From 844a9429475febb80ea39a4f105dbfd0c04a77a2 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Fri, 16 Dec 2011 16:45:25 +0000 Subject: [PATCH] psblas3: Documentation changes. 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docs/src/figures/psblas.pdf | Bin 2066 -> 7196 bytes docs/src/figures/try8x8.fig | 353 + docs/src/intro.tex | 41 +- docs/src/userguide.tex | 2 +- docs/src/userhtml.tex | 2 +- 243 files changed, 14302 insertions(+), 14624 deletions(-) create mode 100644 docs/src/figures/psblas.fig create mode 100644 docs/src/figures/try8x8.fig diff --git a/docs/html/footnode.html b/docs/html/footnode.html index 1fad8e9a..0bb3989c 100644 --- a/docs/html/footnode.html +++ b/docs/html/footnode.html @@ -18,7 +18,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -104,8 +104,8 @@ sample scatter/gather routines. . -
... follows3
+
... follows3
The string is case-insensitive 
.
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De`HvJ

diff --git a/docs/html/img114.png b/docs/html/img114.png
index 8b8bbce788f2241e8eaf8425df45691cb70fa22c..cc0a9a34402dd8d6272433407993669f38c60a59 100644
GIT binary patch
literal 425
zcmV;a0apHrP)BjLjb~?PO-)TFCno>^01XWdw6wIEnwo%sfOK?pT3T8_KtMD!G#VNjY}~9}00001
zbW%=J06^y0W&i*ICrLy>R49?vQcX(4Fckip&N!XUn;Q2bvloUg1ra=gc#=7Qi@^g(
z@Bmr_7h;j(Qa8b$ouG&d#Z8Xj5zI>?r0vG8#1Hyj-uLBuc_{%xBw>+pP*|dc6;{^U
zYztANlD5{ouwmIze}N%;V^bI0X%2G?7)%lEeUT;J3q59n5DQGaE&uWBz6bU};d9I(
z<=f3YGpo}o$P)$-Dt{&>DwKzA!bJkAcZ|qcZr&(kVurym=h2l^1K%Ox9%1wTKl3kf
zQKxHrkt*aP9ag05XBx&M7jJd4{c$Bv;PuIi4G)`T1uE=HkbMOEz!L($m{zHQa0i@^
zk(vl)sN)o)HN;N8&v!0gxA?h<#{)YcEiCzojWc92oOZW!vAae^vL(kI!~erK!M`~g
Tylah!00000NkvXXu0mjfF?+8l

literal 868
zcmV-q1DpJbP)BjLjd5{tXJ=MthEt5z&)qbBc9MHfN-JoU#kE8Uak>`Ng_iAqWjbt8b
zt<>h|!NrizqnLG)+1RHk)utz{sAd>d|5GNg1jt
z9JrX64hO?Ky6ICX26EGd{N-+-r{!o#kKrX`{9hS68umfWY*k(c#J|T<7LJqwq+nrV
zq)*1tZ5D}>fWpRBF%_^{Vvl%I9QHnBPNd(%}9O|f%kBTr(Ju9=pOa-P%vN~MJ
zmX%ztxc#ANlxUOnYbvjuZ{eke1~VpxE(KVg;^wc5etB(kLqM0(0iug@mv_b%ihe1e
zeLbDv+B2+)PHJ0MSMt@?%&teu;{?l==yA2$3d8!aU%uC4Ma(XOkwWzW)M?>AoTziZpw?{0jarsnp5N}Cu07oV$}
u8~N}_v#vGAaE2UTPPgEun{K-4|D`|9A{gH7Q+ZJU0000{X=Bl@MRhPw6K_Vq>Vh!ho_cR6+@%MNICV~C6IobJ_E^yo;
z(VgLDe*c9BU}_;t=6)tJWlgn$i4?GckQRcefp&mn=omwTXX@k=@E9XxIZBkZ1~F8>
zAAZa)3x0*m9O-`3m%A?@xMIIJbZbfJ;h})z$2Z;FGd}y<#2f$s002ovPDHLkV1gY@
BoYw#V

delta 360
zcmV-u0hj)y1E~WciBL{Q4GJ0x0000DNk~Le0000!0000W1Oos70naq%3Xvg9eZui?R}9Y-U~fue}WJTOuQ}s@$0?^_Ceuu%pv95%{?=#(<;al1`sNL
zCMGJBhi<|}0;+e6$XRaQC}U!V!7%61l~e=YA>kfj^Zq~cFL6<)YkQF@PRb+Y|&B~Re>$%_pSn`H$m>`IV*1pB}f0>7A6sey0@oR5*32xX|_J`|%h#7@7@
zcP?MI__>M413MrsEcuCzGh{NHcDHk}yGBK_CC44Z|HC)Izd0JbYmJBi00000onef1Lp!EiBL{Q4GJ0x0000DNk~Le0000b0000W1Oos70T6ne6_FuJe*oo4
zL_t(2kz-&0g9lKI1SX*H*cccT7_b3GW;l!CKmm|yK+}l@umbS`h6Nx4^%x#ZV$ftT
z05WeZIKaukz2E>;kpa*^O27gz$pvy3D-T47ABY7Qm?jvU=K)#_w5WiCfd}Mn28LZ%
zc=#A@Fl+$&TVMhU0|N)t6a@wze2QE_3RnrDHUV8dK?X&J2OOjv55Sz=2RN*6t`nHY
zz`(tSf#DQLh=~UnbU_RZXMhd{VjZx$rJM|04;UHN0F4Wnz+eLwJ8WRP`jQ1G0(guW
s7#UJm25s2K)MYPpJ^`Omo9MJ
zBGH}UW`6&L2ViO;OXhwiGG$G*f{7Hcf{+%1seyKYW9S$|gJEWS(
zWE@>WF@Y1ImPF4Vk8QvPmI{V09<9%PYH*Mrxjvf)g>Rj`jd9PJ|7)oV?m{0RQO~ji
QY5)KL07*qoM6N<$f(R~cQ~&?~

delta 293
zcmV+=0owk|0_OrDiBL{Q4GJ0x0000DNk~Le0000b0000W1Oos70T6ne6_FuKf8|L;
zK~yM_V_*P-2T+UzCZO=x7#I{7umMJ9IE�g!4y(}@MJ0`UQc1t0_U7#>Vw&}1+G
zGH)z6z{$Y9-~d#S0nk87zydJI1#%ZF4@8I`hy@s!CK#OO0a^^SsDOik2jp%BhFw>9
z_!w?5YykROU;+yR0|(R;1qL39dt5;ZSP7vv0bM;o21SMk9Hbl%z?|I&IIM536PU-q
zz`cio;S@-Si3b>TK@1FMfDQ&?9k9BkoD5tK7#Y?8jSHB-U;`FAY+$?kk_9LNc#Ihs
r9wOVp=m54!0o7sw1_p5C3={wW!5%5DFUoKc00000NkvXXu0mjfCV*b}

diff --git a/docs/html/img118.png b/docs/html/img118.png
index 195c0224f865d1458c1e406d13197a7caa4a010c..f8ecccb644a0532da84c8bb380b52ef265e115f7 100644
GIT binary patch
delta 867
zcmV-p1DyQK0{;djiBL{Q4GJ0x0000DNk~Le0002F0000U2m=5B0WfWUt^fc4Gm#}L
ze?me+KtMn=G&C9-8f0brc;ZE2*OjMOPYurQ6?tm3gs9X%(`~Z*CW49Ip8lrJqnFXZ2Z?SyoSq$0!#|wmYbM#_L@9#@cV$DZi7vc>0d)
zIb%GRcE`^wzgf8RaRehzvjKNdF(YaFr%(@8keG6e?P)13X+9vZn?2YP2E634e~);d
z1qFGNZKCXG97k>0r2E7MFeVxdwid}Fq9Wrcv8Yi2(XrR}!37WfQYzV8Y}`f{g&?1#
z2ujS0F8fI;eN^5y`-S*$_{dt`7|hIR-vL%giM%qUW!UA!D1@R|vPSYi9uXz2ml>ep
z%8DGCrJ7!R*!Z?c_S%4z$-<;1f62&e4T!QRN${+q;P-5AD{Dgd87q3L_7osmP3n#b
zC}%AhnNnLcN#SnLAwD15coh|;aaM^9TTn5o)zme72u5L8?X>J8p{3=rqD|GBKo*z+
zt~??Nj?+rwQfUHk_T~vb1UAx_=~8spVSglmKlIQy(i=JRqbNJ6L#ci)e|bT}{pm_+
z2Mqp8XAR#GAl@8Y$2aty(LGQ$+Tr4xE-HN4#bwnOeW0Xk6vXh{CtawmEt*^bOu#lE
zo(vvJgS<9TqQce^X5~v5L~sl~Xo0NRtdMuk@^04?jp
zEmQ8eiNbspCUGL;W-4$DBTU^aTX?$aio1FD;TYDd+H6Idn=QERE$^0My=vVJHCW6s;Y0m1IBA^N
tR&sDx^}?3RVEhC9AFU5P^w2|Z&|l%P7vubrFns_3002ovPDHLkV1ltal`jAQ

delta 299
zcmV+`0o4Bg2FwB_iBL{Q4GJ0x0000DNk~Le0000V0000W1Oos70dK30BHm3xU8^ZU>rv4a(zSFC5wHm$dV%Ql_EUSu3yLNS38p_W9?ACGOo29^qj
xE*`DVeQI!!AGto828C~(y^V3tng4643hqK5AW_e<18M*O002ovPDHLkV1ly)b!z|s

diff --git a/docs/html/img119.png b/docs/html/img119.png
index f8ecccb644a0532da84c8bb380b52ef265e115f7..2c463039e856f2886efdcd120548abca06ef300e 100644
GIT binary patch
delta 305
zcmey*c9BW7Gr-TCmrII^fq{Y7)59eQNGk)e0t+((1EXxp8<2p(L{;s22L}fe6B8*Z
zshm4&Vu6B;B|(0{3=Yq3qyahSJzX3_G$tk|G%&fbr5F@5O*wexz=3lO+zwwqFcuzW
zRI`wlf57yJna5$Pk1)?UW5XPVS?4#r=HgdxX5tTNWo%|(G%jdnO)z43vx!+ivCg3V
zC8NAL|6$e%vP?NV4qP1-^}8z?&eZ0F#n}1LLyk*BZE`PR(wJU~_F_S2_HV
z;mDJFhcE0YzvkRl$-`4EDdE>BThW%tw3>rc;ZE2*OjMOPYurQ6?tm3gs9X%(`~Z*CW49Ip8lrJqnFXZ2Z?SyoSq$0!#|wmYbM#_L@9#@cV$DZi7vc>0d)
zIb%GRcE`^wzgf8RaRehzvjKNdF(YaFr%(@8keG6e?P)13X+9vZn?2YP2E634e~);d
z1qFGNZKCXG97k>0r2E7MFeVxdwid}Fq9Wrcv8Yi2(XrR}!37WfQYzV8Y}`f{g&?1#
z2ujS0F8fI;eN^5y`-S*$_{dt`7|hIR-vL%giM%qUW!UA!D1@R|vPSYi9uXz2ml>ep
z%8DGCrJ7!R*!Z?c_S%4z$-<;1f62&e4T!QRN${+q;P-5AD{Dgd87q3L_7osmP3n#b
zC}%AhnNnLcN#SnLAwD15coh|;aaM^9TTn5o)zme72u5L8?X>J8p{3=rqD|GBKo*z+
zt~??Nj?+rwQfUHk_T~vb1UAx_=~8spVSglmKlIQy(i=JRqbNJ6L#ci)e|bT}{pm_+
z2Mqp8XAR#GAl@8Y$2aty(LGQ$+Tr4xE-HN4#bwnOeW0Xk6vXh{CtawmEt*^bOu#lE
zo(vvJgS<9TqQce^X5~v5L~sl~Xo0NRtdMuk@^04?jp
zEmQ8eiNbspCUGL;W-4$DBTU^aTX?$aio1FD;TYDd+H6Idn=QERE$^0My=vVJHCW6s;Y0m1IBA^N
tR&sDx^}?3RVEhC9AFU5P^w2|Z&|l%P7vubrFns_3002ovPDHLkV1mLal{5eV

diff --git a/docs/html/img120.png b/docs/html/img120.png
index 2c463039e856f2886efdcd120548abca06ef300e..017eea044bf934f25bded7f4bc5886f7c3ede020 100644
GIT binary patch
delta 472
zcmV;}0Vn>^0+$3KiBL{Q4GJ0x0000DNk~Le0000=0000W1Oos70Wg-s=#e2ye*u+A
zL_t(Ijonf`O9Md=eS2pwH6jLn0A8@6WiiOo7
zr*;-{LW+=Bq&603CstQmIeQ=GLqtiL2fMTTc6R2??f?T&Xox`qCVZ1j7TrF_!dV5<
zx>whAmwEUb)^`p)vXSAqq^t}!e=rME|3{!7$cr;Bt)C>IQ3bbhEer3WvItfQNGv?f
zwo%?AE)Y-^a3pm|WN&2^<~Rbz0Yh$-nnF#cSCYNdQ-vQSoIv#S9%>$yq!`RF;51|%
ziUr?;>CxLZb!2#0Ti1Y3WhxnVO2Jd5ybL5zW-^k=vo8Irh*HHlr{_eRe|IvVb&A`-
zUA$ZIM~(~OoUc$Xmbe|0%BWX1Bz9@&{y8=5)MS#(^WE$<%EbZtFT
zxA$-(y&i$jw3Vjiw40+qOEMODDaUX~Uw|W%yf%Rob$yMFE|8f4Hl!DC6`p_;{ff&z
zEG*Zx7spoj4?LiU`77Y9F0YZ5ha{7h`*_K%0iF-HcVi)0m417{$-);G#Z(U7>jljK
O0000k1Dig8~m!g#m*A0W)xe1z<7&?6Lz8A$~B2=>Z=n55onJ9Rh3&KnjR>yLf=kJ-`i8
z)xf|4A|OBkrkB=$3mVFsfLI1aW`+kO!|?#bX9K#e;`Rj
zK~yM_#Zo&?#4r$j$wo=+3|SvwiwLn4XpvTkk^@kt+!`d#KtZwM1U>=E5kQonm8k)V
zBZQ6$ZA-_D9Uxk0_((h{FK=e-neo_w#~BDE`dIMiG*+Qgw?M@r`V|;ozce34ELwZV824{eEcT&}
z5xHQgCr~9KI$(OnuyddDoji(4W#I`X(4$$r^uax$P2N?uxC1gnA=yNTHy)r~{Sq0L%
zSJ!oydH5UFcMd(Wk>R+ctPD0Ve+yIpN1z|bi!&~*pCq7B1-Ei73-6+`2v!M5EIiG&
zQQjji5Kt9xBy~t+Z)FwcI0D82LvECsLQSSulD*VZg&!oGK=kw;Y95uO7|bx>G-Mr$
z1>b||(c3n4WO!Ix*MLuDDj9Z4!BeHY3?xuyGLp%&F8!*AQpGu^=R}-$e=?wTirc_l
zyj$@{jtk+OuTU?RxE+(qs8=>5c4_GTIW_FoLq~eCwj;Ei*HxfdbX=eRnB$Jl=c*(5+o)5QoV#q{Aaq(<8eEL^&jtntz6T5p+z3r+X$cHyfRTrt1xN{S
zFbbec5dpYPD9C}d7aU*&xyB*bU<25lgX9K!e*qv#
zL_t(2k;PIwPQ)+}eaS{i>`rlnD^NXfumAu607*qoM6N<$g8X8a
AQvd(}

diff --git a/docs/html/img123.png b/docs/html/img123.png
index 69253a7820421c3cbae5e138bba5fcf6c740d07c..90d8d9a96d33b371d46ef059caa5bf8dd1adbaa1 100644
GIT binary patch
delta 508
zcmVBdIJgBT5uric?9jnQ
zafqNGSfry^hx`SaRb0Hg#QuxXnFIJ!eh*e=2*0&wAA1$ckJ3fUG9!)JSBBvQzy!+;Z)1ViBHt1eHakE^tO@LaANBqVP<-|v9=kUQ
zFI5aF8lw~EDfKMWSePnQ8au8jB#j;7FLVc377q%0lLJlFX*fsKVYGQIe>R8vd2q~p
zU&RqbzEIVAym3&1qFfhMBfU4va=Pn5c9Xz#TJn!iP;4gBl9QqPq*M39NS1nTDa6oX
z#u(WdOOz*DWZEU@-3hM88|U+FPE6j0GR8FZ)r;kxPWDCPKk4Kcv&H^MXO(iZRKsg*
z3}<|^gZpmZhi>GiO11p}Qkza41y}c+*rw`G2WWt;j7=#w+liB^V&!zr?O+uBBk_ai
yVEDNFcxGpI3N%^_X_C9+ycZ?)4+Q`CBX|cTdu*GPWx7)U0000#q{Aaq(<8eEL^&jtntz6T5p+z3r+X$cHyfRTrt1xN{S
zFbbec5dpYPD9C}d7aU*&xyB*bU<25lg}1k(f|iBL{Q4GJ0x0000DNk~Le0001h0000T1Oos70q5^Y^N}G;f6+-q
zK~y-6?Nd!l96=C$(|+vEWM^j-5xmII;K^tf^9Lp(;&HrsnxCL|52Hs<4LJpZ21zbv
zg#q!9HHQ`y1oz@iP+{;FtpC93?sd1tl?bvRlE=_p{pxjfRdo;0ft->Elrai0^hAmv
z!m_d=`U2bK#gLvdLcOe^`a=JYN)V}&X&g==w-nx@1a2@*1A-7P0+7203lbkFh!0V4sU*%|h!fi2V3e+pJ(mveKR
zD0B{&)!?9;PV&NTVqFa3IrxH8{3|GKY;nKPq4nXczJIr^FX
zBS6$dkPpPs6@DQQ-2lwbX}y95+C=Y+>jz;1I4Q=nZV6r@KA|+>wy=VxYn8Br(uf+Y
zS7ZWUd*i~c>oW%T4)^?=CAh6wjw?*=;^y~Kmtm*tRp+Vg2(7{D<
zh@c=?q@!4e`~{j-T)eyFN|G8BL_zS;=DY8G@B8}ht}T#2fOQc~_R^36UD@^V##h7?
z(j;b}!{tSh<)R+A%{@*%XHESoe|+geJo^PjKo1QRK&UM#Kzo^^&~v6#K@nD!F_gdS
z;fvrOdlk!%(nZTMBaPZuhT#Rk1j`L?V}aKq-x3ryJ3vRQ3G9I%_5KS`eD)w7yEh3h
zRSYQ_qZ8*T^(@p_m?~5nJFY1tjUD1IbO%@#4+?ve15MRwI7iiCw0SKye~0^daLjyP
z#SuilP}O?8aZrMyTo+X%y*JBpy6Zu9lfZOZ@{dnYY$no@lcD>hQ}@G2mU?a}#L!~K
z7}*(1lqXwc+9l}S39iQ*=ksk&Ox}hv#x(WSi{+k9_C@1A>Esx*#r{ZVm2$IG!)t5|
zXMD4R`)=QdZsev)wfz8_QBEBNSNELQrs_}!Xn?JZO({3qiIb{g<#f&MU=;l$@q_4K
x__+LdW@mN^G+GR4lDp%)7bW!%1poLWcn2kWY@3y3x>EoE002ovPDHLkV1oT7=hOfI

diff --git a/docs/html/img125.png b/docs/html/img125.png
index 798e786430d3d0a926eebe4c49268ae7d27a51d9..fcdbb64f9442c2698bad89a265890048a5232213 100644
GIT binary patch
delta 305
zcmV-10nYx@1n~kPiBL{Q4GJ0x0000DNk~Le0000<0000T1Oos70b@mMn2{k%e*o`E
zL_t(IjbmT{1I|@E4A{V|rZZT@85k587`WdvaN>|f2V7A40fR!rAqJiU3=9VtxVYUu
zfW!_EX$Els?2m$k3+y~lw@p$~0E3h{O_e=!(za85wd2=tYJ0MU^!_yE@gywcr78FCIxa_?c_
zJiUa0$7$E;$!l?{QaHo#o56%Z;Wook27YAACn*5|Ochtaqz?>*6F5IGL@}HJhA!_r
zAb5pt7LPH5*XpPRyc?JT7#h5*7#gz!MAd<(>UH$5Hbyal_(1Dzi2$V4jF!V%<
zAi}b;BKiW`<;9SmGD5wqq54A+e~T?52J+tFUJj|pf({KKysaofSdBG7_!B`u&b1Zb
zn&d*|*e|3GaBQu=+s>*IFfAy#S-vU-@R7JsIzBj$w4mK#7a~MvYzNs||5EM?Vk*s%
z80rwR>tlr~FNJGykD8{$9tjdMXWcC)X%*UE-*nIN2LU4iquCkusevuif7J?BW0!Mt
zoG5e-m(}2)oPE=~28U`z(aC4?;k=A)O&GI`kw=AaE;{xoT@m2F`q92WI7gwq^u%+*
zCn%e4-eJlFS_pgV#=blgpi-!jr5KKAy3RED;V=Dqjkq%3IRCn@h?z5^KAEoPI63;6
z{UbosM34`}(G`9n5ZwUGYR|ob2HHgLjOzzs0yrtgvu+7qB0ixs;kK}XrfZe3gVKl^
ztXE_LV0+`juIn=f_YU{`oF%xeS&l1A?&9Y6QkP+;>sGXSlhC74p5kSDL3#bhTf{x0
WFLcLoEun}20000DdQR4yw1qOWq<8u$#3@s%k0~p1b?Psu^GV-0Vk>P}v#|{RSa@!xg
zD(VFbG}9wEOgtk4mwoCBM(UTd*2
Zq;&}Qln80P06K%g)78&q9kWwH6958>H+292

delta 304
zcmV-00nh&L0r3JMiBL{Q4GJ0x0000DNk~Le0000<0000T1Oos70b@mMn2{k&fA2{|
zK~y-6V_*OS&Q&}N*ubo&Gg!qL7!(*7xZg8y;*doLTu}M}gF?e02A%^93^xAnO;S<-i%sBQVBnytRm6Y*RIVMS3O)t~rUwBZMEUs`c+Q+r
zfC@24Hf&(z;fE+uQc?g4@pdvXe;9OdPC(KK^p$`B(UCCt0M`V((%nQEat=&#?_uCP
zy@Y|sY1iq=YjLVlIK%Lp!GuBKHp5Z|eq_rhDFFdY6<5Hd4-AD9I6p8%F`NO0F7G=a
zc!h2jk1>PS>Zk?08<+wZ9vNU*s1tsgDCdt50001zG_(8xdIkUh002ov22Mn-LSTZ5
Cq;I4E

diff --git a/docs/html/img127.png b/docs/html/img127.png
index 1fe14d4673902b406e48c274d44fb7e44cf3e24b..5032beaf50de614cad74a71024d28df374a3cfe8 100644
GIT binary patch
delta 502
zcmVe
zL_t(IjqOyyO2a@9eVYb#leCTEQ7|Y9m5Tj@_yIya>ZyA2*#1HAB!W-{J$Z-+#e-l3
zK@krT5f6saqu7Jd4-h}Wo!v;IwH~CN^g%LjXEO74W|IK#=yNV%1;ip)=mOSs$%F`b
z+AH%@jtYa%;pVH|>U;}RT)v$we>^xO=MTWtT~fB8Llm|#TBRjz7dQ%kr1U-PGB7Ne
z5S~p1XgnG!C=$KLxeW)MXGsZ00Z~#zaBp$+8O$f0Jc7?7I1$
z$v2cj$+(a<%lrqWd@J8lBZ|}mmLjh`n!}%f;p%n8MnbwTii@iWvgqrS@fT@!fF-iK
zSM5-i4unVcS80TXydMC|;0m1e)qSJ0A0
z63rU@1ZtRr_y7gknYp?VOsD#6t@BuW4cdKXT&-Nn#Ae)~iB%`vg81EWkEI-fuc3di
sYtM`}Qcrt^grksf?J?+<_>W(}8!9GUZH-cR2LJ#707*qoM6N<$g3W#8Gynhq

delta 174
zcmdnW@}5z#Gr-TCmrII^fq{Y7)59eQNDBcmKMOMh17ptmP1`3bde<}Ldb&7An6Y`az=?!MmIwAX-egqSHYIp|W312-tDFOyvR-Sk
aF{E_}_ml`}y#Ts{!PC{xg=L*nLK6Vu?l(IC

diff --git a/docs/html/img128.png b/docs/html/img128.png
index 5032beaf50de614cad74a71024d28df374a3cfe8..47913ee15572d4e4cc5dd5595002d7b130ce17db 100644
GIT binary patch
delta 562
zcmV-20?qxk1n~qRiBL{Q4GJ0x0000DNk~Le0001)0000U1Oos70lL7Ee~}?ffA2{|
zK~zYI?Nl*H96=O)JD%?C-fTQUQXR)~U?nC?D$z#4LbM5_NtdZon=X(PYRWWAsw+Ya
zNo%p7l{TX&h%AY=F~yQnLUQR-_-DpF_q@wx;L;rA-F=w(^ZuK+e|8oqLaHdk0z#ew
zwSyR0o;m9z_zSm7?$G}|qk-p*e}Mxdp-J|{({6~qhQ`~Y2nb`I@}Ey0LvlI#J283M
zvVkkzcXE_N!SK<{Tr}OLOC`%@?r^sR)@T@>>ME*c
zrHtzX)cV!3Q?>Us99W3|O1VdG8ANAOB}J{1Mt%2*#;ZuvL)4?D*Yv3Be=T^LhW<%d
zFXc2ww7m5Y6;YA!BQsxqk+Nt6?)YM5pG_FV?ym
z>(8v3z*<(cAwiGZG|&aJgtPxoE=SoM>@Q4RCtmfWv4=T7>ZistO%@mn)nIb5u(UFN
zhT2XfZ97)MieK8-*A2Ax!XHg?7%2WNtS|{ERrC=q@z~
zVOz}+xT~02F8D#XBo4ih_rad4xb)g``7*ZPP7vosmp8oII5+dcqXyJc{@_%{w^@@b
zKI#SPAA&Et1;6b0Wr6{)HAwM)3=Ql)HFgkJu*R<_7ES)D000002uVdwM6N<$g6EJ4
A)Bpeg

delta 501
zcmV8#3ESe0@ifNga~=s
zEAvy13WLw#=BwT6d<#=tzMU*Qe>f!P55Ux2QnsN(6t*#1r6p|_I0}EH^gZk{Ff5r6
zo=pX4JQ^w}63=IVd$Df%(-yYI95uWrwf}2<-{0F6cE8kKhiqr#^BCkD~!=HfR>UG6NLb@-Ci>nE;=(2_+G
z%^Lj#YM6ug00r8axw;XjOZsfB^H_Tg+I?nRtz62)X568PRVUqo_}y`jr5u8d*$

diff --git a/docs/html/img129.png b/docs/html/img129.png
index 47913ee15572d4e4cc5dd5595002d7b130ce17db..2a4a67cc73782264f15976410e1d0dc3911393b7 100644
GIT binary patch
literal 593
zcmV-X0BjLjb~?PU0q#GO-&~!CjbBd4Gj&nw6vObaYx;T0lTRG&D3C8XDEr
z3?={o00DGTPE!Ct=GbNc00GHKL_t(oh3!|{a)clZ4NzU75aa*EfbDwz+7)Ik~soxTyUT=|&wSk2m+xf%z*4gkljFW}vL}ja|Be3xS=Wa5pmH%=RCS6w?vqzE
zL?TBTGW;w^alD%aMtD?YAKhZ~bxsh+dnqzSe=1((JK+U*Q6D-cOM{F&%v%~ZwTyZs
za1Jg&hHIU64YK5+sDo{nJaaX$n<_60ve*B|b5b^5jT?U&#~X^j@laj|eQl$04qavN
zd*GY;;IvW9W5n}6P7F;uO(9gD(Qdl)(J=|eUMv_^+ua#>pBi^DDz7&_j`Eb
f#*GWwtPAi30D>6B2c|Cn00000NkvXXu0mjffxr5y

literal 625
zcmV-%0*?KOP)BjLjb~?PO-)TFCno>^01XWdw6wIEnwo%sfOK?pT3T8_KtMD!G#VNjY}~9}00001
zbW%=J06^y0W&i*I?@2^KR7i>KR53^#K@@#Ep6>15Y&=0y9mjHDB_>NM(MG{SvlE|3&z$}~%=D?$uOYq6k}HlrwrEQz);#gbA&a_Lj}XU0AEyvt?a(j4U7eVF<4
z{+qXdb`~f?swl$(LY@M(gBV$!IqM|&3%5(|(EmN7f#;2Z10$hH_Qca}h`xr#+oK2w
zW1jM#PaZ>ZIr=*>dD^msB!Q#0&AJsTef2F2+7}D*;K-XfR}pt|ltaPr(ac;l-KI+=
z%VzFyw*=N`7@q1Xs%E8(>jTvK)v{By_ca_?i2q8tM{gNKXHz9bt&>K5_ld@`!{+ceMxvxKw%PcBE<9PBSlT_;}kq_KxNKkBE(
zGffs43)Nt9v9PovlL^1dI>$*xgONB=`n%++M>fZ97)MieK8-*A2Ax!XHg?7%2
zWNtS|{ERrC=q@z~VOz}+xT~02F8D#XBo4ih_rad4xb)g``7*ZPP7vosmp8oII5+dc
zqXyJc{@_%{w^@@bKI#SPAA&Et1;6b0Wr6{)HAwM)3=Ql)HFgkJu*R<_7ES)D00000
LNkvXXu0mjfE1w>i

diff --git a/docs/html/img130.png b/docs/html/img130.png
index 2a4a67cc73782264f15976410e1d0dc3911393b7..f63e861ee297c16410e9dda1714b049003bef807 100644
GIT binary patch
literal 217
zcmeAS@N?(olHy`uVBq!ia0vp^LO{&N!py+HxcqY>h+`1o6XJT{z=7qRi14oS;8M!~$?POT-?GTfn!f)pTj0!sy
z9~hdoYBYGOHN6x+tSm4&w&6L$b9RB#EeqE+)~lTmV`Sr7(96Tn$}M=0OJV&XpcM?B
Lu6{1-oD!MBjLjb~?PU0q#GO-&~!CjbBd4Gj&nw6vObaYx;T0lTRG&D3C8XDEr
z3?={o00DGTPE!Ct=GbNc00GHKL_t(oh3!|{a)clZ4NzU75aa*EfbDwz+7)Ik~soxTyUT=|&wSk2m+xf%z*4gkljFW}vL}ja|Be3xS=Wa5pmH%=RCS6w?vqzE
zL?TBTGW;w^alD%aMtD?YAKhZ~bxsh+dnqzSe=1((JK+U*Q6D-cOM{F&%v%~ZwTyZs
za1Jg&hHIU64YK5+sDo{nJaaX$n<_60ve*B|b5b^5jT?U&#~X^j@laj|eQl$04qavN
zd*GY;;IvW9W5n}6P7F;uO(9gD(Qdl)(J=|eUMv_^+ua#>pBi^DDz7&_j`Eb
f#*GWwtPAi30D>6B2c|Cn00000NkvXXu0mjffxr5y

diff --git a/docs/html/img131.png b/docs/html/img131.png
index f63e861ee297c16410e9dda1714b049003bef807..c07a1bcd994852d18f6b0a26b243f1fbd100fb1f 100644
GIT binary patch
delta 567
zcmV-70?7T@0rdnSiBL{Q4GJ0x0000DNk~Le0001y0000U1Oos70jU?!i;*Eqe*yDJ
zL_t(YiS1RtOB_)U{_fpI@Aj7~h$M25ZsJuv+ax7THpgBCB>5%l-itnfLb2-HUP@9twgV?9BV#3^Vg)-tGc1I)Eb%
zwTc!{gs#AWS)_ehc^?+Q4vS*Tf@fag
zr47gQ@%mF+8SfA49f^WmrhylvGXHt_R55087BNlf8nnTj8Z(D=uzX&6;hYYqSYls2
zVuef6J<`kTGk(a0{`CP*@)$UXm%Vp7Q1iMNZkniw$;-|rp^NKGH=-D^e{cHub-i(T
z>-^eHIMo{+7Id1F!6ji{MKiIQx202xV+aTWAK{m3xCfe)5d;;43ni@{DZ7OFFs9z0
zR0c^;N>;u29aYiqG&^_L%=nClg<4cfckORU+0tm(gfCPXn3Fu^Hbnd*gziKn_p@mz
zT}Ijg=1FB;acf-xo7jvRf8tE@I=FDzI2PW*bV6sy&9HFglpo%TG$13XZ+J3EnHyDX
zf8eel-^UsX=(MQP1x!=EJi)$+WR_H^nQO(~n;6m7N(%oNy$eIfiAba9Pp5s&zf}_!
z?HW%xv2C3`*{>46lU!`Fkl~%(iL~v2{cY(l_lzfke_*m~#MBKH4PF2M002ovPDHLk
FV1jB11+xGE

delta 151
zcmey$a+6W9Gr-TCmrII^fq{Y7)59eQNDBcm9}6=B1LN|~i9!<l7DJzX3_IA$g%
zI56(vG7u}bVP+QYDbCocJ7La&qsEPl+#l?AGOYM^h{;dkxAOr;g`J8I49!|K8obq-
zUWy-97ML8{@SNc}yTIv|g=-t@)lP^pvhgkGKIxMg~t;KbLh*2~7aK
CpD%s@

diff --git a/docs/html/img132.png b/docs/html/img132.png
index c07a1bcd994852d18f6b0a26b243f1fbd100fb1f..6b244fdf3d5ba34e7d34cbfe1ddac3dfe7b57ccf 100644
GIT binary patch
delta 681
zcmV;a0#^O?1m^`IiBL{Q4GJ0x0000DNk~Le000220000W1Oos70Saoq-jN|oe*$Gm
zL_t(YiS1OsixWW<{<3T0PV(|YIPHX0un|2{Sg2LB5V1-rSFL}*!CBZ@?8Qd#(B*7S
z1R2mnM1@5w@0#^QF(jaNf+FjcS4ga5;d`^$TynW^NU*r$zMXmV=IzY4@6Eioz#zyp
z#!nz)8lW&1-l!=UzuF+*8*|WRe-!B{3$wEk;%JA>6QW|`NumNe1ti~dtH8k~Smx*9
zr9N0j`ss$6&#Lo({o5Y8w!J+of?X?{X2)`Io&^F4BPCC0vQT$9Dt(P}e+jiQrC=(6
z(n^_@L{m~pG_anw?EMV6F+xeUd!UNB*TZF=8$E*aDxim1a#8QpJHiHAa@fP=gdszm
zBt1P_pMzd>BjvyGL&Gb{9>l=g#QWPSNcFke3XxBNvbad^5XjtdLtaHm%&M;|1b*Pi
zP~k^7OFJEzoeb8{>Fr~ee<8E_kC*qXuN7PtN3RXMb3$Yyqy5H-p6%8co^f_GMc6fw
zR^3=A2JV`>Ai@B){;}mcsSyxfBTES7#qB;gBi3<
z;Tii6v9l8e|DL<7ptNFdkY~R;xW33e*ie01TWIlU{>wO_~W
z;`PZY_&l#XpV89S&*DP>>;26TrAg~|YG_vIjcXIKrvI^F*b}qvWAETEU*@0eWRl^|
P00000NkvXXu0mjfjdxaA

delta 567
zcmV-70?7U61@#0WiBL{Q4GJ0x0000DNk~Le0001y0000U1Oos70jU?!i;*Eqe*yDJ
zL_t(YiS1RtOB_)U{_fpI@Aj7~h$M25ZsJuv+ax7THpgBCB>5%l-itnfLb2-HUP@9twgV?9BV#3^Vg)-tGc1I)Eb%
zwTc!{gs#AWS)_ehc^?+Q4vS*Tf@fag
zr47gQ@%mF+8SfA49f^WmrhylvGXHt_R55087BNlf8nnTj8Z(D=uzX&6;hYYqSYls2
zVuef6J<`kTGk(a0{`CP*@)$UXm%Vp7Q1iMNZkniw$;-|rp^NKGH=-D^e{cHub-i(T
z>-^eHIMo{+7Id1F!6ji{MKiIQx202xV+aTWAK{m3xCfe)5d;;43ni@{DZ7OFFs9z0
zR0c^;N>;u29aYiqG&^_L%=nClg<4cfckORU+0tm(gfCPXn3Fu^Hbnd*gziKn_p@mz
zT}Ijg=1FB;acf-xo7jvRf8tE@I=FDzI2PW*bV6sy&9HFglpo%TG$13XZ+J3EnHyDX
zf8eel-^UsX=(MQP1x!=EJi)$+WR_H^nQO(~n;6m7N(%oNy$eIfiAba9Pp5s&zf}_!
z?HW%xv2C3`*{>46lU!`Fkl~%(iL~v2{cY(l_lzfke_*m~#MBKH4PF2M002ovPDHLk
FV1kk31;qdW

diff --git a/docs/html/img133.png b/docs/html/img133.png
index 6b244fdf3d5ba34e7d34cbfe1ddac3dfe7b57ccf..850dcba0e0715780348d23a8549238be7f098311 100644
GIT binary patch
delta 208
zcmV;>05AXN1(5?#Ce
z2d?vX8h}pR!0Z6R45}b0eFk<(CJ<(L#R=rGtlGK?gc%-LFaQ8F2q5BoaayYY0000<
KMNUMnLSTZnyGp?T

delta 681
zcmV;a0#^Nz0_O!GiBL{Q4GJ0x0000DNk~Le000220000W1Oos70Saoq-jN|oe*$Gm
zL_t(YiS1OsixWW<{<3T0PV(|YIPHX0un|2{Sg2LB5V1-rSFL}*!CBZ@?8Qd#(B*7S
z1R2mnM1@5w@0#^QF(jaNf+FjcS4ga5;d`^$TynW^NU*r$zMXmV=IzY4@6Eioz#zyp
z#!nz)8lW&1-l!=UzuF+*8*|WRe-!B{3$wEk;%JA>6QW|`NumNe1ti~dtH8k~Smx*9
zr9N0j`ss$6&#Lo({o5Y8w!J+of?X?{X2)`Io&^F4BPCC0vQT$9Dt(P}e+jiQrC=(6
z(n^_@L{m~pG_anw?EMV6F+xeUd!UNB*TZF=8$E*aDxim1a#8QpJHiHAa@fP=gdszm
zBt1P_pMzd>BjvyGL&Gb{9>l=g#QWPSNcFke3XxBNvbad^5XjtdLtaHm%&M;|1b*Pi
zP~k^7OFJEzoeb8{>Fr~ee<8E_kC*qXuN7PtN3RXMb3$Yyqy5H-p6%8co^f_GMc6fw
zR^3=A2JV`>Ai@B){;}mcsSyxfBTES7#qB;gBi3<
z;Tii6v9l8e|DL<7ptNFdkY~R;xW33e*ie01TWIlU{>wO_~W
z;`PZY_&l#XpV89S&*DP>>;26TrAg~|YG_vIjcXIKrvI^F*b}qvWAETEU*@0eWRl^|
P00000NkvXXu0mjfeiT*n

diff --git a/docs/html/img134.png b/docs/html/img134.png
index 850dcba0e0715780348d23a8549238be7f098311..a733cc99945723936223f0ae01c2bc3245f0b6bd 100644
GIT binary patch
delta 479
zcmV<50U-X70-gjRiBL{Q4GJ0x0000DNk~Le0000}0000W1Oos70qZSk%8?;Ue*v6H
zL_t(Ijpb84OT<7BeV6+%A8V3QK_Mt=BPwboBB`yeJFz+i3p@P>TYCztm3oI92nwf#
zoG5x&gsVhF#Ln*g2fh8(64E4T
z<;=AJh2U${_rYu+4S1P5;u_VWf9DW@2Ky&j38u;pgvuMBjDTJhte9q=v4m`xm&dY;
z1;54^XTo+)H53?FG>!<#Xp_+&X7HOZKMPrDTsbS*-UNcTqY$lRNwC#xy18xW!8(Gp
zLp^h;%HDRkYhV_^x|L~_zETab!dKlqZwSwJj^UAN;iYQ>zLAjevLt`2f2Kv7h)Vu-
zn4(Fmv^r05AWZ1d#$EiBL{Q4GJ0x0000DNk~Le0000Q0000F1Oos70e^V%Ly;j%e*lk3
zL_t&tnPXsJVBr4%Bp5=0cmjyQz{UUt{6NgXFliD461c#?z{9}6*|4)=!vT;Efe8W(
z*uV!Uy@7!NsE)IXvx^}CXf!VyFNn{_zmI=IH&D6(2q$3C&Ug*QSQ9YG6aXUU>?#Ce
z2d?vX8h}pR!0Z6R45}b0eFk<(CJ<(L#R=rGtlGK?gc%-LFaQ8F2q5BoaayYY0000<
KMNUMnLSTY=oJw~9

diff --git a/docs/html/img135.png b/docs/html/img135.png
index a733cc99945723936223f0ae01c2bc3245f0b6bd..9ffee9ad89b4e125e6ed30c94bcaf456b9a13ea1 100644
GIT binary patch
delta 209
zcmV;?051QY1d;+FiBL{Q4GJ0x0000DNk~Le0000P0000F1Oos70hCWkK#?I!e*ln4
zL_t&tnPXsJVBo(1Bp6~77#Jpi7@QppC}7eAZX_O1?E#>gh7HRafHcDd0Rf0ERPX_e
z7&d?ub9OOwGc+);@iK(+Ffj1(Z)afxN;P29#=yXMO#qo|0wz_#Qu+++lH3jbCklKEK!&oc+PaEI$%=tbxq$%yuaF^6s}uEx00000
LNkvXXu0mjfmp4b-

delta 479
zcmV<50U-X80-gjRiBL{Q4GJ0x0000DNk~Le0000}0000W1Oos70qZSk%8?;Ue*v6H
zL_t(Ijpb84OT<7BeV6+%A8V3QK_Mt=BPwboBB`yeJFz+i3p@P>TYCztm3oI92nwf#
zoG5x&gsVhF#Ln*g2fh8(64E4T
z<;=AJh2U${_rYu+4S1P5;u_VWf9DW@2Ky&j38u;pgvuMBjDTJhte9q=v4m`xm&dY;
z1;54^XTo+)H53?FG>!<#Xp_+&X7HOZKMPrDTsbS*-UNcTqY$lRNwC#xy18xW!8(Gp
zLp^h;%HDRkYhV_^x|L~_zETab!dKlqZwSwJj^UAN;iYQ>zLAjevLt`2f2Kv7h)Vu-
zn4(Fmv^rip0?7m+iBL{Q4GJ0x0000DNk~Le0001!0000U1Oos70j=Tzwvi!Ae*woy
zL_t(YiS1OoOT$1M{w_Y!)Jq#d9VG@_M4_`T)k&NR4z8KRQU8PZ*c2?zq6J+%~%@cKWhH2X;yjsX|k4r6T
zG8?j|=qZp#LD~}59(p-G#c~8@e~kYj=;F=us(Sx~Jip*$zCZ&hTh6C-weL*lHzS+xVCbof
zshhO6ElwWlN3JBfxQ1%=0*T^iCRcZvjp6kEcGD%1Yu;sjIi^_f8RK#9%=g_g!@GA+SktMP+H7_fGAr2(no_I9*Kp%rL1H?XE1LJnS~ZYUhA
z-y%E=_Rq#_NjURXY$L~d)`y&?24~JZ(TByqJY5)KL
M07*qoM6N<$f`GL8AOHXW

delta 209
zcmV;?051Q@1d;+FiBL{Q4GJ0x0000DNk~Le0000P0000F1Oos70hCWkK#?I!e*ln4
zL_t&tnPXsJVBo(1Bp6~77#Jpi7@QppC}7eAZX_O1?E#>gh7HRafHcDd0Rf0ERPX_e
z7&d?ub9OOwGc+);@iK(+Ffj1(Z)afxN;P29#=yXMO#qo|0wz_#Qu+++lH3jbCklKEK!&oc+PaEI$%=tbxq$%yuaF^6s}uEx00000
LNkvXXu0mjfx>866

diff --git a/docs/html/img137.png b/docs/html/img137.png
index 6928567c99f107cf02428584db43c69f79ef08c5..df82028c96a2151cbb9ced6dc9cbc34adf886de6 100644
GIT binary patch
delta 186
zcmV;r07d`F1p5IYiBL{Q4GJ0x0000DNk~Le0000Q0000E1Oos70kk9`=8+*we*k$&
zL_t&tnPXsJVBlZ?f!_=ezyySFz{K#7f%(E=gh1Dt)eNVBbcZGbKLZ|cn8lWH7mz-v
z%fQXZz`)JV&!7P0@@R20FfYKT5fj|tz9sX(j$vxUIS_AYY6H6f17`+UYWf701``Gb
o&JPSdAg&|>g8;}s6Brl(6kZkN5L;p>tpET307*qoM6N<$f_EoEN&o-=

delta 522
zcmV+l0`>j-0m%d*iBL{Q4GJ0x0000DNk~Le0001!0000U1Oos70j=Tzwvi!Ae*woy
zL_t(YiS1OoOT$1M{w_Y!)Jq#d9VG@_M4_`T)k&NR4z8KRQU8PZ*c2?zq6J+%~%@cKWhH2X;yjsX|k4r6T
zG8?j|=qZp#LD~}59(p-G#c~8@e~kYj=;F=us(Sx~Jip*$zCZ&hTh6C-weL*lHzS+xVCbof
zshhO6ElwWlN3JBfxQ1%=0*T^iCRcZvjp6kEcGD%1Yu;sjIi^_f8RK#9%=g_g!@GA+SktMP+H7_fGAr2(no_I9*Kp%rL1H?XE1LJnS~ZYUhA
z-y%E=_Rq#_NjURXY$L~d)`y&?24~JZ(TByqJY5)KL
M07*qoM6N<$f>hM{hyVZp

diff --git a/docs/html/img138.png b/docs/html/img138.png
index df82028c96a2151cbb9ced6dc9cbc34adf886de6..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 100644
GIT binary patch
literal 0
HcmV?d00001

literal 251
zcmeAS@N?(olHy`uVBq!ia0vp^Qb5ed!py+HxJ5w@bYfivSrq+Sq%*hB_$L#H2yr4*y3<~)>WS6jV0}B%=XN31v8FL
zD-@q#x8n4HvnLK5ID7v50){7_G760i^baf-6u$FdpX%oWeTi9zEd}y3vzT`?FsHLc
xWc^~9#wN_hc8;INR$-kAb2GyUdtnI)29Y??C(%h7Yk`hn@O1TaS?83{1OS}VSZDwM

diff --git a/docs/html/img140.png b/docs/html/img140.png
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..43dfe1694cd692b528443bef04386f50f733b299 100644
GIT binary patch
literal 372
zcmV-)0gL{LP)BjLjb~?PO-)TFCno>^01XWdw6wIEnwo%sfOK?pT3T8_KtMD!G#VNjY}~9}00001
zbW%=J06^y0W&i*H@<~KNR49>SU;qIg2L=Wv1~?FS*TC?>fB_jWZ$sv#fj|O`#}6X-
zJQM^b0BIfT3;10PUyLo_g;0UkJuk@oorc{9I1d1s4V35htyOr8UrAJFY&XlfwC?bHEj*Z=^FHB4hx
Sbytl50000e*rs5
zL_t(2k;RfRPQx%1hQByfTQ_c!0d)bSh=GYAN2u6Ay+K1K*m{JV0Ck~r#0g;U;DQ*C
zD#QhlGBPmq2t2116sS5-A^zw++xhLh|9=itFj|u0E9SAJW4^<~B<9E4RkS1;4GeV%
z{0KJ+a`JrRxmEb`khO?w+7*jve-NOtMI8$%scFlk)FC&Yhs42VWxs~!YKp5$h7uWF
zwG(3sBTwPDx<{tWWKPFt;!JWl$x8B>-C4Z~-
b{0H6vY63MM|4Re300000NkvXXu0mjf1ACORyAa5o&Mv?(0bMyo-~f!ld16C?CeNI1R*>xl4hQ(z
z*jXll?0xW{n~#T&uK^@32(-O}e^Gz~$mHF?z|eT$HpLD|gM$PzbTb8@iyYa#r0e{h
zhTR7^4*;1BoTn{8%6K>MJWyp|;yJ*#2*mu&c@m^{J_GxPSDZjf6~x>Gb->-#9t@8x
z82Yq-ftj1NKrzkyaT#e*$8H8~8wLc6
zZD}~K){&(F=28Tx#X2Mr7lRXH^1GNWIq|4ki)ngls=bp9l}Z_)UbohwCW=$@f;P^^
z_k%W{mLa>fnVMp$%*1^RMNA`MlpQmJKE&!Yo{d3siI)vQ8bT6-05c^5f6`^koIVH#
zd-0=CyuG?zqw5~1WfROmpVshZYoLi&%I_{-gy;4kz+qVR@~zJ5Z1P1bh#dn_mPN&`
z`-vs`g3Ccg4$4j7rcVJSxcTG6P-sOe@eB|iyI9q&?0&5Ekd0(H&Iu~cmP=f6@MP{zJwq6y!L$~
z&Q2B3jSYO#h3B3VpsVe;~|q{we8?>R`Gdl>v@bi
zZ*4hG26yb^6Wfyq+LJBjsmXlHbmtjbifWA0Kp!rvKD)5UyhB;&cR2UwrR!VE-b+|9
zYj7v$09*!fHRZx4f2D}nnNi^*a6JXH=RLR%I#pdfVBLOa5t3m(A@15Y{ktX21GvG?
zL~(`1bb?jauZs0=)`Cb9puzklltWUVCwF
z@@0ds9)=%yHtjQ#M<4t2-0s9k?<`vgzc
z(I{6AC*?^8Joxvv8Mie478tkN=Q9GkZLSe*rs5
zL_t(2k;RfRPQx%1hQByfTQ_c!0d)bSh=GYAN2u6Ay+K1K*m{JV0Ck~r#0g;U;DQ*C
zD#QhlGBPmq2t2116sS5-A^zw++xhLh|9=itFj|u0E9SAJW4^<~B<9E4RkS1;4GeV%
z{0KJ+a`JrRxmEb`khO?w+7*jve-NOtMI8$%scFlk)FC&Yhs42VWxs~!YKp5$h7uWF
zwG(3sBTwPDx<{tWWKPFt;!JWl$x8B>-C4Z~-
b{0H6vY63MM|4Re300000NkvXXu0mjf_kX1S

diff --git a/docs/html/img143.png b/docs/html/img143.png
index 9eaf8c6191ab4121f82565bc6c709e2d2b9021fd..a80d3c32d5d5665436e20a48728617edf3698281 100644
GIT binary patch
delta 666
zcmV;L0%iT@2iOH6iBL{Q4GJ0x0000DNk~Le0001a0000i1Oos70mP6xsF5K{e*#uX
zL_t(YiPcp-h}2LJ{<6urKY7VU5J3?{9^O8+=^Rk=0%Yoo5d6_rgd^5B2egaGi8@;t3
zay%6ZpoLpf|E-T80adu7SkmQse;`%85_0hW!Wl4P{2Biq6#ooI(
zvw)Q-%6*vGk#GA~GPNMvkqMW>L=j&LQ8dnjVq9LQN?}E>A?HelE;557q2jU~G
z@(%s5y*-)p47pGl@4K`!1{h?CD0iwI0nS-3*y%!025ygMUA1zi!B%aPu)%DYGmkbq
zv|x|#nlfw?dv@Cx0=s-Ne^fSG|Aj7
z9l$>=@s@Yjt-(HvqmIn&uzlwz
zHe2OMyaT#e*$8H8~8wLc6
zZD}~K){&(F=28Tx#X2Mr7lRXH^1GNWIq|4ki)ngls=bp9l}Z_)UbohwCW=$@f;P^^
z_k%W{mLa>fnVMp$%*1^RMNA`MlpQmJKE&!Yo{d3siI)vQ8bT6-05c^5f6`^koIVH#
zd-0=CyuG?zqw5~1WfROmpVshZYoLi&%I_{-gy;4kz+qVR@~zJ5Z1P1bh#dn_mPN&`
z`-vs`g3Ccg4$4j7rcVJSxcTG6P-sOe@eB|iyI9q&?0&5Ekd0(H&Iu~cmP=f6@MP{zJwq6y!L$~
z&Q2B3jSYO#h3B3VpsVe;~|q{we8?>R`Gdl>v@bi
zZ*4hG26yb^6Wfyq+LJBjsmXlHbmtjbifWA0Kp!rvKD)5UyhB;&cR2UwrR!VE-b+|9
zYj7v$09*!fHRZx4f2D}nnNi^*a6JXH=RLR%I#pdfVBLOa5t3m(A@15Y{ktX21GvG?
zL~(`1bb?jauZs0=)`Cb9puzklltWUVCwF
z@@0ds9)=%yHtjQ#M<4t2-0s9k?<`vgzc
z(I{6AC*?^8Joxvv8Mie478tkN=Q9GkZLSZh%jS>wyCYmM>r4
z+uNI-p6=`GtFEpNl$q!#QSaO?_8!P&ED7=pW^j0RBMr#O_jGX#k(ipCkdW{ot$~@@
zqPtz#Y57uBg(dTi4L0PYIxuQ{QaHe;#wukY>A|>1#>Zh2?~x}@(ll6tSb63h$@KL;
zT)^tBN_qeQ

delta 718
zcmV;<0x|vW0oVmWiBL{Q4GJ0x0000DNk~Le0001a0000i1Oos70mP6xr~m)}Fi=cX
zMZmzor>Ccljg4n#XH88_CnqNW000dQ4Us+=e{9^WT>t<80d!JMQvg8b*k%9#0#->x
zK~zYI)m1%+)KC!qvdOtWdC5i)K@bUNrHG{1%0dF$*jR{-jKZSJ=6a@cmpoLpf|E-T80adu7SkmQsAXUBOoF?Il!OaZj#ztoK(Yp|3Nqr>-r3k0R-n%%n
zfR!l9eVEyiZ~Ip=wIJJ(375k}5nl^YG|q!!TwbS2K8MLqc-6Q^XcZ1bDeh$^bH#+I
z`fbv)^C{-L0rV(FJTm*p_Ke}+wYL?Ve=O1jmhwF{O@s!{7OdGgHJG(a)%+vz^I@up
ze5eI?xTs{`fLjIox>K3EU0s?HC2+o-nb(i|vErxsz|&{%g3og88!Fo1G`tN5;v=o{
z4*jsbJ(=?ixlkGJyRvPSrPB}6AXgWGo4AOV*8hJDi{1D+C>u+;FTbj_Tq(Qj8g$R`mUq{!!9I(lj?C?_edi}O
zTjfdR?R}Gzt|94~c6-^I<6M$BWn1;SwkP=u(Qc{Z{Vp)000000NkvXX1g=70g0Ff~
AXaE2J

diff --git a/docs/html/img145.png b/docs/html/img145.png
index 0cc86fe7ac880844c73059882e1d909a55d2188a..554b59b21951976bc6fb8c9307a231d289435905 100644
GIT binary patch
delta 431
zcmV;g0Z{(#0lWi2iBL{Q4GJ0x0000DNk~Le000150000U1Oos70Vzl%-2eapFi=cX
zMZmzor>Ccljg4n#XH88_CnqNW000dQ4Us+=e{9^WT>t<80d!JMQvg8b*k%9#0Xj)U
zK~y-6V_<*)UIs1(h6M~*fddc=Gk_F8*qDHyk@p>w0Eoqm-3aV}ABfqZnpi=Y7ifk7
z-zx?n#ly#lWE&SL#^SdS1g1eKrV9)T5C#u}l9B=gk1Eg^OhEnyPN=m9z_JN^hu0cR
zf1r*NC<1$-bSIiP6O>*Ap?Fq9`I|3*DQ+H)oew~a4N!$295|JffZo&NWCDc%Cj$=y
z!@GA67#<{mr4O(%ED$&VN))^h^@qVE%YkjWn;O7IVu_ChV+j4H}41>}%
zFm?|q`7tnX!0cmoVBl&+_J|zA86=)11H&?gwJZmCAc}yQkilyKvf(o@z0$ymu4ojH
Z1pppVHxsu#J;DG0002ovPDHLkV1l!pnyvr<

delta 224
zcmdnP{EpGCGr-TCmrII^fq{Y7)59eQNDBk891Al81EcqIj_p8>Zh%jS>wyCYmM>r4
z+uNI-p6=`GtFEpNl$q!#QSaO?_8!P&ED7=pW^j0RBMr#O_jGX#k(ipCkdW{ot$~@@
zqPtz#Y57uBg(dTi4L0PYIxuQ{QaHe;#wukY>A|>1#>Zh2?~x}@(ll6tSb63h$@KL;
zT)@z8N?ZT{

diff --git a/docs/html/img146.png b/docs/html/img146.png
index 554b59b21951976bc6fb8c9307a231d289435905..a2e86fc073c618c5d637d552a81aafe19ffff1f9 100644
GIT binary patch
delta 441
zcmV;q0Y?731Nj3XiBL{Q4GJ0x0000DNk~Le0001F0000H1Oos70j?w@gOMRje|Jel
zK~yM_ol-qW!$25)No-Bhw8^Nr9Cgty>Fm^1U5b--iVmf#qg!Tm$RvtTBRC0apt?B(
zL8MS6YwZ$o5+r1G^Dapv9<+$>@#S*gyYDBL4;UjTBuhJimAhS_*v`DU6S`>ESLyUMNfYGkP`
zk&*VOI&sq{0zx2)LZ-|y@;&_x3b!v|At6QKw^D)8WCXnD!&)!U+=FhWh}faDAo>Je
zGmh&H;S_9z3fz9YrwS-Xk&B9eZAz-t-^(J%T5GhF#yoj%2IG{b+mrCWe>*@6`ZRel
z0xqzcTZ+NdlrK;$6z4OeA0sY@=-~X(Hr)zQHq}_dr|!@nJD_+-LsWXSmKmX*Swr)I
zU0Ui4M|RnRZ1Gh@dbFAu3mNSfZBJ^*9eka1VV16De2oji2d;BNG6D_+z-Dj9Fa(<)
j3Obn8ADevr6Y&iRvW*W84=AFn00000NkvXXu0mjfc4@ok

delta 379
zcmV->0fhef1H1zviBL{Q4GJ0x0000DNk~Le000150000U1Oos70Vzl%-H{zD-
zK~y-6V_<*)UIs1(h6M~*fddc=Gk_F8*qDHyk@p>w0Eoqm-3aV}ABfqZnpi=Y7ifk7
z-zx?n#ly#lWE&SL#^SdS1g1eKrV9)T5C#u}l9B=gk1Eg^OhEnyPN=m9z_JN^hu0cR
zppFwL0(+r!Cz?1DlwJg(cveICf159WDQ+H)oew~a4N!$295|JffZo&NWCDc%Cj$=y
z!@GA67#<{mr4O(%ED$&VN))^h^@qVE%YkjWn;O7IVu_ChE41>}%
zFm?|q`7tnX!0cmoVBl&+_J|zA86=)11H&?gwJZmCAc}yQkilyKvf(o@z0$ymu4ojH
Z1pppVHxsu#J;DG0002ovPDHLkV1g5jiiZFI

diff --git a/docs/html/img147.png b/docs/html/img147.png
index a2e86fc073c618c5d637d552a81aafe19ffff1f9..ee9568425999fcd6b4f91eaeafc8c6581b4214f9 100644
GIT binary patch
delta 386
zcmV-|0e$}Y1H%I$iBL{Q4GJ0x0000DNk~Le0000>0000T1Oos70cWthrI8^_e?dt^
zK~y-6V_<-QxOEVki2(&n_{j-jD4>cnF)%YQa3^rg`*i?K2M)mX0Yn-w@Bxi#WZ(d@
z4*;25%ncJZKtv%xNCB4tgaHqN$-RLAY-Yg$27v<~5-u<#AjBpxFaik#fe_(JPD8LU7422UIxE?TqEnR?YDUUJ3BMXMxKqL8-8N60UEwEjE$pXoZOh;=rFyIDj
g&Hw@aFc^*i07JY_=0wWlwEzGB07*qoM6N<$g1sG!@c;k-

delta 441
zcmV;q0Y?7A1Nj3XiBL{Q4GJ0x0000DNk~Le0001F0000H1Oos70j?w@gOMRje|Jel
zK~yM_ol-qW!$25)No-Bhw8^Nr9Cgty>Fm^1U5b--iVmf#qg!Tm$RvtTBRC0apt?B(
zL8MS6YwZ$o5+r1G^Dapv9<+$>@#S*gyYDBL4;UjTBuhJimAhS_*v`DU6S`>ESLyUMNfYGkP`
zk&*VOI&sq{0zx2)LZ-|y@;&_x3b!v|At6QKw^D)8WCXnD!&)!U+=FhWh}faDAo>Je
zGmh&H;S_9z3fz9YrwS-Xk&B9eZAz-t-^(J%T5GhF#yoj%2IG{b+mrCWe>*@6`ZRel
z0xqzcTZ+NdlrK;$6z4OeA0sY@=-~X(Hr)zQHq}_dr|!@nJD_+-LsWXSmKmX*Swr)I
zU0Ui4M|RnRZ1Gh@dbFAu3mNSfZBJ^*9eka1VV16De2oji2d;BNG6D_+z-Dj9Fa(<)
j3Obn8ADevr6Y&iRvW*W84=AFn00000NkvXXu0mjff_S^`

diff --git a/docs/html/img148.png b/docs/html/img148.png
index ee9568425999fcd6b4f91eaeafc8c6581b4214f9..75d19edba522ce4f33d1c3481048636086f988e4 100644
GIT binary patch
delta 305
zcmV-10nYxz1MvbOiBL{Q4GJ0x0000DNk~Le0000k0000H1Oos70Vlk(>X9K!e*o`E
zL_t&-m1AH4f!iAx($dnvOa>MK1e<|@hhxJk0|gk50m9-5VqoAuz`(4)uwk_UNOf9T
z0s{jV0}|M?{($p^*$&bR4g)z0xF&pHVi00rW55eIQFyFK>oWUZ-r1^j$
zgJI!0<_DY+Tpu_icpgk`-~man3-BCZU?^l@nAX6%VOj$NXOa?F!|g7%h7HUP3=H!a
z^ttCVaGXeB=z)5C0s|w6HG@Hbp_74uV*;w9kpTcA>O-%2+)qjX0000<2SrXqu0mjf
D&|!9;

delta 387
zcmV-}0et@P0>c9#iBL{Q4GJ0x0000DNk~Le0000>0000T1Oos70cWthrI8^^e*r;B
zL_t(IjbmVdfVg!Knu!4gO!&zOVJM)AGchnTFmNYu%=>i!O$QFZ^#Md0Fz^A5YGmL5
zvJU{6T+9sW$0S18s9}+GwBp}2lFfalM4zL^O2?7vI
zULajc0G_HIBZQ#iw*%D}|Cfh&OFC&Oc>}r#5U@;O;5H~pU|`^UfJGJ#xEL5dfEfx88X6cF7Jx+<
z`0!~V40sqgE&wfN0NP%_$iNzK04T=Gzy#t?5CDoZFmQvEHBn{@RuF(-a2X9K!e*o`E
zL_t&-m1AH4f!iAx($dnvOa>MK1e<|@hhxJk0|gk50m9-5VqoAuz`(4)uwk_UNOf9T
z0s{jV0}|M?{($p^*$&bR4g)z0xF&pHVi00rW55eIQFyFK>oWUZ-r1^j$
zgJI!0<_DY+Tpu_icpgk`-~man3-BCZU?^l@nAX6%VOj$NXOa?F!|g7%h7HUP3=H!a
z^ttCVaGXeB=z)5C0s|w6HG@Hbp_74uV*;w9kpTcA>O-%2+)qjX0000<2SrXqu0mjf
DoAq{c

diff --git a/docs/html/img26.png b/docs/html/img26.png
index e69de29bb2d1d6434b8b29ae775ad8c2e48c5391..cf98cfe0687e5d392c1b37a6ee07289e80dc5365 100644
GIT binary patch
literal 506
zcmVBjLjb~?PO-)TFCno>^01XWdw6wIEnwo%sfOK?pT3T8_KtMD!G#VNjY}~9}00001
zbW%=J06^y0W&i*Icu7P-R5*?0Q@ct8F%&&B`(Vb&j#G(tF(UY85j(Nj+QQy1u=5k5
zHdZp7B7%z_AXDn05LlZWD!YVvn7osqS%~B;B5cat^OFY3rD@pgk5+=BS&L~*0`-k6dp<6pk6E8`F=QB8wY*2Skd}9KJ8P-T0kEciQ02dbSDBVQ
z38(CGgd8_PaB4mtifw^&HLo9Nqq=+7(Yu2eFE~-Y00{$3#GDY3
zdBba$sjv*c;Vx-|a?9RrfIaBo(0*&{Pex7bW0VTHKWj@ZY7@s#5i+;c5!umK4(htELEn4~(Dv%(blkM-0hjde=+3W=gjQL;F}RR91007*qoM6N<$f-9TV2mk;8

literal 0
HcmV?d00001

diff --git a/docs/html/img27.png b/docs/html/img27.png
index cf98cfe0687e5d392c1b37a6ee07289e80dc5365..09de5cc5345774f75eb8025e08c631aa0bea759e 100644
GIT binary patch
delta 178
zcmeyxe2~$uGr-TCmrII^fq{Y7)59eQL<2D&3o`=)V`13tav(=Hz$e7@z<~qHmoM+_
z?M+Wl_x1HvS62thOmvjUc5WAY4`ecy1o;IsI6S+N2IM$-x;Tb#%uG&jVDMwsXr9`5
zkWDSaSkU8x(E_G#qT&)3Ga7n0nRslvxg-jh(%Np<@FvJ|Cj66`#(PI$*2V^A4Ccljg4n#XH88_CnqNW000dQ4Us+=e{9^WT>t<80d!JMQvg8b*k%9#0eDG7
zK~y-6SA!M
zbP;Pitwb%hl&!o;c3pKAS$tF;NOCzjIXCx)03W~;x5z_C9cS`o_8}?|#Nk7f!z%wlkEYe(3h~6~po8Bq--AE1uW}`n3CWJtq%Ju*;I}BtINno=j
zjU}SkoJino|JJSk7_tjTz0HJOcts;eV}{vYu|7+STwN4JoccXc~!f2qs?u%>=c<-deinU*~Xr|fcs95+F5YCax{
zZGm$&uODcmx_j5ryMq@mI8nX=uj7%31z|wZGT0^QW8){poDh+D!)uqRunfQ9E@^{u
z%ie8(J?P-jerxMbMosKvlnS{&YfCL^6UR>xGPl(c+0j=H>cG}y6Bvl=U)JlGB&0f(
kv%(blkM-0hjde=+3W=gjQL;F}RR91007*qoM6N<$f`4()5&!@I

diff --git a/docs/html/img28.png b/docs/html/img28.png
index 09de5cc5345774f75eb8025e08c631aa0bea759e..7dac43e21487bad105e15e4088398514bd063893 100644
GIT binary patch
delta 209
zcmV;?051Q*0pJ0U7k?fE0{{R4a)7z)0000gP)t-sz`($#r>BjLjb~?PCnqNW000dQ
z4Yahhnwpw`fPi##bXrX
z#RgVw-~c&>iF*Uj1Q5TMK?N*cqjeMPmCrJ

delta 178
zcmaFBc#v^|cs(BrGXn!-Vc70+1_lP*0G|-o0|yQ)U%tGzw>LdK-PhMwU0oe0vt`Sc
zS+iy}G&Gcylte{EIXF0&n3zaONjbNRy$4D&mIV0)GdMiEkp|>AdAc};aLi0jaA5Fb
z)@YvEc#usk!&uPcgV6$}Z=&K77Bd=pIGK2Cy166@w3*V{ZrAW8$Z{t9lbObQM`6~+
d24)W?hN)Z}&cT{-K+_l)JYD@<);T3K0RUMbH}C)e

diff --git a/docs/html/img29.png b/docs/html/img29.png
index 7dac43e21487bad105e15e4088398514bd063893..9430fcbe698aca4ff4a39e0554606de01496e7f5 100644
GIT binary patch
delta 187
zcmaFBc$!hMGr-TCmrII^fq{Y7)59eQNb`X(3o`=)xl!JqViHV7nl+=%DD?R}gGnNGT1v5B2yO9Ru_v93CDW1Od1nKPdtcX
jYl}_jEMeQm!p5*bjYm){X@YDS&};@zS3j3^P6Unv2w`|!mYu2oW
zhK7=olBlRC6B83DDXD{Z1LT2<8B2ovf*Bm1-ADs+QaoK8LpWw8Cp0j#w($zE3D4l;
zZSDHpu=9*T>Ow{ykA{h|9v&(N0!%)<4#9d1TjdxoyfuUIIK9X`YCWQFo<&rd+na}q7P^xgQu&X%Q~lo
FCIH?TK)e6|

diff --git a/docs/html/img30.png b/docs/html/img30.png
index 9430fcbe698aca4ff4a39e0554606de01496e7f5..aa48fceccb3ff00fee354ec871a7f73ea2af0aad 100644
GIT binary patch
delta 209
zcmV;?051Q_0pJ0U7k?fE0{{R4nYRM(0000gP)t-sz`($bjg4n#XH88_CnqPTr>C^E
zw3?clfPjE>baYx;T0lTRG&D3C8X9ZCy*2;<00DGTPE!Ct=GbNc003l3L_t&tnPXsJ
z;9`J*01z>afsp|T2r#f-U|_hwfC)H(auD4!7GRNv1Ga7u!Ab%o#LR%i1Rjv796+KG
zsErYyPAp~>fGH*h9+2G(6BtS$E@4;+rL94<1_P4;Seg;)P;vkOspbknw?dVD00000
LNkvXXu0mjfNmxjs

delta 188
zcmaFBc$#s7cs(BrGXn$TtVD(q1_lPL0G|-o0|yQ)U%tGzw>LdKU0q!rD7fw&D{|nz1CvFPOpM*^M+H$KTV%F@$4gazes`q=bYS
z3`cm*u<`_4IB>v_@zfL+qZty@3=i&r*k#g~
oD0<>S6kA(tLT3rvHWoI91!_EENfTttfMzpzy85}Sb4q9e0Lw8y8UO$Q

diff --git a/docs/html/img31.png b/docs/html/img31.png
index aa48fceccb3ff00fee354ec871a7f73ea2af0aad..8b03134963d0c35fcfe54bb9e87e19535f911b84 100644
GIT binary patch
literal 467
zcmV;^0WAKBP)BjLjb~?PO-)TFCno>^01XWdw6wIEnwo%sfOK?pT3T8_KtMD!G#VNjY}~9}00001
zbW%=J06^y0W&i*IQAtEWR5*=eV1NN06bb>jftZtlVFH*VfG!IKlO}M3X}$wE6u_VBrtF?
za=>&jG=K<>1~ToX0C4bPgg65OKb+!+i*ds#goZOjxgoE!`c8-Pq^o(~KROb-q)
zBwR?~KES}Eq@)D(n?M7@gWn$>BtX>hIvfD10~&+~0R~18i*Y)pYj_MO@E_g4ZtYFG
z2`b`hU>D$maTu@RO3n->7;IH6stVz(IlBrOWHuYD`FjG$VTOrvSl?U+v4VRK!yE?w
z4a^RF8yMa&1%MP?QUU=5P@)Zjs#iF}@QOj7fn8FcfvJLT0Vv^WA)Nkz5yIg705pJQ
z)z(!!MyD9~lpBy;WV`y31=Q|G`xoHy9Ri3=I73(w1BV6!0{}TgK?MiO5HkP(002ov
JPDHLkV1mNer^EmN

delta 210
zcmcc2{D9HAGr-TCmrII^fq{Y7)59eQNb>=)91Al81LMr?Oz(jltpJ}8*8>L*^!E0q
zr>Fb+`l_p|FJHcVqN7B8_QAboKoyK7L4Lsu4$p3+0XZq2E{-7_Gm{e%9waq1G6)#<
zHcn*Z!MSv;;}$mN$&3-R1YZRdF)*xr#^t!(iEnBx&_V`JS3j3^
HP60000R1Oos70kP>{xRD`De_KgJ
zK~y-6V_<-T4GcH|Cj)~5m~jAyf=Ls&!88*t1yFDRVi*XV1>*Rx2|)5C10PVFyMcj$
z3q?CKezR}`Hf=D)%fP?`7dtZzM9$!z!44F2Qc_Z2U;_y-axid$FjQ3oh>$EG*J26)
z4=<(|mp+){2O}sr010SrB)>5xf1CkPGZxI?V^`v3!vl9CeC
zZyypE9{m3BAOWI|*Wmz=d~kpP5dsX1U=~LMhHE%vDDoiv0O#2QD&9n>d&R&m0An*=
z6TqR0DM-l$!7~Aqs+h|77BCdT*mHIjGRSN;So8M;15zsHu)ettYRT>ca-0Vk_%|>+
z@NHmt!xR8gbx8>X6hPS{2xc?S0idb+4D6En3``Y#3nl=?wBQzUJz#{g=7ZeBvTExp
z9-~tXe98^T&az#7$pXsk)Bc6Si^za6lji^t${3n})&Kw!*+zfaKtW>w00001JeT`iBL{Q4GJ0x0000DNk~Le0000=0000R1Oos70bVOKhLIsme^E(9
zK~y-6V_<**9ux`zxPh3HfnfreBY-Xo1(POlgK544I26DDCxp7dz!3j60myjCpa8U@
zfq{VwS!WLcQwW&Oi|h?Eu*+v~&tM0NIVmYAFtC9HJ|r-3GIGFlFf@P&js`OAr2ug7
zVuUyY13#SNhl_E;DTIbIU~xez@wz31ofLh
z1H*&gA08w?)bTnT0ICBTga`o!Mi7f}I;LxQ3@Gp)-N0_`O}hyy;%Z+CRV=Cs;jB5k3K?WJ8?5!qTnDj&dk@1L2L27q4tyIJXx=adfD~O)
z0s#e3q78zoS2)A)ib0=&T~eQcse*3-DB)@$oc@3j!r=S>G=OE*)>S-4rx^H@8<1UO
wyZVv^)b2<77vS<80*FmGLs$_5hXw-!069ZJ1qaFyGXMYp07*qoM6N<$g4>yrY5)KL

diff --git a/docs/html/img33.png b/docs/html/img33.png
index aa4a804d31eb48b9f2a1fee76605997593d383cf..1a3431668deb0d8671a9ce090e5c918f44dfccd5 100644
GIT binary patch
delta 210
zcmV;@04@LB1Cs(FiBL{Q4GJ0x0000DNk~Le0000P0000F1Oos70hCWkK#?I!e*lq5
zL_t&tnPXsJVBik`5)APP3=9)M42B&HC}7eAZY16X28II+44e%+8w!9l!vui_s4f)n
z0gMu{wFuY*`yIr4wT~eQcD5-*P0mx96Ra;l_7@cC^Q*K}Y0Md#fi1=Zw=l}o!
M07*qoM6N<$f|?aY@&Et;

delta 413
zcmV;O0b>4>0^I{4iBL{Q4GJ0x0000DNk~Le0000>0000R1Oos70kP>{xRD`Ce*s%b
zL_t(IjbmVdgAEKg0Ve~40+?|Chk{8HxWP0NE(K6<0Ad&joCV_euL(f%B?BK&oV$U6
zfeS@DGk&vh12%0i#mm6J0~b3p4Mfi1p1}?jb5c@LU|<6YFmf<(f-qE71Bj3;AlG6F
z01q#w7?(bn;s+xrH~shuf%^ahkCKuS
z)NdaW7#{ro@E`%Aj@RJ;kbH1}0TBWWj9?Z=1BPojWGM0={Q&3L11jD`sC&i0E&yXQ
zUK7BfiYZ9R1;H}`ld71?_!ck}!q{_m6*9%X)iBL{Q4GJ0x0000DNk~Le0001%0000S1Oos70R{tW`H>+@e*#2F
zL_t(YiS1QQYZE~jesZ2N4e%BB8wqZE;*du!OQl(aYAOr{FK}o!QSMi-OgQ_=G(B_p1OvC@U9HW#nK`03M+<>2{msxTo0KJI>!_X
zDfHH4&C8kK5t2lmrxr82Al=k&&L!=KrE#Gx+`?9)c(b5xGR382{Jf~RW3?yA527Jl}bM_7uUe~?+4Do7&Ht;^c
z%FO-I`n7ZBd;4O8J=
isfwc5=bG(*20s7-n3XDZWsCm+0000u{wFuY*`yIr4wT~eQcD5-*P0mx96Ra;l_7@cC^Q*K}Y0Md#fi1=Zw=l}o!
M07*qoM6N<$f{58g-2eap

diff --git a/docs/html/img35.png b/docs/html/img35.png
index a0f61030094fac14194363e8acec086f01bb2749..a758b5013a71f66f2be374de26dc2f685f054369 100644
GIT binary patch
delta 192
zcmX@c+Q_8X8Q|y6%O%Cdz`(%k>ERLtq@{qEkA<0mfpLq9;
z7@9a09(`kEGkB1emejz^>gUGBwl0{1@j3Tqbs4rx@-rlM{FE$Uns=3_-7<_(Qu;^b
z4^s&V3&|T27PBNIDkOJIoyk-1`Y@B&yyUtAk_QVKwkPU$M4vcd;Op7gsI9|vBC#wX
sAtU*LMdZl`j86=ko>(`UToAKoC=wQ3zu=Gs&}9q^p00i_>zopr0Q?L-yZ`_I

delta 648
zcmV;30(bp^0>%X)iBL{Q4GJ0x0000DNk~Le0001%0000S1Oos70R{tW`H>+@e*#2F
zL_t(YiS1QQYZE~jesZ2N4e%BB8wqZE;*du!OQl(aYAOr{FK}o!QSMi-OgQ_=G(B_p1OvC@U9HW#nK`03M+<>2{msxTo0KJI>!_X
zDfHH4&C8kK5t2lmrxr82Al=k&&L!=KrE#Gx+`?9)c(b5xGR382{Jf~RW3?yA527Jl}bM_7uUe~?+4Do7&Ht;^c
z%FO-I`n7ZBd;4O8J=
isfwc5=bG(*20s7-n3XDZWsCm+0000pambFGvL(+jIqlb}QUg+3
zcerREsgl*vMRlmzsw$Mqn6)wK(=9quX{!YpWrXFc%B3N@9(V3>6XamPdmt(_f7+JR
z8n@Zbu%P(zPzx6gKhsW%}Kr*X{K?I4&FvxpCzN*_dnHbAfm!A2QDuH2|3YYR43
zn{N!gA7vWS(o)^}dSD`MaEYrIe~ki?lyEnog*V-J8bF)}rYWe$$H-YmN6!VIa293q-;&e0eb0a+r3q$hcw
z3>t}la@p?|nR?jO4aJejtFaBDxATgyc;h|s^#x?)zr4q_rF%Qt(tYq17JmW2AP!hB
Sga+aO0000ERLtq@{qEkA<0mfpLq9;xiz}V4|vCy@`p5l$2D?
zoi(vQ5yp}rzhDN3XE)M-oO(|e#}JO0$q5WioC=S=F|rvvNJ~p+a>uK5<7lM7BJ1b%F}Kc#waQMqw_aA
S$O7mT1_n=8KbLh*2~7ZZDn=Cm

diff --git a/docs/html/img37.png b/docs/html/img37.png
index 5ed5aee4f3b0f5b91c7750d6c3f35d7110d74578..71286e309f4309a27dc3cb4ec486e795cc2ec467 100644
GIT binary patch
delta 980
zcmV;_11tRH1d<3LiBL{Q4GJ0x0000DNk~Le0002#0000a2m=5B0W6r^Es-Hke*=w4
zL_t(&f$dp|wxb{n4FM~JIQaixJ0XBYi+w$Bn>RDw(k*1MSM_sJycNd|(KwPKcO
z6^aNqZE&biV#AN9>WH
zY!>1ju#%);%|%ez5>)inf2Qp;m|tR&OQco^vt%G;F!q~B4T|X0Oetjt>-Qrr!<%4@
z7QB?kA&ZMEsor~9NH>^~J!#I`^&E`FV>Zz9PCN{6Bw^iP4Pv1sw>Oo3n{^i==MSEX32f}A5L+*xrRH^&puAje@m72r$_x0K`&gm
zaN)vVhFA)ilZHLaV`0}r^)x6n9$j^w%$d7S28R}L*l>VP2R5EoByYItJQXo;q+D$|
zjKncmS~{(_aS4>Ry5`|bfNLUR_K{K!h8A6f=n{fkN?IYc9NCe$E6#1G4aW#lTt4q<
zj9IZyckHV3l*Ls_e_ZRNVq0RZg``w%+FVFZ_jzF#?9jR@ANj{l&e5nEgn64{+-6Y;
z0qQ)+O(+fb2-TzZtoAO4vHBa6fz1nR!M;m(?5gu5q9!^U8R0BUq*h_minr9AyYR6<
z!_@WE&mmuU@a)>HpzV1HT|N>lC2H*2w^F$I{TjV
zlx?=%r#p7lc}m}Mt}qT@xR#WL1{qxC;gQ`ZdA1^rTy>uK9jE^{fJ2vj_QwG~40T=d
zp6)W^mZPiAD$^JI-)0|E|3}fDwSOP=S-WuIJMbH%<{Wbu3maGf0000pambFGvL(+jIqlb}QUg+3cerREsgl*vMRlmzsw$Mqn6)wK(=9quX{!YpWrXFc
z%B3N@9(V3>6XamPdmt(_+LqKBx7p6Hp!o7o3l|MP)oZUW>hyXa=on(Df2mnMK38j5
z|I0l87<^~zI%fQ|G(Py?S7Kk|@2L7aVMzj8r4|EAAj1(>sW%}Kr*X{K?I4&FvxpCz
zN*_dnHbAfm!A2QDuH2|3YYR43n{N!gA7vWS(o)^}dSD`MaEYrIjRKOCa5tcZH{E#S
zrkY8!S|&Y^72>p&iSA89d8&@m=1hhAR)=X5)-P24cs*L%ul>8bF)}rYWe$$H-YmN6
z!VIa293q-;&e0eb0a+r3q$hcw3>t}la@p?|nR?jO4aJejtFaBDxATgyc;h|s^#x?)
lzr4q_rF%Qt(tYq1e*wTC4p=XQ2I2q!002ovPDHLkV1ktk{R{vA

diff --git a/docs/html/img38.png b/docs/html/img38.png
index 71286e309f4309a27dc3cb4ec486e795cc2ec467..4ae3794e55443bc7cdbf1a8d3d87fb998d7d6127 100644
GIT binary patch
delta 286
zcmV+(0pb3V2*Ls-iBL{Q4GJ0x0000DNk~Le0000i0000E1Oos70ny3RnE(I)Fp(uL
ze>5~S8X6jG+^k&y0004WQchC8GN2Q0A)T&oNi
z&;WP*XI2IVt_4i4wrDau3l6QeWjMuPyAWth2{;1RPLcWLO};aKNy7!G?gxT)TKTH4teiK`^ypJ(o-b(=Ucc
zASN&j-tbRgVBpMPxXr*Wz;l4}1DMIckpNQ6`GD!e1`~$12L72dLCm!*2YA5Z4U7x|
k3>*v$6TnQy22KVB02lHzS#6=V)c^nh07*qoM6N<$g4~2=LjV8(

delta 1012
zcmVRDw(k*1MSM_sJycNd|(KwPKcO6^aNqZE&biV#-Qrr!<%4@7QB?kA&ZMEsor~9NH>^~J!#I`
z^&E`FV>Zz9PCN{6Bw^iP4Pv1sw>Oo}JV*`X5elySaut($79l&`Xu}r$_x0K`&gmaN)vVhFA)ilZHLaV`0}r^)x6n
z9$j^w%$d7S28R}L*l>VP2R5EoByYItJQXo;q+D$|jKncmS~{(_aS4>Ry5`|bfNLUR
z_K{K!h8A6f=n{fkN?IYce;nD7xGTN>lC2H*2w^F$I{TjVlx?=%r#p7lc}m}Mt}qT@xR#WL
z1{qxC;gQ`ZdA1^rMqG8C_#LPJH-JNzeD=oyKMZwU@}BN8
zLy>?ecqd2EMG@qA3Z6%ma*G@;Q5W5c;3nexz9iSQSFah0p!h3EzVE%?dwK8meP2Fc
zBtkuEi!Z2El6f0&Ml-Wu)~y99f61ZE7eO0ugJ$v+awsSM<-nJ&W-pWk0*m}C+s)xI
z7fA090iL`&=j#QiJOg}1ASa%{v`{h~WvY^zq(NvS;<4J3iZ3thEhTXgmwzz0$`Fg>
zElM;~xapLd1Y3uw)oPrr6SbP0EbRc5SEWN$E(0e2vc62^%ZI6HvU0<3e@Woy$)vg`
z59=RAd0S~AdD;kRE6Y}EGbEABdl)o05fAq
zlyb#FB2hMj{U-u>H=;bQm}|^$%GgFg9B*{ddK?&QM{oyt#>6$LO!sa5=VIr^a)A2Y
zwsqP$#cDDd8_PCx1ubccelS>?*Of=|Bjid2H-NR!--=&Fju
zHvIAA&!KhbE>`Lxc;|S@iG9pgMt@JQ*Ps6|KG)wizT@l*b~U%OepqrZ=_hP)F|`>i
zyXL8aI(f<-bJf`-JhmCyL4=LpoGOZa|CHgTaEF^=8|*A^Q@S
YUykaSTJ=_rp#T5?07*qoM6N<$f*=1^p8x;=

delta 257
zcmV+c0sj7@2Eqa%iBL{Q4GJ0x0000DNk~Le0000i0000E1Oos70ny3RnUNt&e*nNq
zL_t&-m1AH40%isX_`m=MEU^k)s|*;>0C)UnRt5&H1x&8CXfiwt4z0FjIK^PQ5NJ&0
z1TLQW>=XFVwc`M@9lTF2;M~Ho^8o|H2B!-PIJsFknHU(D7z92998h3nSRlZ_uzJCU
zfX7_BcsDf=X(&N3wP8J%Oa#*}SB6I*CNK=%@K0c1;LKpS&A=|ebAa;$n90DA08-5P
zfa${q6Na`1{+TmD%(W~Bc);Qfj0^${91IK-z)Z#lP6h@57xFV%ZK1Z+00000NkvXX
Hu0mjfh#g-S

diff --git a/docs/html/img40.png b/docs/html/img40.png
index c00b10d4e9d950bf8f4d533aefd8b622cfc2fd40..fc90801217f55222fc19f6d75b0b8dfc3df08658 100644
GIT binary patch
delta 424
zcmV;Z0ayN`2IvDJiBL{Q4GJ0x0000DNk~Le000170000S1Oos70coD~k&z)we*tDm
zL_t(IjqQ`MOT$1E#=j&@lS{5?R>2{rI0@<~1tB$tPUijn;N+iWQKM(i}IyR
z6ks^?5$+|MIABA#(OQ43o6vbufA)B&y)2Prv*!Nlun~%q;0*B@YPz&EzY>ZzE)Nr0QcLJ+>V+MnW+~0_0R}d6RfR$uE48@dZ
z?^}))6^i9-K1`$7=DrF7qC)*X-^1zz{rqb{M$b=V<0qEK>z5ApPXhf4e$%*}YhG02
zq_WtH@3xMfGQ1p04nAf)tBqH&6lyNscwyO2mEpc@0d|TnK$+6L1B-M-*F1(C(1
zG3aaN6sB~Y;)TX}gW6T7&u4eu17=}V^1Vy3ss`GGB_(
SFMk~X0000
zLy>?ecqd2EMG@qA3Z6%ma*G@;Q5W5c;3nexz9iSQSFah0p!h3EzVE%?dwK8meP2Fc
zBtkuEi!Z2El6f0&Ml-Wu)~y99f61ZE7eO0ugJ$v+awsSM<-nJ&W-pWk0*m}C+s)xI
z7fA090iL`&=j#QiJOg}1ASa%{v`{h~WvY^zq(NvS;<4J3iZ3thEhTXgmwzz0$`Fg>
zElM;~xapLd1Y3uw)oPrr6SbP0EbRc5SEWN$E(0e2vc62^%ZI6HvU0<3e@Woy$)vg`
z59=RAd0S~AdD;kRE6Y}EGbEABdl)o05fAq
zlyb#FB2hMj{U-u>H=;bQm}|^$%GgFg9B*{ddK?&QM{oyt#>6$LO!sa5=VIr^a)A2Y
zwsqP$#cDDd8_PCx1ubccelS>?*Of=|Bjid2H-NR!--=&Fju
zHvIAA&!KhbE>`Lxc;|S@iG9pgMt@JQ*Ps6|KG)wizT@l*b~U%OepqrZ=_hP)F|`>i
zyXL8aI(f<-bJf`-JhmCyL4=LpoGOZa|CHgTaEF^=8|*A^Q@S
YUykaSTJ=_rp#T5?07*qoM6N<$f{_SU#sB~S

diff --git a/docs/html/img41.png b/docs/html/img41.png
index fc90801217f55222fc19f6d75b0b8dfc3df08658..227f4a45eda40082c3e0805fb7981688608a2799 100644
GIT binary patch
delta 805
zcmV+=1KRxP1L6iDiBL{Q4GJ0x0000DNk~Le0002Z0000S1Oos70Y~>1Mv);)e*)l1
zL_t(YiS1UuYZO5keY;7_?cUtp7Fq}vn+<79&;y$o4II~6cv#waSfw+6LP(_`x@Z$2
zn1g5&PdWTi7$b}^O-#@rHWGxU*PGsnvAY}`|Tr3Cu$-I*&;|1rZDVe(<+n`t=5&GOC1*CR@xMZH
z;{sjiPN`ztX|nUJ(qw}U<)vd4M>MJ9Q(1S+vf#@G7Q-;0Bn#ImQbFL+f3gvl0?Hik
z6;4b-(p(NzI2jA%nncNmgJMQ2*{MekY&Ot|FHvRd)&P-(U>YsyVh
z?OMa|b&cK9(Im&Gs+s4JtW8#f*bB;)s=SE8C#sNcQe&$Vd3wm0RD
zkSFQVGv<0G5cv^L>NVHH*3~4}bl!tP+rG8PPWyI*BODeyn
znU4>hb+QW(rTLZnPhn)HI{A865nFweLV9&OS9ipJHMkebl&<31E@5$`M-Cza-7G}^>6_R$@uA1waA)-RtPgmwD
zdIMjK*K?+AJ#IO2dm6ZkRmaHWdYg2*=U&Z;a0GV-M~AVF0eJm8?$0{)FHRTetv&kW
z^DywevyM22T-`3?hnbn`><7~a$K#IwnRwqWztclM)iKb@2{rI0@<~1tB$tPUijn;N+iWQKM(i}IyR
z6ks^?5$+|MIABA#(OQ43o6vbufA)B&y)2Prv*!Nlun~%q;0*B@YPz&EzY>ZzE)Nr0QcLJ+>V+MnW+~0_0R}d6RfR$uE48@dZ
z?^}))6^i9-K1`$7=DrF7qC)*X-^1zz{rqb{M$b=V<0qEK>z5ApPXhf4e$%*}YhG02
zq_WtH@3xMfGQ1p04nAf)tBqH&6lyNscwyO2mEpc@0d|TnK$+6L1B-M-*F1(C(1
zG3aaN6sB~Y;)TX}gW6T7&u4eu17=}V^1Vy3ss`GGB_(
SFMk~X00001Mv);)e*)l1
zL_t(YiS1UuYZO5keY;7_?cUtp7Fq}vn+<79&;y$o4II~6cv#waSfw+6LP(_`x@Z$2
zn1g5&PdWTi7$b}^O-#@rHWGxU*PGsnvAY}`|Tr3Cu$-I*&;|1rZDVe(<+n`t=5&GOC1*CR@xMZH
z;{sjiPN`ztX|nUJ(qw}U<)vd4M>MJ9Q(1S+vf#@G7Q-;0Bn#ImQbFL+f3gvl0?Hik
z6;4b-(p(NzI2jA%nncNmgJMQ2*{MekY&Ot|FHvRd)&P-(U>YsyVh
z?OMa|b&cK9(Im&Gs+s4JtW8#f*bB;)s=SE8C#sNcQe&$Vd3wm0RD
zkSFQVGv<0G5cv^L>NVHH*3~4}bl!tP+rG8PPWyI*BODeyn
znU4>hb+QW(rTLZnPhn)HI{A865nFweLV9&OS9ipJHMkebl&<31E@5$`M-Cza-7G}^>6_R$@uA1waA)-RtPgmwD
zdIMjK*K?+AJ#IO2dm6ZkRmaHWdYg2*=U&Z;a0GV-M~AVF0eJm8?$0{)FHRTetv&kW
z^DywevyM22T-`3?hnbn`><7~a$K#IwnRwqWztclM)iKb@0Wbc^0*?eCiBL{Q4GJ0x0000DNk~Le000190000S1Oos70c~p~tdSv0e*uk2
zL_t(IjqOy+O2a@DJ$aNSW}0T{NPyWr9XbnVIy=%V-ye!ze$HxgWl6d4c&MWpCP
zkiuATBO+PrCjLS33!E9_G-;zk7p^>EhI{Whb7$_IBtQww%=#Fi8htUS7`&40Xp3$q
zREq6~ZxU5PWhFp{=MFWAbk>B^e^5=9a@@BOGJ8>=aL*NOAEf+OITgD^?OMg7j;@GaMeuRyckOPa%ZJi#O!
zrp&h_jf
zU=9L;c!ZExC?qgB(j*2sQbp5jO0AA`qJ?i}cK3FZ7%ier{F0lS`R0A^&6{~M9B>R?
zGx=phzgtT=?KnY-C7>!h`y>W9f1t}D`<>8j7sqxgx_3WrNhTCcET+uoC7y)&E1vG*O8X$?3cO
zE>yM3vN3Wbcv)3+divtnc{M+sIP!}3GtP@-bk+5;NIhXC$@4*zcegQ0_30>4yZQ{C
z!Fntw8f`yl(H)JWK$4o}f8*6-O3FjW_dQu>(~xCW6>pF~HcTR|LYJ6hN-U4az{E!M
z2s=b2kxG~fqrnDucBJtlSq0A<2%Iaj3Nc-DJ4#1OvK77#e_H|@vYq*LAY}kE
z&a*nt0%c%H#F@UH-J0lHAFjjP9JgXPE5x*b>?u=*>+`FaU5?1WocOfhV)N)gq+Y+=
zem~yDOW@(^i#_2hwe)s@@74xtowJO?+fqVf+ZXUuAboHVwZ++p3@qFx?uwMJ#3GDe
zzv&OFK;9Nv+D&`|f4Paup7fPkT0Q7fWcSY8w>j))1VgM~q>#}ZaEZEP06V5fWKyzv
zd>|uI&!OC6JQ6>r7U-QacxFk9#qvmiPQ8UD*j4iE9y%k++8LV%8QgfYeGS+;z_z4kr&7JoPNxc97002ovPDHLkV1g~okthHF

delta 464
zcmV;>0WbcW2ag0HiBL{Q4GJ0x0000DNk~Le000190000S1Oos70c~p~tdSv0e*uk2
zL_t(IjqOy+O2a@DJ$aNSW}0T{NPyWr9XbnVIy=%V-ye!ze$HxgWl6d4c&MWpCP
zkiuATBO+PrCjLS33!E9_G-;zk7p^>EhI{Whb7$_IBtQww%=#Fi8htUS7`&40Xp3$q
zREq6~ZxU5PWhFp{=MFWAbk>B^e^5=9a@@BOGJ8>=aL*NOAEf+OITgD^?OMg7j;@GaMeuRyckOPa%ZJi#O!
zrp&hmz?e*v^f
zL_t(Ijnz}XOT$1E{?b(2G?#jd`;p?H1?k{W6hQq1EX75;R9wWxtZu$bYE5di;2`*sd+*-Qd+*%^=z{eMq?s1d8MJnnT-a`_
z+g;)^uph(D9x(-TC`bAB#1vehe`axjYS>U62be)#6S55B7x}h}9tshrBz*=8Y6`;V
zsz-H?CKy)19haoIX`19jb$QNy3I!+yQYf0Q{woxJ?C)F9D48D84BJ5|*b=l{JAI0-
z2dI1d!2#u|ylDy8{-6@HTKmh$-O>;kc!C}g8EU2}pp16Lg`7|k?;j{le>?2~7hpNW
z?&v0XQVEyMeTj$4`QNzuO%M~3>L=B#9qkai;a`sQ|fD_jf
zU=9L;c!ZExC?qgB(j*2sQbp5jO0AA`qJ?i}cK3FZ7%ier{F0lS`R0A^&6{~M9B>R?
zGx=phzgtT=?KnY-C7>!h`y>W9f1t}D`<>8j7sqxgx_3WrNhTCcET+uoC7y)&E1vG*O8X$?3cO
zE>yM3vN3Wbcv)3+divtnc{M+sIP!}3GtP@-bk+5;NIhXC$@4*zcegQ0_30>4yZQ{C
z!Fntw8f`yl(H)JWK$4o}f8*6-O3FjW_dQu>(~xCW6>pF~HcTR|LYJ6hN-U4az{E!M
z2s=b2kxG~fqrnDucBJtlSq0A<2%Iaj3Nc-DJ4#1OvK77#e_H|@vYq*LAY}kE
z&a*nt0%c%H#F@UH-J0lHAFjjP9JgXPE5x*b>?u=*>+`FaU5?1WocOfhV)N)gq+Y+=
zem~yDOW@(^i#_2hwe)s@@74xtowJO?+fqVf+ZXUuAboHVwZ++p3@qFx?uwMJ#3GDe
zzv&OFK;9Nv+D&`|f4Paup7fPkT0Q7fWcSY8w>j))1VgM~q>#}ZaEZEP06V5fWKyzv
zd>|uI&!OC6JQ6>r7U-QacxFk9#qvmiPQ8UD*j4iE9y%k++8LV%8QgfYeGS+;z_z4kr&7JoPNxc97002ovPDHLkV1ltlkxu{s

diff --git a/docs/html/img46.png b/docs/html/img46.png
index 74259acf5eddbd9d5ff8254a60615b5779b7ae92..daed562ba8a5f804397083964e8c152dd10fe58d 100644
GIT binary patch
delta 513
zcmV+c0{;EB1i=I$iBL{Q4GJ0x0000DNk~Le0001N0000O1Oos70h;_ZzmXwKf4@mY
zK~y-6-Bi6x!$1`OU1LAeUSbya5Oq*NIyi_T6wyT##6LiaLr1ZTb5Rfkhu|oJ*)27z
ziV%w+qF{0JW2m@@i(Lf=-{lOZHGb65AKdTd-Mjbhy?1v3THrhbdZKwwqp>mHfcx6I
z+Q+FBF+oFE-z32>9l7*Z$YGDTf9e>33Y3&%uG^Tzuxg52D4BBGA=e5L5vCLku7zjv
zrj&}$UPf?|V+n@WAf>~yELudF2}44LV1OM8!BoMew)6Ze3g6fF6-3#xz5so0SX&5d
zYBn!F(sV-PR}a+`y;6_CI}RZu
zH$$)0lMD7AKR5@U8m*lSl=nw!bnAULC2&b!0*Aor(bhelkffsliALEPbGEhU
zdoneOcZ*)=-E6tA*ixBJM&;(HyCl`I-K*i~zWj_gF=S!lPgXhB00000NkvXXu0mjf
D$0zB&

delta 502
zcmVmz@f3!(N
zK~y-6)la2Q>EKWlK?E035dQ$_RB#bpoJBzp9Exr(W)v(X
zxM>kW5kwR$#YMYRT*Sq!ZoW%uO=`5@Ao!7c@7~XQ@7)FHg7pfdnHJI+w04(V*lw%a
zUE(sZAH&WbF$HrdNBQ=|6kMQYe{q0n*ian@m_c3>vJB%F`L>H53K6CxeFh6^3c}~A
zM|F=T7*@d@m!!C9n&d=vdCqC)KPS?GU@+UzIhF9$^huWKi-s^zZu6h0oQg&f(K%
z*I=^~^^0uzbi7V)!;4Zs>?ykODzJ5a@Q4JJk({`%aEK-
zS~@jT>T92;VNp^SYn%uUOwngCr=;64X&m{iZ@wyN1?_%QEqXGBt-J_>vNbV;bVgY(
su5@*kCZqarp4srE$>T;oaw5I)4s2jvmP1X2oB#j-07*qoM6N<$f_)g_RR910

diff --git a/docs/html/img47.png b/docs/html/img47.png
index daed562ba8a5f804397083964e8c152dd10fe58d..507614678dd02efd209ced9ccc386fef7a04d357 100644
GIT binary patch
delta 275
zcmV+u0qp+41k?f{iBL{Q4GJ0x0000DNk~Le0000h0000E1Oos70W%fI;E^Fqe*n@+
zL_t&-m1AH40xkv!xWoVl+z)sa*cgz(8wLgiUha5iAXA%xsSHWxAP{>WV6i>4+Ln_C
z$o^2s&oF_DXTk;stbpkNg5AN+z`&!m;nW82lM5JtY=#XFxS1|2;A8-*;bah)!0;j9
z05=l@125x(3k(|q9*gB+HxnB;X~bELMU*p{K@CJNJldeou<#u7E13wUUks0cBEP}%
zg$!pv1OvMO&jHR43=F%$qRb9V0S3$t3=Ad=Z4LZ0CrnY&0SPk#eE=dD1Q<9N7$!h$
Z006HhE{y%1kiGx_002ovPDHLkV1jzK0!iBL{Q4GJ0x0000DNk~Le0001N0000O1Oos70h;_ZzmXwJe*wQq
zL_t(IjonneOT$1E|6OB0(q3W~_YieZK{_~yA{5a@6vRJ3ibF@Si*r#B1c%@#g4r!K
ztBMedAfjM#^JA#Eh>KkX2jArkrZs-l(I4FJ<=wmY?!9++0b1ZZ1A3x)PNT6g-+=qt
zy4uI76fr?VSl=YUFdez{SIA+Hf4J%xfC`k9W3Jnn#IS0LTqv1x+acEq5)q~p4X%Y}
z@}`uE&t67wl4A*m*C3_CvMgFenF&KehG2jl3c*ytrMC0@D+=G&_Z39hvc3R)Zdh9g
zYic$xKhktU_FZhkjb0JEFg{OKrO+J|qrFm(!8;Bi
zBR4~@)sqYMA3rz;pBk;543zgrYIN&;HzjaMUjm1~>e1Fco{*%Y8@;X=FmF*26w}=F
zEM6#1R(M@m0%8|l&rm&fSp0oQdiisL8z>q?*g@Rko}F?1zfAu}iZh3TD+p>%*Xi|KM=pbs_Mxm*aGXSHKILJw!U)S_Nw+upPREHvEp<@&4ZG@!){gH?Gx~
zzc$g{RXhRSQsh16Ctd&Tf5qc{wk~*{yyHe|{IhSsdNnue%QN@{rOE#y(VMwoWV6i>4+Ln_C
z$o^2s&oF_DXTk;stbpkNg5AN+z`&!m;nW82lM5JtY=#XFxS1|2;A8-*;bah)!0;j9
z05=l@125x(3k(|q9*gB+HxnB;X~bELMU*p{K@CJNJldeou<#u7E13wUUks0cBEP}%
zg$!pv1OvMO&jHR43=F%$qRb9V0S3$t3=Ad=Z4LZ0CrnY&0SPk#eE=dD1Q<9N7$!h$
Z006HhE{y%1kiGx_002ovPDHLkV1h+7U!wp3

diff --git a/docs/html/img49.png b/docs/html/img49.png
index a6a250ad4697b7295cbce257f9fe39a3d9e47920..c6870ddb4f86d303b73ae4e8d33265db13d899c1 100644
GIT binary patch
delta 454
zcmV;%0XhDT1%(75iBL{Q4GJ0x0000DNk~Le0001G0000S1Oos70sVMfW04_Ce*uF@
zL_t(IjqOxDOT%Cgev+misc+MOxQ9q5K{ARUh@f+Sf%FGB=syT9;vzxa8x#d;kUA(>
zQ9>JVaOvKqvmkVJ^WJ@G~@L*#sK;JDA*
zEuc4xDuFtgD>CxkMHNGyc|6-Tf7WD^X9e~;?smcEJpX&J*kw^Hq>2nGRCgqR>AKGA
zr>l{wBtY9d?96S`VhLWYBA`6+Ns-rlEwr)WV8FLsg0xQz`
zWb8xYtD|CfGhhr&f>fwlo#?b2Y+_n8NQv@Nyi_H+%*>b|bpMzSH>pgaf8P}0$cmyF
z5Om7dT2jNdI&bhUpW&@IkL!Ir`HYd)+~wV*MjPN(th7N^uH#c=oY~NQL>hKc8zwdK
z2nTADf+q4dbFC}>*@<@Q9{QVT_|f@?b=EUcX$$Xk7cf8#$})QKSdm8Daq+UJagBxt
w^XFBJC*o1dvF<%|KM=pbs_Mxm*aGXSHKILJw!U)S_Nw+upPREHvEp<@&4ZG@!){gH?Gx~
zzc$g{RXhRSQsh16Ctd&Tf5qc{wk~*{yyHe|{IhSsdNnue%QN@{rOE#y(VMwoB
zL_t(IjqO!UXw*Oy{*vrZVrGAO5riJnY(>!`z57Gx(Tl~aqN}%phhDu6dJ!xVD2Nn`
zi@kZ!fG2T_;}%6~lpZ{&AgnzU(LLlW9(*s!nnt#XS-fW$Kr^i%_CxgN+lwZF>0+NsW-l
z$g~F-aO^5pDC9=s-^}f{G5uT73y=>ae_9Rdq_U0qaxzr(u-T|UxUP!|RDz7A{LtWH8xEpUHmB!Zs+a{Qe~jypt_I9<
zM1V7ia$QzJNgkdND$1{)5cGTnszHfsbV~%Be#`C0rD{WOxm0v7YQs^ft{Ppu2Tcp@
zDzMm5aUcU;U;QYP$;CB>8qGwDP4g0K#fLV>cbT34_?zesLcTZz^D7HJIPJ(cC
zb?M_al8J>=^0BfMoDiRBeB6ye))|O(i4Q~0b@v?UO1r3Ec9_C#&A1cbhAuXRs&`;T
zI)7JsXQ(uS_ylc^lJTmm_|JmQv6n?HbbZ`Unq;CxchKnE!G3bxT6{9xpJ46Kqc3C6
zzLE1XFnI~~R&V_LQ##TtjQ6W8nUUD{rW9@*{>nkZos#=5KRnsWT6JvkiL^OEgyzAW
eICh6CB<(vAL5df@UO~qI0000
zQ9>JVaOvKqvmkVJ^WJ@G~@L*#sK;JDA*
zEuc4xDuFtgD>CxkMHNGyc|6-Tf7WD^X9e~;?smcEJpX&J*kw^Hq>2nGRCgqR>AKGA
zr>l{wBtY9d?96S`VhLWYBA`6+Ns-rlEwr)WV8FLsg0xQz`
zWb8xYtD|CfGhhr&f>fwlo#?b2Y+_n8NQv@Nyi_H+%*>b|bpMzSH>pgaf8P}0$cmyF
z5Om7dT2jNdI&bhUpW&@IkL!Ir`HYd)+~wV*MjPN(th7N^uH#c=oY~NQL>hKc8zwdK
z2nTADf+q4dbFC}>*@<@Q9{QVT_|f@?b=EUcX$$Xk7cf8#$})QKSdm8Daq+UJagBxt
w^XFBJC*o1dvF<%Ec`-t-psuH?3*`lCct{R
zN;hH4R#FJ~3NoE(4S6D;wo-N7e=0nvv~LYN4yXsmH!n_gQz(653(~=Y+W6JYDaYt6
zi0kx=A28EV=n1q!tZ@)CxWylpSq
zL=;7Epo%=UT!UFIG3-i2Y3%gsz~vMaOEYU!u!7jILb&p;F6m#8`l&!if5{u$rEGQR
z5mGT0QR@$f>%GjrsQob|yqh`rnzdIL=5#?ii6kec97-trp1}yat6;gv@jhM?E#4n5
zVhUG<14R2uT*iS!sLbc$Je`w!frmPE=HVSMdx&bzCTrWg@pAd3_IEqf2RGy+W?cnV
zCT2!dC%XJsD*yhY-J2@6e~G${3uylC%k8yK~4@$T|VBD)Bx8uSTb`FgvD=r$gpM+Mmxq`bN`!|>=4DKhPWReXAq;6T@Sx*efo`@Zvd6^@INi<
z@$ILd&RSK(u>EX
Td9zCZ0000)DNd@sqGMz*n_hzCE&=FQBT?|t*$c`&1?w3iR1A7)f5|A|EpiX)lS*J^>X*BVP@-ppjT69adif7YjgZI4
zv?&3$^MCpz|33Wu(BNVl4x&;vr{`U&m<1<{f9sI02F!9q
zfHR45T~k#WjW+%|we$^Ac;thc?G|nVtXmo9GTgzBmN)GF9?*7`_Ekw%iG@@0v9c7L5T9v$+>Jrj8Hja>4@1s%_Z;a;yQp7wn8Iz%xD()pE;fa#cVI<2
ze^+{Es5FB31Z|Fz@v5u%&w|demqjgfecVr)WTHfO(CFO3esbM>Su)(8VC~SOFJsTX
zk@GSzc?tGbZ~XjII?^nR_p2?Lk=Xa96mA^;%0a@NlKU<{JlV=xb!_p8v^hb9=E0pf
dc84n@?K=`diWk3LLB{|9002ovPDHLkV1hpqHBbNm

diff --git a/docs/html/img52.png b/docs/html/img52.png
index 6577cec8d9f181100e232ae77b825838e54033a3..e3ca633abdbe7dd6d8ddf3fb46a3e6b6a4c8834d 100644
GIT binary patch
delta 699
zcmV;s0!01m1^ERbiBL{Q4GJ0x0000DNk~Le0001!0000R1Oos70sSwK1(6|4e|Jel
zK~y-6?NvQ!6hRdJZufq6b8|mw0z!(-T!NB_1Y4UWSczb;RrItASj5t9&_*!GLLf*u
z@ra#;E?S8f9WN*$t|DTgqHtazqA9Kx3*YSA-yV0#MN(M!!OpyW^X8lPw>v-&-iD(C
zLy9CAiK5q{1=gH}tg##(LiXtUf1!aS{8MOB!#;`S{p_j((uiFaAhatvDSzvM6U-~%4KnkNh~I`M$)6iToQ54
zIptF3l)mb!aaMEiIR}0wW&zimL>_6oqN$DAn#;g}#r=!t9|40ugjI4TfBNo4UrqHH
zm=2@nXv8~eBWjhxJdH9~(Y0zC_=@WYqt+rMvLYD>GIAAbASwHvrm1=oRHQ2B4sNlq
z+iYH=F|242MuAgHx{V?nskyuih4vtC)1o>X%Vim!Xu_?@b}22@1D$FcqzJ8u!V=in
zH8a-ut|tG{h0k6LmF++^8o{~(Oz}yVYW^k&Hv8D#So^RORmP?N
zPAIKj1b!f;{*CW}mt8i745zffX)RPxLU-fEULB)OT*>2L_-&>0XIm@w1sLQauC1?r
z?V_4kIwhV+TfzzGOqlPufrq+*OM(8U1j
h&>*J0;3~QK2O#N{5vJNC50L->002ovPDHLkV1iA{N-+Qc

delta 685
zcmV;e0#g0?1?vSNiBL{Q4GJ0x0000DNk~Le0001z0000R1Oos70TS)|JCPwwe`!fX
zK~y-6?Ulca6G0Tmzq^;)+jS?&+8hWLn@vDbkzirr4+xev9=3``JHg^C?FMWFQ*3q0
zp%AnY3k_O{IUMg$Ec`-t-psuH?3*`lCct{R
zN;hH4R#FJ~3NoE(4S6D;wo-N7e=0nvv~LYN4yXsmH!n_gQz(653(~=Y+W6JYDaYt6
zi0kx=A28EV=n1q!tZ@)CxWylpSq
zL=;7Epo%=UT!UFIG3-i2Y3%gsz~vMaOEYU!u!7jILb&p;F6m#8`l&!if5{u$rEGQR
z5mGT0QR@$f>%GjrsQob|yqh`rnzdIL=5#?ii6kec97-trp1}yat6;gv@jhM?E#4n5
zVhUG<14R2uT*iS!sLbc$Je`w!frmPE=HVSMdx&bzCTrWg@pAd3_IEqf2RGy+W?cnV
zCT2!dC%XJsD*yhY-J2@6e~G${3uylC%k8yK~4@$T|VBD)Bx8uSTb`FgvD=r$gpM+Mmxq`bN`!|>=4DKhPWReXAq;6T@Sx*efo`@Zvd6^@INi<
z@$ILd&RSK(u>EX
Td9zCZ0000wyCYmM>r4
z+uNI-p6=`GtFEpNl$q!#QSaO?_8!P&ED7=pW^j0RBMrzY@^o?%iBL{Q4GJ0x0000DNk~Le0001!0000R1Oos70sSwK1poj5Fi=cX
zMZmzor>Ccljg4n#XH88_CnqNW000dQ4Us+=e{9^WT>t<80d!JMQvg8b*k%9#0(VJ7
zK~y-6?NvQ!6hRdJZufq6b8|mw0z!(-T!NB_1Y4UWSczb;RrItASj5t9&_*!GLLf*u
z@ra#;E?S8f9WN*$t|DTgqHtazqA9Kx3*YSA-yV0#MN(M!!OpyW^X8lPw>v-&-iD(C
ze?y8S7>T0Sq6OBRg{-k09zyo$`=Nm({8MOB!#;`S{p_j((uiFaAhatvDSzvM6U-~%4KnkNh~I`M$)6iToQ54
zIptF3l)mb!aaMEiIR}0wW&zimL>_6of1;_4+M3J2fyMoc=N|!sKZI3sCi?D0UrqHH
zm=2@nXv8~eBWjhxJdH9~(Y0zC_=@WYqt+rMvLYD>GIAAbASwHvrm1=oRHQ2B4sNlq
z+iYH=F|242MuAgHx{V?nskyuih4vtC)1o>X%Vim!Xu_?@b}22@1D$FcqzJ8uf5H;j
z*flfO_^u}Z(S_1yk6LmF++^8o{~(Oz}yVYW^k&Hv8D#So^RORmP?N
zPAIKj1b!f;{*CW}mt8i745zffX)RPxLU-fEULB)OT*>2L_-&>0XIm@w1sLQauC1?r
z?V_4kIwhV+TfzzGOqlPufrC8T1EEzrdP
h>(C&kz2GXj`3E5Bm8RMx50L->002ovPDHLkV1h}+T4(?O

diff --git a/docs/html/img54.png b/docs/html/img54.png
index 6e6a2fab38cb76b843d796c89cd9faeee119ba24..6daecc86f4de7c16e1a3fbf61bb09295fe534892 100644
GIT binary patch
delta 218
zcmV<0044wN0g3{UBponNOjJd{z`&=cr;Uw`XJ=Pp2bhv95NK#Xmm>_ACO~ZYkN~D091!3FQXCD9K=*LSz*KP%FeMEPh_`k30nP((
z7w{b5TL71t&!Eb1ih+R#EYdQk{R=L^n8|a1;WDoSuK|eH)Bq$n6^OSH4@g4-09Cdh
UUZ46zjsO4v07*qoM6N<$f{-UpS^xk5

delta 193
zcmeBT`p7szMM^ioC&cx@fdk8zFYoQ`O;1nv_4QR(S7%^gnCK``@7yl-9>`=Y3GxeO
zaCmkj4ah0-ba4!kn3|k$fZam!U`SMyR7}VA#>PamSw<<98VSt-tUOFitN~)24Ksf;
zPEwO==VhA1!_y&6N$VJT4j&X~Q8`-KI5AP3nfW`5!tJzc
tip3$l?UH>TBoub|%DCL_;9sK1$Z#oGqGO%Qwi2NA44$rjF6*2UngH@^LQ4Pu

diff --git a/docs/html/img55.png b/docs/html/img55.png
index 6daecc86f4de7c16e1a3fbf61bb09295fe534892..984ac7b2b8ac78876aabb3e73e8557cb29264564 100644
GIT binary patch
delta 242
zcmV=>s4Vc(Xhg@J*MVG;vp1CX7-fCTtq3qoc$FkApK0Q(U`U#34jFaQ7m07*qo
IM6N<$f{js$QUCw|

delta 243
zcmVk!#ux%%-J3Za=15pr;_Rt<11!FK1grfY|V&vptB^FsZmqO&{@!O5aXu_eSXwBp3)uH65B5Kb6VD*oNgCrT~+H&zB+Hrvdl!?KdbbWX2)DimDfnhsZ
zTXh~CGMb957pu(}%F#1ke;bT090gWoLWOU>y?F2PixduqggZY{?z+9eS_*E
z`4+7W4DQ>)eFbW}dWZ`aCp!el{w%TyzwV!9^vkez(u{Bs#2-*3utK-#~WUtEJR1o&6#Hjv(2~n@+>L#8zN+q#gE#-9z$H4iqqFM>qojQ(B?!*rP
zRshbm0G7*Dx4%Dw7SvbZ198D;=h?zx><28sIs7y~;F(Aa5{kzV7b_unFe`oqysEjU
zm8e%-2pjcV*y?x{e@86oRfmpAP9k0*7I5Oc=s?6Pqltr1$V_bWMW)qXk9$RTkVrKv
zZ&>sWl6PB8WLDq~Qa_+EBZWTJs{)AOr3{Hb&5XsW(~o#11>T!}ruFLo5>Dt>FVSue
z$0wip^h>bFlNwI5fp3UF#fV2_uLzyERu@-{#YzV;=iMkOpfI3G>#ohD
z?@bHhVnqndwk9t#NobU(Cg|BJ!-*Co#wyG!T}&Kia;&1f8o@$ltU|mZSg?*_6&`h!
z1gk)-N)Mvze`0OLwQxZiq{fP8FI`Z#wlK)UQCF0v#tQ0utWp~$RIL0xT5T9M1KWnu
zX}iZeV%y%S$}#%XL-bNk;_#_McTSE$w8rDgpB%obxOER%H$p2j)39!UMTPE!oT&M6
zzsavKt7N^2#rhV^cpW}-HL2PJ>$L~PYUkd!fOw@}e|$3-ti)I?dc4w_+vxaT>9N`b
z-r|QxSZU5>#wyG!_h`Mu>VW~gYFlo(2o$8n%6O{_kE=b{bvO_x$cPock_Ikw0|l9}
zx(cNFRXN9cIy44bTLrfy4$wL>eGDRqTL%wuJyCyPVd@Y+260v4x-*M|wyKCLpg&qj
z3P4anf6JSB^CVfyv)SD$1bb^fJD*qkI-FNjAdwU+$twc!3WJv(t4;6|7U0#v9tJNf
zR-smRyJ_~?#A*ZAICAe!cnB{%lM@-7!aHC&9s3MkF%nz;G$XW~#4B`gs)~uaP-d~I
z59~06nZVQPV5is|A(UwJIX${UhvPjaO2sV6AgAkJ}nJn1G$iOjM
z>B~KCO#0P6<6c!u;K(+@D;JGg4CD)O>D6BnLlD9MD)ad)*CTYN@Fn3Ztazga@&Wl&
zsh16V;BcA|Q0Pka_$z3=fqd%UsPiR=F56)sx9-Pz)rJx0lc*YyW+h|9uNdgt$T)^q
ze+!aN93$a>Yqtr58c*5Bcr|JupWuMo=|ynv=rG7F@#lrVBV6vYJuEw*Ya
zE8s2aCG=ZkuP7rkI*YMQ+_?aorEjgPz7K!urv1^Ar@bULVMoRx+
zzFuwO$G^zn)g`DLeqC%bDEFaWojq-3@+z!XKCT;H0UKu95PV)883ng$6G#OCUKvQN
zp_ns#Qb8K8ZbD+o&0U{VkijdOYBe=TD#+lKyB+M43etH6A7}7H?YI>ne-&i%Dk@e`
zh$-uaRC%|_d^lsTv&A4Z5AN#(H`M?G9Rq(J#2@`dp;;g@CO(K$=RpE#7H#pOv2s>t
zEOQ>@nl&RcCIeVMVIDM=z3skDD2{dEmDxaACd`8xxbq-tR@=-qg5zvNTe=d4SKj&j(Pp{NghwD|~Nk9^>xL(m-ev|7}S)}4-GOt{{
zBG9Hd5-p2YVZFk?ZU(R53=8O$O+-uQ)g|aDzFuiyT-lS!tI#BHG;n-v@@fMcxZcrU
z>jqS3RjboiY@3!UyX<@Im7dpvTO2{<#2r@QCf){k11B95uDG(zfBPVcJ;-;<{|GZ?
z#KUFqpQlCN@}B?QpaR-AL4BB;c7x~K;_tum%s>4W)SFL#2q&4wd_&WA-*m$U&b0`h
z4>JR>pNE>O)Q!Mp;1&0{&#l(oElPs1lPfBwA^m_WBh`Dl0=I>`fK$VY1vg>rm)^q(
z^Y@{XR9rdp7Qjp5e@#BohZewPcn)p}7*;O4)`tWbcfD}vxAWilGtK;<*xw1h*2#;1
zj{Sc3l`WRv!igj3%1^gn4!L4OHfr(jy_JuA$~)%ysY=~Z9^@~3dwob;)J%>?tktjc
z+C??nWJ>HG?J&T)Clp-cAZH>D0G%hRqG&V44(LQtOa>5?0g
zN#toQbV=g6m#6+(H*l5nrR9sZzv6XKSeMfBB^vWz^^7OfrL=qro<#Ehdpcc8&zGn#
z%0tuXQo0~1e<;0A^`_IMR6$Z+zhdvTrq`t$f+Vq_OIHymw;w;brVUiBx#ntSV==k}
zchg6#AORda@=nnv#&rq4O&=&oM%On}nQ+Jw!`t_8QeEPL^vRx|D#;c$FMY)dRXVXQ
z0sKRJ2}x30TXwhT)z<+SPO#F+bqU8Tek?6}k|g?|f11$fhbo;^mq?H>Ra@{=CDDTZ
zo7-8q(y4R_;7ePY-Z4MgJXYzN=+YXB-8BdO_{r@#UNfHp&*RYUC!c;Se@*uQyln9=
z)DL(ER=hW}I`Z_}L32s2HeATv!gq0GIQ;8=THz`WxbigDl&9|xSiADX#|oi!2z>7T
zGF-Lxe>J#p5K1Eyj1H9cOC>EkAtSfEU1$Fdw1DCI61YA}_)`2XG$XH54cu(tiLcPxpq6s2t_#nc-gX
zSWon!)WCQi34Cr{!W)2-h^a
zlpsj(ANehXYjRym5+t1-I8(mFg{wNHE~N>Q#FV;}Uyvj=bm?k9`zza8_+^J;_(0|v
zfAJ`wNCM-!r0#2d5dy*_F@YipjO$Xp&y~p&CfP3IUwUwqz*M^A3R4L#HhK`JNCK1V
zk|#`+F2pL5?ApY-AI8UAu6Q*g`alSkyBus_Y
zas3ZJkswd+mu^c+mm7IOJ?DOHf<;f5}4U;`Vt7e??u
X1_)mUI)Bq#00000NkvXXu0mjfp=ooF

delta 362
zcmV-w0hRvg8ma>!iBL{Q4GJ0x0000DNk~Le0000_0000F1Oos70U$-cPmv)@e*q{-
zL_t(2kz-(hg1={AEI!r?2N>Xhg@J*MVG;vp1CX7-fCTtq3qoc$FkApK0Q(U`U#34jFaQ7m07*qo
IM6N<$g8CbYp8x;=

diff --git a/docs/html/img58.png b/docs/html/img58.png
index 919319cce4b55359537d121277b9b1ba501cf31b..f759dd46a7f4be1379c038814a460819f8be7366 100644
GIT binary patch
delta 141
zcmaDUb)HeNGr-TCmrII^fq{Y7)59eQNDBZl9}6=B1LI=0jrtQ6y^|SyJzX3_IA$g%
zBs@rFV7$l7bE1LuoEJlq8>`64Hg-Oqm>w?a1*dK}u*i3DvE4SVOF!oeR2q`-EDbBk@E#Q7=n*n${ZpYSX?UvK*qXb*#@tDnm{r-UW|+>|bC

delta 3393
zcmV-H4ZiZv0qGhciBL{Q4GJ0x0000DNk~Le0002O0002*1Oos70VVn-e32nbe+=hI
zL_t(|ob6mqj2y)ke%&*>J3Za=15pr;_Rt<11!FK1grfY|V&vptB^FsZmqO&{@!O5aXu_eSXwBp3)uH65B5Kb6VD*oNgCrT~+H&zB+Hrvdl!?KdbbWX2)DimDfnhsZ
zTXh~CGMb957pu(}%F#1ke;bT090gWoLWOU>y?F2PixduqggZY{?z+9eS_*E
z`4+7W4DQ>)eFbW}dWZ`aCp!el{w%TyzwV!9^vkez(u{Bs#2-*3utK-#~WUtEJR1o&6#Hjv(2~n@+>L#8zN+q#gE#-9z$H4iqqFM>qojQ(B?!*rP
zRshbm0G7*Dx4%Dw7SvbZ198D;=h?zx><28sIs7y~;F(Aa5{kzV7b_unFe`oqysEjU
zm8e%-2pjcV*y?x{e@86oRfmpAP9k0*7I5Oc=s?6Pqltr1$V_bWMW)qXk9$RTkVrKv
zZ&>sWl6PB8WLDq~Qa_+EBZWTJs{)AOr3{Hb&5XsW(~o#11>T!}ruFLo5>Dt>FVSue
z$0wip^h>bFlNwI5fp3UF#fV2_uLzyERu@-{#YzV;=iMkOpfI3G>#ohD
z?@bHhVnqndwk9t#NobU(Cg|BJ!-*Co#wyG!T}&Kia;&1f8o@$ltU|mZSg?*_6&`h!
z1gk)-N)Mvze`0OLwQxZiq{fP8FI`Z#wlK)UQCF0v#tQ0utWp~$RIL0xT5T9M1KWnu
zX}iZeV%y%S$}#%XL-bNk;_#_McTSE$w8rDgpB%obxOER%H$p2j)39!UMTPE!oT&M6
zzsavKt7N^2#rhV^cpW}-HL2PJ>$L~PYUkd!fOw@}e|$3-ti)I?dc4w_+vxaT>9N`b
z-r|QxSZU5>#wyG!_h`Mu>VW~gYFlo(2o$8n%6O{_kE=b{bvO_x$cPock_Ikw0|l9}
zx(cNFRXN9cIy44bTLrfy4$wL>eGDRqTL%wuJyCyPVd@Y+260v4x-*M|wyKCLpg&qj
z3P4anf6JSB^CVfyv)SD$1bb^fJD*qkI-FNjAdwU+$twc!3WJv(t4;6|7U0#v9tJNf
zR-smRyJ_~?#A*ZAICAe!cnB{%lM@-7!aHC&9s3MkF%nz;G$XW~#4B`gs)~uaP-d~I
z59~06nZVQPV5is|A(UwJIX${UhvPjaO2sV6AgAkJ}nJn1G$iOjM
z>B~KCO#0P6<6c!u;K(+@D;JGg4CD)O>D6BnLlD9MD)ad)*CTYN@Fn3Ztazga@&Wl&
zsh16V;BcA|Q0Pka_$z3=fqd%UsPiR=F56)sx9-Pz)rJx0lc*YyW+h|9uNdgt$T)^q
ze+!aN93$a>Yqtr58c*5Bcr|JupWuMo=|ynv=rG7F@#lrVBV6vYJuEw*Ya
zE8s2aCG=ZkuP7rkI*YMQ+_?aorEjgPz7K!urv1^Ar@bULVMoRx+
zzFuwO$G^zn)g`DLeqC%bDEFaWojq-3@+z!XKCT;H0UKu95PV)883ng$6G#OCUKvQN
zp_ns#Qb8K8ZbD+o&0U{VkijdOYBe=TD#+lKyB+M43etH6A7}7H?YI>ne-&i%Dk@e`
zh$-uaRC%|_d^lsTv&A4Z5AN#(H`M?G9Rq(J#2@`dp;;g@CO(K$=RpE#7H#pOv2s>t
zEOQ>@nl&RcCIeVMVIDM=z3skDD2{dEmDxaACd`8xxbq-tR@=-qg5zvNTe=d4SKj&j(Pp{NghwD|~Nk9^>xL(m-ev|7}S)}4-GOt{{
zBG9Hd5-p2YVZFk?ZU(R53=8O$O+-uQ)g|aDzFuiyT-lS!tI#BHG;n-v@@fMcxZcrU
z>jqS3RjboiY@3!UyX<@Im7dpvTO2{<#2r@QCf){k11B95uDG(zfBPVcJ;-;<{|GZ?
z#KUFqpQlCN@}B?QpaR-AL4BB;c7x~K;_tum%s>4W)SFL#2q&4wd_&WA-*m$U&b0`h
z4>JR>pNE>O)Q!Mp;1&0{&#l(oElPs1lPfBwA^m_WBh`Dl0=I>`fK$VY1vg>rm)^q(
z^Y@{XR9rdp7Qjp5e@#BohZewPcn)p}7*;O4)`tWbcfD}vxAWilGtK;<*xw1h*2#;1
zj{Sc3l`WRv!igj3%1^gn4!L4OHfr(jy_JuA$~)%ysY=~Z9^@~3dwob;)J%>?tktjc
z+C??nWJ>HG?J&T)Clp-cAZH>D0G%hRqG&V44(LQtOa>5?0g
zN#toQbV=g6m#6+(H*l5nrR9sZzv6XKSeMfBB^vWz^^7OfrL=qro<#Ehdpcc8&zGn#
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zchg6#AORda@=nnv#&rq4O&=&oM%On}nQ+Jw!`t_8QeEPL^vRx|D#;c$FMY)dRXVXQ
z0sKRJ2}x30TXwhT)z<+SPO#F+bqU8Tek?6}k|g?|f11$fhbo;^mq?H>Ra@{=CDDTZ
zo7-8q(y4R_;7ePY-Z4MgJXYzN=+YXB-8BdO_{r@#UNfHp&*RYUC!c;Se@*uQyln9=
z)DL(ER=hW}I`Z_}L32s2HeATv!gq0GIQ;8=THz`WxbigDl&9|xSiADX#|oi!2z>7T
zGF-Lxe>J#p5K1Eyj1H9cOC>EkAtSfEU1$Fdw1DCI61YA}_)`2XG$XH54cu(tiLcPxpq6s2t_#nc-gX
zSWon!)WCQi34Cr{!W)2-h^a
zlpsj(ANehXYjRym5+t1-I8(mFg{wNHE~N>Q#FV;}Uyvj=bm?k9`zza8_+^J;_(0|v
zfAJ`wNCM-!r0#2d5dy*_F@YipjO$Xp&y~p&CfP3IUwUwqz*M^A3R4L#HhK`JNCK1V
zk|#`+F2pL5?ApY-AI8UAu6Q*g`alSkyBus_Y
zas3ZJkswd+mu^c+mm7IOJ?DOHf<;f5}4U;`Vt7e??u
X1_)mUI)Bq#00000NkvXXu0mjfacpz5

diff --git a/docs/html/img59.png b/docs/html/img59.png
index f759dd46a7f4be1379c038814a460819f8be7366..6b825d668c5b33e7a8ad7a290ef61dcfbcc39f46 100644
GIT binary patch
delta 158
zcmX@l_>fVtGr-TCmrII^fq{Y7)59eQNDBfn9}6=B1EbH8TY?i6eM;gzT^vI=W+o>%
zFytvbV%a>yQsPIXgoH?f(HowcgrCejCmQA}GH7KS_|VAM(Qt?VkA|1Tj`MRZij
zJV<6>yvNLQqJj0C7ekU8tH{YVc0Qh%9xmwxr*1f~$aitE-8QaEKj#Zn8j|qi@Bv=2
qM}7^bJ|13ki*2FA`6=_*f*4w#@GLrCZ~GKz4TGnvpUXO@geCyO!7fVx

diff --git a/docs/html/img60.png b/docs/html/img60.png
index 6b825d668c5b33e7a8ad7a290ef61dcfbcc39f46..6cdf6149cd70c3c37231dd182e5ecd2a13c2cc34 100644
GIT binary patch
delta 380
zcmV-?0fYYG0lWhtiBL{Q4GJ0x0000DNk~Le0000?0000F1Oos70n2g(Opzf=e*rp4
zL_t(2k(H7$OT;i7#b0{o*|h1ki=z;P1MwC?hg$@3RFKX$RX@S`4GK;oNJeq7gWw=&
zClPfB=XgawfQJ;v8}xP;b4jtK4&ob=Z~jEZMk43f!Tl
zn__NfOZFMd;3(e=lh1nYml$R|f71XUWS(IlTb|jJY8TXo4FSZaX8nn*D^v{QBIl>6qddzoLxfdS`u2-I-Cg;

delta 159
zcmdnP{E$(xGr-TCmrII^fq{Y7)59eQNDBfn9}6=B1EbH8TY?i6y-OM5JzX3_IA$g%
zI56ZXJYv~A!&2f$q=bY>g3%kEnuMRsJSQ6FD>7(h9Qe@4*wJu@|Br^3#E$cGEsL2B
z?KyPdKo&z%ftr!Q2U~`X6|xc%N5mQ;l9+hrOjT&}`7={lftSJL7XN*}O_m)%n;AS^
L{an^LB{Ts5itsao

diff --git a/docs/html/img61.png b/docs/html/img61.png
index 6cdf6149cd70c3c37231dd182e5ecd2a13c2cc34..f73e47fab7dcc9fe6bf09665471e7ba87d2aaa36 100644
GIT binary patch
delta 760
zcmVee*&{f
zL_t(YiS1O+Yt%p#{*vvsNj96L(1L=Lh$nwwgL<(-S^NtYJa}Di9_>N!&_nPb=oT4o
z6%>Qu!CE9JT3Hpwu7b9U?nw#-2?!okB=p*g^D^0OHoF#u9*XqKX6DVj_q};}@67@k
zl)I7x1@IG5$F_)*@itjit}~@ie{b~dXiF@WOlX(E#9`puAM%gLpBZy;geB!_GBVUZ
zan5OXmKAGtS7{|5atoC-NLo1XwH*!YFTj%E6&&y6WSa8Rfg$5J#arEAMcXQxNS;>9
z72m=auOhD2^*NzYqj8}YUUU@=<{EWN*p;Lk3(-*VG?s>Jjk#{w_k+v2y9f>nUAe!VJsRS)2-B1(0X51tu!SJmq#^9?MN-JvbyF)kQ@^1`^MO&K
zB6?I!VX0!=*8RKXqBS1`hmH5HQ4*02m*LdfZN`PAoBA}Nn8RpXoJXx)9l<5uX2P{)
zzxJcecFd?TQcE44Yg@N9e`ZFTUrRydTsx*}`bopbbcv%*aLmyl?z1KyUni5;>ZqEO
zqOII`xg0gK9lM8J4CS+9uwekBJsa#Q^d*;NjM)LpznV`5@kpz|9__8A-(e
zw0c&OcBe5@dPP$Ob7!XXNV+tGoJ*lF&o)+p15Z6|WeUn_gE(3Ze=j-S9$gHHEopXG
zsJN|UD#f^9a_Lg#IhR7=uH!MR5I^nZefWV<;+R|&zjA0q#Fn&4jO;h6j3z56RE*SR
zf#xs21On+&DD)UJ&Lq?;FSHFcmegws9_YA-kx^nx+R(zY1@mMwDeKQ2`sY7(eic^s
za;fiTL!l^#%6Hd1PO*aJLjjscJmO3|LDR!JChjL}D|aU!QLe|NyxdoZvBBl(W#?(?
qK^ouCQ0QZ%ia&$cgJ^sB-|-s>9K!;j(y?y<0000=Z~jEZMk43f!Tl
zn__NfOZFMd;3(e=lh1nYml$R|f71XUWS(IlTb|jJY8TXo4FSZaX8nn*D^v{QBIl>6qddzoLxfdS`u2-I-CL*EMLC7
zx3@PvJ>A#WS6y8lC^OMfqTab(>^+dlSQ6wH%;50sMjDW_%G1R$L}OxdLIZOj+dXa$
zxx=h&4Qy;B2GTBb?ldU&iHbOA_yl{faPsi@d3kZkuCcljg4n#XH88_CnqNW000dQ4Us+=e{9^WT>t<80d!JMQvg8b*k%9#0<%d(
zK~zYI?NrZe)Ib#elI^xhHk+i-f`XKYCx2jrda*)T{0kO5cwKKE?LqL+L+~Kz78!39
z6ocTwS|li1Srx{vg0_q9NeTrC2p&`<^xBK_GTCi5yB38WiuB87=FPnKy?J@>%>o&e
zf4hz@{h=$8FO)jCFN=|GSokD
z&S`g+6>D`@X(b?q<9Pi|0n)1_uA>%j2Tiswq+bWt!o>t2h
z-@+HKBCgi;IiXRbaiJDobQKNe8g)z9f0d*g3(-*VG?s>Jjk#{w_kQH!(i55!50P;8B;nu1{JC(KhAl{F_%^so|NyPxP
zdRCHlr!iA{MNx-^5Fe@me-&o)+p15Z6|WeUn_gE(3ZFFD>GT?~mWX?9qs
zxUFO=#kgQ{=~Cr6mqOvL<1wrdKkemx_<>R4m|PXVa%e=vmb6KX>^G{6CMzgZjMQa;
z<}bel0_jpH^cXYFB-AS}v<)?u)N2YJ=(vZGQDRHl(899?^JFq9>(3qfVdp<~eic^s
za;fiTL!l^#%6Hd1v4Z780h&iV;!He2)5AI@?k8+3cPAfFuE(Uj+*gOO!R6^?=V|Ie
p8sE@R=wqacKZDqVXnXkI@f!&o!vdhvv2OqX002ovPDHLkV1n^icWeLv

diff --git a/docs/html/img63.png b/docs/html/img63.png
index 1ec88bf6664deefdf26bd479ad9107a0486aaa16..8e1ae26a8f170becd7f1842f72d13bbd3333ef6b 100644
GIT binary patch
delta 410
zcmV;L0cHNF0;dB(iBL{Q4GJ0x0000DNk~Le0000;0000U1Oos70SXg!2mk;8Fi=cX
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Ef(o{lL*EMLC7
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literal 97
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zXzW9FYRaBv?DV+r^PK1Rob&tr{rORK9Kpio>
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z5-)Zeg9RicGsdIu3abxa?|SoRTWIwwC@oiiS{}iv5LGSPzo0UrEC*>Bs
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diff --git a/docs/html/img67.png b/docs/html/img67.png
index b36bd89cfc7fd0e1396da662fba79cb72b538b3f..e85b77f0e363bbe91c4a3ab586b535d08cb35b23 100644
GIT binary patch
delta 198
zcmaFK)WM|K8Q|y6%O%Cdz`(%k>ERLtqy>Ojj)j?lfpNiw&08ia`qa01x;TbNOifN;
zV6qc9D8Q~JS!QHVYIK0{Ih(*q!^Xyk49rqD4t{88^lVfF@~(8Um3XQgSj?@$B*7yQ
zA<L^{jY)C|%I_at?BblkazNxeFWWgTg|jnQRPHevN}pIGr4SaJkdRQx
yu<2Uj;dAp7j`nz&&royNBBRf(a?(tNf#FD~n6SLI?_!_>89ZJ6T-G@yGywp6(m=uh

delta 295
zcmV+?0oeYC0_g%FiBL{Q4GJ0x0000DNk~Le0000t0000R1Oos70bQIru8|>3f9FX=
zK~yM_V_<*-&JAFSivbBdU^vcz1+X(PtYO%|z_J0GBm(flSuepP_pbvGZUBCL$bb=r
zmjHATnBq}VQet3IV0ggBz`y~MWx6n-fq0WC0SYL*9h}J4GAe)_X>gu_6T}5N@G#E@
zkRw?@Zf0X(VF0SW!UIvv!!VQAec=Fuzyzpfp(aL7WTO+Q?{>O?Ih*!Qz$Le}fq~&M
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kXQ(-B(dSkzopr03?A-x&QzG

diff --git a/docs/html/img69.png b/docs/html/img69.png
index 4f8dbfd9c895a8f5c464ad6b7f6704c530925850..11b3c242b52f6a9c702792ec59b5db10dc5c7743 100644
GIT binary patch
delta 239
zcmey%*v_Qd8Q|y6%O%Cdz`(%k>ERLtq@{pZgoT-bfl(}zK^n+0n5e2$-_X!dQc@BX
z73JXIU}9n-B_)+}XH6_nma!zrFPOpM*^M+Hr`6NNF+^f&a)JZX8lDJ-a8YLKW(H>C
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delta 229
zcmZo?`pc-=8Q|y6%O%Cdz`(%k>ERLtq{V<(j)j?lfpP7*!=Hg1-HED7^(7@GQBhG2
z4h|+JCQ?#Tg*$(U1Em;Cg8YIR9G=}s19Iv-T^vIsrY0u<0ZS4y8%IJ?L*s28k3#|n
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zm3WA;L)l*-UCr^ppN7Wc=8UJ(;tw3CVmxJbdv7(n&)MXbBE1QV^NJ4Jp4-yMFBo@)
ag&}yMU~%ZVTW&z7FnGH9xvXS9vt4DfU3<&xrJU|`_&^l%9R($YXI!otkJ!1!}@w(3MhpZX3@7sn8ZsmTcm
z2@ld7n0sF^@$l5J^6>o8P?}xVe1c!+j6&DXGmIM)tX=eYnF6l7zs43E^Cm{&E01`D
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zaI9_eJ;$Q)U9U^CXQsxU#d7s51rhAu<*tM>O#i7kUAN(lJzopr08W-f
A!~g&Q

delta 197
zcmV;$06PDQ0*3-2iBL{Q4GJ0x0000DNk~Le0000Q0000K1Oos70TyWh8<8PQe}zdz
zK~xx(V_-l6tPEHHR}}+0g8&0FlF)8#Ai>OVfd#~2JJSFb+yIeF1A_!)6S%b@avY2x
zlApoB04&Pzpa4YMoPntN099RpYCRV75TJ+QHp2n1Vdu`AIl;gQGvf*a!!ZV4sEarg
z8JH@WkDY|@crPFuAT|MsBNKlR8@n|yS3m&(<~<@XkwcoT00000NkvXXu0mjfPJ%!1

diff --git a/docs/html/img71.png b/docs/html/img71.png
index 30dbd771877180fddde8e701a246f2ec13d3cea7..2a8221eca08df88294a3de62e1d37ef031ea6f48 100644
GIT binary patch
delta 272
zcmV+r0q_2b0@4B@iBL{Q4GJ0x0000DNk~Le0000i0000Z1Oos70c!ijagiZRf6z%p
zK~yM_V_*OQULd~1fC6|JHZVjApo;Y#0Ff6M@B?0uW{8jK=K)zO$-r#DI02@L=>|!L5)Te+022GoG%#?#Il&1MU|~pLU~pgq`(`53
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zj5|$$L4ATv&IBm;E{Z9PnJB!Y9)ARISO@nW)KvhN`5~7rfb2g20000?{;TycWnYe2pdx=nk?9b2x&bcXctmlp-0NtCEcPZhBTWd
z1`9nU0Y$+rM9c+YL$1&m<;su~T}T%pE;bfvoSECzC3i>g2U3_1-peZ9wO8MY~1-D~@{eQK*BSTLYp0-~cCEoqqL4}>;Z@57vSAa~i9;>rx>)
z^a8K}f9j^g2@-_Vh@8mDnY>Euvj+UHak=>6nyJ9dlE9A2f{3noG@6NK^aVZ$&76jp
zfU&p7Yi89nRG4`$a;l@kfAq`N_GoFMG(qMD)XI)gD=yIi8ML^>&M>EPb-B8Wrd5$#
z`u6k&X3{l(v3h$2cesTeHsTmZj|Z*h=P8@r3=@nU9w+Bjs~$&^wsn*uf<7;Mpo(qO!TgcCPZ9HW|x->AH$e_FVXOABt%7s9h!
zIAzBPo0jTIWs6C`87yCOdywNZNvFI;@iEyv45Ci6Ar0?ihzh|Zy^Vs%Q+548K7&xk
zObo%?^%S>H?v8XCZVwUG|WATH*`HzS>+9OJ*h4{LwAv1~yk!2kdN07*qoM6N<$f{39~>Hq)$

delta 273
zcmV+s0q*{X2GRl{iBL{Q4GJ0x0000DNk~Le0000i0000Z1Oos70c!ijagiZQe*n-)
zL_t(2kz-&00bU@!!+-*K7&b6O3ZRPh9srRS81MsLkYis=SPh7u1BYycAb&NMJ^zd6AP5@2CSU|?`y1N&wo
z(*y=i0ZlWIGeDsL^&(J3vjH2_XZar)0w$b?hudWX8o859z`bd=_6AJh6%2(83&1RU
z28JsL2D1ZHK{W$I9D>0P^&fN28DK~uGr)k~0G$B_+ku#G!eIyl73eU0P$0uMgAM=y
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diff --git a/docs/html/img73.png b/docs/html/img73.png
index 5b3493320e4656ae8b9259fbbd0311e7d732cd97..2f029ed72ab26bcb1fdc2265df236041f88ec808 100644
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diff --git a/docs/html/img74.png b/docs/html/img74.png
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diff --git a/docs/html/img76.png b/docs/html/img76.png
index 19eb28999a678470660dbab7fb2fe8e551ec696a..2111312c7c47f658f72c52e4609418b068965b25 100644
GIT binary patch
delta 329
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delta 724
zcmV;_0xSKA1Ca(HiBL{Q4GJ0x0000DNk~Le0001^0000S1Oos70f^Zmg^?jke*%w5
zL_t(YiS1NPXw*Oy{*wJM*~BD*M_I;-3L?1FlXV60C_UutDfO^tk9r#vih{`CK}xAO
zAf76+w6vg59Ctx#TX4^MiHc&WXz(uhCY#-M%kEli1rZ-)=Dj!H_uiX%GXVw(_u*c0
zJ+}h1x=u9+Er18{JzF$75H>LIe`c7H9%S2L5g|{0pVvS8H{pNdEn`@S9gFO0F%V?x
z$Mw9bq7DlvEJImS@TrDb|Ep?|7lKuk^PX_yybiu6W$apHuUP=LpHFD&QTYhFE(5M_
z7O_ZZ4m3ta7$TcrVc}gCLAhX&6G5K>T-vokZR9ZQjBJw;aEoS^L0LrcnV?6
zSqVuP#_((l6|_V+wJ)HqM!*H?yUmMO0K05+7ph?MYrLJ3p_P0PPM{!FJBy9io;Ql<
z7G6SlXYdrNPoB}s2Xe|le1;SiR-85E0>ay@f;)iIhw4k@>(?#&DTFMo>|pVH}h
z>ldJMw8eHyRe|v5u71B0vz^mg6
zf!5&HX9U@1s4LEBWOryLgQ?)j-1$kvOmO^qY)t52Ptt#jDYGJJ38!FQoiwZ{IM%j3
zDM|_%EotL4tr{SwV7y%n%5!L*lvt^vR;#^PI>LKSr+K2{j;^3QXKXNM^r5yrf`rIu
zWOr!yDO-TqzK6U6DmmE4cTu82`#Ai25rG%|oVk9^UCU2e0lcW|C#+on0000w%xLjW-qe;PZs2wBHDU?9ga-bmyp{eJ^jV#D?ekiPtF9W&+zP^|UP3TEL^gCGqx
zB53&1gv=y%Ih}n|9`zPmHYLjz>w2vjD`;fO7baVte~NG$EKTi{OcC=qf488#`99P0
zdhZw##vPa8nIglf*TZvq2<0<2Ws0hucGl2jzNwK9!0l4VKW2_dLE4bEk-aKmtIbr{
z!_zKxp-b%^c?CfV@WN4*4KDku>=rR~P0l)ZprKmU-90sGSB0oUWdFTnx7|FPuy!7c
z*h$TCHdAx9U{39`;KRWmAe-<8hkGH8A|4BT0q7lH?F0tH!2kdN07*qoM6N<$f~~a2
A$^ZZW

delta 328
zcmV-O0k{5&1c?J7iBL{Q4GJ0x0000DNk~Le0000l0000U1Oos70XZmY0g)k0e+NlK
zK~yM_V_*ORZU$Zk9tH&9*u}`O0mfkjlYC|hiVP1Jumd)R4?vP^pV^8u~{X<3(n97Pfh#R48MFzkhM4lpni-TGA5u1@-1N9u#SQA2SX&w1s($i24;pg{1ZSDcNpd~1Tjo&V5k;j
zU_Ag7;DBnp#qpczfx&zRz728=XMp^*EC-;0!1;lpk%6HT$eIDRseuzL9?W~fhMNAP
aEdT&0x;K_Nvv*Yh0000
zL_t(2kz-&0g9|{+#Q+1{8wB8NMhL~Gpuq3|A&LUnptP_Q^8%m-b_ND!hyV+A^{9Xc
ziG6^Zj~i%V0D}Sp!z1Pc%nQ=8E^`uN2p;eN*?c5+0*?XD28Ql=VDSe$K+jE3U}9k4
zVECZ%0T>vJKzA{2IJDr9S=wz4ZeApPTnqySxE^2?W>vr{ypDnM2SX%h1kVFdguLOO
zzyVel#4xRap&E!mfFl8_nCXGRd4Ci5d+xa(+`Ir01VxIi&od-YDcZ61XgM8L
zgV(WT>-`CMT_VO|GI;>}Z$khve-#=#wg_3rIpljZ+P-)vAKR1GXR
zM%YEo_~sP8!S!jluQxxe>k_Gy!k%U
z^LpCcljg4n#XOTD|e`wS{0RR910d!JMQvg8b*k%9#0PIObK~xx(V_*OR-dCcljg4n#XH88_ku@QIY}~9}00001bW%=J06^y0W&i*H*GWV{R49>SU;u*)
zK+MGe1Kk@0;A}<+#ipRZ@Bkr-0@$FmuoUwGpaymZ24;u=3wHIWfCq_vfSZpSXkh?@
z0t3S%<^#+N(y}gd5@QG+@BrC-Bz6Li0nY}8?s;JG2RuN}O;BKBVBlbX_@MCt7#NH|
zcQI}_wBV3g+HDP9Bz;^A0|vMrU=?Onz$(0sf%6ALBxeNA15kv#;h(?(Ru{xDt%0E$
zh(UlO0jikkfx&zRz76vkI1Vr{tYtaC!_^9o?M4QMP6h~OU~B-!h1UYAc!j0_00k#1
VEG&SxQUCw|07*qoM6N;tV1hywbff?P

diff --git a/docs/html/img80.png b/docs/html/img80.png
index 337d43ee38ecc038533d98fdc5612abab0714e68..af302e8bd5ef41883df942f6e64bca019c050045 100644
GIT binary patch
delta 298
zcmV+_0oDHN0>J_}iBL{Q4GJ0x0000DNk~Le0000Y0000U1Oos70nFCnu>b%7Fi=cX
zMZmzor>Ccljg4n#XH88_ku@QIY}~9}00001bW%=J06^y0W&i*Hzez+vR49>SU;qLh
zCLqDV00RafAvlkLmkYs81A+twB=Cb_4gm2(*cdhoO;&LE!+9+rZ$(#2{G!QOd+{m@F%4(x4!LY)3Zl
zo%ImH;@$%cJ0O_As=&aY1Y#+iVR!|WTE`&3d=SLo{J<0dq?m8*Rc_$Cz;J8=1IMHN
w3t(oktYYA1U=W*d2F(r*4YHj_6i7n{09sEf-)>FlWdHyG07*qoM6N<$f|h}8>;M1&

delta 341
zcmV-b0jmDN0_y@biBL{Q4GJ0x0000DNk~Le0000m0000F1Oos70VfAxS^xk5El^BU
zMZmzor>Ccljg4n#XOTD|e`wS{0RR910d!JMQvg8b*k%9#0PIObK~xx(V_*OR-dBjLjb~?PU0q#GO-&~!CjbBd4Gj&nw6vObaYx;T0lTRG&D3C8XDEr
z3?={o00DGTPE!Ct=GbNc008nyL_t(YiS1O;4uc>NtH*T0@I3ziXLpFYF^RHedvZ-o
z3BplI0eFIR4vZRbu$FbG>s0^|wS8;+NQtvcMl~a25qN#C|0RnVS6(cRe2)|Hrvd^?p?0
Y4jV!Xllgp7DF6Tf07*qoM6N<$f-G~JC;$Ke

literal 321
zcmV-H0lxl;P)BjLjb~?PO-)TFCno>^01XWdw6wIEnwo%sfOK?pT3T8_KtMD!G#VNjY}~9}00001
zbW%=J06^y0W&i*Hzez+vR49>SU;qLhCLqDV00RafAvlkLmkYs81A+twB=Cb_4gm2(*cdhoO;&LE!+9
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zbW%=J06^y0W&i*Iu1Q2eR7i>KRKH8ZKoowLR%6u5W(5X}0)Jk<$hvHa7^C$T3aw(Ujk%$fz{KC6;_rCY*(w73n(YR&G
z0H|q@g%Zj_=^}-D0*W$;rmf7RhbfHq>w}8xG%r$Ng(g7#IM~O=oGvgL
zYpX@@JoGBOa}!84rc3}Yvx^*k+4*B>-812!_z4o)ra^TbKn7QKWpt2Gj(oXDIo`Q|
zDSRS0ME}M`#un>z@dbmLB*WkNItq^jDhm
zv;7HLzZBWydUhk>CN(mMWTbdnykSb+S$l-JOABT7;l&Y%%}y88-OhG8Pun!T5aNgDBJ0`CyF@g*X
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z3?={o00DGTPE!Ct=GbNc008nyL_t(YiS1O;4uc>NtH*T0@I3ziXLpFYF^RHedvZ-o
z3BplI0eFIR4vZRbu$FbG>s0^|wS8;+NQtvcMl~a25qN#C|0RnVS6(cRe2)|Hrvd^?p?0
Y4jV!Xllgp7DF6Tf07*qoM6N<$f-G~JC;$Ke

diff --git a/docs/html/img83.png b/docs/html/img83.png
index ffe4cf524189bc57d269a657af61599198922289..7dee1cf4319233e5a6786ed5f91e59b0b2d099c8 100644
GIT binary patch
literal 195
zcmeAS@N?(olHy`uVBq!ia0vp^5Eak7F*P~i0H??U
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zbW%=J06^y0W&i*Iu1Q2eR7i>KRKH8ZKoowLR%6u5W(5X}0)Jk<$hvHa7^C$T3aw(Ujk%$fz{KC6;_rCY*(w73n(YR&G
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zYpX@@JoGBOa}!84rc3}Yvx^*k+4*B>-812!_z4o)ra^TbKn7QKWpt2Gj(oXDIo`Q|
zDSRS0ME}M`#un>z@dbmLB*WkNItq^jDhm
zv;7HLzZBWydUhk>CN(mMWTbdnykSb+S$l-JOABT7;l&Y%%}y88-OhG8Pun!T5aNgDBJ0`CyF@g*X
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diff --git a/docs/html/img87.png b/docs/html/img87.png
index e7a86242bfe1f513763e2194865c91f641a55eec..4b39f077c786934afb9ec9eb2a0ed7d7288758c2 100644
GIT binary patch
delta 306
zcmV-20nPsZ1M&hPiBL{Q4GJ0x0000DNk~Le0000c0000W1Oos70sBoS7Lg%Ke*o}F
zL_t(2k;RccP6IIzg}?O{!C7yz1qTRpbgrSq1}Bz_u1K|=}yRixY?
zjccksK#Gj5{DDFhMLcQ7<9W|BqcLnT+J&uH%^o__WyV2t*JqWy=S&~g{YJ&mgKFw9
z^ePz1gzDiXl%pcD3BTyR2
z#6+&GuR7tGFe(}wp?E)w^IH&qd$ZNXH?_-T$K{0$p%^yLkWj1YGiKdsArijydLW*Q
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zY9@*L%2+I)v{IsIiCblO@HIClVV&XY@fFbD+0G?In~vvsQbiwwlEj^004KDk*hk|-
z|11Vn4%a!)MM*-Z*h4~Fk+lmeE9^mCH#!N5!pPHs0P6wI(1r`r#k*gd+_Z~c7WKCP
q7f34TB&v{*4S57fRlt8N7QrXoKv*0|&PWsh0000?F@R1=*e~(E-
zK~xx(V_-l93JeT9a1N912QZzMmIfE&v)TY*Fe5ajr6r&l!@$UJVFHliWMKG!E=2$^
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JPDHLkV1hjtOu_&F

delta 305
zcmV-10nYxB0`dYOiBL{Q4GJ0x0000DNk~Le0000c0000W1Oos70sBoS7Lg%LfAC2}
zK~yM_#gRQu12GVVzx5WuS#Poh2MBa@uA$i@Gl{ei}qULka^`q}(8l
zYpOj!ij1xNfkG8UJZZ+`dCxPWF>Eo~g{@f49y-%y#zAz~XO+C?Odr<$M#a#BYU(ib
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z?e_&u>
zV?Y827?{8`%LG0K2F^D;P~o(+v;>$E1qOx%3^)L?ItEUL1dxG16CpH16G$)dfQyBJ
zf%yT*fdUK+U|Io%=Hp@l(?IS7n2n@>G%!fOl#t#Cp}WB(zW`GJm~jqFsxdGm;pU1l
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AR{#J2

delta 198
zcmV;%06G7W0+9kCiBL{Q4GJ0x0000DNk~Le0000L0000U1Oos70Y>?F@R1=^e?SEa
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zYWP+yV36IN2-Cu~f#(2Rzmfp496rM9S};fe04-D@D?rZc?*IS*07*qoM6N<$g0a|1
AKmY&$

diff --git a/docs/html/img90.png b/docs/html/img90.png
index 97c77ca2b50aaad1aa3277592344288f41f40964..f89a8e47a1be3125f20255c0d7ec705fab8e8ddc 100644
GIT binary patch
literal 203
zcmeAS@N?(olHy`uVBq!ia0vp^JV4CH!py+HIB&`YPasD$nNa*QQGe!&b5&u*jvIYFK-jv*W~
zlM@)48QA1l*}k#z1S~jkfKA1cwL!?oL5EFnDoYY0JDb{qEP*tZq_$oro`MT!68KbZ
yGD}1>Hpw`6H8wVKIvM7qzhKi$3{Fa5VCZ_pzHiZ!_A5Zs89ZJ6T-G@yGywqnPdj=5

literal 273
zcmeAS@N?(olHy`uVBq!ia0vp^(m*W7!py+H7-8Vy4CELD_=LC~IB;P3^5wm~z3J)c
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zW(KV7_{Rua+{WCNnG`;#X+0E23~rBz8bkD`
ke-vtg#Xl?blCJ-ZZ*Lbua(JC2&;S4c07*qoM6N<$f&u%zJOBUy

literal 203
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diff --git a/docs/html/index.html b/docs/html/index.html
index 21e6f6b1..fc0b17cf 100644
--- a/docs/html/index.html
+++ b/docs/html/index.html
@@ -23,18 +23,18 @@ original version by:  Nikos Drakos, CBLU, University of Leeds
 
 
 
-
 next 
 up 
 previous 
-
 contents  
 

- Next:  Next: Contents
-       Contents 
 

 

@@ -58,296 +58,292 @@ University of Rome ``Tor Vergata'', Italy
 

 Software version: 3.0-beta
 

-May 15th, 2010
+December 15th, 2011
desc_a
-
the problem communication descriptor. +
the problem communication descriptor. Scope: local
Type: required
-Intent: in, target. +Intent: in. +
+Specified as: a communication data structure descdatapsb_desc_type. +
+
trans
+
Scope: +
+Type: optional +
+Intent: in. +
+Specified as: a character. +
+
work
+
an optional work space +Scope: local +
+Type: optional
-Specified as: a communication descriptor data structure descdatapsb_desc_type. +Intent: inout. +
+Specified as: a double precision array.
@@ -106,17 +125,16 @@ Specified as: a communication descriptor data structure descdatapsb_desc_typ
On Return
-
prec
-
the preconditioner. -
+
y
+
the destination vector. Scope: local
Type: required
Intent: inout.
-Specified as: a precondtioner data structure precdatapsb_prec_type -
+Specified as: a double precision array. +
info
Error code.
diff --git a/docs/html/node104.html b/docs/html/node104.html index 62561612..021b52e1 100644 --- a/docs/html/node104.html +++ b/docs/html/node104.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_precaply -- Preconditioner application routine - +psb_precdescr -- Prints a description of current preconditioner + @@ -18,53 +18,53 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: psb_precdescr Prints - Up: Preconditioner routines - Previous: psb_precbld Builds -   Next: Iterative Methods + Up: Preconditioner routines + Previous: psb_precaply Preconditioner +   Contents

-

-psb_precaply -- Preconditioner application routine +

+psb_precdescr -- Prints a description of current + preconditioner 

-call psb_precaply(prec,x,y,desc_a,info,trans,work)
-call psb_precaply(prec,x,desc_a,info,trans)
+call psb_precdescr(prec)
+call psb_precdescr(prec, iout)

Type:
-
Synchronous. +
Asynchronous.
On Entry
@@ -79,72 +79,15 @@ Intent: in.
Specified as: a preconditioner data structure precdatapsb_prec_type.
-
x
-
the source vector. -Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a double precision array. -
-
desc_a
-
the problem communication descriptor. +
iout
+
output unit. Scope: local
-Type: required +Type: optiona
Intent: in.
-Specified as: a communication data structure descdatapsb_desc_type. -
-
trans
-
Scope: -
-Type: optional -
-Intent: in. -
-Specified as: a character. -
-
work
-
an optional work space -Scope: local -
-Type: optional -
-Intent: inout. -
-Specified as: a double precision array. -
-
- -

-

-
On Return
-
-
-
y
-
the destination vector. -Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a double precision array. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. +Specified as: an integer number.
diff --git a/docs/html/node105.html b/docs/html/node105.html index 763bda29..3ba7a91c 100644 --- a/docs/html/node105.html +++ b/docs/html/node105.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_precdescr -- Prints a description of current preconditioner - +Iterative Methods + @@ -18,80 +18,61 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Iterative Methods - Up: Preconditioner routines - Previous: psb_precaply Preconditioner -   Next: psb_krylov Krylov + Up: userhtml + Previous: psb_precdescr Prints +   Contents

-

-psb_precdescr -- Prints a description of current - preconditioner -

+

+ +
+Iterative Methods +

-

-call psb_precdescr(prec)
-call psb_precdescr(prec, iout)
-
+In this chapter we provide routines for preconditioners and iterative +methods. The interfaces for Krylov subspace methods are available in +the module psb_krylov_mod.

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
prec
-
the preconditioner. -Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a preconditioner data structure precdatapsb_prec_type. -
-
iout
-
output unit. -Scope: local -
-Type: optiona -
-Intent: in. -
-Specified as: an integer number. -
-
+
+ +Subsections -

+

+
diff --git a/docs/html/node106.html b/docs/html/node106.html index 0904e909..12954c0f 100644 --- a/docs/html/node106.html +++ b/docs/html/node106.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Iterative Methods - +psb_krylov -- Krylov Methods Driver Routine + @@ -18,62 +18,372 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - - + + - next - + up - previous - contents
- Next: psb_krylov Krylov - Up: userhtml - Previous: psb_precdescr Prints -   Next: Bibliography + Up: Iterative Methods + Previous: Iterative Methods +   Contents

-

- +


-Iterative Methods -

+psb_krylov -- Krylov Methods Driver + Routine + + +

+This subroutine is a driver that provides a general interface for all +the Krylov-Subspace family methods implemented in PSBLAS version 2. + +

+The stopping criterion is the normwise backward error, in the infinity +norm, i.e. the iteration is stopped when +

+
+ + +\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath} +
+
+

+or the 2-norm residual reduction +

+
+ + +\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath} +
+
+

+according to the value passed through the istop argument (see +later). In the above formulae, $x_i$ is the tentative solution and +$r_i=b-Ax_i$ the corresponding residual at the $i$-th iteration. + +

+

+call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&
+     & itmax,iter,err,itrace,irst,istop,cond)
+

-In this chapter we provide routines for preconditioners and iterative -methods. The interfaces for Krylov subspace methods are available in -the module psb_krylov_mod. +

+
Type:
+
Synchronous. +
+
On Entry
+
+
+
method
+
a string that defines the iterative method to be + used. Supported values are: +
+
CG:
+
the Conjugate Gradient method; + +
+
CGS:
+
the Conjugate Gradient Stabilized method;

-

- -Subsections - - - -
+
+
BICG:
+
the Bi-Conjugate Gradient method; + +
+
BICGSTAB:
+
the Bi-Conjugate Gradient Stabilized method; + +
+
BICGSTABL:
+
the Bi-Conjugate Gradient Stabilized method with restarting; + +
+
RGMRES:
+
the Generalized Minimal Residual method with restarting. + +
+
+
+
a
+
the local portion of global sparse matrix +$A$. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a structured data of type spdatapsb_spmat_type. +
+
prec
+
The data structure containing the preconditioner. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a structured data of type precdatapsb_prec_type. +
+
b
+
The RHS vector. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a rank one array. +
+
x
+
The initial guess. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a rank one array. +
+
eps
+
The stopping tolerance. +
+Scope: global +
+Type: required +
+Intent: in. +
+Specified as: a real number. +
+
desc_a
+
contains data structures for communications. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a structured data of type descdatapsb_desc_type. +
+
itmax
+
The maximum number of iterations to perform. +
+Scope: global +
+Type: optional +
+Intent: in. +
+Default: $itmax = 1000$. +
+Specified as: an integer variable $itmax \ge 1$. +
+
itrace
+
If $>0$ print out an informational message about + convergence every $itrace$ iterations. +
+Scope: global +
+Type: optional +
+Intent: in. +
+
irst
+
An integer specifying the restart parameter. +
+Scope: global +
+Type: optional. +
+Intent: in. +
+Values: $irst>0$. This is employed for the BiCGSTABL or RGMRES +methods, otherwise it is ignored. + +

+

+
istop
+
An integer specifying the stopping criterion. +
+Scope: global +
+Type: optional. +
+Intent: in. +
+Values: 1: use the normwise backward error, 2: use the scaled 2-norm +of the residual. Default: 2. +
+
On Return
+
+
+
x
+
The computed solution. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a rank one array. +
+
iter
+
The number of iterations performed. +
+Scope: global +
+Type: optional +
+Intent: out. +
+Returned as: an integer variable. +
+
err
+
The convergence estimate on exit. +
+Scope: global +
+Type: optional +
+Intent: out. +
+Returned as: a real number. +
+
cond
+
An estimate of the condition number of matrix $A$; only + available with the $CG$ method. +
+Scope: global +
+Type: optional +
+Intent: out. +
+Returned as: a real number. +
+
info
+
Error code. +
+Scope: local +
+Type: required +
+Intent: out. +
+An integer value; 0 means no error has been detected. +
+
+ +

+ +

+ +

+ +

+

+ + +next + +up + +previous + +contents +
+ Next: Bibliography + Up: Iterative Methods + Previous: Iterative Methods +   Contents + diff --git a/docs/html/node107.html b/docs/html/node107.html index a5d00464..d9949883 100644 --- a/docs/html/node107.html +++ b/docs/html/node107.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_krylov -- Krylov Methods Driver Routine - +Bibliography + @@ -18,372 +18,158 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Bibliography - Up: Iterative Methods - Previous: Iterative Methods -   Next: About this document ... + Up: userhtml + Previous: psb_krylov Krylov +   Contents -
-
+

- -

-
-psb_krylov -- Krylov Methods Driver - Routine -

- -

-This subroutine is a driver that provides a general interface for all -the Krylov-Subspace family methods implemented in PSBLAS version 2. - -

-The stopping criterion is the normwise backward error, in the infinity -norm, i.e. the iteration is stopped when -

-
- - -\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath} -
-
-

-or the 2-norm residual reduction -

-
- - -\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath} -
-
-

-according to the value passed through the istop argument (see -later). In the above formulae, $x_i$ is the tentative solution and -$r_i=b-Ax_i$ the corresponding residual at the $i$-th iteration. - -

-

-call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&
-     & itmax,iter,err,itrace,irst,istop,cond)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
+ +

+Bibliography +

1
-
-
method
-
a string that defines the iterative method to be - used. Supported values are: -
-
CG:
-
the Conjugate Gradient method; - -
-
CGS:
-
the Conjugate Gradient Stabilized method; + D. Barbieri, V. Cardellini, S. Filippone and D. Rouson +Design Patterns for Scientific Computations on Sparse Matrices, + HPSS 2011, Algorithms and Programming Tools for Next-Generation High-Performance Scientific Software, Bordeaux, Sep. 2011

-

-
BICG:
-
the Bi-Conjugate Gradient method; - -
-
BICGSTAB:
-
the Bi-Conjugate Gradient Stabilized method; - -
-
BICGSTABL:
-
the Bi-Conjugate Gradient Stabilized method with restarting; - -
-
RGMRES:
-
the Generalized Minimal Residual method with restarting. - -
-
-
-
a
-
the local portion of global sparse matrix -$A$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type spdatapsb_spmat_type. -
-
prec
-
The data structure containing the preconditioner. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type precdatapsb_prec_type. -
-
b
-
The RHS vector. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one array. -
-
x
-
The initial guess. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one array. -
-
eps
-
The stopping tolerance. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a real number. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
itmax
-
The maximum number of iterations to perform. -
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $itmax = 1000$. -
-Specified as: an integer variable $itmax \ge 1$. -
-
itrace
-
If $>0$ print out an informational message about - convergence every $itrace$ iterations. -
-Scope: global -
-Type: optional -
-Intent: in. -
-
irst
-
An integer specifying the restart parameter. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Values: $irst>0$. This is employed for the BiCGSTABL or RGMRES -methods, otherwise it is ignored. +

2 +
+G. Bella, S. Filippone, A. De Maio and M. Testa, +A Simulation Model for Forest Fires, +in J. Dongarra, K. Madsen, J. Wasniewski, editors, +Proceedings of PARA 04 Workshop on State of the Art +in Scientific Computing, pp. 546-553, Lecture Notes in Computer Science, +Springer, 2005. +

3 +
A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,
+2LEV-D2P4: a package of high-performance preconditioners,
+Applicable Algebra in Engineering, Communications and Computing, +Volume 18, Number 3, May, 2007, pp. 223-239 +

4 +
P. D'Ambra, S. Filippone, D. Di Serafino
+On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners +
+Applied Numerical Mathematics, Elsevier Science, +Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196.

-

-
istop
-
An integer specifying the stopping criterion. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Values: 1: use the normwise backward error, 2: use the scaled 2-norm -of the residual. Default: 2. -
-
On Return
+

5
-
-
x
-
The computed solution. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one array. -
-
iter
-
The number of iterations performed. -
-Scope: global -
-Type: optional -
-Intent: out. -
-Returned as: an integer variable. -
-
err
-
The convergence estimate on exit. -
-Scope: global -
-Type: optional -
-Intent: out. -
-Returned as: a real number. -
-
cond
-
An estimate of the condition number of matrix $A$; only - available with the $CG$ method. -
-Scope: global -
-Type: optional -
-Intent: out. -
-Returned as: a real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required + Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R., +An Extended Set of Fortran Basic Linear Algebra Subprograms, +ACM Trans. Math. Softw. vol. 14, 1-17, 1988. +

6 +
+ Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I., +A Set of level 3 Basic Linear Algebra Subprograms, +ACM Trans. Math. Softw. vol. 16, 1-17, 1990. +

7 +
+J. J. Dongarra and R. C. Whaley, +A User's Guide to the BLACS v. 1.1, +Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of +Tennessee, March 1995 (updated May 1997). +

8 +
+I. Duff, M. Marrone, G. Radicati and C. Vittoli, +Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: +a User Level Interface, +ACM Transactions on Mathematical Software, 23(3), pp. 379-401, 1997. +

9 +
+I. Duff, M. Heroux and R. Pozo, +An Overview of the Sparse Basic Linear +Algebra Subprograms: the New Standard from the BLAS Technical Forum, +ACM Transactions on Mathematical Software, 28(2), pp. 239-267, 2002. +

10 +
+S. Filippone and M. Colajanni, +PSBLAS: A Library for Parallel Linear Algebra +Computation on Sparse Matrices,
-Intent: out. +ACM Transactions on Mathematical Software, 26(4), pp. 527-550, 2000. +

11 +
+S. Filippone and A. Buttari, +Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003,
-An integer value; 0 means no error has been detected. -
-
- -

+ACM Transactions on Mathematical Software, to appear. +

12 +
+S. Filippone, P. D'Ambra, M. Colajanni, +Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics +Applications Code on Linux Clusters, +in G. Joubert, A. Murli, F. Peters, M. Vanneschi, editors, +Parallel Computing - Advances & Current Issues, +pp. 441-448, Imperial College Press, 2002. +

13 +
+Karypis, G. and Kumar, V., +METIS: Unstructured Graph Partitioning and Sparse Matrix + Ordering System. +Minneapolis, MN 55455: University of Minnesota, Department of + Computer Science, 1995. +Internet Address: http://www.cs.umn.edu/~karypis. +

14 +
+Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., + Basic Linear Algebra Subprograms for Fortran usage, +ACM Trans. Math. Softw. vol. 5, 38-329, 1979.

+

15 +
+Machiels, L. and Deville, M. +Fortran 90: An entry to object-oriented programming for the solution + of partial differential equations. +ACM Trans. Math. Softw. vol. 23, 32-49. +

16 +
+Metcalf, M., Reid, J. and Cohen, M. +Fortran 95/2003 explained. +Oxford University Press, 2004. +

17 +
+Rouson, D.W.I., Xia, J., Xu, X.: Scientific Software Design: The + Object-Oriented Way. Cambridge University Press (2011)

+

18 +
+M. Snir, S. Otto, S. Huss-Lederman, D. Walker and J. Dongarra, +MPI: The Complete Reference. Volume 1 - The MPI Core, second edition, +MIT Press, 1998. +

-

- - -next - -up - -previous - -contents -
- Next: Bibliography - Up: Iterative Methods - Previous: Iterative Methods -   Contents - +
diff --git a/docs/html/node108.html b/docs/html/node108.html index 777b58bc..1789a129 100644 --- a/docs/html/node108.html +++ b/docs/html/node108.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Bibliography - +About this document ... + @@ -18,157 +18,52 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - - -next - + up - previous - contents
- Next: About this document ... - Up: Up: userhtml - Previous: psb_krylov Krylov -   Previous: Bibliography +   Contents -

- - -

-Bibliography -

1 -
- D. Barbieri, V. Cardellini, S. Filippone and D. Rouson -Design Patterns for Scientific Computations on Sparse Matrices, - HPSS 2011, Algorithms and Programming Tools for Next-Generation High-Performance Scientific Software, Bordeaux, Sep. 2011 - -

-

2 -
-G. Bella, S. Filippone, A. De Maio and M. Testa, -A Simulation Model for Forest Fires, -in J. Dongarra, K. Madsen, J. Wasniewski, editors, -Proceedings of PARA 04 Workshop on State of the Art -in Scientific Computing, pp. 546-553, Lecture Notes in Computer Science, -Springer, 2005. -

3 -
A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,
-2LEV-D2P4: a package of high-performance preconditioners,
-Applicable Algebra in Engineering, Communications and Computing, -Volume 18, Number 3, May, 2007, pp. 223-239 -

4 -
P. D'Ambra, S. Filippone, D. Di Serafino
-On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners -
-Applied Numerical Mathematics, Elsevier Science, -Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196. - -

-

5 -
- Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R., -An Extended Set of Fortran Basic Linear Algebra Subprograms, -ACM Trans. Math. Softw. vol. 14, 1-17, 1988. -

6 -
- Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I., -A Set of level 3 Basic Linear Algebra Subprograms, -ACM Trans. Math. Softw. vol. 16, 1-17, 1990. -

7 -
-J. J. Dongarra and R. C. Whaley, -A User's Guide to the BLACS v. 1.1, -Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of -Tennessee, March 1995 (updated May 1997). -

8 -
-I. Duff, M. Marrone, G. Radicati and C. Vittoli, -Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: -a User Level Interface, -ACM Transactions on Mathematical Software, 23(3), pp. 379-401, 1997. -

9 -
-I. Duff, M. Heroux and R. Pozo, -An Overview of the Sparse Basic Linear -Algebra Subprograms: the New Standard from the BLAS Technical Forum, -ACM Transactions on Mathematical Software, 28(2), pp. 239-267, 2002. -

10 -
-S. Filippone and M. Colajanni, -PSBLAS: A Library for Parallel Linear Algebra -Computation on Sparse Matrices,
-ACM Transactions on Mathematical Software, 26(4), pp. 527-550, 2000. -

11 -
-S. Filippone and A. Buttari, -Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003,
-ACM Transactions on Mathematical Software, to appear. -

12 -
-S. Filippone, P. D'Ambra, M. Colajanni, -Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics -Applications Code on Linux Clusters, -in G. Joubert, A. Murli, F. Peters, M. Vanneschi, editors, -Parallel Computing - Advances & Current Issues, -pp. 441-448, Imperial College Press, 2002. -

13 -
-Karypis, G. and Kumar, V., -METIS: Unstructured Graph Partitioning and Sparse Matrix - Ordering System. -Minneapolis, MN 55455: University of Minnesota, Department of - Computer Science, 1995. -Internet Address: http://www.cs.umn.edu/~karypis. -

14 -
-Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., - Basic Linear Algebra Subprograms for Fortran usage, -ACM Trans. Math. Softw. vol. 5, 38-329, 1979. + +

+About this document ... +

+

+This document was generated using the +LaTeX2HTML translator Version 2008 (1.71)

-

15 -
-Machiels, L. and Deville, M. -Fortran 90: An entry to object-oriented programming for the solution - of partial differential equations. -ACM Trans. Math. Softw. vol. 23, 32-49. -

16 -
-Metcalf, M., Reid, J. and Cohen, M. -Fortran 95/2003 explained. -Oxford University Press, 2004. -

17 -
-Rouson, D.W.I., Xia, J., Xu, X.: Scientific Software Design: The - Object-Oriented Way. Cambridge University Press (2011) - +Copyright © 1993, 1994, 1995, 1996, +Nikos Drakos, +Computer Based Learning Unit, University of Leeds. +
+Copyright © 1997, 1998, 1999, +Ross Moore, +Mathematics Department, Macquarie University, Sydney.

-

18 -
-M. Snir, S. Otto, S. Huss-Lederman, D. Walker and J. Dongarra, -MPI: The Complete Reference. Volume 1 - The MPI Core, second edition, -MIT Press, 1998. -
- +The command line arguments were:
+ latex2html -local_icons -noaddress -dir ../../html userhtml.tex

+The translation was initiated by Salvatore Filippone on 2011-12-16

diff --git a/docs/html/node11.html b/docs/html/node11.html index e7a95356..555c4e71 100644 --- a/docs/html/node11.html +++ b/docs/html/node11.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Named Constants - Up: Up: Data Structures - Previous: Previous: Named Constants -   Contents

@@ -57,11 +57,14 @@ original version by: Nikos Drakos, CBLU, University of Leeds Sparse Matrix data structure The spdatapsb_spmat_type data structure -contains all information about local portion of the sparse matrix and +contains all information about the local portion of the sparse matrix and its storage mode. Most of these fields are set by the tools routines when inserting a new sparse matrix; the user needs only choose, if he/she so whishes, a specific matrix storage mode. -
+ +

+The +

aspk
Contains values of the local distributed sparse matrix. @@ -125,11 +128,11 @@ Specified as: integer variable.
The Fortran 95 interface for distributed sparse matrices containing double precision real entries is defined as shown in -figure 5. The definitions for single precision and +figure 4. The definitions for single precision and complex data are identical except for the real declaration and for the kind type parameter. -
+
Figure 4: The PSBLAS defined data type that @@ -223,32 +226,32 @@ values: Subsections
- next - up - previous - contents
- Next: Next: Named Constants - Up: Up: Data Structures - Previous: Previous: Named Constants -   Contents diff --git a/docs/html/node12.html b/docs/html/node12.html index 5783c3b9..8825b9cc 100644 --- a/docs/html/node12.html +++ b/docs/html/node12.html @@ -25,26 +25,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Dense Vector Data Structure - Up: Up: Sparse Matrix data structure - Previous: Previous: Sparse Matrix data structure -   Contents

diff --git a/docs/html/node13.html b/docs/html/node13.html index 4fa95e39..b854d547 100644 --- a/docs/html/node13.html +++ b/docs/html/node13.html @@ -18,7 +18,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Named Constants - Up: Next: Preconditioner data structure + Up: Data Structures - Previous: Previous: Named Constants -   Contents

@@ -61,196 +61,9 @@ contains all information about local portion of the sparse matrix and its storage mode. Most of these fields are set by the tools routines when inserting a new sparse matrix; the user needs only choose, if he/she so whishes, a specific matrix storage mode. -
-
aspk
-
Contains values of the local distributed sparse -matrix. -
-Specified as: an allocatable array of rank one of type corresponding -to matrix entries type. -
-
ia1
-
Holds integer information on distributed sparse -matrix. Actual information will depend on data format used. -
-Specified as: an allocatable integer array of rank one. -
-
ia2
-
Holds integer information on distributed sparse -matrix. Actual information will depend on data format used. -
-Specified as: an allocatable integer array of rank one. -
-
infoa
-
On entry can hold auxiliary information on distributed sparse -matrix. Actual information will depend on data format used. -
-Specified as: an integer array of length psb_ifasize_. -
-
fida
-
Defines the format of the distributed sparse matrix. -
-Specified as: a string of length 5 -
-
descra
-
Describe the characteristic of the distributed sparse matrix. -
-Specified as: array of character of length 9. -
-
pl
-
Specifies the local row permutation of distributed sparse -matrix. If pl(1) is equal to 0, then there isn't row permutation.
-Specified as: an allocatable integer array of dimension equal to number of local row (matrix_data[psb_n_row_]) -
-
pr
-
Specifies the local column permutation of distributed sparse -matrix. If PR(1) is equal to 0, then there isn't columnm permutation. -
-Specified as: an allocatable integer array of dimension equal to number of -local row (matrix_data[psb_n_col_]) -
-
m
-
Number of rows; if row indices are stored explicitly, -as in Coordinate Storage, should be greater than or equal to the -maximum row index actually present in the sparse matrix. -Specified as: integer variable. -
-
k
-
Number of columns; if column indices are stored explicitly, -as in Coordinate Storage or Compressed Sparse Rows, should be greater -than or equal to the maximum column index actually present in the sparse matrix. -Specified as: integer variable. -
-
-The Fortran 95 interface for distributed sparse matrices containing -double precision real entries is defined as shown in -figure 5. The definitions for single precision and -complex data are identical except for the real declaration and -for the kind type parameter. - -
- - - -
Figure 5: - The PSBLAS defined data type that - contains a sparse matrix.
-
- -
- -\fbox{\TheSbox} -
-
-

-The following two cases are among the most commonly used: -

-
fida=``CSR''
-
Compressed storage by rows. In this case the -following should hold: - -
    -
  1. ia2(i) contains the index of the first element of row -i; the last element of the sparse matrix is thus stored at -index $ia2(m+1)-1$. It should contain m+1 entries in -nondecreasing order (strictly increasing, if there are no empty rows). -
    2. -
  2. ia1(j) contains the column index and aspk(j) -contains the corresponding coefficient value, for all -$ia2(1) \le j -\le ia2(m+1)-1$. -
    3. -
-
-
fida=``COO''
-
Coordinate storage. In this case the following -should hold: - -
    -
  1. infoa(1) contains the number of nonzero elements in the -matrix; -
    2. -
  2. For all -$1 \le j \le infoa(1)$, the coefficient, row index and -column index are stored into apsk(j), ia1(j) and -ia2(j) respectively. -
    3. -
-
-
-A sparse matrix has an associated state, which can take the following -values: -
-
Build:
-
State entered after the first allocation, and before the - first assembly; in this state it is possible to add nonzero entries. -
-
Assembled:
-
State entered after the assembly; computations using - the sparse matrix, such as matrix-vector products, are only possible - in this state; -
-
Update:
-
State entered after a reinitalization; this is used to - handle applications in which the same sparsity pattern is used - multiple times with different coefficients. In this state it is only - possible to enter coefficients for already existing nonzero entries. -
-

- -Subsections - - - -
- - -next - -up - -previous - -contents -
- Next: Named Constants - Up: Data Structures - Previous: Named Constants -   Contents - diff --git a/docs/html/node14.html b/docs/html/node14.html index d5714c05..f01a0035 100644 --- a/docs/html/node14.html +++ b/docs/html/node14.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Named Constants - +Preconditioner data structure + @@ -18,65 +18,79 @@ original version by: Nikos Drakos, CBLU, University of Leeds + - + - next - + up - previous - contents
- Next: Preconditioner data structure - Up: Next: Data structure query routines + Up: Data Structures + Previous: Dense Vector Data Structure - Previous: Dense Vector Data Structure -   Contents

-

- +

+ +
+Preconditioner data structure +

+Our base library offers support for simple well known preconditioners +like Diagonal Scaling or Block Jacobi with incomplete +factorization ILU(0). + +

+A preconditioner is held in the precdata psb_prec_type data structure reported in +figure 5. The psb_prec_type +data type may contain a simple preconditioning matrix with the +associated communication descriptor.The values contained in +the iprcparm and rprcparm define tha type of +preconditioner along with all the parameters related to it; thus, +iprcparm and rprcparm define how the other records have +to be interpreted. This data structure is the basis of more complex +preconditioning strategies, which are the subject of further +research. + +

+ + + +
Figure 5: +The PSBLAS defined data type that contains a preconditioner.

+
-Named Constants - -
-
psb_dupl_ovwrt_
-
Duplicate coefficients should be overwritten - (i.e. ignore duplications) -
-
psb_dupl_add_
-
Duplicate coefficients should be added; -
-
psb_dupl_err_
-
Duplicate coefficients should trigger an error conditino -
-
psb_upd_dflt_
-
Default update strategy for matrix coefficients; -
-
psb_upd_srch_
-
Update strategy based on search into the data structure; -
-
psb_upd_perm_
-
Update strategy based on additional - permutation data (see tools routine description). -
-
+ + +
+\fbox{\TheSbox}
+
+


diff --git a/docs/html/node15.html b/docs/html/node15.html index 7ef6ed8a..719ee509 100644 --- a/docs/html/node15.html +++ b/docs/html/node15.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Preconditioner data structure - +Data structure query routines + @@ -18,81 +18,59 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + - next - up - previous - contents
- Next: Data structure query routines - Up: Next: get_local_rows Get + Up: Data Structures - Previous: Named Constants -   Previous: Preconditioner data structure +   Contents

-

- +

+
-Preconditioner data structure +Data structure query routines

-Our base library offers support for simple well known preconditioners -like Diagonal Scaling or Block Jacobi with incomplete -factorization ILU(0). - -

-A preconditioner is held in the precdata psb_prec_type data structure reported in -figure 6. The psb_prec_type -data type may contain a simple preconditioning matrix with the -associated communication descriptor.The values contained in -the iprcparm and rprcparm define tha type of -preconditioner along with all the parameters related to it; thus, -iprcparm and rprcparm define how the other records have -to be interpreted. This data structure is the basis of more complex -preconditioning strategies, which are the subject of further -research. - -

- - - -
Figure 6: -The PSBLAS defined data type that contains a preconditioner.

- -
- - -
-\fbox{\TheSbox}
-
-
+
+ +Subsections -

+

+
diff --git a/docs/html/node16.html b/docs/html/node16.html index a1d03c01..cbf0d441 100644 --- a/docs/html/node16.html +++ b/docs/html/node16.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Data structure query routines - +get_local_rows -- Get number of local rows + @@ -18,59 +18,89 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - + - next - + up - previous - contents
- Next: get_local_rows Get - Up: Data Structures - Previous: Preconditioner data structure -   Next: get_local_cols Get + Up: Data structure query routines + Previous: Data structure query routines +   Contents

-

- +

+get_local_rows -- Get number of local rows +

+ +

+

+nr = desc%get_local_rows()
+
+ +

+

+
Type:
+
Asynchronous. +
+
On Entry
+
+
+
desc
+
the communication descriptor.
-Data structure query routines - -
- -Subsections +Scope: local. +
+Type: required. +
+Intent: in. +
+Specified as: a structured data of type descdatapsb_desc_type. +
+
+ +

+

+
On Return
+
+
+
Function value
+
The number of local rows, i.e. the number of + rows owned by the current process; as explained in 1, + it is equal to +$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert$. The returned value is + specific to the calling process. +
+
- - +


diff --git a/docs/html/node17.html b/docs/html/node17.html index 1f8b780d..4f29c33d 100644 --- a/docs/html/node17.html +++ b/docs/html/node17.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_local_rows -- Get number of local rows - +get_local_cols -- Get number of local cols + @@ -20,54 +20,54 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: get_local_cols Get - Up: Data structure query routines - Previous: Data structure query routines -   Next: get_global_rows Get + Up: Data structure query routines + Previous: get_local_rows Get +   Contents

-

-get_local_rows -- Get number of local rows +

+get_local_cols -- Get number of local cols 

-nr = desc%get_local_rows()
+nc = desc%get_local_cols()

-
Type:
-
Asynchronous. -
On Entry
+
Type:
+
Asynchronous. +
desc
the communication descriptor.
@@ -87,16 +87,17 @@ Specified as: a structured data of type descdatapsb_desc_type.
Function value
-
The number of local rows, i.e. the number of - rows owned by the current process; as explained in 1, - it is equal to $\vert{\cal I}_i\vert + \vert{\cal B}_i\vert$. The returned value is - specific to the calling process. + WIDTH="118" HEIGHT="32" ALIGN="MIDDLE" BORDER="0" + SRC="img11.png" + ALT="$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert +\vert{\cal H}_i\vert$">. The + returned value is specific to the calling process.
diff --git a/docs/html/node18.html b/docs/html/node18.html index 6088ff7e..a642776c 100644 --- a/docs/html/node18.html +++ b/docs/html/node18.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_local_cols -- Get number of local cols - +get_global_rows -- Get number of global rows + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: get_global_rows Get - Up: Data structure query routines - Previous: get_local_rows Get -   Next: get_global_cols Get + Up: Data structure query routines + Previous: get_local_cols Get +   Contents

-

-get_local_cols -- Get number of local cols +

+get_global_rows -- Get number of global rows 

-nc = desc%get_local_cols()
+nr = desc%get_global_rows()

@@ -87,17 +87,7 @@ Specified as: a structured data of type descdatapsb_desc_type.

Function value
-
The number of local cols, i.e. the number of - indices used by the current process, including both local and halo - indices; as explained in 1, - it is equal to -$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert +\vert{\cal H}_i\vert$. The - returned value is specific to the calling process. +
The number of global rows in the mesh
diff --git a/docs/html/node19.html b/docs/html/node19.html index ad0ed183..bb56ea20 100644 --- a/docs/html/node19.html +++ b/docs/html/node19.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_global_rows -- Get number of global rows - +get_global_cols -- Get number of global cols + @@ -18,56 +18,55 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: get_global_cols Get - Up: Data structure query routines - Previous: get_local_cols Get -   Next: get_context Get communication context + Up: Data structure query routines + Previous: get_global_rows Get +   Contents

-

-get_global_rows -- Get number of global rows +

+get_global_cols -- Get number of global cols 

-nr = desc%get_global_rows()
+nr = desc%get_global_cols()

-
On Entry
-
-
Type:
Asynchronous.
+
On Entry
+
+
desc
the communication descriptor.
@@ -87,7 +86,7 @@ Specified as: a structured data of type descdatapsb_desc_type.
Function value
-
The number of global rows in the mesh +
The number of global cols in the mesh
diff --git a/docs/html/node2.html b/docs/html/node2.html index 15cf7b33..b3003ade 100644 --- a/docs/html/node2.html +++ b/docs/html/node2.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: General overview - Up: Up: userhtml - Previous: Previous: Contents -   Contents

@@ -71,7 +71,7 @@ passing.

The PSBLAS library version 3 is internally implemented in the Fortran 2003 [16] programming language, with reuse and/or + HREF="node107.html#metcalf">16] programming language, with reuse and/or adaptation of some existing Fortran 77 software, and a handful of C routines. @@ -81,37 +81,36 @@ mostly in the handling of requirements for evolution and adaptation of the library to new computing architectures and integration of new algorithms. For a detailed discussion of our design see [11]; other -works tackling advanced programming in Fortran 2003 include [1,17] + HREF="node107.html#Sparse03">11]; other +works discussing advanced programming in Fortran 2003 +include [1,17]; sufficient support for +Fortran 2003 is now available from many compilers, including the GNU +Fortran compiler from the Free Software Foundation (as of version 4.6).

Previous approaches have been based on mixing Fortran 95, with its support for object-based design, with other languages; these have been advocated by a number of authors, e.g. [15]. Moreover, the Fortran 95 facilities for dynamic + HREF="node107.html#machiels">15]. Moreover, the Fortran 95 facilities for dynamic memory management and interface overloading greatly enhance the usability of the PSBLAS subroutines. In this way, the library can take care of runtime memory requirements that are quite difficult or even impossible to predict at implementation or compilation time. -In the current release we rely on the availability of the so-called -allocatable extensions, specified in TR 15581. Strictly speaking they -are outside the Fortran 95 standard; however they have been included -in the Fortran 2003 language standard, and are available in -practically all Fortran 95 compilers on the market, including the GNU -Fortran compiler from the Free Software Foundation (as of version 4.2). + +

The presentation of the PSBLAS library follows the general structure of the proposal for serial Sparse BLAS [8,9], which in its turn is based on the + HREF="node107.html#sblas97">8,9], which in its turn is based on the proposal for BLAS on dense matrices [14,5,6]. + HREF="node107.html#BLAS1">14,5,6].

The applicability of sparse iterative solvers to many different areas @@ -145,26 +144,26 @@ computational fluid dynamics applications.

- next - up - previous - contents
- Next: Next: General overview - Up: Up: userhtml - Previous: Previous: Contents -   Contents diff --git a/docs/html/node20.html b/docs/html/node20.html index 16428cb3..f8312f99 100644 --- a/docs/html/node20.html +++ b/docs/html/node20.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_global_cols -- Get number of global cols - +get_context--Get communication context + @@ -18,45 +18,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + - next - -up +up + previous - contents
- Next: get_context Get communication context - Up: Data structure query routines - Previous: get_global_rows Get -   Next: psb_cd_get_large_threshold Get + Up: Data Structures + Previous: get_global_cols Get +   Contents

-

-get_global_cols -- Get number of global cols -

- -

+

+
+get_context--Get communication context +
 +

-nr = desc%get_global_cols()
+ictxt = desc%get_context()

@@ -86,12 +86,32 @@ Specified as: a structured data of type descdatapsb_desc_type.

Function value
-
The number of global cols in the mesh +
The communication context.


+ +Subsections + + + +
diff --git a/docs/html/node21.html b/docs/html/node21.html index f67e2fea..42155ebc 100644 --- a/docs/html/node21.html +++ b/docs/html/node21.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_context--Get communication context - +psb_cd_get_large_threshold -- Get threshold for index mapping switch + @@ -18,45 +18,46 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: psb_cd_get_large_threshold Get - Up: Data Structures - Previous: get_global_cols Get -   Next: psb_cd_set_large_threshold Set + Up: get_context Get communication context + Previous: get_context Get communication context +   Contents

-

-
-get_context--Get communication context -
 -

+

+psb_cd_get_large_threshold -- Get threshold for + index mapping switch +

+ 
-ictxt = desc%get_context()
+ith = psb_cd_get_large_threshold()

@@ -64,54 +65,18 @@ ictxt = desc%get_context()

Type:
Asynchronous.
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
- - -

-

On Return
Function value
-
The communication context. +
The current value for the size threshold. + +


- -Subsections - - - -
diff --git a/docs/html/node22.html b/docs/html/node22.html index 1773ed2d..0ad007a6 100644 --- a/docs/html/node22.html +++ b/docs/html/node22.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cd_get_large_threshold -- Get threshold for index mapping switch - +psb_cd_set_large_threshold -- Set threshold for index mapping switch + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_cd_set_large_threshold Set - Up: get_context Get communication context - Previous: get_context Get communication context -   Next: get_nrows Get + Up: get_context Get communication context + Previous: psb_cd_get_large_threshold Get +   Contents

-

-psb_cd_get_large_threshold -- Get threshold for +

+psb_cd_set_large_threshold -- Set threshold for index mapping switch 

-ith = psb_cd_get_large_threshold()
+call psb_cd_set_large_threshold(ith)

@@ -65,15 +65,24 @@ ith = psb_cd_get_large_threshold()

Type:
Asynchronous.
-
On Return
+
On Entry
-
Function value
-
The current value for the size threshold. - -

+

ith
+
the new threshold for communication descriptors. +
+Scope: global. +
+Type: required. +
+Intent: in. +
+Specified as: an integer value greater than zero.
+Note: the threshold value is only queried by the library at the time a +call to psb_cdall is executed, therefore changing the threshold +has no effect on communication descriptors that have already been initialized.


diff --git a/docs/html/node23.html b/docs/html/node23.html index d663d445..15da1733 100644 --- a/docs/html/node23.html +++ b/docs/html/node23.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cd_set_large_threshold -- Set threshold for index mapping switch - +get_nrows -- Get number of rows in a sparse matrix + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: get_nrows Get - Up: get_context Get communication context - Previous: psb_cd_get_large_threshold Get -   Next: get_ncols Get + Up: get_context Get communication context + Previous: psb_cd_set_large_threshold Set +   Contents

-

-psb_cd_set_large_threshold -- Set threshold for - index mapping switch +

+get_nrows -- Get number of rows in a sparse matrix

+

-call psb_cd_set_large_threshold(ith)
+nr = a%get_nrows()

@@ -68,21 +68,28 @@ call psb_cd_set_large_threshold(ith)

On Entry
-
ith
-
the new threshold for communication descriptors. +
a
+
the sparse matrix
-Scope: global. +Scope: local
-Type: required. +Type: required
Intent: in.
-Specified as: an integer value greater than zero. +Specified as: a structured data of type spdatapsb_spmat_type. +
+ + +

+

+
On Return
+
+
+
Function value
+
The number of rows of sparse matrix a.
-Note: the threshold value is only queried by the library at the time a -call to psb_cdall is executed, therefore changing the threshold -has no effect on communication descriptors that have already been initialized.


diff --git a/docs/html/node24.html b/docs/html/node24.html index f7c660bb..91915427 100644 --- a/docs/html/node24.html +++ b/docs/html/node24.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_nrows -- Get number of rows in a sparse matrix - +get_ncols -- Get number of columns in a sparse matrix + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: get_ncols Get - Up: get_context Get communication context - Previous: psb_cd_set_large_threshold Set -   Next: get_nnzeros Get + Up: get_context Get communication context + Previous: get_nrows Get +   Contents

-

-get_nrows -- Get number of rows in a sparse matrix +

+get_ncols -- Get number of columns in a sparse matrix 

-nr = a%get_nrows()
+nr = a%get_ncols()

@@ -87,7 +87,7 @@ Specified as: a structured data of type spdatapsb_spmat_type.

Function value
-
The number of rows of sparse matrix a. +
The number of columns of sparse matrix a.
diff --git a/docs/html/node25.html b/docs/html/node25.html index 5316f32b..9ea89d12 100644 --- a/docs/html/node25.html +++ b/docs/html/node25.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_ncols -- Get number of columns in a sparse matrix - +get_nnzeros -- Get number of nonzero elements in a sparse matrix + @@ -18,46 +18,46 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: get_nnzeros Get - Up: get_context Get communication context - Previous: get_nrows Get -   Next: Computational routines + Up: get_context Get communication context + Previous: get_ncols Get +   Contents

-

-get_ncols -- Get number of columns in a sparse matrix +

+get_nnzeros -- Get number of nonzero elements + in a sparse matrix 

-nr = a%get_ncols()
+nr = a%get_nnzeros()

@@ -87,10 +87,20 @@ Specified as: a structured data of type spdatapsb_spmat_type.

Function value
-
The number of columns of sparse matrix a. +
The number of nonzero elements stored in sparse matrix a.
+

+Notes + +

    +
  1. The function value is specific to the storage format of matrix + a; some storage formats employ padding, thus the returned + value for the same matrix may be different for different storage choices. +
    2. +
+


diff --git a/docs/html/node26.html b/docs/html/node26.html index 82c9a030..7c467b4c 100644 --- a/docs/html/node26.html +++ b/docs/html/node26.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -get_nnzeros -- Get number of nonzero elements in a sparse matrix - +Computational routines + @@ -18,90 +18,75 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Computational routines - Up: get_context Get communication context - Previous: get_ncols Get -   Next: psb_geaxpby General + Up: userhtml + Previous: get_nnzeros Get +   Contents

-

-get_nnzeros -- Get number of nonzero elements - in a sparse matrix -

+

+Computational routines +

-

-nr = a%get_nnzeros()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type spdatapsb_spmat_type. -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of nonzero elements stored in sparse matrix a. -
-
- -

-Notes - -

    -
  1. The function value is specific to the storage format of matrix - a; some storage formats employ padding, thus the returned - value for the same matrix may be different for different storage choices. -
    2. -
+
+ +Subsections -

+

+
diff --git a/docs/html/node27.html b/docs/html/node27.html index 262ee489..f8c7c410 100644 --- a/docs/html/node27.html +++ b/docs/html/node27.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Computational routines - +psb_geaxpby -- General Dense Matrix Sum + @@ -18,76 +18,264 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - - + + + - next - + up - previous - contents
- Next: psb_geaxpby General - Up: userhtml - Previous: get_nnzeros Get -   Next: psb_gedot Dot + Up: Computational routines + Previous: Computational routines +   Contents

-

-Computational routines -

+

+psb_geaxpby -- General Dense Matrix Sum +

+ +

+This subroutine is an interface to the computational kernel for +dense matrix sum: +

+
+ + +\begin{displaymath}y \leftarrow \alpha\> x+ \beta y \end{displaymath} +
+
+

+ +

+

+call psb_geaxpby(alpha, x, beta, y, desc_a, info)
+
+ +

+

+
+ + + +
Table 1: +Data types
+
+ + + + + + + + + + + + + + + + +
$x$, $y$, $\alpha$, $\beta$Subroutine
Short Precision Realpsb_geaxpby
Long Precision Realpsb_geaxpby
Short Precision Complexpsb_geaxpby
Long Precision Complexpsb_geaxpby
+
+
+

+
+ +

+

+
Type:
+
Synchronous. +
+
On Entry
+
+
+
alpha
+
the scalar $\alpha$. +
+Scope: global +
+Type: required +
+Intent: in. +
+Specified as: a number of the data type indicated in Table 1. +
+
x
+
the local portion of global dense matrix +$x$. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a rank one or two array +containing numbers of type +specified in Table 1. The rank of $x$ must be the same of $y$. +
+
beta
+
the scalar $\beta$. +
+Scope: global +
+Type: required +
+Intent: in. +
+Specified as: a number of the data type indicated in Table 1. +
+
y
+
the local portion of the global dense matrix +$y$. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a rank one or two array containing numbers of the type +indicated in Table 1. The rank of $y$ must be the same of $x$. +
+
desc_a
+
contains data structures for communications. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a structured data of type descdatapsb_desc_type. + +

+

+

-

- -Subsections +
+
On Return
+
+
+
y
+
the local portion of result submatrix $y$. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a rank one or two array containing numbers of the type +indicated in Table 1. +
+
info
+
Error code. +
+Scope: local +
+Type: required +
+Intent: out. +
+An integer value; 0 means no error has been detected. +
+
- - -
+

+

+ + +next + +up + +previous + +contents +
+ Next: psb_gedot Dot + Up: Computational routines + Previous: Computational routines +   Contents + diff --git a/docs/html/node28.html b/docs/html/node28.html index c4211b2c..2152c782 100644 --- a/docs/html/node28.html +++ b/docs/html/node28.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geaxpby -- General Dense Matrix Sum - +psb_gedot -- Dot Product + @@ -20,100 +20,132 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_gedot Dot - Up: Computational routines - Previous: Computational routines -   Next: psb_gedots Generalized + Up: Computational routines + Previous: psb_geaxpby General +   Contents

-

-psb_geaxpby -- General Dense Matrix Sum +

+psb_gedot -- Dot Product

-This subroutine is an interface to the computational kernel for -dense matrix sum: +This function computes dot product between two vectors $x$ and +$y$. +
+If $x$ and $y$ are real vectors +it computes dot-product as:

\begin{displaymath}dot \leftarrow x^T y\end{displaymath} +
+
+

+Else if \begin{displaymath}y \leftarrow \alpha\> x+ \beta y \end{displaymath} + ALT="$x$"> and $y$ are complex vectors then it computes dot-product as: +

+
+ + +\begin{displaymath}dot \leftarrow x^H y\end{displaymath}

-

+

-call psb_geaxpby(alpha, x, beta, y, desc_a, info)
+psb_gedot(x, y, desc_a, info)
- -


-
+
-
Table 1: +Table 2: Data types
- + SRC="img28.png" + ALT="$y$"> + - + - + - + - +
$dot$, $x$, $y$, $\alpha$, $\beta$SubroutineFunction
Short Precision Realpsb_geaxpbypsb_gedot
Long Precision Realpsb_geaxpbypsb_gedot
Short Precision Complexpsb_geaxpbypsb_gedot
Long Precision Complexpsb_geaxpbypsb_gedot
@@ -130,25 +162,11 @@ Data types
On Entry
-
alpha
-
the scalar $\alpha$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in Table 1. -
x
the local portion of global dense matrix $x$.
Scope: local @@ -157,50 +175,37 @@ Type: required
Intent: in.
-Specified as: a rank one or two array -containing numbers of type -specified in Table 1. The rank of 2. The rank of $x$ must be the same of $y$.
-
beta
-
the scalar $\beta$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in Table 1. -
y
-
the local portion of the global dense matrix +
the local portion of global dense matrix $y$.
Scope: local
Type: required
-Intent: inout. +Intent: in.
-Specified as: a rank one or two array containing numbers of the type -indicated in Table 1. The rank of 2. The rank of $y$ must be the same of $x$.
desc_a
@@ -216,27 +221,21 @@ Specified as: a structured data of type descdatapsb_desc_type.

- - -

-

On Return
-
y
-
the local portion of result submatrix Function value +
is the dot product of subvectors $x$ and $y$.
-Scope: local -
-Type: required -
-Intent: inout. +Scope: global
-Specified as: a rank one or two array containing numbers of the type -indicated in Table 1. +Specified as: a number of the data type indicated in Table 2.
info
Error code. @@ -254,26 +253,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_gedot Dot - Up: Computational routines - Previous: Computational routines -   Next: psb_gedots Generalized + Up: Computational routines + Previous: psb_geaxpby General +   Contents diff --git a/docs/html/node29.html b/docs/html/node29.html index 668bf2ff..970d2717 100644 --- a/docs/html/node29.html +++ b/docs/html/node29.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_gedot -- Dot Product - +psb_gedots -- Generalized Dot Product + @@ -20,132 +20,117 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_gedots Generalized - Up: Computational routines - Previous: psb_geaxpby General -   Next: psb_geamax Infinity-Norm + Up: Computational routines + Previous: psb_gedot Dot +   Contents

-

-psb_gedot -- Dot Product +

+psb_gedots -- Generalized Dot Product

-This function computes dot product between two vectors $x$ and -$y$. -
-If $x$ and $y$ are real vectors -it computes dot-product as: + SRC="img28.png" + ALT="$y$">:

\begin{displaymath}dot \leftarrow x^T y\end{displaymath} + WIDTH="150" HEIGHT="28" BORDER="0" + SRC="img34.png" + ALT="\begin{displaymath}res(i) \leftarrow x(:,i)^T y(:,i)\end{displaymath}">

-Else if $x$ is +used. If $x$ and $y$ are complex vectors then it computes dot-product as: -

-
- - -\begin{displaymath}dot \leftarrow x^H y\end{displaymath} -
-
-

+ SRC="img28.png" + ALT="$y$"> are of rank one, then $res$ is a scalar, else it +is a rank one array. 

-psb_gedot(x, y, desc_a, info)
+call psb_gedots(res, x, y, desc_a, info)

-
+
-
Table 2: +Table 3: Data types
- + - + - + - + - +
$dot$, $res$, $x$, $y$FunctionSubroutine
Short Precision Realpsb_gedotpsb_gedots
Long Precision Realpsb_gedotpsb_gedots
Short Precision Complexpsb_gedotpsb_gedots
Long Precision Complexpsb_gedotpsb_gedots
@@ -166,8 +151,8 @@ Data types
the local portion of global dense matrix $x$. + SRC="img27.png" + ALT="$x$">.
Scope: local
@@ -177,19 +162,19 @@ Intent: in.
Specified as: an array of rank one or two containing numbers of type specified in -Table 2. The rank of 3. The rank of $x$ must be the same of $y$.
y
the local portion of global dense matrix $y$.
Scope: local @@ -200,12 +185,12 @@ Intent: in.
Specified as: an array of rank one or two containing numbers of type specified in -Table 2. The rank of 3. The rank of $y$ must be the same of $x$.
desc_a
@@ -218,24 +203,25 @@ Type: required Intent: in.
Specified as: a structured data of type descdatapsb_desc_type. - -

On Return
-
Function value
+
res
is the dot product of subvectors $x$ and $y$.
Scope: global
-Specified as: a number of the data type indicated in Table 2. +Intent: out. +
+Specified as: a number or a rank-one array of the data type indicated +in Table 2.
info
Error code. @@ -253,26 +239,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_gedots Generalized - Up: Computational routines - Previous: psb_geaxpby General -   Next: psb_geamax Infinity-Norm + Up: Computational routines + Previous: psb_gedot Dot +   Contents diff --git a/docs/html/node3.html b/docs/html/node3.html index 5a58dc55..0e7a9c7a 100644 --- a/docs/html/node3.html +++ b/docs/html/node3.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Basic Nomenclature - Up: Up: userhtml - Previous: Previous: Introduction -   Contents

@@ -71,22 +71,17 @@ influenced by the structure of the ScaLAPACK parallel library. The layered structure of the PSBLAS library is shown in figure 1; lower layers of the library indicate an encapsulation relationship with upper layers. The ongoing -discussion focuses on the Fortran 95 layer immediately below the +discussion focuses on the Fortran 2003 layer immediately below the application layer. The serial parts of the computation on each process are executed through -calls to the serial sparse BLAS subroutines. In a similar way, the -inter-process message exchanges are implemented through the Basic +calls to the serial sparse BLAS subroutines. +In a similar way, the inter-process message exchanges are encapsulated +in an applicaiton layer that has been strongly inspired by the Basic Linear Algebra Communication Subroutines (BLACS) library [7] -that guarantees a portable and efficient communication layer. The -Message Passing Interface code is encapsulated within the BLACS -layer. However, in some cases, MPI routines are directly used either -to improve efficiency or to implement communication patterns for which -the BLACS package doesn't provide any method. - -

-In any case we provide wrappers around the BLACS routines so that the -user does not need to delve into their details (see Sec. 7). + HREF="node107.html#BLACS">7]. +Usually there is no need to deal directly with MPI; however, in some +cases, MPI routines are used directly to improve efficiency. For +further details on our communication layer see Sec. 7.

@@ -135,13 +130,14 @@ is equivalent to a partition of the discretization mesh into sub-domainsCYCLIC(N) and BLOCK, +This choice is consistent with simple data distributions +such as CYCLIC(N) and BLOCK, as well as completely arbitrary assignments of -equation indices to processes. In particular it is consistent with the +equation indices to processes. +In particular it is consistent with the usage of graph partitioning tools commonly available in the literature, e.g. METIS [13]. + HREF="node107.html#METIS">13]. Dense vectors conform to sparse matrices, that is, the entries of a vector follow the same distribution of the matrix rows. @@ -161,38 +157,38 @@ bottleneck would make this option unattractive in most cases. Subsections

- next - up - previous - contents
- Next: Next: Basic Nomenclature - Up: Up: userhtml - Previous: Previous: Introduction -   Contents diff --git a/docs/html/node30.html b/docs/html/node30.html index 979cd3bd..f69ad8e2 100644 --- a/docs/html/node30.html +++ b/docs/html/node30.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_gedots -- Generalized Dot Product - +psb_geamax -- Infinity-Norm of Vector + @@ -20,117 +20,127 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_geamax Infinity-Norm - Up: Computational routines - Previous: psb_gedot Dot -   Next: psb_geamaxs Generalized + Up: Computational routines + Previous: psb_gedots Generalized +   Contents

-

-psb_gedots -- Generalized Dot Product +

+psb_geamax -- Infinity-Norm of Vector

-This subroutine computes a series of dot products among the columns of -two dense matrices $x$. +
+If $x$ and $y$: + SRC="img27.png" + ALT="$x$"> is a real vector +it computes infinity norm as:

\begin{displaymath}res(i) \leftarrow x(:,i)^T y(:,i)\end{displaymath} + WIDTH="118" HEIGHT="36" BORDER="0" + SRC="img36.png" + ALT="\begin{displaymath}amax \leftarrow \max_i \vert x_i\vert\end{displaymath}">

-If the matrices are complex, then the -usual convention applies, i.e. the conjugate transpose of $x$ is -used. If $x$ and $y$ are of rank one, then $res$ is a scalar, else it -is a rank one array. + SRC="img27.png" + ALT="$x$"> is a complex vector then it computes infinity-norm as: +

+
+ + +\begin{displaymath}amax \leftarrow \max_i {(\vert re(x_i)\vert + \vert im(x_i)\vert)}\end{displaymath} +
+
+

-call psb_gedots(res, x, y, desc_a, info)
+psb_geamax(x, desc_a, info)
+ +


-
+
-
Table 3: +Table 4: Data types
+ - + SRC="img27.png" + ALT="$x$"> + - + + - + + - - + + + - - + + +
$res$, $amax$$x$, $y$SubroutineFunction
Short Precision Realpsb_gedotsShort Precision Realpsb_geamax
Long Precision Realpsb_gedotsLong Precision Realpsb_geamax
Short Precision Complexpsb_gedots
Short Precision RealShort Precision Complexpsb_geamax
Long Precision Complexpsb_gedots
Long Precision RealLong Precision Complexpsb_geamax
@@ -151,8 +161,9 @@ Data types
the local portion of global dense matrix $x$. +
Scope: local
@@ -160,38 +171,9 @@ Type: required
Intent: in.
-Specified as: an array of rank one or two -containing numbers of type specified in -Table 3. The rank of $x$ must be the same of $y$. -
-
y
-
the local portion of global dense matrix -$y$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an array of rank one or two +Specified as: a rank one or two array containing numbers of type specified in -Table 3. The rank of $y$ must be the same of $x$. +Table 4.
desc_a
contains data structures for communications. @@ -203,25 +185,21 @@ Type: required Intent: in.
Specified as: a structured data of type descdatapsb_desc_type. + +

On Return
-
res
-
is the dot product of subvectors Function value +
is the infinity norm of subvector $x$ and $y$. + SRC="img27.png" + ALT="$x$">.
Scope: global
-Intent: out. -
-Specified as: a number or a rank-one array of the data type indicated -in Table 2. +Specified as: a long precision real number.
info
Error code. @@ -239,26 +217,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_geamax Infinity-Norm - Up: Computational routines - Previous: psb_gedot Dot -   Next: psb_geamaxs Generalized + Up: Computational routines + Previous: psb_gedots Generalized +   Contents diff --git a/docs/html/node31.html b/docs/html/node31.html index 6ac743e5..900ffaec 100644 --- a/docs/html/node31.html +++ b/docs/html/node31.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geamax -- Infinity-Norm of Vector - +psb_geamaxs -- Generalized Infinity Norm + @@ -20,127 +20,102 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_geamaxs Generalized - Up: Computational routines - Previous: psb_gedots Generalized -   Next: psb_geasum 1-Norm + Up: Computational routines + Previous: psb_geamax Infinity-Norm +   Contents

-

-psb_geamax -- Infinity-Norm of Vector +

+psb_geamaxs -- Generalized Infinity Norm

-This function computes - the infinity-norm of a vector $x$. -
-If $x$ is a real vector -it computes infinity norm as: -

-
- - -\begin{displaymath}amax \leftarrow \max_i \vert x_i\vert\end{displaymath} -
-
-

-else if $x$ is a complex vector then it computes infinity-norm as: + SRC="img27.png" + ALT="$x$">:

\begin{displaymath}amax \leftarrow \max_i {(\vert re(x_i)\vert + \vert im(x_i)\vert)}\end{displaymath} + WIDTH="148" HEIGHT="36" BORDER="0" + SRC="img39.png" + ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}"> 

-psb_geamax(x, desc_a, info)
+call psb_geamaxs(res, x, desc_a, info)


-
+
-
Table 4: +Table 5: Data types
+ WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img35.png" + ALT="$res$"> - + - + - + - + - +
$amax$ $x$FunctionSubroutine
Short Precision Real Short Precision Realpsb_geamaxpsb_geamaxs
Long Precision Real Long Precision Realpsb_geamaxpsb_geamaxs
Short Precision Real Short Precision Complexpsb_geamaxpsb_geamaxs
Long Precision Real Long Precision Complexpsb_geamaxpsb_geamaxs
@@ -161,9 +136,8 @@ Data types
the local portion of global dense matrix $x$. -
Scope: local
@@ -171,9 +145,9 @@ Type: required
Intent: in.
-Specified as: a rank one or two array +Specified as: a rank one or two array containing numbers of type specified in -Table 4. +Table 5.
desc_a
contains data structures for communications. @@ -185,21 +159,21 @@ Type: required Intent: in.
Specified as: a structured data of type descdatapsb_desc_type. - -

On Return
-
Function value
-
is the infinity norm of subvector res +
is the infinity norm of the columns of $x$.
Scope: global
-Specified as: a long precision real number. +Intent: out. +
+Specified as: a number or a rank-one array of long precision real numbers.
info
Error code. @@ -217,26 +191,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_geamaxs Generalized - Up: Computational routines - Previous: psb_gedots Generalized -   Next: psb_geasum 1-Norm + Up: Computational routines + Previous: psb_geamax Infinity-Norm +   Contents diff --git a/docs/html/node32.html b/docs/html/node32.html index 93d76a3b..dfa141d0 100644 --- a/docs/html/node32.html +++ b/docs/html/node32.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geamaxs -- Generalized Infinity Norm - +psb_geasum -- 1-Norm of Vector + @@ -20,102 +20,126 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_geasum 1-Norm - Up: Computational routines - Previous: psb_geamax Infinity-Norm -   Next: psb_geasums Generalized + Up: Computational routines + Previous: psb_geamaxs Generalized +   Contents

-

-psb_geamaxs -- Generalized Infinity Norm +

+psb_geasum -- 1-Norm of Vector

-This subroutine computes a series of infinity norms on the columns of -a dense matrix $x$. +
+If $x$: + SRC="img27.png" + ALT="$x$"> is a real vector +it computes 1-norm as:

\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath} + ALT="\begin{displaymath}asum \leftarrow \Vert x_i\Vert\end{displaymath}"> +
+
+

+else if $x$ is a vector then it computes 1-norm as: +

+
+ + +\begin{displaymath}asum \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath} 

-call psb_geamaxs(res, x, desc_a, info)
+psb_geasum(x, desc_a, info)


-
+
-
Table 5: +Table 6: Data types
+ WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img42.png" + ALT="$asum$"> - + - + - + - + - +
$res$ $x$SubroutineFunction
Short Precision Real Short Precision Realpsb_geamaxspsb_geasum
Long Precision Real Long Precision Realpsb_geamaxspsb_geasum
Short Precision Real Short Precision Complexpsb_geamaxspsb_geasum
Long Precision Real Long Precision Complexpsb_geamaxspsb_geasum
@@ -136,8 +160,9 @@ Data types
the local portion of global dense matrix $x$. +
Scope: local
@@ -147,7 +172,7 @@ Intent: in.
Specified as: a rank one or two array containing numbers of type specified in -Table 5. +Table 6.
desc_a
contains data structures for communications. @@ -159,21 +184,21 @@ Type: required Intent: in.
Specified as: a structured data of type descdatapsb_desc_type. + +

On Return
-
res
-
is the infinity norm of the columns of Function value +
is the 1-norm of vector $x$.
Scope: global
-Intent: out. -
-Specified as: a number or a rank-one array of long precision real numbers. +Specified as: a long precision real number.
info
Error code. @@ -191,26 +216,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_geasum 1-Norm - Up: Computational routines - Previous: psb_geamax Infinity-Norm -   Next: psb_geasums Generalized + Up: Computational routines + Previous: psb_geamaxs Generalized +   Contents diff --git a/docs/html/node33.html b/docs/html/node33.html index acc2859a..dab9733c 100644 --- a/docs/html/node33.html +++ b/docs/html/node33.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geasum -- 1-Norm of Vector - +psb_geasums -- Generalized 1-Norm of Vector + @@ -20,126 +20,146 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_geasums Generalized - Up: Computational routines - Previous: psb_geamaxs Generalized -   Next: psb_genrm2 2-Norm + Up: Computational routines + Previous: psb_geasum 1-Norm +   Contents

-

-psb_geasum -- 1-Norm of Vector +

+psb_geasums -- Generalized 1-Norm of Vector

+This subroutine computes a series of 1-norms on the columns of +a dense matrix $x$: +

+
+ + +\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath} +
+
+

This function computes the 1-norm of a vector $x$.
If $x$ is a real vector + SRC="img27.png" + ALT="$x$"> is a real vector it computes 1-norm as:

\begin{displaymath}asum \leftarrow \Vert x_i\Vert\end{displaymath} + WIDTH="94" HEIGHT="28" BORDER="0" + SRC="img43.png" + ALT="\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath}">

else if $x$ is a vector then it computes 1-norm as: + SRC="img27.png" + ALT="$x$"> is a complex vector then it computes 1-norm as:

\begin{displaymath}asum \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath} + WIDTH="207" HEIGHT="28" BORDER="0" + SRC="img44.png" + ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}"> 

-psb_geasum(x, desc_a, info)
+call psb_geasums(res, x, desc_a, info)


-
+
-
Table 6: +Table 7: Data types
+ WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img35.png" + ALT="$res$"> - + - + - + - + - +
$asum$ $x$FunctionSubroutine
Short Precision Real Short Precision Realpsb_geasumpsb_geasums
Long Precision Real Long Precision Realpsb_geasumpsb_geasums
Short Precision Real Short Precision Complexpsb_geasumpsb_geasums
Long Precision Real Long Precision Complexpsb_geasumpsb_geasums
@@ -160,7 +180,7 @@ Data types
the local portion of global dense matrix $x$.
@@ -172,7 +192,7 @@ Intent: in.
Specified as: a rank one or two array containing numbers of type specified in -Table 6. +Table 7.
desc_a
contains data structures for communications. @@ -190,14 +210,17 @@ Specified as: a structured data of type descdatapsb_desc_type.
On Return
-
Function value
-
is the 1-norm of vector res +
contains the 1-norm of (the columns of) $x$.
Scope: global
+Intent: out. +
+Short as: a long precision real number. Specified as: a long precision real number.
info
@@ -216,26 +239,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_geasums Generalized - Up: Computational routines - Previous: psb_geamaxs Generalized -   Next: psb_genrm2 2-Norm + Up: Computational routines + Previous: psb_geasum 1-Norm +   Contents diff --git a/docs/html/node34.html b/docs/html/node34.html index 3ac45e78..29ca2461 100644 --- a/docs/html/node34.html +++ b/docs/html/node34.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geasums -- Generalized 1-Norm of Vector - +psb_genrm2 -- 2-Norm of Vector + @@ -20,146 +20,121 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_genrm2 2-Norm - Up: Computational routines - Previous: psb_geasum 1-Norm -   Next: psb_genrm2s Generalized + Up: Computational routines + Previous: psb_geasums Generalized +   Contents

-

-psb_geasums -- Generalized 1-Norm of Vector +

+psb_genrm2 -- 2-Norm of Vector

-This subroutine computes a series of 1-norms on the columns of -a dense matrix $x$: -

-
- - -\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath} -
-
-

-This function computes the 1-norm of a vector $x$.
If $x$ is a real vector -it computes 1-norm as: + SRC="img27.png" + ALT="$x$"> is a double precision real vector +it computes 2-norm as:

\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath} + WIDTH="106" HEIGHT="24" BORDER="0" + SRC="img45.png" + ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\end{displaymath}">

else if $x$ is a complex vector then it computes 1-norm as: + SRC="img27.png" + ALT="$x$"> is double precision complex vector then it computes 2-norm as:

\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath} + WIDTH="108" HEIGHT="24" BORDER="0" + SRC="img46.png" + ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\end{displaymath}">

-

-

-call psb_geasums(res, x, desc_a, info)
-
-


-
+
-
Table 7: +Table 8: Data types
+ WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img47.png" + ALT="$nrm2$"> - + - + - + - + - +
$res$ $x$SubroutineFunction
Short Precision Real Short Precision Realpsb_geasumspsb_genrm2
Long Precision Real Long Precision Realpsb_geasumspsb_genrm2
Short Precision Real Short Precision Complexpsb_geasumspsb_genrm2
Long Precision Real Long Precision Complexpsb_geasumspsb_genrm2
@@ -168,6 +143,11 @@ Data types


+

+

+psb_genrm2(x, desc_a, info)
+
+

Type:
@@ -180,9 +160,8 @@ Data types
the local portion of global dense matrix $x$. - + SRC="img27.png" + ALT="$x$">.
Scope: local
@@ -190,9 +169,9 @@ Type: required
Intent: in.
-Specified as: a rank one or two array +Specified as: a rank one or two array containing numbers of type specified in -Table 7. +Table 8.
desc_a
contains data structures for communications. @@ -210,18 +189,17 @@ Specified as: a structured data of type descdatapsb_desc_type.
On Return
-
res
-
contains the 1-norm of (the columns of) Function Value +
is the 2-norm of subvector $x$.
Scope: global
-Intent: out. +Type: required
-Short as: a long precision real number. -Specified as: a long precision real number. +Specified as: a long precision real number.
info
Error code. @@ -239,26 +217,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_genrm2 2-Norm - Up: Computational routines - Previous: psb_geasum 1-Norm -   Next: psb_genrm2s Generalized + Up: Computational routines + Previous: psb_geasums Generalized +   Contents diff --git a/docs/html/node35.html b/docs/html/node35.html index a13f9c78..07de357b 100644 --- a/docs/html/node35.html +++ b/docs/html/node35.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_genrm2 -- 2-Norm of Vector - +psb_genrm2s -- Generalized 2-Norm of Vector + @@ -20,121 +20,102 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_genrm2s Generalized - Up: Computational routines - Previous: psb_geasums Generalized -   Next: psb_spnrmi Infinity + Up: Computational routines + Previous: psb_genrm2 2-Norm +   Contents

-

-psb_genrm2 -- 2-Norm of Vector +

+psb_genrm2s -- Generalized 2-Norm of Vector

-This function computes the 2-norm of a vector $x$. -
-If $x$ is a double precision real vector -it computes 2-norm as: + SRC="img27.png" + ALT="$x$">:

\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\end{displaymath} + WIDTH="126" HEIGHT="28" BORDER="0" + SRC="img48.png" + ALT="\begin{displaymath}res(i) \leftarrow \Vert x(:,i)\Vert _2 \end{displaymath}">

-else if $x$ is double precision complex vector then it computes 2-norm as: -

-
- -\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\end{displaymath} -
-
-

+

+

+call psb_genrm2s(res, x, desc_a, info)
+


-
+
-
Table 8: +Table 9: Data types
+ WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img35.png" + ALT="$res$"> - + - + - + - + - +
$nrm2$ $x$FunctionSubroutine
Short Precision Real Short Precision Realpsb_genrm2psb_genrm2s
Long Precision Real Long Precision Realpsb_genrm2psb_genrm2s
Short Precision Real Short Precision Complexpsb_genrm2psb_genrm2s
Long Precision Real Long Precision Complexpsb_genrm2psb_genrm2s
@@ -143,11 +124,6 @@ Data types


-

-

-psb_genrm2(x, desc_a, info)
-
-

Type:
@@ -160,8 +136,9 @@ psb_genrm2(x, desc_a, info)
the local portion of global dense matrix $x$. + SRC="img27.png" + ALT="$x$">. +
Scope: local
@@ -169,9 +146,9 @@ Type: required
Intent: in.
-Specified as: a rank one or two array +Specified as: a rank one or two array containing numbers of type specified in -Table 8. +Table 9.
desc_a
contains data structures for communications. @@ -189,17 +166,17 @@ Specified as: a structured data of type descdatapsb_desc_type.
On Return
-
Function Value
-
is the 2-norm of subvector res +
contains the 1-norm of (the columns of) $x$.
Scope: global
-Type: required +Intent: out.
-Specified as: a long precision real number. +Specified as: a long precision real number.
info
Error code. @@ -217,26 +194,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_genrm2s Generalized - Up: Computational routines - Previous: psb_geasums Generalized -   Next: psb_spnrmi Infinity + Up: Computational routines + Previous: psb_genrm2 2-Norm +   Contents diff --git a/docs/html/node36.html b/docs/html/node36.html index 8f060a67..540a458c 100644 --- a/docs/html/node36.html +++ b/docs/html/node36.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_genrm2s -- Generalized 2-Norm of Vector - +psb_spnrmi -- Infinity Norm of Sparse Matrix + @@ -20,102 +20,102 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_spnrmi Infinity - Up: Computational routines - Previous: psb_genrm2 2-Norm -   Next: psb_spmm Sparse + Up: Computational routines + Previous: psb_genrm2s Generalized +   Contents

-

-psb_genrm2s -- Generalized 2-Norm of Vector +

+psb_spnrmi -- Infinity Norm of Sparse Matrix

-This subroutine computes a series of 2-norms on the columns of -a dense matrix $x$: +This function computes the infinity-norm of a matrix $A$: +
+


\begin{displaymath}res(i) \leftarrow \Vert x(:,i)\Vert _2 \end{displaymath} + ALT="\begin{displaymath}nrmi \leftarrow \Vert A\Vert _\infty \end{displaymath}">

- -

-

-call psb_genrm2s(res, x, desc_a, info)
-
+where: +
+
$A$
+
represents the global matrix $A$ +
+


-
+
- + +
Table 9: +Table 10: Data types
- - + WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img1.png" + ALT="$A$"> + - - + - - + - - - + + - - - + +
$res$$x$SubroutineFunction
Short Precision RealShort Precision Realpsb_genrm2spsb_spnrmi
Long Precision RealLong Precision Realpsb_genrm2spsb_spnrmi
Short Precision RealShort Precision Complexpsb_genrm2s
Short Precision Complexpsb_spnrmi
Long Precision RealLong Precision Complexpsb_genrm2s
Long Precision Complexpsb_spnrmi
@@ -124,6 +124,11 @@ Data types


+

+

+psb_spnrmi(A, desc_a, info)
+
+

Type:
@@ -132,23 +137,20 @@ Data types
On Entry
-
x
-
the local portion of global dense matrix +
a
+
the local portion of the global sparse matrix $x$. - + WIDTH="16" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img1.png" + ALT="$A$">.
Scope: local
-Type: required +Type: required
Intent: in.
-Specified as: a rank one or two array -containing numbers of type specified in -Table 9. +Specified as: a structured data of type spdatapsb_spmat_type.
desc_a
contains data structures for communications. @@ -160,23 +162,19 @@ Type: required Intent: in.
Specified as: a structured data of type descdatapsb_desc_type. - -

On Return
-
res
-
contains the 1-norm of (the columns of) $x$. +
Function value
+
is the infinity-norm of sparse submatrix $A$.
Scope: global
-Intent: out. -
-Specified as: a long precision real number. +Specified as: a long precision real number.
info
Error code. @@ -194,26 +192,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_spnrmi Infinity - Up: Computational routines - Previous: psb_genrm2 2-Norm -   Next: psb_spmm Sparse + Up: Computational routines + Previous: psb_genrm2s Generalized +   Contents diff --git a/docs/html/node37.html b/docs/html/node37.html index 170572dd..2c436ced 100644 --- a/docs/html/node37.html +++ b/docs/html/node37.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_spnrmi -- Infinity Norm of Sparse Matrix - +psb_spmm -- Sparse Matrix by Dense Matrix Product + @@ -20,81 +20,146 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_spmm Sparse - Up: Computational routines - Previous: psb_genrm2s Generalized -   Next: psb_spsm Triangular + Up: Computational routines + Previous: psb_spnrmi Infinity +   Contents

-

-psb_spnrmi -- Infinity Norm of Sparse Matrix +

+psb_spmm -- Sparse Matrix by Dense Matrix Product

-This function computes the infinity-norm of a matrix $A$: -
+This subroutine computes the Sparse Matrix by Dense Matrix Product: +

-

-
+
+
+ - - +
\begin{displaymath}nrmi \leftarrow \Vert A\Vert _\infty \end{displaymath} - -
-

+ ALT="\begin{displaymath} +y \leftarrow \alpha P_r A P_c x + \beta y +\end{displaymath}">		 +(1)
+

+
+
+ + + + + +
\begin{displaymath} +y \leftarrow \alpha P_r A^T P_c x + \beta y +\end{displaymath} +(2)
+

+
+
+ + + + + +
\begin{displaymath} +y \leftarrow \alpha P_r A^H P_c x + \beta y +\end{displaymath} +(3)
+

+ +

where:

+
$x$
+
is the global dense submatrix $x_{:, :}$ +
+
$y$
+
is the global dense submatrix $y_{:, :}$ +
$A$
-
represents the global matrix is the global sparse submatrix $A$
+
$P_r, P_c$
+
are the permutation matrices. +


-
+
- - + ALT="$A$">, $x$, $y$, $\alpha$, $\beta$ + - + - + - + - +
Table 10: +Table 11: Data types
@@ -102,20 +167,32 @@ Data types
$A$FunctionSubroutine
Short Precision Realpsb_spnrmipsb_spmm
Long Precision Realpsb_spnrmipsb_spmm
Short Precision Complexpsb_spnrmipsb_spmm
Long Precision Complexpsb_spnrmipsb_spmm
@@ -126,8 +203,10 @@ Data types 

-psb_spnrmi(A, desc_a, info)
-
+call psb_spmm(alpha, a, x, beta, y, desc_a, info) +call psb_spmm(alpha, a, x, beta, y,desc_a, info, & + & trans, work) +

@@ -137,8 +216,23 @@ psb_spnrmi(A, desc_a, info)
On Entry
+
alpha
+
the scalar $\alpha$. +
+Scope: global +
+Type: required +
+Intent: in. +
+Specified as: a number of the data type indicated in +Table 11. +
a
-
the local portion of the global sparse matrix +
the local portion of the sparse matrix in.
Specified as: a structured data of type spdatapsb_spmat_type.
+
x
+
the local portion of global dense matrix +$x$. + +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a rank one or two array +containing numbers of type specified in +Table 11. The rank of $x$ must be the same of $y$. +
+
beta
+
the scalar $\beta$. +
+Scope: global +
+Type: required +
+Intent: in. +
+Specified as: a number of the data type indicated in Table 11. +
+
y
+
the local portion of global dense matrix +$y$. + +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a rank one or two array +containing numbers of type specified in +Table 11. The rank of $y$ must be the same of $x$. +
desc_a
contains data structures for communications.
@@ -163,18 +319,74 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
+
trans
+
indicate what kind of operation to perform. +
+
trans = N
+
the operation is specified by equation 1 +
+
trans = T
+
the operation is specified by equation +2 +
+
trans = C
+
the operation is specified by equation +3 +
+
+Scope: global +
+Type: optional +
+Intent: in. +
+Default: $trans = N$ +
+Specified as: a character variable. + +

+

+
work
+
work array. +
+Scope: local +
+Type: optional +
+Intent: inout. +
+Specified as: a rank one array of the same type of $x$ and $y$ with +the TARGET attribute. + +

+

On Return
-
Function value
-
is the infinity-norm of sparse submatrix $A$. +
y
+
the local portion of result submatrix $y$.
-Scope: global +Scope: local +
+Type: required +
+Intent: inout.
-Specified as: a long precision real number. +Specified as: an array of rank one or two +containing numbers of type specified in +Table 11.
info
Error code. @@ -192,26 +404,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_spmm Sparse - Up: Computational routines - Previous: psb_genrm2s Generalized -   Next: psb_spsm Triangular + Up: Computational routines + Previous: psb_spnrmi Infinity +   Contents diff --git a/docs/html/node38.html b/docs/html/node38.html index e5499645..5acca937 100644 --- a/docs/html/node38.html +++ b/docs/html/node38.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_spmm -- Sparse Matrix by Dense Matrix Product - +psb_spsm -- Triangular System Solve + @@ -18,181 +18,164 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: psb_spsm Triangular - Up: Computational routines - Previous: psb_spnrmi Infinity -   Next: Communication routines + Up: Computational routines + Previous: psb_spmm Sparse +   Contents

-

-psb_spmm -- Sparse Matrix by Dense Matrix Product +

+psb_spsm -- Triangular System Solve

-This subroutine computes the Sparse Matrix by Dense Matrix Product: +This subroutine computes the Triangular System Solve:

-
-

- - - - - -
\begin{displaymath} -y \leftarrow \alpha P_r A P_c x + \beta y -\end{displaymath} -(1)
-

-
-
- - - - - -
\begin{displaymath} -y \leftarrow \alpha P_r A^T P_c x + \beta y -\end{displaymath} -(2)
-

-
-
- +

+
- - - -
\begin{displaymath} -y \leftarrow \alpha P_r A^H P_c x + \beta y -\end{displaymath} -(3)
-

+\begin{eqnarray*} +y &\leftarrow& \alpha P_r T^{-1} P_c x + \beta y\\ +y &\leftar... +...\beta y\\ +y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\ +\end{eqnarray*}
+

where:

$x$
is the global dense submatrix $x_{:, :}$
$y$
is the global dense submatrix $y_{:, :}$
$A$
-
is the global sparse submatrix $T$ +
is the global sparse block triangular submatrix $A$ + SRC="img58.png" + ALT="$T$"> +
+
$D$
+
is the scaling diagonal matrix.
$P_r, P_c$
are the permutation matrices.
+

+

+call psb_spsm(alpha, t, x, beta, y, desc_a, info)
+call psb_spsm(alpha, t, x, beta, y, desc_a, info,&
+             & trans, unit, choice, diag, work)
+
+


-
+
-
Table 11: +Table 12: Data types
- + - + - + - +
$A$, $T$, $x$, $y$, $D$, $\alpha$, $\beta$ Subroutine
Short Precision Realpsb_spmmpsb_spsm
Long Precision Realpsb_spmmpsb_spsm
Short Precision Complexpsb_spmmpsb_spsm
Long Precision Complexpsb_spmmpsb_spsm
@@ -201,13 +184,6 @@ Data types


-

-

-call psb_spmm(alpha, a, x, beta, y, desc_a, info)
-call psb_spmm(alpha, a, x, beta, y,desc_a, info, &
-             & trans, work)
-
-

Type:
@@ -219,7 +195,7 @@ call psb_spmm(alpha, a, x, beta, y,desc_a, info, &
alpha
the scalar $\alpha$.
Scope: global @@ -229,14 +205,14 @@ Type: required Intent: in.
Specified as: a number of the data type indicated in -Table 11. +Table 12.
-
a
-
the local portion of the sparse matrix +
t
+
the global portion of the sparse matrix $A$. + SRC="img58.png" + ALT="$T$">.
Scope: local
@@ -244,13 +220,14 @@ Type: required
Intent: in.
-Specified as: a structured data of type spdatapsb_spmat_type. +Specified as: a structured data type specified in +§ 3.
x
the local portion of global dense matrix $x$.
@@ -260,20 +237,20 @@ Type: required
Intent: in.
-Specified as: a rank one or two array +Specified as: a rank one or two array containing numbers of type specified in -Table 11. The rank of 12. The rank of $x$ must be the same of $y$.
beta
the scalar $\beta$.
Scope: global @@ -282,13 +259,13 @@ Type: required
Intent: in.
-Specified as: a number of the data type indicated in Table 11. +Specified as: a number of the data type indicated in Table 12.
y
the local portion of global dense matrix $y$.
@@ -300,12 +277,12 @@ Intent: inout.
Specified as: a rank one or two array containing numbers of type specified in -Table 11. The rank of 12. The rank of $y$ must be the same of $x$.
desc_a
@@ -320,18 +297,16 @@ Intent: in. Specified as: a structured data of type descdatapsb_desc_type.
trans
-
indicate what kind of operation to perform. +
specify with unitd the operation to perform.
-
trans = N
-
the operation is specified by equation 1 +
trans = 'N'
+
the operation is with no transposed matrix
-
trans = T
-
the operation is specified by equation -2 +
trans = 'T'
+
the operation is with transposed matrix.
-
trans = C
-
the operation is specified by equation -3 +
trans = 'C'
+
the operation is with conjugate transposed matrix.
Scope: global @@ -342,15 +317,86 @@ Intent: in.
Default: $trans = N$
Specified as: a character variable. - -

+

+
unitd
+
specify with trans the operation to perform. +
+
unitd = 'U'
+
the operation is with no scaling +
+
unitd = 'L'
+
the operation is with left scaling +
+
unitd = 'R'
+
the operation is with right scaling. +
+
+Scope: global +
+Type: optional +
+Intent: in. +
+Default: $unitd = U$ +
+Specified as: a character variable. +
+
choice
+
specifies the update of overlap elements to be performed + on exit: +
+
+
psb_none_ +
+
+
psb_sum_ +
+
+
psb_avg_ +
+
+
psb_square_root_ +
+
+Scope: global +
+Type: optional +
+Intent: in. +
+Default: psb_avg_ +
+Specified as: an integer variable. +
+
diag
+
the diagonal scaling matrix. +
+Scope: local +
+Type: optional +
+Intent: in. +
+Default: +$diag(1) = 1 (no scaling)$ +
+Specified as: a rank one array containing numbers of the type +indicated in Table 12.
work
-
work array. +
a work array.
Scope: local
@@ -360,12 +406,9 @@ Intent: inout.
Specified as: a rank one array of the same type of $x$ and $y$ with -the TARGET attribute. + SRC="img27.png" + ALT="$x$"> with the +TARGET attribute.

@@ -373,10 +416,12 @@ the TARGET attribute.
y
-
the local portion of result submatrix the local portion of global dense matrix +$y$. + SRC="img28.png" + ALT="$y$">. +
Scope: local
@@ -386,7 +431,7 @@ Intent: inout.
Specified as: an array of rank one or two containing numbers of type specified in -Table 11. +Table 12.
info
Error code. @@ -404,26 +449,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_spsm Triangular - Up: Computational routines - Previous: psb_spnrmi Infinity -   Next: Communication routines + Up: Computational routines + Previous: psb_spmm Sparse +   Contents diff --git a/docs/html/node39.html b/docs/html/node39.html index a2259d8d..4f878be8 100644 --- a/docs/html/node39.html +++ b/docs/html/node39.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_spsm -- Triangular System Solve - +Communication routines + @@ -18,459 +18,63 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Communication routines - Up: Computational routines - Previous: psb_spmm Sparse -   Next: psb_halo Halo + Up: userhtml + Previous: psb_spsm Triangular +   Contents

-

-psb_spsm -- Triangular System Solve -

- -

-This subroutine computes the Triangular System Solve: - -

-

-
- -\begin{eqnarray*} -y &\leftarrow& \alpha P_r T^{-1} P_c x + \beta y\\ -y &\leftar... -...\beta y\\ -y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\ -\end{eqnarray*}
-

- -

-where: -

-
$x$
-
is the global dense submatrix $x_{:, :}$ -
-
$y$
-
is the global dense submatrix $y_{:, :}$ -
-
$T$
-
is the global sparse block triangular submatrix $T$ -
-
$D$
-
is the scaling diagonal matrix. -
-
$P_r, P_c$
-
are the permutation matrices. -
-
- -

-

-call psb_spsm(alpha, t, x, beta, y, desc_a, info)
-call psb_spsm(alpha, t, x, beta, y, desc_a, info,&
-             & trans, unit, choice, diag, work)
-
- -

-

-
- - - -
Table 12: -Data types
-
- - - - - - - - - - - - - - - - -
$T$, $x$, $y$, $D$, $\alpha$, $\beta$Subroutine
Short Precision Realpsb_spsm
Long Precision Realpsb_spsm
Short Precision Complexpsb_spsm
Long Precision Complexpsb_spsm
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
alpha
-
the scalar $\alpha$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in -Table 12. -
-
t
-
the global portion of the sparse matrix -$T$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data type specified in -§ 3. -
-
x
-
the local portion of global dense matrix -$x$. - -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array -containing numbers of type specified in -Table 12. The rank of $x$ must be the same of $y$. -
-
beta
-
the scalar $\beta$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in Table 12. -
-
y
-
the local portion of global dense matrix -$y$. - -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array -containing numbers of type specified in -Table 12. The rank of $y$ must be the same of $x$. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
trans
-
specify with unitd the operation to perform. -
-
trans = 'N'
-
the operation is with no transposed matrix -
-
trans = 'T'
-
the operation is with transposed matrix. -
-
trans = 'C'
-
the operation is with conjugate transposed matrix. -
-
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $trans = N$ -
-Specified as: a character variable. -
-
unitd
-
specify with trans the operation to perform. -
-
unitd = 'U'
-
the operation is with no scaling -
-
unitd = 'L'
-
the operation is with left scaling -
-
unitd = 'R'
-
the operation is with right scaling. -
-
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $unitd = U$ -
-Specified as: a character variable. -
-
choice
-
specifies the update of overlap elements to be performed - on exit: -
-
-
psb_none_ -
-
-
psb_sum_ -
-
-
psb_avg_ -
-
-
psb_square_root_ -
-
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: psb_avg_ -
-Specified as: an integer variable. -
-
diag
-
the diagonal scaling matrix. -
-Scope: local -
-Type: optional -
-Intent: in. -
-Default: -$diag(1) = 1 (no scaling)$ -
-Specified as: a rank one array containing numbers of the type -indicated in Table 12. -
-
work
-
a work array. -
-Scope: local -
-Type: optional -
-Intent: inout. -
-Specified as: a rank one array of the same type of $x$ with the -TARGET attribute. - -

-

-
On Return
-
-
-
y
-
the local portion of global dense matrix -$y$. - -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: an array of rank one or two -containing numbers of type specified in -Table 12. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
+

+Communication routines +

+The routines in this chapter implement various global communication operators +on vectors associated with a discretization mesh. For auxiliary communication +routines not tied to a discretization space see 6.

-

- - -next - -up - -previous - -contents -
- Next: Communication routines - Up: Computational routines - Previous: psb_spmm Sparse -   Contents - +
+ +Subsections + + + +
diff --git a/docs/html/node4.html b/docs/html/node4.html index 24148455..7920add7 100644 --- a/docs/html/node4.html +++ b/docs/html/node4.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Library contents - Up: Up: General overview - Previous: Previous: General overview -   Contents

@@ -126,8 +126,8 @@ Overlap points do not usually exist in the basic data distributions; however they are a feature of Domain Decomposition Schwarz preconditioners which are the subject of related research work [4,3]. + HREF="node107.html#2007c">4,3].

We denote the sets of internal, boundary and halo points for a given @@ -197,26 +197,26 @@ points in the literature.

- next - up - previous - contents
- Next: Next: Library contents - Up: Up: General overview - Previous: Previous: General overview -   Contents diff --git a/docs/html/node40.html b/docs/html/node40.html index fbf7720a..ef06fc8a 100644 --- a/docs/html/node40.html +++ b/docs/html/node40.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Communication routines - +psb_halo -- Halo Data Communication + @@ -18,63 +18,636 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - - + + + - next - + up - previous - contents
- Next: psb_halo Halo - Up: userhtml - Previous: psb_spsm Triangular -   Next: psb_ovrl Overlap + Up: Communication routines + Previous: Communication routines +   Contents

-

-Communication routines -

-The routines in this chapter implement various global communication operators -on vectors associated with a discretization mesh. For auxiliary communication -routines not tied to a discretization space see 6. +

+psb_halo -- Halo Data Communication +

+ +

+These subroutines gathers the values of the halo +elements, and (optionally) scale the result: + +

+

+
+ + +\begin{displaymath}x \leftarrow \alpha x \end{displaymath} +
+
+

+where: +
+
$x$
+
is a global dense submatrix. +
+
+ +

+

+
+ + + +
Table 13: +Data types
+
+ + + + + + + + + + + + + + + + + + + +
$\alpha$, $x$Subroutine
Integerpsb_halo
Short Precision Realpsb_halo
Long Precision Realpsb_halo
Short Precision Complexpsb_halo
Long Precision Complexpsb_halo
+
+
+

+

-

- -Subsections - - - -
+
+call psb_halo(x, desc_a, info)
+call psb_halo(x, desc_a, info, alpha, work, data)
+
+ +

+

+
Type:
+
Synchronous. +
+
On Entry
+
+
+
x
+
global dense matrix $x$. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a rank one or two array with the TARGET attribute +containing numbers of type specified in +Table 13. +
+
desc_a
+
contains data structures for communications. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a structured data of type descdatapsb_desc_type. +
+
alpha
+
the scalar $\alpha$. +
+Scope: global +
+Type: optional +
+Intent: in. +
+Default: $alpha = 1 $ +
+Specified as: a number of the data type indicated in Table 13. +
+
work
+
the work array. +
+Scope: local +
+Type: optional +
+Intent: inout. +
+Specified as: a rank one array of the same type of $x$ with the +POINTER attribute. +
+
data
+
index list selector. +
+Scope: global +
+Type: optional +
+Specified as: an integer. Values:psb_comm_halo_,psb_comm_mov_, +psb_comm_ext_, default: psb_comm_halo_. Chooses the +index list on which to base the data exchange. + +

+

+
On Return
+
+
+
x
+
global dense result matrix $x$. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Returned as: a rank one or two array +containing numbers of type specified in +Table 13. +
+
info
+
the local portion of result submatrix $y$. +
+Scope: local +
+Type: required +
+Intent: out. +
+An integer value that contains an error code. +
+
+ +
+ + + +
Figure 6: +Sample discretization mesh.
+
+\includegraphics[scale=0.45]{figures/try8x8.eps} + + +\rotatebox{-90}{\includegraphics[scale=0.45]{figures/try8x8}} + +
+
+ +

+Usage Example +Consider the discretization mesh depicted in fig. 6, +partitioned among two processes as shown by the dashed line; the data +distribution is such that each process will own 32 entries in the +index space, with a halo made of 8 entries placed at local indices 33 +through 40. If process 0 assigns an initial value of 1 to its entries +in the $x$ vector, and process 1 assigns a value of 2, then after a +call to psb_halo the contents of the local vectors will be the +following: +
+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+Process 0  +Process 1
+ I GLOB(I) X(I)   I GLOB(I) X(I)
+ 1 1 1.0   1 33 2.0
+ 2 2 1.0   2 34 2.0
+ 3 3 1.0   3 35 2.0
+ 4 4 1.0   4 36 2.0
+ 5 5 1.0   5 37 2.0
+ 6 6 1.0   6 38 2.0
+ 7 7 1.0   7 39 2.0
+ 8 8 1.0   8 40 2.0
+ 9 9 1.0   9 41 2.0
+ 10 10 1.0   10 42 2.0
+ 11 11 1.0   11 43 2.0
+ 12 12 1.0   12 44 2.0
+ 13 13 1.0   13 45 2.0
+ 14 14 1.0   14 46 2.0
+ 15 15 1.0   15 47 2.0
+ 16 16 1.0   16 48 2.0
+ 17 17 1.0   17 49 2.0
+ 18 18 1.0   18 50 2.0
+ 19 19 1.0   19 51 2.0
+ 20 20 1.0   20 52 2.0
+21 21 1.0   21 53 2.0
+22 22 1.0   22 54 2.0
+23 23 1.0   23 55 2.0
+24 24 1.0   24 56 2.0
+25 25 1.0   25 57 2.0
+26 26 1.0   26 58 2.0
+27 27 1.0   27 59 2.0
+28 28 1.0   28 60 2.0
+29 29 1.0   29 61 2.0
+30 30 1.0   30 62 2.0
+31 31 1.0   31 63 2.0
+32 32 1.0   32 64 2.0
+33 33 2.0   33 25 1.0
+34 34 2.0   34 26 1.0
+35 35 2.0   35 27 1.0
+36 36 2.0   36 28 1.0
+37 37 2.0   37 29 1.0
+38 38 2.0   38 30 1.0
+39 39 2.0   39 31 1.0
+40 40 2.0   40 32 1.0
+
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: psb_ovrl Overlap + Up: Communication routines + Previous: Communication routines +   Contents + diff --git a/docs/html/node41.html b/docs/html/node41.html index 86003dab..adae6ae8 100644 --- a/docs/html/node41.html +++ b/docs/html/node41.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_halo -- Halo Data Communication - +psb_ovrl -- Overlap Update + @@ -20,58 +20,57 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_ovrl Overlap - Up: Communication routines - Previous: Communication routines -   Next: psb_gather Gather + Up: Communication routines + Previous: psb_halo Halo +   Contents

-

-psb_halo -- Halo Data Communication +

+psb_ovrl -- Overlap Update

-These subroutines gathers the values of the halo -elements, and (optionally) scale the result: +These subroutines applies an overlap operator to the input vector:


\begin{displaymath}x \leftarrow \alpha x \end{displaymath} + WIDTH="55" HEIGHT="27" BORDER="0" + SRC="img66.png" + ALT="\begin{displaymath}x \leftarrow Q x \end{displaymath}">

@@ -79,44 +78,54 @@ where:
$x$
-
is a global dense submatrix. +
is the global dense submatrix $x$ +
+
$Q$
+
is the overlap operator; it is the composition of two +operators $ P_a$ and $ P^{T}$.


-
+
-

- next - + up - previous - contents
- Next:psb_ovrl Overlap - Up:Communication routines - Previous:Communication routines -   Next:psb_gather Gather + Up:Communication routines + Previous:psb_halo Halo +   Contents diff --git a/docs/html/node42.html b/docs/html/node42.html index 269eda31..98e1b3e5 100644 --- a/docs/html/node42.html +++ b/docs/html/node42.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_ovrl -- Overlap Update - +psb_gather -- Gather Global Dense Matrix + @@ -20,112 +20,123 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next:psb_gather Gather - Up:Communication routines - Previous:psb_halo Halo -   Next:psb_scatter Scatter + Up:Communication routines + Previous:psb_ovrl Overlap +   Contents

-

-psb_ovrl -- Overlap Update +

+psb_gather -- Gather Global Dense Matrix

-These subroutines applies an overlap operator to the input vector: +These subroutines collect the portions of global dense matrix +distributed over all process into one single array stored on one +process.


\begin{displaymath}x \leftarrow Q x \end{displaymath} + WIDTH="163" HEIGHT="28" BORDER="0" + SRC="img75.png" + ALT="\begin{displaymath}glob\_x \leftarrow collect(loc\_x_i) \end{displaymath}">

where:
$x$
-
is the global dense submatrix $x$ + WIDTH="47" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" + SRC="img76.png" + ALT="$glob\_x$"> +
is the global submatrix +$glob\_x_{1:m,1:n}$
$Q$
-
is the overlap operator; it is the composition of two -operators $ P_a$ and $ P^{T}$. + WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" + SRC="img78.png" + ALT="$loc\_x_i$"> +
is the local portion of global dense matrix on +process $i$. +
+
$collect$
+
is the collect function.


-
+
Table 13: +Table 14: Data types
- - - - + - + - + - +
$\alpha$, $x$ Subroutine
Integerpsb_halo
Short Precision Realpsb_halopsb_ovrl
Long Precision Realpsb_halopsb_ovrl
Short Precision Complexpsb_halopsb_ovrl
Long Precision Complexpsb_halopsb_ovrl
@@ -127,9 +136,9 @@ Data types 

-call psb_halo(x, desc_a, info)
-call psb_halo(x, desc_a, info, alpha, work, data)
-
+call psb_ovrl(x, desc_a, info) +call psb_ovrl(x, desc_a, info, update=update_type, work=work) +

@@ -142,7 +151,7 @@ call psb_halo(x, desc_a, info, alpha, work, data)
x
global dense matrix $x$.
Scope: local @@ -151,9 +160,9 @@ Type: required
Intent: inout.
-Specified as: a rank one or two array with the TARGET attribute +Specified as: a rank one or two array containing numbers of type specified in -Table 13. +Table 14.
desc_a
contains data structures for communications. @@ -166,24 +175,40 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
-
alpha
-
the scalar $\alpha$. -
+
update
+
Update operator. +
+
update = psb_none_
+
Do nothing; +
+
update = psb_add_
+
Sum overlap entries, i.e. apply $P^T$; +
+
update = psb_avg_
+
Average overlap entries, i.e. apply $P_aP^T$; +
+
Scope: global
-Type: optional -
Intent: in.
-Default: $alpha = 1 $ +Default: +$update\_type = psb\_avg\_ $ +
+Scope: global
-Specified as: a number of the data type indicated in Table 13. +Specified as: a integer variable.
work
the work array. @@ -194,22 +219,10 @@ Type: optional
Intent: inout.
-Specified as: a rank one array of the same type of $x$ with the -POINTER attribute. -
-
data
-
index list selector. -
-Scope: global -
-Type: optional -
-Specified as: an integer. Values:psb_comm_halo_,psb_comm_mov_, -psb_comm_ext_, default: psb_comm_halo_. Chooses the -index list on which to base the data exchange. + SRC="img27.png" + ALT="$x$">.

@@ -219,7 +232,7 @@ index list on which to base the data exchange.
x
global dense result matrix $x$.
Scope: local @@ -228,15 +241,12 @@ Type: required
Intent: inout.
-Returned as: a rank one or two array +Specified as: an array of rank one or two containing numbers of type specified in -Table 13. +Table 14.
info
-
the local portion of result submatrix $y$. +
Error code.
Scope: local
@@ -244,46 +254,80 @@ Type: required
Intent: out.
-An integer value that contains an error code. +An integer value; 0 means no error has been detected.
-
+

+Notes + +

    +
  1. If there is no overlap in the data distribution associated with + the descriptor, no operations are performed; +
    2. +
  2. The operator $ P^{T}$ performs the reduction sum of overlap +elements; it is a ``prolongation'' operator $P^T$ that +replicates overlap elements, accounting for the physical replication +of data; +
    3. +
  3. The operator $ P_a$ performs a scaling on the overlap elements by +the amount of replication; thus, when combined with the reduction +operator, it implements the average of replicated elements over all of +their instances. +
    4. +
+ +

+ +

Figure 7: Sample discretization mesh.
\includegraphics[scale=0.45]{figures/try8x8.eps} + WIDTH="533" HEIGHT="454" ALIGN="BOTTOM" BORDER="0" + SRC="img74.png" + ALT="\includegraphics[scale=0.65]{figures/try8x8_ov.eps}"> \rotatebox{-90}{\includegraphics[scale=0.45]{figures/try8x8}} + WIDTH="76" HEIGHT="2" ALIGN="BOTTOM" BORDER="0" + SRC="img73.png" + ALT="\rotatebox{-90}{\includegraphics[scale=0.65]{figures/try8x8_ov}}">
-

-Usage Example -Consider the discretization mesh depicted in fig. 7, -partitioned among two processes as shown by the dashed line; the data -distribution is such that each process will own 32 entries in the -index space, with a halo made of 8 entries placed at local indices 33 -through 40. If process 0 assigns an initial value of 1 to its entries +Example of use +Consider the discretization mesh depicted in fig. 7, +partitioned among two processes as shown by the dashed lines, with an +overlap of 1 extra layer with respect to the partition of +fig. 6; the data +distribution is such that each process will own 40 entries in the +index space, with an overlap of 16 entries placed at local indices 25 +through 40; the halo will run from local index 41 through local index 48.. If process 0 assigns an initial value of 1 to its entries in the $x$ vector, and process 1 assigns a value of 2, then after a -call to psb_halo the contents of the local vectors will be the -following: +call to psb_ovrl with psb_avg_ and a call to +psb_halo_ the contents of the local vectors will be the +following (showing a transition among the two subdomains) + +


@@ -306,7 +350,7 @@ Process 1 - + @@ -314,7 +358,7 @@ Process 1 - + @@ -322,7 +366,7 @@ Process 1 - + @@ -330,7 +374,7 @@ Process 1 - + @@ -338,7 +382,7 @@ Process 1 - + @@ -346,7 +390,7 @@ Process 1 - + @@ -354,7 +398,7 @@ Process 1 - + @@ -362,7 +406,7 @@ Process 1 - + @@ -461,7 +505,7 @@ Process 1 + 21 @@ -469,7 +513,7 @@ Process 1 + 22 @@ -477,7 +521,7 @@ Process 1 + 23 @@ -485,7 +529,7 @@ Process 1 + 24 @@ -493,131 +537,195 @@ Process 1 + 25 - + + 26 - + + 27 - + + 28 - + + 29 - + + 30 - + + 31 - + + 32 - + + 33 - + - + + 34 - + - + + 35 - + - + + 36 - + - + + 37 - + - + + 38 - + - + + 39 - + - + + 40 - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
1.0   1 33 2.0 1.5
2 1.0   2 34 2.0 1.5
3 1.0   3 35 2.0 1.5
4 1.0   4 36 2.0 1.5
5 1.0   5 37 2.0 1.5
6 1.0   6 38 2.0 1.5
7 1.0   7 39 2.0 1.5
8 1.0   8 40 2.0 1.5
9 2.0
-21 21 1.0   21 2.0
-22 22 1.0   22 2.0
-23 23 1.0   23 2.0
-24 24 1.0   24 2.0
-25 25 1.0 1.5   25 57 2.0
-26 26 1.0 1.5   26 58 2.0
-27 27 1.0 1.5   27 59 2.0
-28 28 1.0 1.5   28 60 2.0
-29 29 1.0 1.5   29 61 2.0
-30 30 1.0 1.5   30 62 2.0
-31 31 1.0 1.5   31 63 2.0
-32 32 1.0 1.5   32 64 2.0
-33 33 2.0 1.5   33 25 1.0 1.5
-34 34 2.0 1.5   34 26 1.0 1.5
-35 35 2.0 1.5   35 27 1.0 1.5
-36 36 2.0 1.5   36 28 1.0 1.5
-37 37 2.0 1.5   37 29 1.0 1.5
-38 38 2.0 1.5   38 30 1.0 1.5
-39 39 2.0 1.5   39 31 1.0 1.5
-40 40 2.0 1.5   40 32 1.5
+ 41 41 2.0   41 17 1.0
+ 42 42 2.0   42 18 1.0
+ 43 43 2.0   43 19 1.0
+ 44 44 2.0   44 20 1.0
+ 45 45 2.0   45 21 1.0
+ 46 46 2.0   46 22 1.0
+ 47 47 2.0   47 23 1.0
+ 48 48 2.0   48 24 1.0
@@ -626,26 +734,26 @@ Process 1
-
Table 14: +Table 15: Data types
+ WIDTH="34" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" + SRC="img80.png" + ALT="$x_i, y$"> + + + - + - + - + - +
$x$ Subroutine
Integerpsb_gather
Short Precision Realpsb_ovrlpsb_gather
Long Precision Realpsb_ovrlpsb_gather
Short Precision Complexpsb_ovrlpsb_gather
Long Precision Complexpsb_ovrlpsb_gather
@@ -136,9 +147,9 @@ Data types 

-call psb_ovrl(x, desc_a, info)
-call psb_ovrl(x, desc_a, info, update=update_type, work=work)
-
+call psb_gather(glob_x, loc_x, desc_a, info, root) +call psb_gather(glob_x, loc_x, desc_a, info, root) +

@@ -148,21 +159,21 @@ call psb_ovrl(x, desc_a, info, update=update_type, work=work)
On Entry
-
x
-
global dense matrix $x$. +
loc_x
+
the local portion of global dense matrix +$glob\_x$.
Scope: local
-Type: required +Type: required
-Intent: inout. +Intent: in.
-Specified as: a rank one or two array -containing numbers of type specified in -Table 14. +Specified as: a rank one or two array containing numbers of the type +indicated in Table 15.
desc_a
contains data structures for communications. @@ -175,75 +186,43 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
-
update
-
Update operator. -
-
update = psb_none_
-
Do nothing; -
-
update = psb_add_
-
Sum overlap entries, i.e. apply $P^T$; -
-
update = psb_avg_
-
Average overlap entries, i.e. apply $P_aP^T$; -
-
-Scope: global -
-Intent: in. -
-Default: -$update\_type = psb\_avg\_ $ +
root
+
The process that holds the global copy. If $root=-1$ all + the processes will have a copy of the global vector.
Scope: global
-Specified as: a integer variable. -
-
work
-
the work array. -
-Scope: local -
Type: optional
-Intent: inout. +Intent: in.
-Specified as: a one dimensional array of the same type of $x$. - -

+Specified as: an integer variable +$-1\le root\le np-1$, default $-1$.

On Return
-
x
-
global dense result matrix $x$. +
glob_x
+
The array where the local parts must be gathered.
-Scope: local +Scope: global
-Type: required +Type: required
-Intent: inout. +Intent: out.
-Specified as: an array of rank one or two -containing numbers of type specified in -Table 14. +Specified as: a rank one or two array.
info
Error code. @@ -258,502 +237,29 @@ An integer value; 0 means no error has been detected.
-

-Notes - -

    -
  1. If there is no overlap in the data distribution associated with - the descriptor, no operations are performed; -
    2. -
  2. The operator $ P^{T}$ performs the reduction sum of overlap -elements; it is a ``prolongation'' operator $P^T$ that -replicates overlap elements, accounting for the physical replication -of data; -
    3. -
  3. The operator $ P_a$ performs a scaling on the overlap elements by -the amount of replication; thus, when combined with the reduction -operator, it implements the average of replicated elements over all of -their instances. -
    4. -
- -

- -

- - - -
Figure 8: -Sample discretization mesh.
-
-\includegraphics[scale=0.65]{figures/try8x8_ov.eps} - - -\rotatebox{-90}{\includegraphics[scale=0.65]{figures/try8x8_ov}} - -
-
- -Example of use -Consider the discretization mesh depicted in fig. 8, -partitioned among two processes as shown by the dashed lines, with an -overlap of 1 extra layer with respect to the partition of -fig. 7; the data -distribution is such that each process will own 40 entries in the -index space, with an overlap of 16 entries placed at local indices 25 -through 40; the halo will run from local index 41 through local index 48.. If process 0 assigns an initial value of 1 to its entries -in the $x$ vector, and process 1 assigns a value of 2, then after a -call to psb_ovrl with psb_avg_ and a call to -psb_halo_ the contents of the local vectors will be the -following (showing a transition among the two subdomains) - -

-
-

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Process 0  -Process 1
- I GLOB(I) X(I)   I GLOB(I) X(I)
- 1 1 1.0   1 33 1.5
- 2 2 1.0   2 34 1.5
- 3 3 1.0   3 35 1.5
- 4 4 1.0   4 36 1.5
- 5 5 1.0   5 37 1.5
- 6 6 1.0   6 38 1.5
- 7 7 1.0   7 39 1.5
- 8 8 1.0   8 40 1.5
- 9 9 1.0   9 41 2.0
- 10 10 1.0   10 42 2.0
- 11 11 1.0   11 43 2.0
- 12 12 1.0   12 44 2.0
- 13 13 1.0   13 45 2.0
- 14 14 1.0   14 46 2.0
- 15 15 1.0   15 47 2.0
- 16 16 1.0   16 48 2.0
- 17 17 1.0   17 49 2.0
- 18 18 1.0   18 50 2.0
- 19 19 1.0   19 51 2.0
- 20 20 1.0   20 52 2.0
- 21 21 1.0   21 53 2.0
- 22 22 1.0   22 54 2.0
- 23 23 1.0   23 55 2.0
- 24 24 1.0   24 56 2.0
- 25 25 1.5   25 57 2.0
- 26 26 1.5   26 58 2.0
- 27 27 1.5   27 59 2.0
- 28 28 1.5   28 60 2.0
- 29 29 1.5   29 61 2.0
- 30 30 1.5   30 62 2.0
- 31 31 1.5   31 63 2.0
- 32 32 1.5   32 64 2.0
- 33 33 1.5   33 25 1.5
- 34 34 1.5   34 26 1.5
- 35 35 1.5   35 27 1.5
- 36 36 1.5   36 28 1.5
- 37 37 1.5   37 29 1.5
- 38 38 1.5   38 30 1.5
- 39 39 1.5   39 31 1.5
- 40 40 1.5   40 32 1.5
- 41 41 2.0   41 17 1.0
- 42 42 2.0   42 18 1.0
- 43 43 2.0   43 19 1.0
- 44 44 2.0   44 20 1.0
- 45 45 2.0   45 21 1.0
- 46 46 2.0   46 22 1.0
- 47 47 2.0   47 23 1.0
- 48 48 2.0   48 24 1.0
-
-

- next - + up - previous - contents
- Next: psb_gather Gather - Up: Communication routines - Previous: psb_halo Halo -   Next: psb_scatter Scatter + Up: Communication routines + Previous: psb_ovrl Overlap +   Contents diff --git a/docs/html/node43.html b/docs/html/node43.html index a5bb9e66..3ab5b145 100644 --- a/docs/html/node43.html +++ b/docs/html/node43.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_gather -- Gather Global Dense Matrix - +psb_scatter -- Scatter Global Dense Matrix + @@ -18,61 +18,59 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: psb_scatter Scatter - Up: Communication routines - Previous: psb_ovrl Overlap -   Next: Data management routines + Up: Communication routines + Previous: psb_gather Gather +   Contents

-

-psb_gather -- Gather Global Dense Matrix +

+psb_scatter -- Scatter Global Dense Matrix

-These subroutines collect the portions of global dense matrix -distributed over all process into one single array stored on one -process. +These subroutines scatters the portions of global dense matrix owned +by a process to all the processes in the processes grid.


\begin{displaymath}glob\_x \leftarrow collect(loc\_x_i) \end{displaymath} + WIDTH="168" HEIGHT="28" BORDER="0" + SRC="img84.png" + ALT="\begin{displaymath}loc\_x_i \leftarrow scatter(glob\_x) \end{displaymath}">

@@ -80,19 +78,19 @@ where:
$glob\_x$
-
is the global submatrix $glob\_x_{1:m,1:n}$
$loc\_x_i$
is the local portion of global dense matrix on process $i$.
$collect$
-
is the collect function. + WIDTH="53" HEIGHT="14" ALIGN="BOTTOM" BORDER="0" + SRC="img85.png" + ALT="$scatter$"> +
is the scatter function.


-
+
- +
Table 15: +Table 16: Data types
- + - + - + - + - +
$x_i, y$ Subroutine
Integerpsb_gatherpsb_scatter
Short Precision Realpsb_gatherpsb_scatter
Long Precision Realpsb_gatherpsb_scatter
Short Precision Complexpsb_gatherpsb_scatter
Long Precision Complexpsb_gatherpsb_scatter
@@ -147,8 +145,8 @@ Data types 

-call psb_gather(glob_x, loc_x, desc_a, info, root)
-call psb_gather(glob_x, loc_x, desc_a, info, root)
+call psb_scatter(glob_x, loc_x, desc_a, info, root)
+call psb_scatter(glob_x, loc_x, desc_a, info, root)

@@ -159,21 +157,16 @@ call psb_gather(glob_x, loc_x, desc_a, info, root)

On Entry
-
loc_x
-
the local portion of global dense matrix -$glob\_x$. +
glob_x
+
The array that must be scattered into local pieces.
-Scope: local +Scope: global
Type: required
Intent: in.
-Specified as: a rank one or two array containing numbers of the type -indicated in Table 15. +Specified as: a rank one or two array.
desc_a
contains data structures for communications. @@ -189,9 +182,9 @@ Specified as: a structured data of type descdatapsb_desc_type.
root
The process that holds the global copy. If $root=-1$ all - the processes will have a copy of the global vector. + the processes have a copy of the global vector.
Scope: global
@@ -204,25 +197,30 @@ Specified as: an integer variable $-1\le root\le np-1$, default $-1$.
On Return
-
glob_x
-
The array where the local parts must be gathered. +
loc_x
+
the local portion of global dense matrix +$glob\_x$.
-Scope: global +Scope: local
Type: required
Intent: out.
-Specified as: a rank one or two array. +Specified as: a rank one or two array containing numbers of the type +indicated in Table 16.
info
Error code. @@ -240,26 +238,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: psb_scatter Scatter - Up: Communication routines - Previous: psb_ovrl Overlap -   Next: Data management routines + Up: Communication routines + Previous: psb_gather Gather +   Contents diff --git a/docs/html/node44.html b/docs/html/node44.html index bd7b3f66..de4b64e3 100644 --- a/docs/html/node44.html +++ b/docs/html/node44.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_scatter -- Scatter Global Dense Matrix - +Data management routines + @@ -18,248 +18,114 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Data management routines - Up: Communication routines - Previous: psb_gather Gather -   Next: psb_cdall Allocates + Up: userhtml + Previous: psb_scatter Scatter +   Contents

-

-psb_scatter -- Scatter Global Dense Matrix -

- -

-These subroutines scatters the portions of global dense matrix owned -by a process to all the processes in the processes grid. - -

-

-
- - -\begin{displaymath}loc\_x_i \leftarrow scatter(glob\_x) \end{displaymath} -
-
-

-where: -
-
$glob\_x$
-
is the global matrix -$glob\_x_{1:m,1:n}$ -
-
$loc\_x_i$
-
is the local portion of global dense matrix on -process $i$. -
-
$scatter$
-
is the scatter function. -
-
- -

-

-
- - - -
Table 16: -Data types
-
- - - - - - - - - - - - - - - - - - - -
$x_i, y$Subroutine
Integerpsb_scatter
Short Precision Realpsb_scatter
Long Precision Realpsb_scatter
Short Precision Complexpsb_scatter
Long Precision Complexpsb_scatter
-
-
-

+

+
+Data management routines +

-

-call psb_scatter(glob_x, loc_x, desc_a, info, root)
-call psb_scatter(glob_x, loc_x, desc_a, info, root)
-
+
+ +Subsections -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
glob_x
-
The array that must be scattered into local pieces. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
root
-
The process that holds the global copy. If $root=-1$ all - the processes have a copy of the global vector. -
-Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: an integer variable -$-1\le root\le np-1$, default $-1$. -
-
On Return
-
-
-
loc_x
-
the local portion of global dense matrix -$glob\_x$. -
-Scope: local -
-Type: required -
-Intent: out. -
-Specified as: a rank one or two array containing numbers of the type -indicated in Table 16. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - -next - -up - -previous - -contents -
- Next: Data management routines - Up: Communication routines - Previous: psb_gather Gather -   Contents - + + +
diff --git a/docs/html/node45.html b/docs/html/node45.html index 424b886c..6fdf28b2 100644 --- a/docs/html/node45.html +++ b/docs/html/node45.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Data management routines - +psb_cdall -- Allocates a communication descriptor + @@ -18,114 +18,407 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - - + + + - next - + up - previous - contents
- Next: psb_cdall Allocates - Up: userhtml - Previous: psb_scatter Scatter -   Next: psb_cdins Communication + Up: Data management routines + Previous: Data management routines +   Contents

-

- +

+psb_cdall -- Allocates a communication descriptor +

+ +

+

+call psb_cdall(icontxt, desc_a, info,mg=mg,parts=parts)
+call psb_cdall(icontxt, desc_a, info,vg=vg,[mg=mg,flag=flag])
+call psb_cdall(icontxt, desc_a, info,vl=vl,[nl=nl,globalcheck=.true.])
+call psb_cdall(icontxt, desc_a, info,nl=nl)
+call psb_cdall(icontxt, desc_a, info,mg=mg,repl=.true.)
+
+ +

+This subroutine initializes the communication descriptor associated +with an index space. One of the optional arguments +parts, vg, vl, nl or repl +must be specified, thereby choosing +the specific initialization strategy. +

+
On Entry
+
+
+
Type:
+
Synchronous. +
+
icontxt
+
the communication context. +
+Scope:global. +
+Type:required. +
+Intent: in. +
+Specified as: an integer value. +
+
vg
+
Data allocation: each index +$i\in \{1\dots mg\}$ is allocated + to process $vg(i)$. +
+Scope:global. +
+Type:optional. +
+Intent: in. +
+Specified as: an integer array. +
+
flag
+
Specifies whether entries in $vg$ are zero- or one-based. +
+Scope:global. +
+Type:optional. +
+Intent: in. +
+Specified as: an integer value $0,1$, default $0$. + +

+

+
mg
+
the (global) number of rows of the problem. +
+Scope:global. +
+Type:optional. +
+Intent: in. +
+Specified as: an integer value. It is required if parts or +repl is specified, it is optional if vg is specified. +
+
parts
+
the subroutine that defines the partitioning scheme. +
+Scope:global. +
+Type:required. +
+Specified as: a subroutine. +
+
vl
+
Data allocation: the set of global indices + $vl(1:nl)$ belonging to the calling process. +
+Scope:local. +
+Type:optional. +
+Intent: in. +
+Specified as: an integer array. +
+
nl
+
Data allocation: in a generalized block-row distribution the + number of indices belonging to the current process. +
+Scope:local. +
+Type:optional. +
+Intent: in. +
+Specified as: an integer value. May be specified together with +vl. +
+
repl
+
Data allocation: build a replicated index space (i.e. all + processes own all indices). +
+Scope:global. +
+Type:optional. +
+Intent: in. +
+Specified as: the logical value .true. +
+
globalcheck
+
Data allocation: do global checks on the local + index lists vl +
+Scope:global. +
+Type:optional. +
+Intent: in. +
+Specified as: a logical value, default: .true. +
+
+ +

+

+
On Return
+
+
+
desc_a
+
the communication descriptor. +
+Scope:local. +
+Type:required. +
+Intent: out. +
+Specified as: a structured data of type descdatapsb_desc_type. +
+
info
+
Error code. +
+Scope: local
-Data management routines - +Type: required +
+Intent: out. +
+An integer value; 0 means no error has been detected. +
+

-

- -Subsections +Notes - - -
+
    +
  1. One of the optional arguments parts, vg, + vl, nl or repl must be specified, thereby choosing the + initialization strategy as follows: +
    +
    parts
    +
    In this case we have a subroutine specifying the mapping + between global indices and process/local index pairs. If this + optional argument is specified, then it is mandatory to + specify the argument mg as well. + The subroutine must conform to the following interface: +
    +  interface 
+     subroutine psb_parts(glob_index,mg,np,pv,nv)
+       integer, intent (in)  :: glob_index,np,mg
+       integer, intent (out) :: nv, pv(*)
+     end subroutine psb_parts
+  end interface
+
    + The input arguments are: +
    +
    glob_index
    +
    The global index to be mapped; + +
    +
    np
    +
    The number of processes in the mapping; + +
    +
    mg
    +
    The total number of global rows in the mapping; + +
    +
    + The output arguments are: +
    +
    nv
    +
    The number of entries in pv; + +
    +
    pv
    +
    A vector containing the indices of the processes to + which the global index should be assigend; each entry must satisfy + +$0\le pv(i) < np$; if $nv>1$ we have an index assigned to multiple + processes, i.e. we have an overlap among the subdomains. + +
    +
    +
    +
    vg
    +
    In this case the association between an index and a process + is specified via an integer vector vg(1:mg); + each index +$i\in \{1\dots mg\}$ is assigned to process $vg(i)$. + The vector vg must be identical on all + calling processes; its entries may have the ranges $(0\dots np-1)$ + or $(1\dots np)$ according to the value of flag. + The size $mg$ may be specified via the optional argument mg; + the default is to use the entire vector vg, thus having + mg=size(vg). +
    +
    vl
    +
    In this case we are specifying the list of indices + vl(1:nl) assigned to the current process; thus, the global + problem size $mg$ is given by + the range of the aggregate of the individual vectors vl specified + in the calling processes. The size may be specified via the optional + argument nl; the default is to use the entire vector vl, thus having + nl=size(vl). + If globalcheck=.true. the subroutine will check how many + times each entry in the global index space $(1\dots mg)$ is + specified in the input lists vl, thus allowing for the + presence of overlap in the input, and checking for ``orphan'' + indices. If globalcheck=.false., the subroutine will not + check for overlap, and may be significantly faster, but the user + is implicitly guaranteeing that there are neither orphan nor + overlap indices. +
    +
    nl
    +
    If this argument is specified alone (i.e. without vl) + the result is a generalized row-block distribution in which each + process $I$ gets assigned a consecutive chunk of $N_I=nl$ global + indices. +
    +
    repl
    +
    This arguments specifies to replicate all indices on + all processes. This is a special purpose data allocation that is + useful in the construction of some multilevel preconditioners. +
    +
    +
    2. +
  2. On exit from this routine the descriptor is in the build + state. +
    3. +
  3. Calling the routine with vg or parts implies that + every process will scan the entire index space to figure out the + local indices. +
    4. +
  4. Overlapped indices are possible with both parts and + vl invocations. +
    5. +
  5. When the subroutine is invoked with vl in + conjunction with globalcheck=.true., it will perform a scan + of the index space to search for overlap or orphan indices. +
    6. +
  6. When the subroutine is invoked with vl in + conjunction with globalcheck=.false., no index space scan + will take place. Thus it is the responsibility of the user to make + sure that the indices specified in vl have neither orphans nor + overlaps; if this assumption fails, results will be + unpredictable. +
    7. +
  7. Orphan and overlap indices are + impossible by construction when the subroutine is invoked with + nl (alone), or vg. +
    8. +
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: psb_cdins Communication + Up: Data management routines + Previous: Data management routines +   Contents + diff --git a/docs/html/node46.html b/docs/html/node46.html index 8a693160..3bc5a73c 100644 --- a/docs/html/node46.html +++ b/docs/html/node46.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cdall -- Allocates a communication descriptor - +psb_cdins -- Communication descriptor insert routine + @@ -20,189 +20,98 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_cdins Communication - Up: Data management routines - Previous: Data management routines -   Next: psb_cdasb Communication + Up: Data management routines + Previous: psb_cdall Allocates +   Contents

-

-psb_cdall -- Allocates a communication descriptor +

+psb_cdins -- Communication descriptor insert routine 

-call psb_cdall(icontxt, desc_a, info,mg=mg,parts=parts)
-call psb_cdall(icontxt, desc_a, info,vg=vg,[mg=mg,flag=flag])
-call psb_cdall(icontxt, desc_a, info,vl=vl,[nl=nl,globalcheck=.true.])
-call psb_cdall(icontxt, desc_a, info,nl=nl)
-call psb_cdall(icontxt, desc_a, info,mg=mg,repl=.true.)
+call psb_cdins(nz, ia, ja, desc_a, info)

-This subroutine initializes the communication descriptor associated -with an index space. One of the optional arguments -parts, vg, vl, nl or repl -must be specified, thereby choosing -the specific initialization strategy. -

-
On Entry
-
-
-
Type:
-
Synchronous. -
-
icontxt
-
the communication context. -
-Scope:global. -
-Type:required. -
-Intent: in. -
-Specified as: an integer value. -
-
vg
-
Data allocation: each index -$i\in \{1\dots mg\}$ is allocated - to process $vg(i)$. -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer array. -
-
flag
-
Specifies whether entries in $vg$ are zero- or one-based. -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer value $0,1$, default $0$. +This subroutine examines the edges of the graph associated with the +discretization mesh (and isomorphic to the sparsity pattern of a +linear system coefficient matrix), storing them as necessary into the +communication descriptor.

+

+
Type:
+
Asynchronous.
-
mg
-
the (global) number of rows of the problem. -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer value. It is required if parts or -repl is specified, it is optional if vg is specified. -
-
parts
-
the subroutine that defines the partitioning scheme. -
-Scope:global. -
-Type:required. -
-Specified as: a subroutine. -
-
vl
-
Data allocation: the set of global indices - $vl(1:nl)$ belonging to the calling process. -
-Scope:local. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer array. +
On Entry
+
-
nl
-
Data allocation: in a generalized block-row distribution the - number of indices belonging to the current process. +
nz
+
the number of points being inserted.
-Scope:local. +Scope: local.
-Type:optional. +Type: required.
Intent: in.
-Specified as: an integer value. May be specified together with -vl. +Specified as: an integer value.
-
repl
-
Data allocation: build a replicated index space (i.e. all - processes own all indices). +
ia
+
the indices of the starting vertex of the edges being inserted.
-Scope:global. +Scope: local.
-Type:optional. +Type: required.
Intent: in.
-Specified as: the logical value .true. +Specified as: an integer array of length $nz$.
-
globalcheck
-
Data allocation: do global checks on the local - index lists vl +
ja
+
the indices of the end vertex of the edges being inserted.
-Scope:global. +Scope: local.
-Type:optional. +Type: required.
Intent: in.
-Specified as: a logical value, default: .true. +Specified as: an integer array of length $nz$.
@@ -212,13 +121,13 @@ Specified as: a logical value, default: .true.
desc_a
-
the communication descriptor. +
the updated communication descriptor.
Scope:local.
Type:required.
-Intent: out. +Intent: inout.
Specified as: a structured data of type descdatapsb_desc_type.
@@ -234,189 +143,41 @@ Intent: out. An integer value; 0 means no error has been detected.
- -

Notes

    -
  1. One of the optional arguments parts, vg, - vl, nl or repl must be specified, thereby choosing the - initialization strategy as follows: -
    -
    parts
    -
    In this case we have a subroutine specifying the mapping - between global indices and process/local index pairs. If this - optional argument is specified, then it is mandatory to - specify the argument mg as well. - The subroutine must conform to the following interface: -
    -  interface 
-     subroutine psb_parts(glob_index,mg,np,pv,nv)
-       integer, intent (in)  :: glob_index,np,mg
-       integer, intent (out) :: nv, pv(*)
-     end subroutine psb_parts
-  end interface
-
    - The input arguments are: -
    -
    glob_index
    -
    The global index to be mapped; - -
    -
    np
    -
    The number of processes in the mapping; - -
    -
    mg
    -
    The total number of global rows in the mapping; - -
    -
    - The output arguments are: -
    -
    nv
    -
    The number of entries in pv; - -
    -
    pv
    -
    A vector containing the indices of the processes to - which the global index should be assigend; each entry must satisfy - -$0\le pv(i) < np$; if $nv>1$ we have an index assigned to multiple - processes, i.e. we have an overlap among the subdomains. - -
    -
    -
    -
    vg
    -
    In this case the association between an index and a process - is specified via an integer vector vg(1:mg); - each index -$i\in \{1\dots mg\}$ is assigned to process $vg(i)$. - The vector vg must be identical on all - calling processes; its entries may have the ranges $(0\dots np-1)$ - or $(1\dots np)$ according to the value of flag. - The size $mg$ may be specified via the optional argument mg; - the default is to use the entire vector vg, thus having - mg=size(vg). -
    -
    vl
    -
    In this case we are specifying the list of indices - vl(1:nl) assigned to the current process; thus, the global - problem size $mg$ is given by - the range of the aggregate of the individual vectors vl specified - in the calling processes. The size may be specified via the optional - argument nl; the default is to use the entire vector vl, thus having - nl=size(vl). - If globalcheck=.true. the subroutine will check how many - times each entry in the global index space $(1\dots mg)$ is - specified in the input lists vl, thus allowing for the - presence of overlap in the input, and checking for ``orphan'' - indices. If globalcheck=.false., the subroutine will not - check for overlap, and may be significantly faster, but the user - is implicitly guaranteeing that there are neither orphan nor - overlap indices. -
    -
    nl
    -
    If this argument is specified alone (i.e. without vl) - the result is a generalized row-block distribution in which each - process $I$ gets assigned a consecutive chunk of $N_I=nl$ global - indices. -
    -
    repl
    -
    This arguments specifies to replicate all indices on - all processes. This is a special purpose data allocation that is - useful in the construction of some multilevel preconditioners. -
    -
    +
  2. This routine may only be called if the descriptor is in the + build state;
    3. -
  3. On exit from this routine the descriptor is in the build - state. -
    4. -
  4. Calling the routine with vg or parts implies that - every process will scan the entire index space to figure out the - local indices. -
    5. -
  5. Overlapped indices are possible with both parts and - vl invocations. -
    6. -
  6. When the subroutine is invoked with vl in - conjunction with globalcheck=.true., it will perform a scan - of the index space to search for overlap or orphan indices. -
    7. -
  7. When the subroutine is invoked with vl in - conjunction with globalcheck=.false., no index space scan - will take place. Thus it is the responsibility of the user to make - sure that the indices specified in vl have neither orphans nor - overlaps; if this assumption fails, results will be - unpredictable. -
    8. -
  8. Orphan and overlap indices are - impossible by construction when the subroutine is invoked with - nl (alone), or vg. +
  9. This routine automatically ignores edges that do not +insist on the current process, i.e. edges for which neither the starting +nor the end vertex belong to the current process.

- next - + up - previous - contents
- Next: psb_cdins Communication - Up: Data management routines - Previous: Data management routines -   Next: psb_cdasb Communication + Up: Data management routines + Previous: psb_cdall Allocates +   Contents diff --git a/docs/html/node47.html b/docs/html/node47.html index da6cde42..f59a2e29 100644 --- a/docs/html/node47.html +++ b/docs/html/node47.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cdins -- Communication descriptor insert routine - +psb_cdasb -- Communication descriptor assembly routine + @@ -20,98 +20,64 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_cdasb Communication - Up: Data management routines - Previous: psb_cdall Allocates -   Next: psb_cdcpy Copies + Up: Data management routines + Previous: psb_cdins Communication +   Contents

-

-psb_cdins -- Communication descriptor insert routine +

+psb_cdasb -- Communication descriptor assembly routine 

-call psb_cdins(nz, ia, ja, desc_a, info)
+call psb_cdasb(desc_a, info)
-

-This subroutine examines the edges of the graph associated with the -discretization mesh (and isomorphic to the sparsity pattern of a -linear system coefficient matrix), storing them as necessary into the -communication descriptor. -

Type:
-
Asynchronous. +
Synchronous.
On Entry
-
nz
-
the number of points being inserted. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer value. -
-
ia
-
the indices of the starting vertex of the edges being inserted. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer array of length $nz$. -
-
ja
-
the indices of the end vertex of the edges being inserted. +
desc_a
+
the communication descriptor.
-Scope: local. +Scope:local.
-Type: required. +Type:required.
-Intent: in. +Intent: inout.
-Specified as: an integer array of length $nz$. +Specified as: a structured data of type descdatapsb_desc_type.
@@ -121,7 +87,7 @@ Specified as: an integer array of length
desc_a
-
the updated communication descriptor. +
the communication descriptor.
Scope:local.
@@ -146,40 +112,13 @@ An integer value; 0 means no error has been detected. Notes
    -
  1. This routine may only be called if the descriptor is in the - build state; -
    2. -
  2. This routine automatically ignores edges that do not -insist on the current process, i.e. edges for which neither the starting -nor the end vertex belong to the current process. +
  3. On exit from this routine the descriptor is in the assembled + state.

-

- - -next - -up - -previous - -contents -
- Next: psb_cdasb Communication - Up: Data management routines - Previous: psb_cdall Allocates -   Contents - +
diff --git a/docs/html/node48.html b/docs/html/node48.html index c37ecea8..494fb301 100644 --- a/docs/html/node48.html +++ b/docs/html/node48.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cdasb -- Communication descriptor assembly routine - +psb_cdcpy -- Copies a communication descriptor + @@ -20,64 +20,66 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_cdcpy Copies - Up: Data management routines - Previous: psb_cdins Communication -   Next: psb_cdfree Frees + Up: Data management routines + Previous: psb_cdasb Communication +   Contents

-

-psb_cdasb -- Communication descriptor assembly routine +

+psb_cdcpy -- Copies a communication descriptor 

-call psb_cdasb(desc_a, info)
+call psb_cdcpy(desc_in, desc_out, info)

Type:
-
Synchronous. +
Asynchronous.
On Entry
-
desc_a
+
desc_in
the communication descriptor.
Scope:local.
Type:required.
-Intent: inout. +Intent: in.
Specified as: a structured data of type descdatapsb_desc_type. + +

@@ -86,14 +88,14 @@ Specified as: a structured data of type descdatapsb_desc_type.
On Return
-
desc_a
-
the communication descriptor. +
desc_out
+
the communication descriptor copy.
Scope:local.
Type:required.
-Intent: inout. +Intent: out.
Specified as: a structured data of type descdatapsb_desc_type.
@@ -109,13 +111,6 @@ Intent: out. An integer value; 0 means no error has been detected. -Notes - -
    -
  1. On exit from this routine the descriptor is in the assembled - state. -
    2. -


diff --git a/docs/html/node49.html b/docs/html/node49.html index d228b272..00fa09f8 100644 --- a/docs/html/node49.html +++ b/docs/html/node49.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cdcpy -- Copies a communication descriptor - +psb_cdfree -- Frees a communication descriptor + @@ -20,66 +20,64 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_cdfree Frees - Up: Data management routines - Previous: psb_cdasb Communication -   Next: psb_cdbldext Build + Up: Data management routines + Previous: psb_cdcpy Copies +   Contents

-

-psb_cdcpy -- Copies a communication descriptor +

+psb_cdfree -- Frees a communication descriptor 

-call psb_cdcpy(desc_in, desc_out, info)
+call psb_cdfree(desc_a, info)

Type:
-
Asynchronous. +
Synchronous.
On Entry
-
desc_in
-
the communication descriptor. +
desc_a
+
the communication descriptor to be freed.
Scope:local.
Type:required.
-Intent: in. +Intent: inout.
Specified as: a structured data of type descdatapsb_desc_type. - -

@@ -88,17 +86,6 @@ Specified as: a structured data of type descdatapsb_desc_type.
On Return
-
desc_out
-
the communication descriptor copy. -
-Scope:local. -
-Type:required. -
-Intent: out. -
-Specified as: a structured data of type descdatapsb_desc_type. -
info
Error code.
diff --git a/docs/html/node5.html b/docs/html/node5.html index 3712399f..08ddb656 100644 --- a/docs/html/node5.html +++ b/docs/html/node5.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Application structure - Up: Up: General overview - Previous: Previous: Basic Nomenclature -   Contents

@@ -128,7 +128,7 @@ internally defined in the PSBLAS software package: For example the psb_geins, psb_spins and - psb_cdins perform the same action (see 6) on + psb_cdins perform the same action (see 6) on dense matrices, sparse matrices and communication descriptors respectively. Interface overloading allows the usage of the same subroutine @@ -169,26 +169,26 @@ whose current value is 3.0.0

- next - up - previous - contents
- Next: Next: Application structure - Up: Up: General overview - Previous: Previous: Basic Nomenclature -   Contents diff --git a/docs/html/node50.html b/docs/html/node50.html index fde48e79..95eb82ff 100644 --- a/docs/html/node50.html +++ b/docs/html/node50.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cdfree -- Frees a communication descriptor - +psb_cdbldext -- Build an extended communication descriptor + @@ -20,47 +20,51 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_cdbldext Build - Up: Data management routines - Previous: psb_cdcpy Copies -   Next: psb_spall Allocates + Up: Data management routines + Previous: psb_cdfree Frees +   Contents

-

-psb_cdfree -- Frees a communication descriptor +

+psb_cdbldext -- Build an extended communication + descriptor 

-call psb_cdfree(desc_a, info)
+call psb_cdbldext(a,desc_a,nl,desc_out, info, extype)

+This subroutine builds an extended communication descriptor, based on +the input descriptor desc_a and on the stencil specified +through the input sparse matrix a.

Type:
Synchronous. @@ -68,16 +72,54 @@ call psb_cdfree(desc_a, info)
On Entry
+
a
+
A sparse matrix +Scope:local. +
+Type:required. +
+Intent: in. +
+Specified as: a structured data type. +
desc_a
-
the communication descriptor to be freed. +
the communication descriptor.
Scope:local.
Type:required.
-Intent: inout. +Intent: in.
-Specified as: a structured data of type descdatapsb_desc_type. +Specified as: a structured data of type spdatapsb_spmat_type. +
+
nl
+
the number of additional layers desired. +
+Scope:global. +
+Type:required. +
+Intent: in. +
+Specified as: an integer value $nl\ge 0$. +
+
extype
+
the kind of estension required. +
+Scope:global. +
+Type:optional . +
+Intent: in. +
+Specified as: an integer value +psb_ovt_xhal_, psb_ovt_asov_, default: psb_ovt_xhal_ + +

@@ -86,6 +128,17 @@ Specified as: a structured data of type descdatapsb_desc_type.
On Return
+
desc_out
+
the extended communication descriptor. +
+Scope:local. +
+Type:required. +
+Intent: inout. +
+Specified as: a structured data of type descdatapsb_desc_type. +
info
Error code.
@@ -100,7 +153,48 @@ An integer value; 0 means no error has been detected.

-

+Notes + +
    +
  1. Specifying psb_ovt_xhal_ for the extype argument + the user will obtain a descriptor for a domain partition in which + the additional layers are fetched as part of an (extended) halo; + however the index-to-process mapping is identical to that of the + base descriptor; +
    2. +
  2. Specifying psb_ovt_asov_ for the extype argument + the user will obtain a descriptor with an overlapped decomposition: + the additional layer is aggregated to the local subdomain (and thus + is an overlap), and a new halo extending beyond the last additional + layer is formed. +
    3. +
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: psb_spall Allocates + Up: Data management routines + Previous: psb_cdfree Frees +   Contents + diff --git a/docs/html/node51.html b/docs/html/node51.html index 061c50d7..9560d5ad 100644 --- a/docs/html/node51.html +++ b/docs/html/node51.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_cdbldext -- Build an extended communication descriptor - +psb_spall -- Allocates a sparse matrix + @@ -20,51 +20,47 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_spall Allocates - Up: Data management routines - Previous: psb_cdfree Frees -   Next: psb_spins Insert + Up: Data management routines + Previous: psb_cdbldext Build +   Contents

-

-psb_cdbldext -- Build an extended communication - descriptor +

+psb_spall -- Allocates a sparse matrix 

-call psb_cdbldext(a,desc_a,nl,desc_out, info, extype)
+call psb_spall(a, desc_a, info, nnz)

-This subroutine builds an extended communication descriptor, based on -the input descriptor desc_a and on the stencil specified -through the input sparse matrix a.

Type:
Synchronous. @@ -72,16 +68,6 @@ through the input sparse matrix a.
On Entry
-
a
-
A sparse matrix -Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data type. -
desc_a
the communication descriptor.
@@ -91,35 +77,19 @@ Type:required.
Intent: in.
-Specified as: a structured data of type spdatapsb_spmat_type. -
-
nl
-
the number of additional layers desired. -
-Scope:global. -
-Type:required. -
-Intent: in. -
-Specified as: an integer value $nl\ge 0$. +Specified as: a structured data of type descdatapsb_desc_type.
-
extype
-
the kind of estension required. +
nnz
+
An estimate of the number of nonzeroes in the local + part of the assembled matrix.
-Scope:global. +Scope: global.
-Type:optional . +Type: optional.
Intent: in.
-Specified as: an integer value -psb_ovt_xhal_, psb_ovt_asov_, default: psb_ovt_xhal_ - -

+Specified as: an integer value.

@@ -128,16 +98,16 @@ Specified as: an integer value
On Return
-
desc_out
-
the extended communication descriptor. +
a
+
the matrix to be allocated.
-Scope:local. +Scope:local
-Type:required. +Type:required
-Intent: inout. +Intent: out.
-Specified as: a structured data of type descdatapsb_desc_type. +Specified as: a structured data of type spdatapsb_spmat_type.
info
Error code. @@ -151,48 +121,47 @@ Intent: out. An integer value; 0 means no error has been detected.
- -

Notes

    -
  1. Specifying psb_ovt_xhal_ for the extype argument - the user will obtain a descriptor for a domain partition in which - the additional layers are fetched as part of an (extended) halo; - however the index-to-process mapping is identical to that of the - base descriptor; +
  2. On exit from this routine the sparse matrix is in the build + state.
    3. -
  3. Specifying psb_ovt_asov_ for the extype argument - the user will obtain a descriptor with an overlapped decomposition: - the additional layer is aggregated to the local subdomain (and thus - is an overlap), and a new halo extending beyond the last additional - layer is formed. +
  4. The descriptor may be in either the build or assembled state. +
    5. +
  5. Providing a good estimate for the number of nonzeroes $nnz$ in + the assembled matrix may substantially improve performance in the + matrix build phase, as it will reduce or eliminate the need for + (potentially multiple) data reallocations.

- next - + up - previous - contents
- Next: psb_spall Allocates - Up: Data management routines - Previous: psb_cdfree Frees -   Next: psb_spins Insert + Up: Data management routines + Previous: psb_cdbldext Build +   Contents diff --git a/docs/html/node52.html b/docs/html/node52.html index f3150cba..d654ec48 100644 --- a/docs/html/node52.html +++ b/docs/html/node52.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_spall -- Allocates a sparse matrix - +psb_spins -- Insert a cloud of elements into a sparse matrix + @@ -20,56 +20,57 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_spins Insert - Up: Data management routines - Previous: psb_cdbldext Build -   Next: psb_spasb Sparse + Up: Data management routines + Previous: psb_spall Allocates +   Contents

-

-psb_spall -- Allocates a sparse matrix +

+psb_spins -- Insert a cloud of elements into a sparse + matrix 

-call psb_spall(a, desc_a, info, nnz)
+call psb_spins(nz, ia, ja, val, a, desc_a, info)

Type:
-
Synchronous. +
Asynchronous.
On Entry
-
desc_a
-
the communication descriptor. +
nz
+
the number of elements to be inserted.
Scope:local.
@@ -77,20 +78,65 @@ Type:required.
Intent: in.
-Specified as: a structured data of type descdatapsb_desc_type. +Specified as: an integer scalar.
-
nnz
-
An estimate of the number of nonzeroes in the local - part of the assembled matrix. +
ia
+
the row indices of the elements to be inserted.
-Scope: global. +Scope:local.
-Type: optional. +Type:required.
Intent: in.
-Specified as: an integer value. +Specified as: an integer array of size $nz$.
+
ja
+
the column indices of the elements to be inserted. +
+Scope:local. +
+Type:required. +
+Intent: in. +
+Specified as: an integer array of size $nz$. +
+
val
+
the elements to be inserted. +
+Scope:local. +
+Type:required. +
+Intent: in. +
+Specified as: an array of size $nz$. Must be of the same type and kind +of the aspk component of the sparse matrix $a$. +
+
desc_a
+
The communication descriptor. +
+Scope: local. +
+Type: required. +
+Intent: inout. +
+Specified as: a variable of type descdatapsb_desc_type. +

@@ -99,16 +145,27 @@ Specified as: an integer value.

a
-
the matrix to be allocated. +
the matrix into which elements will be inserted.
Scope:local
Type:required
-Intent: out. +Intent: inout.
Specified as: a structured data of type spdatapsb_spmat_type.
+
desc_a
+
The communication descriptor. +
+Scope: local. +
+Type: required. +
+Intent: inout. +
+Specified as: a variable of type descdatapsb_desc_type. +
info
Error code.
@@ -121,47 +178,59 @@ Intent: out. An integer value; 0 means no error has been detected.
+ +

Notes

    -
  1. On exit from this routine the sparse matrix is in the build - state. +
  2. On entry to this routine the descriptor may be in either the + build or assembled state.
    3. -
  3. The descriptor may be in either the build or assembled state. +
  4. On entry to this routine the sparse matrix may be in either the + build or update state.
    5. -
  5. Providing a good estimate for the number of nonzeroes $nnz$ in - the assembled matrix may substantially improve performance in the - matrix build phase, as it will reduce or eliminate the need for - (potentially multiple) data reallocations. +
  6. If the descriptor is in the build state, then the sparse matrix + must also be in the build state; the action of the routine is to + (implicitly) call psb_cdins to add entries to the sparsity + pattern; each sparse matrix entry implicitly defines a graph edge, + that is passed to the descriptor routine for the appropriate + processing. +
    7. +
  7. Any coefficients from matrix rows not assigned to the calling + process are silently ignored; +
    8. +
  8. If the descriptor is in the assembled state, then any entries in + the sparse matrix that would generate additional communication + requirements will be ignored; +
    9. +
  9. If the matrix is in the update state, any entries in positions + that were not present in the original matrix will be ignored.

- next - + up - previous - contents
- Next: psb_spins Insert - Up: Data management routines - Previous: psb_cdbldext Build -   Next: psb_spasb Sparse + Up: Data management routines + Previous: psb_spall Allocates +   Contents diff --git a/docs/html/node53.html b/docs/html/node53.html index 0f314239..645f2d12 100644 --- a/docs/html/node53.html +++ b/docs/html/node53.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_spins -- Insert a cloud of elements into a sparse matrix - +psb_spasb -- Sparse matrix assembly routine + @@ -20,57 +20,56 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_spasb Sparse - Up: Data management routines - Previous: psb_spall Allocates -   Next: psb_spfree Frees + Up: Data management routines + Previous: psb_spins Insert +   Contents

-

-psb_spins -- Insert a cloud of elements into a sparse - matrix +

+psb_spasb -- Sparse matrix assembly routine 

-call psb_spins(nz, ia, ja, val, a, desc_a, info)
+call psb_spasb(a, desc_a, info, afmt, upd, dupl)

Type:
-
Asynchronous. +
Synchronous.
On Entry
-
nz
-
the number of elements to be inserted. +
desc_a
+
the communication descriptor.
Scope:local.
@@ -78,65 +77,42 @@ Type:required.
Intent: in.
-Specified as: an integer scalar. +Specified as: a structured data of type descdatapsb_desc_type.
-
ia
-
the row indices of the elements to be inserted. +
afmt
+
the storage format for the sparse matrix.
-Scope:local. +Scope: global.
-Type:required. +Type: optional.
Intent: in.
-Specified as: an integer array of size $nz$. +Specified as: an array of characters. Defalt: 'CSR'.
-
ja
-
the column indices of the elements to be inserted. +
upd
+
Provide for updates to the matrix coefficients.
-Scope:local. +Scope: global.
-Type:required. +Type: optional.
Intent: in.
-Specified as: an integer array of size $nz$. +Specified as: integer, possible values: psb_upd_srch_, psb_upd_perm_
-
val
-
the elements to be inserted. +
dupl
+
How to handle duplicate coefficients.
-Scope:local. +Scope: global.
-Type:required. +Type: optional.
Intent: in.
-Specified as: an array of size $nz$. Must be of the same type and kind -of the aspk component of the sparse matrix $a$. +Specified as: integer, possible values: psb_dupl_ovwrt_, +psb_dupl_add_, psb_dupl_err_.
-
desc_a
-
The communication descriptor. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: a variable of type descdatapsb_desc_type. -

@@ -145,7 +121,7 @@ Specified as: a variable of type descdatapsb_desc_type.

a
-
the matrix into which elements will be inserted. +
the matrix to be assembled.
Scope:local
@@ -155,17 +131,6 @@ Intent: inout.
Specified as: a structured data of type spdatapsb_spmat_type.
-
desc_a
-
The communication descriptor. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: a variable of type descdatapsb_desc_type. -
info
Error code.
@@ -183,54 +148,48 @@ An integer value; 0 means no error has been detected. Notes
    -
  1. On entry to this routine the descriptor may be in either the - build or assembled state. +
  2. On entry to this routine the descriptor must be in the + assembled state, i.e. psb_cdasb must already have been called.
    3. -
  3. On entry to this routine the sparse matrix may be in either the - build or update state. +
  4. The sparse matrix may be in either the build or update state;
    5. -
  5. If the descriptor is in the build state, then the sparse matrix - must also be in the build state; the action of the routine is to - (implicitly) call psb_cdins to add entries to the sparsity - pattern; each sparse matrix entry implicitly defines a graph edge, - that is passed to the descriptor routine for the appropriate - processing. +
  6. Duplicate entries are detected and handled in both build and + update state, with the exception of the error action that is only + taken in the build state, i.e. on the first assembly;
    7. -
  7. Any coefficients from matrix rows not assigned to the calling - process are silently ignored; +
  8. If the update choice is psb_upd_perm_, then subsequent + calls to psb_spins to update the matrix must be arranged in + such a way as to produce exactly the same sequence of coefficient + values as encountered at the first assembly;
    9. -
  9. If the descriptor is in the assembled state, then any entries in - the sparse matrix that would generate additional communication - requirements will be ignored; -
    10. -
  10. If the matrix is in the update state, any entries in positions - that were not present in the original matrix will be ignored. +
  11. On exit from this routine the matrix is in the assembled state, + and thus is suitable for the computational routines.

- next - + up - previous - contents
- Next: psb_spasb Sparse - Up: Data management routines - Previous: psb_spall Allocates -   Next: psb_spfree Frees + Up: Data management routines + Previous: psb_spins Insert +   Contents diff --git a/docs/html/node54.html b/docs/html/node54.html index a5029e33..b20062ac 100644 --- a/docs/html/node54.html +++ b/docs/html/node54.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_spasb -- Sparse matrix assembly routine - +psb_spfree -- Frees a sparse matrix + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_spfree Frees - Up: Data management routines - Previous: psb_spins Insert -   Next: psb_sprn Reinit + Up: Data management routines + Previous: psb_spasb Sparse +   Contents

-

-psb_spasb -- Sparse matrix assembly routine +

+psb_spfree -- Frees a sparse matrix 

-call psb_spasb(a, desc_a, info, afmt, upd, dupl)
+call psb_spfree(a, desc_a, info)

@@ -68,50 +68,27 @@ call psb_spasb(a, desc_a, info, afmt, upd, dupl)

On Entry
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
afmt
-
the storage format for the sparse matrix. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an array of characters. Defalt: 'CSR'. -
-
upd
-
Provide for updates to the matrix coefficients. +
a
+
the matrix to be freed.
-Scope: global. +Scope:local
-Type: optional. +Type:required
-Intent: in. +Intent: inout.
-Specified as: integer, possible values: psb_upd_srch_, psb_upd_perm_ +Specified as: a structured data of type spdatapsb_spmat_type.
-
dupl
-
How to handle duplicate coefficients. +
desc_a
+
the communication descriptor.
-Scope: global. +Scope:local.
-Type: optional. +Type:required.
Intent: in.
-Specified as: integer, possible values: psb_dupl_ovwrt_, -psb_dupl_add_, psb_dupl_err_. +Specified as: a structured data of type descdatapsb_desc_type.
@@ -120,17 +97,6 @@ Specified as: integer, possible values: psb_dupl_ovwrt_,
On Return
-
a
-
the matrix to be assembled. -
-Scope:local -
-Type:required -
-Intent: inout. -
-Specified as: a structured data of type spdatapsb_spmat_type. -
info
Error code.
@@ -145,53 +111,7 @@ An integer value; 0 means no error has been detected.

-Notes - -

    -
  1. On entry to this routine the descriptor must be in the - assembled state, i.e. psb_cdasb must already have been called. -
    2. -
  2. The sparse matrix may be in either the build or update state; -
    3. -
  3. Duplicate entries are detected and handled in both build and - update state, with the exception of the error action that is only - taken in the build state, i.e. on the first assembly; -
    4. -
  4. If the update choice is psb_upd_perm_, then subsequent - calls to psb_spins to update the matrix must be arranged in - such a way as to produce exactly the same sequence of coefficient - values as encountered at the first assembly; -
    5. -
  5. On exit from this routine the matrix is in the assembled state, - and thus is suitable for the computational routines. -
    6. -
- -

-

- - -next - -up - -previous - -contents -
- Next: psb_spfree Frees - Up: Data management routines - Previous: psb_spins Insert -   Contents - +
diff --git a/docs/html/node55.html b/docs/html/node55.html index b84fe625..27c4e778 100644 --- a/docs/html/node55.html +++ b/docs/html/node55.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_spfree -- Frees a sparse matrix - +psb_sprn -- Reinit sparse matrix structure for psblas routines. + @@ -20,44 +20,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_sprn Reinit - Up: Data management routines - Previous: psb_spasb Sparse -   Next: psb_geall Allocates + Up: Data management routines + Previous: psb_spfree Frees +   Contents

-

-psb_spfree -- Frees a sparse matrix +

+psb_sprn -- Reinit sparse matrix structure for psblas + routines. 

-call psb_spfree(a, desc_a, info)
+call psb_sprn(a, decsc_a, info, clear)

@@ -69,7 +70,7 @@ call psb_spfree(a, desc_a, info)

a
-
the matrix to be freed. +
the matrix to be reinitialized.
Scope:local
@@ -90,6 +91,17 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
+
clear
+
Choose whether to zero out matrix coefficients +
+Scope:local. +
+Type:optional. +
+Intent: in. +
+Default: true. +

@@ -109,6 +121,13 @@ Intent: out. An integer value; 0 means no error has been detected. +Notes + +

    +
  1. On exit from this routine the sparse matrix is in the update + state. +
    2. +


diff --git a/docs/html/node56.html b/docs/html/node56.html index e4064a1e..3c7cfdd7 100644 --- a/docs/html/node56.html +++ b/docs/html/node56.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_sprn -- Reinit sparse matrix structure for psblas routines. - +psb_geall -- Allocates a dense matrix + @@ -20,45 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_geall Allocates - Up: Data management routines - Previous: psb_spfree Frees -   Next: psb_geins Dense + Up: Data management routines + Previous: psb_sprn Reinit +   Contents

-

-psb_sprn -- Reinit sparse matrix structure for psblas - routines. +

+psb_geall -- Allocates a dense matrix 

-call psb_sprn(a, decsc_a, info, clear)
+call psb_geall(x, desc_a, info, n, lb)

@@ -69,38 +68,52 @@ call psb_sprn(a, decsc_a, info, clear)

On Entry
-
a
-
the matrix to be reinitialized. +
desc_a
+
The communication descriptor.
-Scope:local +Scope: local
-Type:required +Type: required
-Intent: inout. +Intent: in.
-Specified as: a structured data of type spdatapsb_spmat_type. -
-
desc_a
-
the communication descriptor. +Specified as: a variable of type descdatapsb_desc_type. +
+
n
+
The number of columns of the dense matrix to be allocated.
-Scope:local. +Scope: local
-Type:required. +Type: optional
Intent: in.
-Specified as: a structured data of type descdatapsb_desc_type. +Specified as: Integer scalar, default $1$. It is not a valid argument if $x$ is a +rank-1 array.
-
clear
-
Choose whether to zero out matrix coefficients +
lb
+
The lower bound for the column index range of the dense matrix to be allocated.
-Scope:local. +Scope: local
-Type:optional. +Type: optional
Intent: in.
-Default: true. +Specified as: Integer scalar, default $1$. It is not a valid argument if $x$ is a +rank-1 array.
@@ -109,6 +122,18 @@ Default: true.
On Return
+
x
+
The dense matrix to be allocated. +
+Scope: local +
+Type: required +
+Intent: out. +
+Specified as: a rank one or two array with the ALLOCATABLE +attribute, of type real, complex or integer. +
info
Error code.
@@ -121,13 +146,6 @@ Intent: out. An integer value; 0 means no error has been detected.
-Notes - -
    -
  1. On exit from this routine the sparse matrix is in the update - state. -
    2. -


diff --git a/docs/html/node57.html b/docs/html/node57.html index dc8458b0..f8a07e95 100644 --- a/docs/html/node57.html +++ b/docs/html/node57.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geall -- Allocates a dense matrix - +psb_geins -- Dense matrix insertion routine + @@ -20,100 +20,123 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_geins Dense - Up: Data management routines - Previous: psb_sprn Reinit -   Next: psb_geasb Assembly + Up: Data management routines + Previous: psb_geall Allocates +   Contents

-

-psb_geall -- Allocates a dense matrix +

+psb_geins -- Dense matrix insertion routine 

-call psb_geall(x, desc_a, info, n, lb)
+call psb_geins(m, irw, val, x, desc_a, info,dupl)

Type:
-
Synchronous. +
Asynchronous.
On Entry
-
desc_a
-
The communication descriptor. +
m
+
Number of rows in $val$ to be inserted.
-Scope: local +Scope:local.
-Type: required +Type:required.
Intent: in.
-Specified as: a variable of type descdatapsb_desc_type. -
-
n
-
The number of columns of the dense matrix to be allocated. +Specified as: an integer value. +
+
irw
+
Indices of the rows to be inserted. Specifically, row $i$ + of $val$ will be inserted into the local row corresponding to the + global row index $irw(i)$. +Scope:local.
-Scope: local +Type:required. +
+Intent: in. +
+Specified as: an integer array. +
+
val
+
the dense submatrix to be inserted. +
+Scope:local.
-Type: optional +Type:required.
Intent: in.
-Specified as: Integer scalar, default $1$. It is not a valid argument if $x$ is a -rank-1 array. +Specified as: a rank 1 or 2 array. +Specified as: an integer value.
-
lb
-
The lower bound for the column index range of the dense matrix to be allocated. +
desc_a
+
the communication descriptor.
-Scope: local +Scope:local.
-Type: optional +Type:required.
Intent: in.
-Specified as: Integer scalar, default $1$. It is not a valid argument if $x$ is a -rank-1 array. +Specified as: a structured data of type descdatapsb_desc_type. +
+
dupl
+
How to handle duplicate coefficients. +
+Scope: global. +
+Type: optional. +
+Intent: in. +
+Specified as: integer, possible values: psb_dupl_ovwrt_, +psb_dupl_add_.
@@ -123,13 +146,13 @@ rank-1 array.
x
-
The dense matrix to be allocated. +
the output dense matrix.
Scope: local
Type: required
-Intent: out. +Intent: inout.
Specified as: a rank one or two array with the ALLOCATABLE attribute, of type real, complex or integer. @@ -148,7 +171,41 @@ An integer value; 0 means no error has been detected.

-

+Notes + +
    +
  1. Dense vectors/matrices do not have an associated state; +
    2. +
  2. Duplicate entries are either overwritten or added, there is no + provision for raising an error condition. +
    3. +
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: psb_geasb Assembly + Up: Data management routines + Previous: psb_geall Allocates +   Contents + diff --git a/docs/html/node58.html b/docs/html/node58.html index 63efe820..70d5c058 100644 --- a/docs/html/node58.html +++ b/docs/html/node58.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geins -- Dense matrix insertion routine - +psb_geasb -- Assembly a dense matrix + @@ -20,124 +20,65 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_geasb Assembly - Up: Data management routines - Previous: psb_geall Allocates -   Next: psb_gefree Frees + Up: Data management routines + Previous: psb_geins Dense +   Contents

-

-psb_geins -- Dense matrix insertion routine +

+psb_geasb -- Assembly a dense matrix 

-call psb_geins(m, irw, val, x, desc_a, info,dupl)
+call psb_geasb(x, desc_a, info)

Type:
-
Asynchronous. +
Synchronous.
On Entry
-
m
-
Number of rows in $val$ to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer value. -
-
irw
-
Indices of the rows to be inserted. Specifically, row $i$ - of $val$ will be inserted into the local row corresponding to the - global row index $irw(i)$. -Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer array. -
-
val
-
the dense submatrix to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a rank 1 or 2 array. -Specified as: an integer value. -
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. +
The communication descriptor.
-Specified as: a structured data of type descdatapsb_desc_type. -
-
dupl
-
How to handle duplicate coefficients. -
-Scope: global. +Scope: local
-Type: optional. +Type: required
Intent: in.
-Specified as: integer, possible values: psb_dupl_ovwrt_, -psb_dupl_add_. -
+Specified as: a variable of type descdatapsb_desc_type. +

@@ -146,7 +87,7 @@ Specified as: integer, possible values: psb_dupl_ovwrt_,

x
-
the output dense matrix. +
The dense matrix to be assembled.
Scope: local
@@ -169,43 +110,7 @@ Intent: out. An integer value; 0 means no error has been detected.
- -

-Notes - -

    -
  1. Dense vectors/matrices do not have an associated state; -
    2. -
  2. Duplicate entries are either overwritten or added, there is no - provision for raising an error condition. -
    3. -
- -

-

- - -next - -up - -previous - -contents -
- Next: psb_geasb Assembly - Up: Data management routines - Previous: psb_geall Allocates -   Contents - +
diff --git a/docs/html/node59.html b/docs/html/node59.html index ee570e06..5be73a71 100644 --- a/docs/html/node59.html +++ b/docs/html/node59.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_geasb -- Assembly a dense matrix - +psb_gefree -- Frees a dense matrix + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_gefree Frees - Up: Data management routines - Previous: psb_geins Dense -   Next: psb_gelp Applies + Up: Data management routines + Previous: psb_geasb Assembly +   Contents

-

-psb_geasb -- Assembly a dense matrix +

+psb_gefree -- Frees a dense matrix 

-call psb_geasb(x, desc_a, info)
+call psb_gefree(x, desc_a, info)

@@ -68,6 +68,21 @@ call psb_geasb(x, desc_a, info)

On Entry
+
x
+
The dense matrix to + be freed. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a rank one or two array with the ALLOCATABLE +attribute, of type real, complex or integer. +
+

+

desc_a
The communication descriptor.
@@ -86,18 +101,6 @@ Specified as: a variable of type descdatapsb_desc_type.
On Return
-
x
-
The dense matrix to be assembled. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array with the ALLOCATABLE -attribute, of type real, complex or integer. -
info
Error code.
@@ -110,6 +113,8 @@ Intent: out. An integer value; 0 means no error has been detected.
+ +


diff --git a/docs/html/node6.html b/docs/html/node6.html index dc134fd9..dc86daf7 100644 --- a/docs/html/node6.html +++ b/docs/html/node6.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Programming model - Up: Up: General overview - Previous: Previous: Library contents -   Contents

@@ -244,26 +244,26 @@ from optimal.

- next - up - previous - contents
- Next: Next: Programming model - Up: Up: General overview - Previous: Previous: Library contents -   Contents diff --git a/docs/html/node60.html b/docs/html/node60.html index 8b978d17..5438798f 100644 --- a/docs/html/node60.html +++ b/docs/html/node60.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_gefree -- Frees a dense matrix - +psb_gelp -- Applies a left permutation to a dense matrix + @@ -20,71 +20,80 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_gelp Applies - Up: Data management routines - Previous: psb_geasb Assembly -   Next: psb_glob_to_loc Global + Up: Data management routines + Previous: psb_gefree Frees +   Contents

-

-psb_gefree -- Frees a dense matrix +

+psb_gelp -- Applies a left permutation to a dense + matrix 

-call psb_gefree(x, desc_a, info)
+call psb_gelp(trans, iperm, x, info)

Type:
-
Synchronous. +
Asynchronous.
On Entry
-
x
-
The dense matrix to - be freed. +
trans
+
A character that specifies whether to permute $A$ or $A^T$.
Scope: local
Type: required
-Intent: inout. -
-Specified as: a rank one or two array with the ALLOCATABLE -attribute, of type real, complex or integer. +Intent: in.
-

-

-
desc_a
-
The communication descriptor. +Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$. +
+
iperm
+
An integer array containing permutation information.
Scope: local
@@ -92,7 +101,18 @@ Type: required
Intent: in.
-Specified as: a variable of type descdatapsb_desc_type. +Specified as: an integer one-dimensional array. +
+
x
+
The dense matrix to be permuted. +
+Scope: local +
+Type: required +
+Intent: inout. +
+Specified as: a one or two dimensional array.
diff --git a/docs/html/node61.html b/docs/html/node61.html index 36ee0116..14ebdb5a 100644 --- a/docs/html/node61.html +++ b/docs/html/node61.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_gelp -- Applies a left permutation to a dense matrix - +psb_glob_to_loc -- Global to local indices convertion + @@ -20,45 +20,46 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_glob_to_loc Global - Up: Data management routines - Previous: psb_gefree Frees -   Next: psb_loc_to_glob Local + Up: Data management routines + Previous: psb_gelp Applies +   Contents

-

-psb_gelp -- Applies a left permutation to a dense - matrix +

+psb_glob_to_loc -- Global to local indices + convertion 

-call psb_gelp(trans, iperm, x, info)
+call psb_glob_to_loc(x, y, desc_a, info, iact,owned)
+call psb_glob_to_loc(x, desc_a, info, iact,owned)

@@ -69,51 +70,51 @@ call psb_gelp(trans, iperm, x, info)

On Entry
-
trans
-
A character that specifies whether to permute $A$ or $A^T$. +
x
+
An integer vector of indices to be converted.
Scope: local
Type: required
-Intent: in. +Intent: in, inout.
-Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$. +Specified as: a rank one integer array.
-
iperm
-
An integer array containing permutation information. +
desc_a
+
the communication descriptor.
-Scope: local +Scope:local.
-Type: required +Type:required.
Intent: in.
-Specified as: an integer one-dimensional array. -
-
x
-
The dense matrix to be permuted. +Specified as: a structured data of type descdatapsb_desc_type. +
+
iact
+
specifies action to be taken in case of range errors. +Scope: global
-Scope: local +Type: optional
-Type: required +Intent: in.
-Intent: inout. +Specified as: a character variable Ignore, Warning or +Abort, default Ignore. +
+
owned
+
Specfies valid range of input +Scope: global
-Specified as: a one or two dimensional array. -
+Type: optional +
+Intent: in. +
+If true, then only indices strictly owned by the current process are +considered valid, if false then halo indices are also +accepted. Default: false. +

@@ -121,6 +122,44 @@ Specified as: a one or two dimensional array.

On Return
+
x
+
If $y$ is not present, + then $x$ is overwritten with the translated integer indices. +Scope: global +
+Type: required +
+Intent: inout. +
+Specified as: a rank one integer array. +
+
y
+
If $y$ is present, + then $y$ is overwritten with the translated integer indices, and $x$ + is left unchanged. +Scope: global +
+Type: optional +
+Intent: out. +
+Specified as: a rank one integer array. +
info
Error code.
@@ -135,7 +174,42 @@ An integer value; 0 means no error has been detected.

-

+Notes + +
    +
  1. If an input index is out of range, then the corresponding output + index is set to a negative number; +
    2. +
  2. The default Ignore means that the negative output is the + only action taken on an out-of-range input. +
    3. +
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: psb_loc_to_glob Local + Up: Data management routines + Previous: psb_gelp Applies +   Contents + diff --git a/docs/html/node62.html b/docs/html/node62.html index 3ec5cbd7..2023f791 100644 --- a/docs/html/node62.html +++ b/docs/html/node62.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_glob_to_loc -- Global to local indices convertion - +psb_loc_to_glob -- Local to global indices conversion + @@ -20,46 +20,46 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_loc_to_glob Local - Up: Data management routines - Previous: psb_gelp Applies -   Next: psb_is_owned + Up: Data management routines + Previous: psb_glob_to_loc Global +   Contents

-

-psb_glob_to_loc -- Global to local indices - convertion +

+psb_loc_to_glob -- Local to global indices + conversion 

-call psb_glob_to_loc(x, y, desc_a, info, iact,owned)
-call psb_glob_to_loc(x, desc_a, info, iact,owned)
+call psb_loc_to_glob(x, y, desc_a, info, iact)
+call psb_loc_to_glob(x, desc_a, info, iact)

@@ -103,18 +103,6 @@ Intent: in. Specified as: a character variable Ignore, Warning or Abort, default Ignore.

-
owned
-
Specfies valid range of input -Scope: global -
-Type: optional -
-Intent: in. -
-If true, then only indices strictly owned by the current process are -considered valid, if false then halo indices are also -accepted. Default: false. -

@@ -125,11 +113,11 @@ accepted. Default: false.

x
If $y$ is not present, then $x$ is overwritten with the translated integer indices. Scope: global
@@ -142,14 +130,14 @@ Specified as: a rank one integer array.
y
If $y$ is present, + SRC="img28.png" + ALT="$y$"> is not present, then $y$ is overwritten with the translated integer indices, and $x$ is left unchanged. Scope: global @@ -173,41 +161,29 @@ An integer value; 0 means no error has been detected.
-

-Notes - -

    -
  1. If an input index is out of range, then the corresponding output - index is set to a negative number; -
    2. -
  2. The default Ignore means that the negative output is the - only action taken on an out-of-range input. -
    3. -
-

- next - + up - previous - contents
- Next: psb_loc_to_glob Local - Up: Data management routines - Previous: psb_gelp Applies -   Next: psb_is_owned + Up: Data management routines + Previous: psb_glob_to_loc Global +   Contents diff --git a/docs/html/node63.html b/docs/html/node63.html index 02adc208..8d314d3f 100644 --- a/docs/html/node63.html +++ b/docs/html/node63.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_loc_to_glob -- Local to global indices conversion - +psb_is_owned + @@ -20,46 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_is_owned - Up: Data management routines - Previous: psb_glob_to_loc Global -   Next: psb_owned_index + Up: Data management routines + Previous: psb_loc_to_glob Local +   Contents

-

-psb_loc_to_glob -- Local to global indices - conversion +

+psb_is_owned 

-call psb_loc_to_glob(x, y, desc_a, info, iact)
-call psb_loc_to_glob(x, desc_a, info, iact)
+call psb_is_owned(x, desc_a)

@@ -71,15 +69,15 @@ call psb_loc_to_glob(x, desc_a, info, iact)

x
-
An integer vector of indices to be converted. +
Integer index.
Scope: local
Type: required
-Intent: in, inout. +Intent: in.
-Specified as: a rank one integer array. +Specified as: a scalar integer.
desc_a
the communication descriptor. @@ -92,17 +90,6 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
-
iact
-
specifies action to be taken in case of range errors. -Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: a character variable Ignore, Warning or -Abort, default Ignore. -

@@ -110,82 +97,32 @@ Specified as: a character variable Ignore, Warning or

On Return
-
x
-
If $y$ is not present, - then $x$ is overwritten with the translated integer indices. -Scope: global -
-Type: required -
-Intent: inout. -
-Specified as: a rank one integer array. -
-
y
-
If $y$ is not present, - then $y$ is overwritten with the translated integer indices, and Function value +
A logical mask which is true if + $x$ - is left unchanged. -Scope: global -
-Type: optional -
-Intent: out. -
-Specified as: a rank one integer array. -
-
info
-
Error code. -
+ SRC="img27.png" + ALT="$x$"> is owned by the current process Scope: local
-Type: required +Type: required
Intent: out. -
-An integer value; 0 means no error has been detected. -
+

-

- - -next - -up - -previous - -contents -
- Next: psb_is_owned - Up: Data management routines - Previous: psb_glob_to_loc Global -   Contents - +Notes + +
    +
  1. This routine returns a .true. value for an index + that is strictly owned by the current process, excluding the halo + indices +
    2. +
+ +

+

diff --git a/docs/html/node64.html b/docs/html/node64.html index edf09ef0..effa9e8e 100644 --- a/docs/html/node64.html +++ b/docs/html/node64.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_is_owned - +psb_owned_index + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_owned_index - Up: Data management routines - Previous: psb_loc_to_glob Local -   Next: psb_is_local + Up: Data management routines + Previous: psb_is_owned +   Contents

-

-psb_is_owned +

+psb_owned_index 

-call psb_is_owned(x, desc_a)
+call psb_owned_index(y, x, desc_a, info)

@@ -69,15 +69,15 @@ call psb_is_owned(x, desc_a)

x
-
Integer index. +
Integer indices.
Scope: local
Type: required
-Intent: in. +Intent: in, inout.
-Specified as: a scalar integer. +Specified as: a scalar or a rank one integer array.
desc_a
the communication descriptor. @@ -90,6 +90,17 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
+
iact
+
specifies action to be taken in case of range errors. +Scope: global +
+Type: optional +
+Intent: in. +
+Specified as: a character variable Ignore, Warning or +Abort, default Ignore. +

@@ -97,26 +108,39 @@ Specified as: a structured data of type descdatapsb_desc_type.

On Return
-
Function value
-
A logical mask which is true if +
y
+
A logical mask which is true for all corresponding entries of $x$ is owned by the current process + SRC="img27.png" + ALT="$x$"> that are owned by the current process Scope: local
Type: required
Intent: out. -
+
+Specified as: a scalar or rank one logical array. + +
info
+
Error code. +
+Scope: local +
+Type: required +
+Intent: out. +
+An integer value; 0 means no error has been detected. +

Notes

    -
  1. This routine returns a .true. value for an index - that is strictly owned by the current process, excluding the halo +
  2. This routine returns a .true. value for those indices + that are strictly owned by the current process, excluding the halo indices
diff --git a/docs/html/node65.html b/docs/html/node65.html index cbabc713..dc100621 100644 --- a/docs/html/node65.html +++ b/docs/html/node65.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_owned_index - +psb_is_local + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_is_local - Up: Data management routines - Previous: psb_is_owned -   Next: psb_local_index + Up: Data management routines + Previous: psb_owned_index +   Contents

-

-psb_owned_index +

+psb_is_local 

-call psb_owned_index(y, x, desc_a, info)
+call psb_is_local(x, desc_a)

@@ -69,15 +69,15 @@ call psb_owned_index(y, x, desc_a, info)

x
-
Integer indices. +
Integer index.
Scope: local
Type: required
-Intent: in, inout. +Intent: in.
-Specified as: a scalar or a rank one integer array. +Specified as: a scalar integer.
desc_a
the communication descriptor. @@ -90,17 +90,6 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
-
iact
-
specifies action to be taken in case of range errors. -Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: a character variable Ignore, Warning or -Abort, default Ignore. -

@@ -108,39 +97,26 @@ Specified as: a character variable Ignore, Warning or

On Return
-
y
-
A logical mask which is true for all corresponding entries of +
Function value
+
A logical mask which is true if $x$ that are owned by the current process + SRC="img27.png" + ALT="$x$"> is local to the current process Scope: local
Type: required
Intent: out. -
-Specified as: a scalar or rank one logical array. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
+

Notes

    -
  1. This routine returns a .true. value for those indices - that are strictly owned by the current process, excluding the halo +
  2. This routine returns a .true. value for an index + that is local to the current process, including the halo indices
diff --git a/docs/html/node66.html b/docs/html/node66.html index 7e4a7d06..ece8a0cd 100644 --- a/docs/html/node66.html +++ b/docs/html/node66.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_is_local - +psb_local_index + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_local_index - Up: Data management routines - Previous: psb_owned_index -   Next: psb_get_boundary Extract + Up: Data management routines + Previous: psb_is_local +   Contents

-

-psb_is_local +

+psb_local_index 

-call psb_is_local(x, desc_a)
+call psb_local_index(y, x, desc_a, info)

@@ -69,15 +69,15 @@ call psb_is_local(x, desc_a)

x
-
Integer index. +
Integer indices.
Scope: local
Type: required
-Intent: in. +Intent: in, inout.
-Specified as: a scalar integer. +Specified as: a scalar or a rank one integer array.
desc_a
the communication descriptor. @@ -90,6 +90,17 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
+
iact
+
specifies action to be taken in case of range errors. +Scope: global +
+Type: optional +
+Intent: in. +
+Specified as: a character variable Ignore, Warning or +Abort, default Ignore. +

@@ -97,27 +108,40 @@ Specified as: a structured data of type descdatapsb_desc_type.

On Return
-
Function value
-
A logical mask which is true if +
y
+
A logical mask which is true for all corresponding entries of $x$ is local to the current process + SRC="img27.png" + ALT="$x$"> that are local to the current process Scope: local
Type: required
Intent: out. -
+
+Specified as: a scalar or rank one logical array. + +
info
+
Error code. +
+Scope: local +
+Type: required +
+Intent: out. +
+An integer value; 0 means no error has been detected. +

Notes

    -
  1. This routine returns a .true. value for an index - that is local to the current process, including the halo - indices +
  2. This routine returns a .true. value for those indices + that are local to the current process, including the halo + indices.
diff --git a/docs/html/node67.html b/docs/html/node67.html index 51d15938..7c971837 100644 --- a/docs/html/node67.html +++ b/docs/html/node67.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_local_index - +psb_get_boundary -- Extract list of boundary elements + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_get_boundary Extract - Up: Data management routines - Previous: psb_is_local -   Next: psb_get_overlap Extract + Up: Data management routines + Previous: psb_local_index +   Contents

-

-psb_local_index +

+psb_get_boundary -- Extract list of boundary elements 

-call psb_local_index(y, x, desc_a, info)
+call psb_get_boundary(bndel, desc, info)

@@ -68,18 +68,7 @@ call psb_local_index(y, x, desc_a, info)

On Entry
-
x
-
Integer indices. -
-Scope: local -
-Type: required -
-Intent: in, inout. -
-Specified as: a scalar or a rank one integer array. -
-
desc_a
+
desc
the communication descriptor.
Scope:local. @@ -90,17 +79,6 @@ Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.
-
iact
-
specifies action to be taken in case of range errors. -Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: a character variable Ignore, Warning or -Abort, default Ignore. -

@@ -108,20 +86,19 @@ Specified as: a character variable Ignore, Warning or

On Return
-
y
-
A logical mask which is true for all corresponding entries of - $x$ that are local to the current process +
bndel
+
The list of boundary elements on the calling process, in + local numbering. +
Scope: local
Type: required
Intent: out.
-Specified as: a scalar or rank one logical array. -
+Specified as: a rank one array with the ALLOCATABLE +attribute, of type integer. +
info
Error code.
@@ -139,9 +116,12 @@ An integer value; 0 means no error has been detected. Notes
    -
  1. This routine returns a .true. value for those indices - that are local to the current process, including the halo - indices. +
  2. If there are no boundary elements (i.e., if the local part of + the connectivity graph is self-contained) the output vector is set + to the ``not allocated'' state. +
    3. +
  3. Otherwise the size of bndel will be exactly equal to the + number of boundary elements.
diff --git a/docs/html/node68.html b/docs/html/node68.html index f7683aa0..541a261b 100644 --- a/docs/html/node68.html +++ b/docs/html/node68.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_get_boundary -- Extract list of boundary elements - +psb_get_overlap -- Extract list of overlap elements + @@ -20,44 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_get_overlap Extract - Up: Data management routines - Previous: psb_local_index -   Next: psb_sp_getrow Extract + Up: Data management routines + Previous: psb_get_boundary Extract +   Contents

-

-psb_get_boundary -- Extract list of boundary elements +

+psb_get_overlap -- Extract list of overlap elements 

-call psb_get_boundary(bndel, desc, info)
+call psb_get_overlap(ovrel, desc, info)

@@ -86,8 +86,8 @@ Specified as: a structured data of type descdatapsb_desc_type.

On Return
-
bndel
-
The list of boundary elements on the calling process, in +
ovrel
+
The list of overlap elements on the calling process, in local numbering.
Scope: local @@ -116,12 +116,11 @@ An integer value; 0 means no error has been detected. Notes
    -
  1. If there are no boundary elements (i.e., if the local part of - the connectivity graph is self-contained) the output vector is set - to the ``not allocated'' state. +
  2. If there are no overlap elements the output vector is set + to the ``not allocated'' state.
    3. -
  3. Otherwise the size of bndel will be exactly equal to the - number of boundary elements. +
  4. Otherwise the size of ovrel will be exactly equal to the + number of overlap elements.
diff --git a/docs/html/node69.html b/docs/html/node69.html index c63d8c80..8e12aee7 100644 --- a/docs/html/node69.html +++ b/docs/html/node69.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_get_overlap -- Extract list of overlap elements - +psb_sp_getrow -- Extract row(s) from a sparse matrix + @@ -20,44 +20,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_sp_getrow Extract - Up: Data management routines - Previous: psb_get_boundary Extract -   Next: psb_sizeof Memory + Up: Data management routines + Previous: psb_get_overlap Extract +   Contents

-

-psb_get_overlap -- Extract list of overlap elements +

+psb_sp_getrow -- Extract row(s) from a sparse matrix 

-call psb_get_overlap(ovrel, desc, info)
+call psb_sp_getrow(row, a, nz, ia, ja, val, info, &
+              & append, nzin, lrw)

@@ -68,16 +69,75 @@ call psb_get_overlap(ovrel, desc, info)

On Entry
-
desc
-
the communication descriptor. +
row
+
The (first) row to be extracted.
-Scope:local. +Scope:local
-Type:required. +Type:required +
+Intent: in. +
+Specified as: an integer $>0$. +
+
a
+
the matrix from which to get rows. +
+Scope:local +
+Type:required +
+Intent: in. +
+Specified as: a structured data of type spdatapsb_spmat_type. +
+
append
+
Whether to append or overwrite existing output. +
+Scope:local +
+Type:optional
Intent: in.
-Specified as: a structured data of type descdatapsb_desc_type. +Specified as: a logical value default: false (overwrite). +
+
nzin
+
Input size to be appended to. +
+Scope:local +
+Type:optional +
+Intent: in. +
+Specified as: an integer $>0$. When append is true, specifies how many +entries in the output vectors are already filled. +
+
lrw
+
The last row to be extracted. +
+Scope:local +
+Type:optional +
+Intent: in. +
+Specified as: an integer $>0$, default: $row$. + +

@@ -86,19 +146,50 @@ Specified as: a structured data of type descdatapsb_desc_type.
On Return
-
ovrel
-
The list of overlap elements on the calling process, in - local numbering. +
nz
+
the number of elements returned by this call.
-Scope: local +Scope:local.
-Type: required +Type:required.
Intent: out.
-Specified as: a rank one array with the ALLOCATABLE -attribute, of type integer. -
+Returned as: an integer scalar. + +
ia
+
the row indices. +
+Scope:local. +
+Type:required. +
+Intent: inout. +
+Specified as: an integer array with the ALLOCATABLE attribute. +
+
ja
+
the column indices of the elements to be inserted. +
+Scope:local. +
+Type:required. +
+Intent: inout. +
+Specified as: an integer array with the ALLOCATABLE attribute. +
+
val
+
the elements to be inserted. +
+Scope:local. +
+Type:required. +
+Intent: inout. +
+Specified as: a real array with the ALLOCATABLE attribute. +
info
Error code.
@@ -116,16 +207,51 @@ An integer value; 0 means no error has been detected. Notes
    -
  1. If there are no overlap elements the output vector is set - to the ``not allocated'' state. +
  2. The output $nz$ is always the size of the output generated by + the current call; thus, if append=.true., the total output + size will be $nzin+nz$, with the newly extracted coefficients stored in + entries nzin+1:nzin+nz of the array arguments;
    3. -
  3. Otherwise the size of ovrel will be exactly equal to the - number of overlap elements. +
  4. When append=.true. the output arrays are reallocated as + necessary; +
    5. +
  5. The row and column indices are returned in the local numbering + scheme; if the global numbering is desired, the user may employ the + psb_loc_to_glob routine on the output.

-

+
+ + +next + +up + +previous + +contents +
+ Next: psb_sizeof Memory + Up: Data management routines + Previous: psb_get_overlap Extract +   Contents + diff --git a/docs/html/node7.html b/docs/html/node7.html index 182e2bd3..1733c683 100644 --- a/docs/html/node7.html +++ b/docs/html/node7.html @@ -25,26 +25,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Data Structures - Up: Up: General overview - Previous: Previous: Application structure -   Contents

@@ -72,7 +72,7 @@ the tools routines.

However there are many cases where no synchronization, and indeed no communication among processes, is implied; for instance, all the routines in -sec. 3.5 are only acting on the local data structures, +sec. 3.5 are only acting on the local data structures, and thus may be called independently. The most important case is that of the coefficient insertion routines: since the number of coefficients in the sparse and dense matrices varies among the @@ -96,26 +96,26 @@ as:

- next - up - previous - contents
- Next: Next: Data Structures - Up: Up: General overview - Previous: Previous: Application structure -   Contents diff --git a/docs/html/node70.html b/docs/html/node70.html index 71cb73cb..311730e3 100644 --- a/docs/html/node70.html +++ b/docs/html/node70.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_sp_getrow -- Extract row(s) from a sparse matrix - +psb_sizeof -- Memory occupation + @@ -20,45 +20,49 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_sizeof Memory - Up: Data management routines - Previous: psb_get_overlap Extract -   Next: Sorting utilities + Up: Data management routines + Previous: psb_sp_getrow Extract +   Contents

-

-psb_sp_getrow -- Extract row(s) from a sparse matrix +

+psb_sizeof -- Memory occupation

+

+This function computes the memory occupation of a PSBLAS object. + 

-call psb_sp_getrow(row, a, nz, ia, ja, val, info, &
-              & append, nzin, lrw)
+isz = psb_sizeof(a)
+isz = psb_sizeof(desc_a)
+isz = psb_sizeof(prec)

@@ -69,189 +73,56 @@ call psb_sp_getrow(row, a, nz, ia, ja, val, info, &

On Entry
-
row
-
The (first) row to be extracted. -
-Scope:local -
-Type:required -
-Intent: in. -
-Specified as: an integer $>0$. -
a
-
the matrix from which to get rows. +
A sparse matrix +$A$.
-Scope:local +Scope: local
-Type:required +Type: required
Intent: in.
Specified as: a structured data of type spdatapsb_spmat_type.
-
append
-
Whether to append or overwrite existing output. -
-Scope:local -
-Type:optional -
-Intent: in. +
desc_a
+
Communication descriptor.
-Specified as: a logical value default: false (overwrite). -
-
nzin
-
Input size to be appended to. -
-Scope:local +Scope: local
-Type:optional +Type: required
Intent: in.
-Specified as: an integer $>0$. When append is true, specifies how many -entries in the output vectors are already filled. +Specified as: a structured data of type descdatapsb_desc_type.
-
lrw
-
The last row to be extracted. -
-Scope:local +
prec
+
Scope: local
-Type:optional +Type: required
Intent: in.
-Specified as: an integer $>0$, default: $row$. - -

+Specified as: a preconditioner data structure precdatapsb_prec_type.

- - -

-

On Return
-
nz
-
the number of elements returned by this call. -
-Scope:local. -
-Type:required. -
-Intent: out. -
-Returned as: an integer scalar. -
-
ia
-
the row indices. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: an integer array with the ALLOCATABLE attribute. -
-
ja
-
the column indices of the elements to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: an integer array with the ALLOCATABLE attribute. -
-
val
-
the elements to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: a real array with the ALLOCATABLE attribute. -
-
info
-
Error code. +
Function value
+
The memory occupation of the object specified in + the calling sequence, in bytes.
Scope: local
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. +Returned as: an integer(psb_long_int_k_) number.

-Notes - -

    -
  1. The output $nz$ is always the size of the output generated by - the current call; thus, if append=.true., the total output - size will be $nzin+nz$, with the newly extracted coefficients stored in - entries nzin+1:nzin+nz of the array arguments; -
    2. -
  2. When append=.true. the output arrays are reallocated as - necessary; -
    3. -
  3. The row and column indices are returned in the local numbering - scheme; if the global numbering is desired, the user may employ the - psb_loc_to_glob routine on the output. -
    4. -
- -

-

- - -next - -up - -previous - -contents -
- Next: psb_sizeof Memory - Up: Data management routines - Previous: psb_get_overlap Extract -   Contents - +
diff --git a/docs/html/node71.html b/docs/html/node71.html index 1c34bc51..ffb6d548 100644 --- a/docs/html/node71.html +++ b/docs/html/node71.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_sizeof -- Memory occupation - +Sorting utilities + @@ -18,111 +18,276 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: Sorting utilities - Up: Data management routines - Previous: psb_sp_getrow Extract -   Next: Parallel environment routines + Up: Data management routines + Previous: psb_sizeof Memory +   Contents

-

-psb_sizeof -- Memory occupation +

+Sorting utilities

-This function computes the memory occupation of a PSBLAS object. +psb_msort -- Sorting by the Merge-sort + algorithm

+psb_qsort -- Sorting by the Quicksort + algorithm + +

+psb_hsort -- Sorting by the Heapsort algorithm 

-isz = psb_sizeof(a)
-isz = psb_sizeof(desc_a)
-isz = psb_sizeof(prec)
+call psb_msort(x,ix,dir,flag)
+call psb_qsort(x,ix,dir,flag)
+call psb_hsort(x,ix,dir,flag)

+These serial routines sort a sequence $X$ into ascending or +descending order. The argument meaning is identical for the three +calls; the only difference is the algorithm used to accomplish the +task (see Usage Notes below).

Type:
Asynchronous.
-
On Entry
+
On Entry
-
a
-
A sparse matrix -$A$. +
x
+
The sequence to be sorted.
-Scope: local +Type:required.
-Type: required -
-Intent: in. -
-Specified as: a structured data of type spdatapsb_spmat_type. +Specified as: an integer, real or complex array of rank 1.
-
desc_a
-
Communication descriptor. +
ix
+
A vector of indices.
-Scope: local +Type:optional.
-Type: required +Specified as: an integer array of (at least) the same size as $X$. +
+
dir
+
The desired ordering.
-Intent: in. +Type:optional.
-Specified as: a structured data of type descdatapsb_desc_type. +Specified as: an integer value:
+
Integer and real data:
+
psb_sort_up_, +psb_sort_down_, psb_asort_up_, psb_asort_down_; +default psb_sort_up_.
-
prec
-
Scope: local -
-Type: required +
Complex data:
+
psb_lsort_up_, +psb_lsort_down_, psb_asort_up_, psb_asort_down_; +default psb_lsort_up_. +
+
+
+
flag
+
Whether to keep the original values in $IX$.
-Intent: in. +Type:optional.
-Specified as: a preconditioner data structure precdatapsb_prec_type. +Specified as: an integer value psb_sort_ovw_idx_ or +psb_sort_keep_idx_; default psb_sort_ovw_idx_. + +

+
+ +

+

On Return
-
Function value
-
The memory occupation of the object specified in - the calling sequence, in bytes. +
x
+
The sequence of values, in the chosen ordering.
-Scope: local +Type:required.
-Returned as: an integer(psb_long_int_k_) number. +Specified as: an integer, real or complex array of rank 1. +
+
ix
+
A vector of indices. +
+Type: Optional +
+An integer array of rank 1, whose entries are moved to the same +position as the corresponding entries in $x$.

-

+ +

+Notes + +

    +
  1. For integer or real data the sorting can be performed in the up/down direction, on the + natural or absolute values; +
    2. +
  2. For complex data the sorting can be done in a lexicographic + order (i.e.: sort on the real part with ties broken according to + the imaginary part) or on the absolute values; +
    3. +
  3. The routines return the items in the chosen ordering; the + output difference is the handling of ties (i.e. items with an + equal value) in the original input. With the merge-sort algorithm + ties are preserved in the same relative order as they had in the + original sequence, while this is not guaranteed for quicksort or + heapsort; +
    4. +
  4. If +$flag = psb\_sort\_ovw\_idx\_$ then the entries in $ix(1:n)$ + where $n$ is the size of $x$ are initialized to +$ix(i) \leftarrow +i$; thus, upon return from the subroutine, for each + index $i$ we have in $ix(i)$ the position that the item $x(i)$ + occupied in the original data sequence; +
    5. +
  5. If +$flag = psb\_sort\_keep\_idx\_$ the routine will assume that + the entries in $ix(:)$ have already been initialized by the user; +
    6. +
  6. The three sorting algorithms have a similar $O(n \log n)$ expected + running time; in the average case quicksort will be the + fastest and merge-sort the slowest. However note that: + +
      +
    1. The worst case running time for quicksort is $O(n^2)$; the algorithm + implemented here follows the well-known median-of-three heuristics, + but the worst case may still apply; +
      2. +
    2. The worst case running time for merge-sort and heap-sort is + $O(n \log n)$ as the average case; +
      3. +
    3. The merge-sort algorithm is implemented to take advantage of + subsequences that may be already in the desired ordering prior to + the subroutine call; this situation is relatively common when + dealing with groups of indices of sparse matrix entries, thus + merge-sort is often the preferred choice when a sorting is needed + by other routines in the library. +
      4. +
    +
    7. +
+ +

+ +

+

+ + +next + +up + +previous + +contents +
+ Next: Parallel environment routines + Up: Data management routines + Previous: psb_sizeof Memory +   Contents + diff --git a/docs/html/node72.html b/docs/html/node72.html index dd9331c4..1eb18f5b 100644 --- a/docs/html/node72.html +++ b/docs/html/node72.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Sorting utilities - +Parallel environment routines + @@ -18,276 +18,88 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Parallel environment routines - Up: Data management routines - Previous: psb_sizeof Memory -   Next: psb_init Initializes + Up: userhtml + Previous: Sorting utilities +   Contents

-

-Sorting utilities -

- -

-psb_msort -- Sorting by the Merge-sort - algorithm - -

-psb_qsort -- Sorting by the Quicksort - algorithm - -

-psb_hsort -- Sorting by the Heapsort algorithm -

-call psb_msort(x,ix,dir,flag)
-call psb_qsort(x,ix,dir,flag)
-call psb_hsort(x,ix,dir,flag)
-
- -

-These serial routines sort a sequence $X$ into ascending or -descending order. The argument meaning is identical for the three -calls; the only difference is the algorithm used to accomplish the -task (see Usage Notes below). -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
The sequence to be sorted. -
-Type:required. -
-Specified as: an integer, real or complex array of rank 1. -
-
ix
-
A vector of indices. -
-Type:optional. -
-Specified as: an integer array of (at least) the same size as $X$. -
-
dir
-
The desired ordering. -
-Type:optional. -
-Specified as: an integer value:
-
Integer and real data:
-
psb_sort_up_, -psb_sort_down_, psb_asort_up_, psb_asort_down_; -default psb_sort_up_. -
-
Complex data:
-
psb_lsort_up_, -psb_lsort_down_, psb_asort_up_, psb_asort_down_; -default psb_lsort_up_. -
-
-
-
flag
-
Whether to keep the original values in $IX$. -
-Type:optional. -
-Specified as: an integer value psb_sort_ovw_idx_ or -psb_sort_keep_idx_; default psb_sort_ovw_idx_. - -

-

-
- -

-

-
On Return
-
-
-
x
-
The sequence of values, in the chosen ordering. +

+
-Type:required. -
-Specified as: an integer, real or complex array of rank 1. -

-
ix
-
A vector of indices. -
-Type: Optional -
-An integer array of rank 1, whose entries are moved to the same -position as the corresponding entries in $x$. -
-
- -

- -

-Notes - -

    -
  1. For integer or real data the sorting can be performed in the up/down direction, on the - natural or absolute values; -
    2. -
  2. For complex data the sorting can be done in a lexicographic - order (i.e.: sort on the real part with ties broken according to - the imaginary part) or on the absolute values; -
    3. -
  3. The routines return the items in the chosen ordering; the - output difference is the handling of ties (i.e. items with an - equal value) in the original input. With the merge-sort algorithm - ties are preserved in the same relative order as they had in the - original sequence, while this is not guaranteed for quicksort or - heapsort; -
    4. -
  4. If -$flag = psb\_sort\_ovw\_idx\_$ then the entries in $ix(1:n)$ - where $n$ is the size of $x$ are initialized to -$ix(i) \leftarrow -i$; thus, upon return from the subroutine, for each - index $i$ we have in $ix(i)$ the position that the item $x(i)$ - occupied in the original data sequence; -
    5. -
  5. If -$flag = psb\_sort\_keep\_idx\_$ the routine will assume that - the entries in $ix(:)$ have already been initialized by the user; -
    6. -
  6. The three sorting algorithms have a similar $O(n \log n)$ expected - running time; in the average case quicksort will be the - fastest and merge-sort the slowest. However note that: - -
      -
    1. The worst case running time for quicksort is $O(n^2)$; the algorithm - implemented here follows the well-known median-of-three heuristics, - but the worst case may still apply; -
      2. -
    2. The worst case running time for merge-sort and heap-sort is - $O(n \log n)$ as the average case; -
      3. -
    3. The merge-sort algorithm is implemented to take advantage of - subsequences that may be already in the desired ordering prior to - the subroutine call; this situation is relatively common when - dealing with groups of indices of sparse matrix entries, thus - merge-sort is often the preferred choice when a sorting is needed - by other routines in the library. -
      4. -
    -
    7. -
+Parallel environment routines +

- -

-

- - -next - -up - -previous - -contents -
- Next: Parallel environment routines - Up: Data management routines - Previous: psb_sizeof Memory -   Contents - +
+ +Subsections + + + +
diff --git a/docs/html/node73.html b/docs/html/node73.html index 1a5b7433..3d0cfa8a 100644 --- a/docs/html/node73.html +++ b/docs/html/node73.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Parallel environment routines - +psb_init -- Initializes PSBLAS parallel environment + @@ -18,88 +18,161 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - - + + + - next - + up - previous - contents
- Next: psb_init Initializes - Up: userhtml - Previous: Sorting utilities -   Next: psb_info Return + Up: Parallel environment routines + Previous: Parallel environment routines +   Contents

-

- +

+psb_init -- Initializes PSBLAS parallel environment +

+ +

+

+call psb_init(icontxt, np, basectxt, ids)
+
+ +

+This subroutine initializes the PSBLAS parallel environment, defining +a virtual parallel machine. +

+
Type:
+
Synchronous. +
+
On Entry
+
+
+
np
+
Number of processes in the PSBLAS virtual parallel machine. +
+Scope: global. +
+Type: optional. +
+Intent: in. +
+Specified as: an integer value. Default: use all available processes. +
+
basectxt
+
the initial communication context. The new context + will be defined from the processes participating in the initial one.
-Parallel environment routines - +Scope: global. +
+Type: optional. +
+Intent: in. +
+Specified as: an integer value. Default: use MPI_COMM_WORLD. +
+
ids
+
Identities of the processes to use for the new context; the + argument is ignored when np is not specified. This allows the + processes in the new environment to be in an order different from the + original one. +
+Scope: global. +
+Type: optional. +
+Intent: in. +
+Specified as: an integer array. Default: use the indices $(0\dots np-1)$. +
+

-

- -Subsections +
+
On Return
+
+
+
icontxt
+
the communication context identifying the virtual + parallel machine. Note that this is always a duplicate of + basectxt, so that library communications are completely + separated from other communication operations. +
+Scope: global. +
+Type: required. +
+Intent: out. +
+Specified as: an integer variable. +
+
+ +

+Notes + +

    +
  1. A call to this routine must precede any other PSBLAS call. +
    2. +
  2. It is an error to specify a value for $np$ greater than the + number of processes available in the underlying base parallel + environment. +
    3. +
- - -
+

+

+ + +next + +up + +previous + +contents +
+ Next: psb_info Return + Up: Parallel environment routines + Previous: Parallel environment routines +   Contents + diff --git a/docs/html/node74.html b/docs/html/node74.html index a5490e31..0661fe90 100644 --- a/docs/html/node74.html +++ b/docs/html/node74.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_init -- Initializes PSBLAS parallel environment - +psb_info -- Return information about PSBLAS parallel environment + @@ -20,95 +20,68 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_info Return - Up: Parallel environment routines - Previous: Parallel environment routines -   Next: psb_exit Exit + Up: Parallel environment routines + Previous: psb_init Initializes +   Contents

-

-psb_init -- Initializes PSBLAS parallel environment +

+psb_info -- Return information about PSBLAS parallel + environment 

-call psb_init(icontxt, np, basectxt, ids)
+call psb_info(icontxt, iam, np)

-This subroutine initializes the PSBLAS parallel environment, defining +This subroutine returns information about the PSBLAS parallel environment, defining a virtual parallel machine.

Type:
-
Synchronous. +
Asynchronous.
On Entry
-
np
-
Number of processes in the PSBLAS virtual parallel machine. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value. Default: use all available processes. -
-
basectxt
-
the initial communication context. The new context - will be defined from the processes participating in the initial one. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value. Default: use MPI_COMM_WORLD. -
-
ids
-
Identities of the processes to use for the new context; the - argument is ignored when np is not specified. This allows the - processes in the new environment to be in an order different from the - original one. +
icontxt
+
the communication context identifying the virtual + parallel machine.
Scope: global.
-Type: optional. +Type: required.
Intent: in.
-Specified as: an integer array. Default: use the indices $(0\dots np-1)$. +Specified as: an integer variable.
@@ -117,11 +90,24 @@ Specified as: an integer array. Default: use the indices On Return
-
icontxt
-
the communication context identifying the virtual - parallel machine. Note that this is always a duplicate of - basectxt, so that library communications are completely - separated from other communication operations. +
iam
+
Identifier of current process in the PSBLAS virtual parallel machine. +
+Scope: local. +
+Type: required. +
+Intent: out. +
+Specified as: an integer value. +$-1 \le iam \le np-1$
+
np
+
Number of processes in the PSBLAS virtual parallel machine.
Scope: global.
@@ -129,48 +115,56 @@ Type: required.
Intent: out.
-Specified as: an integer variable. -
+Specified as: an integer variable.

Notes

    -
  1. A call to this routine must precede any other PSBLAS call. +
  2. For processes in the virtual parallel machine the identifier + will satisfy +$0 \le iam \le np-1$;
    3. -
  3. It is an error to specify a value for $np$ greater than the - number of processes available in the underlying base parallel - environment. +
  4. If the user has requested on psb_init a number of + processes less than the total available in the parallel execution + environment, the remaining processes will have on return $iam=-1$; + the only call involving icontxt that any such process may + execute is to psb_exit.

- next - + up - previous - contents
- Next: psb_info Return - Up: Parallel environment routines - Previous: Parallel environment routines -   Next: psb_exit Exit + Up: Parallel environment routines + Previous: psb_init Initializes +   Contents diff --git a/docs/html/node75.html b/docs/html/node75.html index 6284718f..c6a54eac 100644 --- a/docs/html/node75.html +++ b/docs/html/node75.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_info -- Return information about PSBLAS parallel environment - +psb_exit -- Exit from PSBLAS parallel environment + @@ -20,53 +20,52 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_exit Exit - Up: Parallel environment routines - Previous: psb_init Initializes -   Next: psb_get_mpicomm Get + Up: Parallel environment routines + Previous: psb_info Return +   Contents

-

-psb_info -- Return information about PSBLAS parallel - environment +

+psb_exit -- Exit from PSBLAS parallel environment 

-call psb_info(icontxt, iam, np)
+call psb_exit(icontxt)
+call psb_exit(icontxt,close)

-This subroutine returns information about the PSBLAS parallel environment, defining -a virtual parallel machine. +This subroutine exits from the PSBLAS parallel virtual machine.

Type:
-
Asynchronous. +
Synchronous.
On Entry
@@ -83,88 +82,67 @@ Intent: in.
Specified as: an integer variable.
-
- -

-

-
On Return
-
-
-
iam
-
Identifier of current process in the PSBLAS virtual parallel machine. -
-Scope: local. -
-Type: required. -
-Intent: out. -
-Specified as: an integer value. -$-1 \le iam \le np-1$
-
np
-
Number of processes in the PSBLAS virtual parallel machine. +
close
+
Whether to close all data structures related to the + virtual parallel machine, besides those associated with icontxt.
Scope: global.
-Type: required. +Type: optional.
-Intent: out. +Intent: in.
-Specified as: an integer variable.
+Specified as: a logical variable, default value: true. +

Notes

    -
  1. For processes in the virtual parallel machine the identifier - will satisfy -This routine may be called even if a previous call to + psb_info has returned with $0 \le iam \le np-1$; + ALT="$iam=-1$">; indeed, it it is the only + routine that may be called with argument icontxt in this + situation.
    2. -
  2. If the user has requested on psb_init a number of - processes less than the total available in the parallel execution - environment, the remaining processes will have on return $iam=-1$; - the only call involving icontxt that any such process may - execute is to psb_exit. +
  3. A call to this routine with close=.true. implies a call + to MPI_Finalize, after which no parallel routine may be called. +
    4. +
  4. If the user whishes to use multiple communication contexts in the + same program, or to enter and exit multiple times into the parallel + environment, this routine may be called to + selectively close the contexts with close=.false., while on + the last call it should be called with close=.true. to + shutdown in a clean way the entire parallel environment.

- next - + up - previous - contents
- Next: psb_exit Exit - Up: Parallel environment routines - Previous: psb_init Initializes -   Next: psb_get_mpicomm Get + Up: Parallel environment routines + Previous: psb_info Return +   Contents diff --git a/docs/html/node76.html b/docs/html/node76.html index ca8b3727..590d57fe 100644 --- a/docs/html/node76.html +++ b/docs/html/node76.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_exit -- Exit from PSBLAS parallel environment - +psb_get_mpicomm -- Get the MPI communicator + @@ -20,52 +20,51 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_get_mpicomm Get - Up: Parallel environment routines - Previous: psb_info Return -   Next: psb_get_rank Get + Up: Parallel environment routines + Previous: psb_exit Exit +   Contents

-

-psb_exit -- Exit from PSBLAS parallel environment +

+psb_get_mpicomm -- Get the MPI communicator 

-call psb_exit(icontxt)
-call psb_exit(icontxt,close)
+call psb_get_mpicomm(icontxt, icomm)

-This subroutine exits from the PSBLAS parallel virtual machine. +This subroutine returns the MPI communicator associated with a PSBLAS context

Type:
-
Synchronous. +
Asynchronous.
On Entry
@@ -82,69 +81,26 @@ Intent: in.
Specified as: an integer variable.
-
close
-
Whether to close all data structures related to the - virtual parallel machine, besides those associated with icontxt. +
+ +

+

+
On Return
+
+
+
icomm
+
The MPI communicator associated with the PSBLAS virtual parallel machine.
Scope: global.
-Type: optional. -
-Intent: in. +Type: required.
-Specified as: a logical variable, default value: true. -
+Intent: out. +

-Notes - -

    -
  1. This routine may be called even if a previous call to - psb_info has returned with $iam=-1$; indeed, it it is the only - routine that may be called with argument icontxt in this - situation. -
    2. -
  2. A call to this routine with close=.true. implies a call - to MPI_Finalize, after which no parallel routine may be called. -
    3. -
  3. If the user whishes to use multiple communication contexts in the - same program, or to enter and exit multiple times into the parallel - environment, this routine may be called to - selectively close the contexts with close=.false., while on - the last call it should be called with close=.true. to - shutdown in a clean way the entire parallel environment. -
    4. -
- -

-

- - -next - -up - -previous - -contents -
- Next: psb_get_mpicomm Get - Up: Parallel environment routines - Previous: psb_info Return -   Contents - +
diff --git a/docs/html/node77.html b/docs/html/node77.html index 65f59e21..1522930a 100644 --- a/docs/html/node77.html +++ b/docs/html/node77.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_get_mpicomm -- Get the MPI communicator - +psb_get_rank -- Get the MPI rank + @@ -20,48 +20,51 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_get_rank Get - Up: Parallel environment routines - Previous: psb_exit Exit -   Next: psb_wtime Wall + Up: Parallel environment routines + Previous: psb_get_mpicomm Get +   Contents

-

-psb_get_mpicomm -- Get the MPI communicator +

+psb_get_rank -- Get the MPI rank 

-call psb_get_mpicomm(icontxt, icomm)
+call psb_get_rank(rank, icontxt, id)

-This subroutine returns the MPI communicator associated with a PSBLAS context +This subroutine returns the MPI rank of the PSBLAS process $id$

Type:
Asynchronous. @@ -81,6 +84,22 @@ Intent: in.
Specified as: an integer variable.
+
id
+
Identifier of a process in the PSBLAS virtual parallel machine. +
+Scope: local. +
+Type: required. +
+Intent: in. +
+Specified as: an integer value. +$0 \le id \le np-1$

@@ -88,10 +107,13 @@ Specified as: an integer variable.

On Return
-
icomm
-
The MPI communicator associated with the PSBLAS virtual parallel machine. +
rank
+
The MPI rank associated with the PSBLAS process $id$.
-Scope: global. +Scope: local.
Type: required.
diff --git a/docs/html/node78.html b/docs/html/node78.html index d90565bf..39783067 100644 --- a/docs/html/node78.html +++ b/docs/html/node78.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_get_rank -- Get the MPI rank - +psb_wtime -- Wall clock timing + @@ -20,105 +20,61 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_wtime Wall - Up: Parallel environment routines - Previous: psb_get_mpicomm Get -   Next: psb_barrier Sinchronization + Up: Parallel environment routines + Previous: psb_get_rank Get +   Contents

-

-psb_get_rank -- Get the MPI rank +

+psb_wtime -- Wall clock timing 

-call psb_get_rank(rank, icontxt, id)
+time = psb_wtime()

-This subroutine returns the MPI rank of the PSBLAS process $id$ +This function returns a wall clock timer. The resolution of the timer +is dependent on the underlying parallel environment implementation.

Type:
Asynchronous.
-
On Entry
+
On Exit
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
id
-
Identifier of a process in the PSBLAS virtual parallel machine. -
-Scope: local. +
Function value
+
the elapsed time in seconds.
-Type: required. -
-Intent: in. -
-Specified as: an integer value. -$0 \le id \le np-1$
-
- -

-

-
On Return
-
+Returned as: a real(psb_dpk_) variable.
-
rank
-
The MPI rank associated with the PSBLAS process $id$. -
-Scope: local. -
-Type: required. -
-Intent: out. -

diff --git a/docs/html/node79.html b/docs/html/node79.html index d577720f..60e904d8 100644 --- a/docs/html/node79.html +++ b/docs/html/node79.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_wtime -- Wall clock timing - +psb_barrier -- Sinchronization point parallel environment + @@ -20,60 +20,68 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_barrier Sinchronization - Up: Parallel environment routines - Previous: psb_get_rank Get -   Next: psb_abort Abort + Up: Parallel environment routines + Previous: psb_wtime Wall +   Contents

-

-psb_wtime -- Wall clock timing +

+psb_barrier -- Sinchronization point parallel + environment 

-time = psb_wtime()
+call psb_barrier(icontxt)

-This function returns a wall clock timer. The resolution of the timer -is dependent on the underlying parallel environment implementation. +This subroutine acts as an explicit synchronization point for the PSBLAS +parallel virtual machine.

Type:
-
Asynchronous. +
Synchronous.
-
On Exit
+
On Entry
-
Function value
-
the elapsed time in seconds. +
icontxt
+
the communication context identifying the virtual + parallel machine. +
+Scope: global. +
+Type: required. +
+Intent: in.
-Returned as: a real(psb_dpk_) variable. +Specified as: an integer variable.
diff --git a/docs/html/node8.html b/docs/html/node8.html index c3ff2fa1..69c0646a 100644 --- a/docs/html/node8.html +++ b/docs/html/node8.html @@ -18,7 +18,7 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Descriptor data structure - Up: Up: userhtml - Previous: Previous: Programming model -   Contents

@@ -91,60 +91,55 @@ it is only used for the psb_sizeof utility. Subsections diff --git a/docs/html/node80.html b/docs/html/node80.html index 1f08bafc..be179d4d 100644 --- a/docs/html/node80.html +++ b/docs/html/node80.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_barrier -- Sinchronization point parallel environment - +psb_abort -- Abort a computation + @@ -20,53 +20,51 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_abort Abort - Up: Parallel environment routines - Previous: psb_wtime Wall -   Next: psb_bcast Broadcast + Up: Parallel environment routines + Previous: psb_barrier Sinchronization +   Contents

-

-psb_barrier -- Sinchronization point parallel - environment +

+psb_abort -- Abort a computation 

-call psb_barrier(icontxt)
+call psb_abort(icontxt)

-This subroutine acts as an explicit synchronization point for the PSBLAS -parallel virtual machine. +This subroutine aborts computation on the parallel virtual machine.

Type:
-
Synchronous. +
Asynchronous.
On Entry
diff --git a/docs/html/node81.html b/docs/html/node81.html index d3e85383..8e69eaca 100644 --- a/docs/html/node81.html +++ b/docs/html/node81.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_abort -- Abort a computation - +psb_bcast -- Broadcast data + @@ -20,51 +20,52 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_bcast Broadcast - Up: Parallel environment routines - Previous: psb_barrier Sinchronization -   Next: psb_sum Global + Up: Parallel environment routines + Previous: psb_abort Abort +   Contents

-

-psb_abort -- Abort a computation +

+psb_bcast -- Broadcast data 

-call psb_abort(icontxt)
+call psb_bcast(icontxt, dat, root)

-This subroutine aborts computation on the parallel virtual machine. +This subroutine implements a broadcast operation based on the +underlying communication library.

Type:
-
Asynchronous. +
Synchronous.
On Entry
@@ -81,10 +82,81 @@ Intent: in.
Specified as: an integer variable.
+
dat
+
On the root process, the data to be broadcast. +
+Scope: global. +
+Type: required. +
+Intent: inout. +
+Specified as: an integer, real or complex variable, which may be a +scalar, or a rank 1 or 2 array, or a character or logical variable, +which may be a scalar or rank 1 array. Type, kind, rank and size must agree on all processes. +
+
root
+
Root process holding data to be broadcast. +
+Scope: global. +
+Type: optional. +
+Intent: in. +
+Specified as: an integer value +$0<= root <= np-1$, default 0

-

+
+
On Return
+
+
+
dat
+
On processes other than root, the data to be broadcast. +
+Scope: global. +
+Type: required. +
+Intent: inout. +
+Specified as: an integer, real or complex variable, which may be a +scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind, rank and size must agree on all processes. +
+
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: psb_sum Global + Up: Parallel environment routines + Previous: psb_abort Abort +   Contents + diff --git a/docs/html/node82.html b/docs/html/node82.html index f27df5a7..892f3389 100644 --- a/docs/html/node82.html +++ b/docs/html/node82.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_bcast -- Broadcast data - +psb_sum -- Global sum + @@ -20,48 +20,48 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_sum Global - Up: Parallel environment routines - Previous: psb_abort Abort -   Next: psb_max Global + Up: Parallel environment routines + Previous: psb_bcast Broadcast +   Contents

-

-psb_bcast -- Broadcast data +

+psb_sum -- Global sum 

-call psb_bcast(icontxt, dat, root)
+call psb_sum(icontxt, dat, root)

-This subroutine implements a broadcast operation based on the +This subroutine implements a sum reduction operation based on the underlying communication library.

Type:
@@ -83,7 +83,7 @@ Intent: in. Specified as: an integer variable.
dat
-
On the root process, the data to be broadcast. +
The local contribution to the global sum.
Scope: global.
@@ -92,11 +92,14 @@ Type: required. Intent: inout.
Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical variable, -which may be a scalar or rank 1 array. Type, kind, rank and size must agree on all processes. +scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes.
root
-
Root process holding data to be broadcast. +
Process to hold the final sum, or $-1$ to make it available + on all processes.
Scope: global.
@@ -105,12 +108,12 @@ Type: optional. Intent: in.
Specified as: an integer value $0<= root <= np-1$, default 0
+ ALT="$-1<= root <= np-1$">, default -1.

@@ -119,7 +122,7 @@ Specified as: an integer value - next - + up - previous - contents
- Next: psb_sum Global - Up: Parallel environment routines - Previous: psb_abort Abort -   Next: psb_max Global + Up: Parallel environment routines + Previous: psb_bcast Broadcast +   Contents diff --git a/docs/html/node83.html b/docs/html/node83.html index d817218b..9addeac9 100644 --- a/docs/html/node83.html +++ b/docs/html/node83.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_sum -- Global sum - +psb_max -- Global maximum + @@ -20,49 +20,49 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_max Global - Up: Parallel environment routines - Previous: psb_bcast Broadcast -   Next: psb_min Global + Up: Parallel environment routines + Previous: psb_sum Global +   Contents

-

-psb_sum -- Global sum +

+psb_max -- Global maximum 

-call psb_sum(icontxt, dat, root)
+call psb_max(icontxt, dat, root)

-This subroutine implements a sum reduction operation based on the -underlying communication library. +This subroutine implements a maximum valuereduction +operation based on the underlying communication library.

Type:
Synchronous. @@ -83,21 +83,21 @@ Intent: in. Specified as: an integer variable.
dat
-
The local contribution to the global sum. +
The local contribution to the global maximum.
-Scope: global. +Scope: local.
Type: required.
Intent: inout.
-Specified as: an integer, real or complex variable, which may be a +Specified as: an integer or real variable, which may be a scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes.
root
-
Process to hold the final sum, or Process to hold the final maximum, or $-1$ to make it available on all processes.
@@ -112,8 +112,9 @@ Specified as: an integer value $-1<= root <= np-1$, default -1.
+ SRC="img129.png" + ALT="$-1<= root <= np-1$">, default -1. +

@@ -122,18 +123,16 @@ Specified as: an integer value - next - + up - previous - contents
- Next: psb_max Global - Up: Parallel environment routines - Previous: psb_bcast Broadcast -   Next: psb_min Global + Up: Parallel environment routines + Previous: psb_sum Global +   Contents diff --git a/docs/html/node84.html b/docs/html/node84.html index 0b27f94e..578c01e7 100644 --- a/docs/html/node84.html +++ b/docs/html/node84.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_max -- Global maximum - +psb_min -- Global minimum + @@ -20,48 +20,48 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_min Global - Up: Parallel environment routines - Previous: psb_sum Global -   Next: psb_amx Global + Up: Parallel environment routines + Previous: psb_max Global +   Contents

-

-psb_max -- Global maximum +

+psb_min -- Global minimum 

-call psb_max(icontxt, dat, root)
+call psb_min(icontxt, dat, root)

-This subroutine implements a maximum valuereduction +This subroutine implements a minimum value reduction operation based on the underlying communication library.

Type:
@@ -83,7 +83,7 @@ Intent: in. Specified as: an integer variable.
dat
-
The local contribution to the global maximum. +
The local contribution to the global minimum.
Scope: local.
@@ -91,13 +91,13 @@ Type: required.
Intent: inout.
-Specified as: an integer or real variable, which may be a +Specified as: an integer or real variable, which may be a scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes.
root
-
Process to hold the final maximum, or Process to hold the final value, or $-1$ to make it available on all processes.
@@ -112,7 +112,7 @@ Specified as: an integer value $-1<= root <= np-1$, default -1.
@@ -123,16 +123,18 @@ Specified as: an integer value - next - + up - previous - contents
- Next: psb_min Global - Up: Parallel environment routines - Previous: psb_sum Global -   Next: psb_amx Global + Up: Parallel environment routines + Previous: psb_max Global +   Contents diff --git a/docs/html/node85.html b/docs/html/node85.html index a7ab4668..77bc82f6 100644 --- a/docs/html/node85.html +++ b/docs/html/node85.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_min -- Global minimum - +psb_amx -- Global maximum absolute value + @@ -20,48 +20,48 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_amx Global - Up: Parallel environment routines - Previous: psb_max Global -   Next: psb_amn Global + Up: Parallel environment routines + Previous: psb_min Global +   Contents

-

-psb_min -- Global minimum +

+psb_amx -- Global maximum absolute value 

-call psb_min(icontxt, dat, root)
+call psb_amx(icontxt, dat, root)

-This subroutine implements a minimum value reduction +This subroutine implements a maximum absolute value reduction operation based on the underlying communication library.

Type:
@@ -83,7 +83,7 @@ Intent: in. Specified as: an integer variable.
dat
-
The local contribution to the global minimum. +
The local contribution to the global maximum.
Scope: local.
@@ -91,13 +91,13 @@ Type: required.
Intent: inout.
-Specified as: an integer or real variable, which may be a +Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes.
root
Process to hold the final value, or $-1$ to make it available on all processes.
@@ -112,7 +112,7 @@ Specified as: an integer value $-1<= root <= np-1$, default -1.
@@ -123,7 +123,7 @@ Specified as: an integer value - next - + up - previous - contents
- Next: psb_amx Global - Up: Parallel environment routines - Previous: psb_max Global -   Next: psb_amn Global + Up: Parallel environment routines + Previous: psb_min Global +   Contents diff --git a/docs/html/node86.html b/docs/html/node86.html index 95c34f13..6286cdd8 100644 --- a/docs/html/node86.html +++ b/docs/html/node86.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_amx -- Global maximum absolute value - +psb_amn -- Global minimum absolute value + @@ -20,48 +20,48 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_amn Global - Up: Parallel environment routines - Previous: psb_min Global -   Next: psb_snd Send + Up: Parallel environment routines + Previous: psb_amx Global +   Contents

-

-psb_amx -- Global maximum absolute value +

+psb_amn -- Global minimum absolute value 

-call psb_amx(icontxt, dat, root)
+call psb_amn(icontxt, dat, root)

-This subroutine implements a maximum absolute value reduction +This subroutine implements a minimum absolute value reduction operation based on the underlying communication library.

Type:
@@ -83,7 +83,7 @@ Intent: in. Specified as: an integer variable.
dat
-
The local contribution to the global maximum. +
The local contribution to the global minimum.
Scope: local.
@@ -97,7 +97,7 @@ scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all pro
root
Process to hold the final value, or $-1$ to make it available on all processes.
@@ -112,7 +112,7 @@ Specified as: an integer value $-1<= root <= np-1$, default -1.
@@ -123,7 +123,7 @@ Specified as: an integer value - next - + up - previous - contents
- Next: psb_amn Global - Up: Parallel environment routines - Previous: psb_min Global -   Next: psb_snd Send + Up: Parallel environment routines + Previous: psb_amx Global +   Contents diff --git a/docs/html/node87.html b/docs/html/node87.html index 776b3c95..4da69119 100644 --- a/docs/html/node87.html +++ b/docs/html/node87.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_amn -- Global minimum absolute value - +psb_snd -- Send data + @@ -20,52 +20,51 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_snd Send - Up: Parallel environment routines - Previous: psb_amx Global -   Next: psb_rcv Receive + Up: Parallel environment routines + Previous: psb_amn Global +   Contents

-

-psb_amn -- Global minimum absolute value +

+psb_snd -- Send data 

-call psb_amn(icontxt, dat, root)
+call psb_snd(icontxt, dat, dst, m)

-This subroutine implements a minimum absolute value reduction -operation based on the underlying communication library. +This subroutine sends a packet of data to a destination.

Type:
-
Synchronous. +
Synchronous: see usage notes.
On Entry
@@ -83,38 +82,65 @@ Intent: in. Specified as: an integer variable.
dat
-
The local contribution to the global minimum. +
The data to be sent.
Scope: local.
Type: required.
-Intent: inout. +Intent: in.
Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. +scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if $m$ is +not specified, size must agree as well.
-
root
-
Process to hold the final value, or $-1$ to make it available - on all processes. +
dst
+
Destination process.
Scope: global.
-Type: optional. +Type: required.
Intent: in.
Specified as: an integer value $-1<= root <= np-1$, default -1. + WIDTH="145" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" + SRC="img131.png" + ALT="$0<= dst <= np-1$">.
+
m
+
Number of rows. +
+Scope: global. +
+Type: Optional. +
+Intent: in. +
+Specified as: an integer value +$0<= m <= size(dat,1)$. +
+When $dat$ is a rank 2 array, specifies the number of rows to be sent +independently of the leading dimension $size(dat,1)$; must have the +same value on sending and receiving processes. +

@@ -122,57 +148,43 @@ Specified as: an integer value - next - + up - previous - contents
- Next: psb_snd Send - Up: Parallel environment routines - Previous: psb_amx Global -   Next: psb_rcv Receive + Up: Parallel environment routines + Previous: psb_amn Global +   Contents diff --git a/docs/html/node88.html b/docs/html/node88.html index 824aeb55..171b803a 100644 --- a/docs/html/node88.html +++ b/docs/html/node88.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_snd -- Send data - +psb_rcv -- Receive data + @@ -18,53 +18,52 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: psb_rcv Receive - Up: Parallel environment routines - Previous: psb_amn Global -   Next: Error handling + Up: Parallel environment routines + Previous: psb_snd Send +   Contents

-

-psb_snd -- Send data +

+psb_rcv -- Receive data 

-call psb_snd(icontxt, dat, dst, m)
+call psb_rcv(icontxt, dat, src, m)

-This subroutine sends a packet of data to a destination. +This subroutine receives a packet of data to a destination.

Type:
-
Synchronous: see usage notes. +
Synchronous: see usage notes.
On Entry
@@ -81,24 +80,8 @@ Intent: in.
Specified as: an integer variable.
-
dat
-
The data to be sent. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if $m$ is -not specified, size must agree as well. -
-
dst
-
Destination process. +
src
+
Source process.
Scope: global.
@@ -107,12 +90,12 @@ Type: required. Intent: in.
Specified as: an integer value $0<= dst <= np-1$. + WIDTH="147" HEIGHT="30" ALIGN="MIDDLE" BORDER="0" + SRC="img136.png" + ALT="$0<= src <= np-1$">.
m
Number of rows. @@ -128,16 +111,16 @@ Specified as: an integer value $0<= m <= size(dat,1)$.
When $dat$ is a rank 2 array, specifies the number of rows to be sent independently of the leading dimension $size(dat,1)$; must have the same value on sending and receiving processes.
@@ -148,6 +131,22 @@ same value on sending and receiving processes.
On Return
+
dat
+
The data to be received. +
+Scope: local. +
+Type: required. +
+Intent: inout. +
+Specified as: an integer, real or complex variable, which may be a +scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if $m$ is +not specified, size must agree as well. +

@@ -155,36 +154,36 @@ same value on sending and receiving processes.

  1. This subroutine implies a synchronization, but only between the - calling process and the destination process $dst$. + calling process and the source process $src$.

- next - + up - previous - contents
- Next: psb_rcv Receive - Up: Parallel environment routines - Previous: psb_amn Global -   Next: Error handling + Up: Parallel environment routines + Previous: psb_snd Send +   Contents diff --git a/docs/html/node89.html b/docs/html/node89.html index 117fc806..139e8115 100644 --- a/docs/html/node89.html +++ b/docs/html/node89.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_rcv -- Receive data - +Error handling + @@ -18,172 +18,174 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Error handling - Up: Parallel environment routines - Previous: psb_snd Send -   Next: psb_errpush Pushes + Up: userhtml + Previous: psb_rcv Receive +   Contents

-

-psb_rcv -- Receive data -

+

+Error handling +

-

-call psb_rcv(icontxt, dat, src, m)
-
+The PSBLAS library error handling policy has been completely rewritten +in version 2.0. The idea behind the design of this new error handling +strategy is to keep error messages on a stack allowing the user to +trace back up to the point where the first error message has been +generated. Every routine in the PSBLAS-2.0 library has, as last +non-optional argument, an integer info variable; whenever, +inside the routine, an error is detected, this variable is set to a +value corresponding to a specific error code. Then this error code is +also pushed on the error stack and then either control is returned to +the caller routine or the execution is aborted, depending on the users +choice. At the time when the execution is aborted, an error message is +printed on standard output with a level of verbosity than can be +chosen by the user. If the execution is not aborted, then, the caller +routine checks the value returned in the info variable and, if +not zero, an error condition is raised. This process continues on all the +levels of nested calls until the level where the user decides to abort +the program execution.

-This subroutine receives a packet of data to a destination. -

-
Type:
-
Synchronous: see usage notes. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
src
-
Source process. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer value -$0<= src <= np-1$. -
-
m
-
Number of rows. -
-Scope: global. -
-Type: Optional. -
-Intent: in. -
-Specified as: an integer value $0<= m <= size(dat,1)$. -
-When $dat$ is a rank 2 array, specifies the number of rows to be sent -independently of the leading dimension $size(dat,1)$; must have the -same value on sending and receiving processes. -
-
+ WIDTH="535" HEIGHT="218" ALIGN="MIDDLE" BORDER="0" + SRC="img20.png" + ALT="\fbox{\TheSbox}"> +
+

-

-
On Return
-
-
-
dat
-
The data to be received. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if $m$ is -not specified, size must agree as well. -
-
+Figure 9 reports a sample error message generated by +the PSBLAS-2.0 library. This error has been generated by the fact that +the user has chosen the invalid ``FOO'' storage format to represent +the sparse matrix. From this error message it is possible to see that +the error has been detected inside the psb_cest subroutine +called by psb_spasb ... by process 0 (i.e. the root process).

-Notes -

    -
  1. This subroutine implies a synchronization, but only between the - calling process and the source process $src$. -
    2. -
+
+ + + +
Figure 9: +A sample PSBLAS-2.0 error + message. Process 0 detected an error condition inside the psb_cest subroutine
+
+ +
+ +\fbox{\TheSbox} +
+

+

+ +Subsections + + +
- next - + up - previous - contents
- Next: Error handling - Up: Parallel environment routines - Previous: psb_snd Send -   Next: psb_errpush Pushes + Up: userhtml + Previous: psb_rcv Receive +   Contents diff --git a/docs/html/node9.html b/docs/html/node9.html index 6ae20844..c6f17983 100644 --- a/docs/html/node9.html +++ b/docs/html/node9.html @@ -26,26 +26,26 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next - up - previous - contents
- Next: Next: Named Constants - Up: Up: Data Structures - Previous: Previous: Data Structures -   Contents

@@ -59,25 +59,73 @@ Descriptor data structure All the general matrix informations and elements to be exchanged among processes are stored within a data structure of the type descdatapsb_desc_type. -Every structure of this type is associated to a sparse matrix, it -contains data about general matrix informations and elements to be -exchanged among processes. +Every structure of this type is associated with a discretization +pattern and enables data communications and other operations that are +necessary for implementing the various algorithms of interest to us.

-It is not necessary for the user to know the internal structure of -psb_desc_type, it is set in a transparent mode by the tools -routines of Sec. 6, and its fields may be accessed -if necessary via the routines of sec. 3.5; -nevertheless we include a description for the curious -reader: +The data structure itself psb_desc_type can be treated as an +opaque object handled via the tools routines of +Sec. 6 and 3.5; +nevertheless we include here a description for the curious +reader. + +

+First we describe the psb_indx_map type. This is a data +structure that keeps track of a certain number of basic issues such +as: + +

    +
  • The value of the communication/MPI context; +
    • +
  • The number of indices in the index space, i.e. global number of + rows and columns of a sparse matrix; +
    • +
  • The local set of indices, including: + +
      +
    • The number of local indices (and local rows); +
      • +
    • The number of halo indices (and therefore local columns); +
      • +
    • The global indices corresponding to the local ones. +
      • +
    +
    • +
+There are many different schemes for storing these data; therefore +there are a number of types extending the base one, and the descriptor +structure holds a polymorphic object whose dynamic type can be any of +the extended types. +The methods associated with this data type answer the following +queries: + +
    +
  • For a given set of local indices, find the corresponding indices + in the global numbering; +
    • +
  • For a given set of global indices, find the corresponding + indices in the local numbering, if any, or return an invalid +
    • +
  • Add a global index to the set of halo indices; +
    • +
  • Find the process owner of each member of a set of global + indices. +
    • +
+All methods but the last are purely local; the last method potentially +requires communication among processes, and thus is a synchronous +method. The choice of a specific dynamic type for the index map is +made at the time the descriptor is initially allocated, according to +the mode of initialization (see also 6). + +

+The descriptor contents are as follows:

-
matrix_data
-
includes general information about matrix and -process grid, such as the communication context, the size of the -global matrix, the size of the portion of matrix stored on the current -process, and so on. -Specified as: an allocatable integer array of dimension psb_mdata_size_. -
+
indxmap
+
A polymorphic variable of a type that is any + extension of the indx_map type described above. +
halo_index
A list of the halo and boundary elements for the current process to be exchanged with other processes; for each @@ -146,27 +194,15 @@ ecurrent process: Specified as: an allocatable integer array of rank two.
-
loc_to_glob
-
each element $i$ of this array contains -global identifier of the local variable $i$. -
-Specified as: an allocatable integer array of rank one. -
-
glob_to_loc, glb_lc, hashv
-
Contain a mapping from - global to local indices. +
bnd_elem
+
A list of all boundary points, i.e. points + that have a connection with other processes.
-The Fortran 95 definition for psb_desc_type structures is +The Fortran 2003 declaration for psb_desc_type structures is as follows: -
+
Figure 3: The PSBLAS defined data type that @@ -201,14 +237,6 @@ state, which can take the following values: only possible in this state. -The global to local index mapping may be stored in two different -formats: the first is simpler but more expensive, as it requires on -each process an amount of memory proportional to the global size of -the index space; the second is more complex, but only requires memory -proportional to the local index space size. The choice is made at the -time of the initialization according to a threshold; this threshold -may be queried and set using the functions in -sec. 3.5.


@@ -216,32 +244,32 @@ sec. 3.5. Subsections
- next - up - previous - contents
- Next: Next: Named Constants - Up: Up: Data Structures - Previous: Previous: Data Structures -   Contents diff --git a/docs/html/node90.html b/docs/html/node90.html index 54dbf34f..b60cc623 100644 --- a/docs/html/node90.html +++ b/docs/html/node90.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Error handling - +psb_errpush -- Pushes an error code onto the error stack + @@ -18,176 +18,101 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - - + + + - next - + up - previous - contents
- Next: psb_errpush Pushes - Up: userhtml - Previous: psb_rcv Receive -   Next: psb_error Prints + Up: Error handling + Previous: Error handling +   Contents

-

-Error handling -

- -

-The PSBLAS library error handling policy has been completely rewritten -in version 2.0. The idea behind the design of this new error handling -strategy is to keep error messages on a stack allowing the user to -trace back up to the point where the first error message has been -generated. Every routine in the PSBLAS-2.0 library has, as last -non-optional argument, an integer info variable; whenever, -inside the routine, an error is detected, this variable is set to a -value corresponding to a specific error code. Then this error code is -also pushed on the error stack and then either control is returned to -the caller routine or the execution is aborted, depending on the users -choice. At the time when the execution is aborted, an error message is -printed on standard output with a level of verbosity than can be -chosen by the user. If the execution is not aborted, then, the caller -routine checks the value returned in the info variable and, if -not zero, an error condition is raised. This process continues on all the -levels of nested calls until the level where the user decides to abort -the program execution. - -

-Figure 9 shows the layout of a generic psb_foo -routine with respect to the PSBLAS-2.0 error handling policy. It is -possible to see how, whenever an error condition is detected, the -info variable is set to the corresponding error code which is, -then, pushed on top of the stack by means of the -psb_errpush. An error condition may be directly detected inside -a routine or indirectly checking the error code returned returned by a -called routine. Whenever an error is encountered, after it has been -pushed on stack, the program execution skips to a point where the -error condition is handled; the error condition is handled either by -returning control to the caller routine or by calling the -psb\_error routine which prints the content of the error stack -and aborts the program execution, according to the choice made by the -user with psb_set_erraction. The default is to print the error -and terminate the program, but the user may choose to handle the error -explicitly. - -

- -

- - - -
Figure 9: -The layout of a generic psb_foo - routine with respect to PSBLAS-2.0 error handling policy.
-
- -
- -\fbox{\TheSbox} -
-
+

+psb_errpush -- Pushes an error code onto the error + stack +

-Figure 10 reports a sample error message generated by -the PSBLAS-2.0 library. This error has been generated by the fact that -the user has chosen the invalid ``FOO'' storage format to represent -the sparse matrix. From this error message it is possible to see that -the error has been detected inside the psb_cest subroutine -called by psb_spasb ... by process 0 (i.e. the root process). +

+call psb_errpush(err_c, r_name, i_err, a_err)
+

- -

- - - -
Figure 10: -A sample PSBLAS-2.0 error - message. Process 0 detected an error condition inside the psb_cest subroutine
-
- -
- -\fbox{\TheSbox} -
-
+
+
Type:
+
Asynchronous. +
+
On Entry
+
+
+
err_c
+
the error code +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: an integer. +
+
r_name
+
the soutine where the error has been caught. +
+Scope: local +
+Type: required +
+Intent: in. +
+Specified as: a string. +
+
i_err
+
addional info for error code +
+Scope: local +
+Type: optional +
+Specified as: an integer array +
+
a_err
+
addional info for error code +
+Scope: local +
+Type: optional +
+Specified as: a string. +
+


- -Subsections - - - -
- - -next - -up - -previous - -contents -
- Next: psb_errpush Pushes - Up: userhtml - Previous: psb_rcv Receive -   Contents - diff --git a/docs/html/node91.html b/docs/html/node91.html index 6b1ccd27..0b109c6b 100644 --- a/docs/html/node91.html +++ b/docs/html/node91.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_errpush -- Pushes an error code onto the error stack - +psb_error -- Prints the error stack content and aborts execution + @@ -20,45 +20,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_error Prints - Up: Error handling - Previous: Error handling -   Next: psb_set_errverbosity Sets + Up: Error handling + Previous: psb_errpush Pushes +   Contents

-

-psb_errpush -- Pushes an error code onto the error - stack +

+psb_error -- Prints the error stack content and aborts + execution 

-call psb_errpush(err_c, r_name, i_err, a_err)
+call psb_error(icontxt)

@@ -69,46 +69,17 @@ call psb_errpush(err_c, r_name, i_err, a_err)

On Entry
-
err_c
-
the error code +
icontxt
+
the communication context.
-Scope: local +Scope: global
-Type: required +Type: optional
Intent: in.
Specified as: an integer.
-
r_name
-
the soutine where the error has been caught. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a string. -
-
i_err
-
addional info for error code -
-Scope: local -
-Type: optional -
-Specified as: an integer array -
-
a_err
-
addional info for error code -
-Scope: local -
-Type: optional -
-Specified as: a string. -

diff --git a/docs/html/node92.html b/docs/html/node92.html index 4b91bd99..5e0e1523 100644 --- a/docs/html/node92.html +++ b/docs/html/node92.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_error -- Prints the error stack content and aborts execution - +psb_set_errverbosity -- Sets the verbosity of error messages. + @@ -20,45 +20,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: psb_set_errverbosity Sets - Up: Error handling - Previous: psb_errpush Pushes -   Next: psb_set_erraction Set + Up: Error handling + Previous: psb_error Prints +   Contents

-

-psb_error -- Prints the error stack content and aborts - execution +

+psb_set_errverbosity -- Sets the verbosity of error + messages. 

-call psb_error(icontxt)
+call psb_set_errverbosity(v)

@@ -69,12 +69,12 @@ call psb_error(icontxt)

On Entry
-
icontxt
-
the communication context. +
v
+
the verbosity level
-Scope: global +Scope: global
-Type: optional +Type: required
Intent: in.
diff --git a/docs/html/node93.html b/docs/html/node93.html index bcdc4d0f..8b4f5052 100644 --- a/docs/html/node93.html +++ b/docs/html/node93.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_set_errverbosity -- Sets the verbosity of error messages. - +psb_set_erraction -- Set the type of action to be taken upon error condition. + @@ -18,47 +18,46 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: psb_set_erraction Set - Up: Error handling - Previous: psb_error Prints -   Next: Utilities + Up: Error handling + Previous: psb_set_errverbosity Sets +   Contents

-

-psb_set_errverbosity -- Sets the verbosity of error - messages. +

+psb_set_erraction -- Set the type of action to be + taken upon error condition. 

-call psb_set_errverbosity(v)
+call psb_set_erraction(err_act)

@@ -69,19 +68,25 @@ call psb_set_errverbosity(v)

On Entry
-
v
-
the verbosity level +
err_act
+
the type of action.
-Scope: global +Scope: global
Type: required
Intent: in.
-Specified as: an integer. +Specified as: an integer. Possible values: psb_act_ret, +psb_act_abort.
+

+

+call psb_errcomm(icontxt, err)
+
+


diff --git a/docs/html/node94.html b/docs/html/node94.html index 10d98ab1..d7a71f94 100644 --- a/docs/html/node94.html +++ b/docs/html/node94.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -psb_set_erraction -- Set the type of action to be taken upon error condition. - +Utilities + @@ -18,77 +18,74 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + + + - next - + up - previous - contents
- Next: Utilities - Up: Error handling - Previous: psb_set_errverbosity Sets -   Next: hb_read Read + Up: userhtml + Previous: psb_set_erraction Set +   Contents

-

-psb_set_erraction -- Set the type of action to be - taken upon error condition. -

- -

-

-call psb_set_erraction(err_act)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
err_act
-
the type of action. -
-Scope: global -
-Type: required +

+
-Intent: in. -
-Specified as: an integer. Possible values: psb_act_ret, -psb_act_abort. -

-
+Utilities +

-

-call psb_errcomm(icontxt, err)
-
+We have some utitlities available for input and output of +sparsematrices; the interfaces to these routines are available in the +module psb_util_mod.


+ +Subsections + + + +
diff --git a/docs/html/node95.html b/docs/html/node95.html index a948e534..cc868f5b 100644 --- a/docs/html/node95.html +++ b/docs/html/node95.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -Utilities - +hb_read -- Read a sparse matrix from a file in the Harwell-Boeing format + @@ -18,74 +18,139 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - - + + + - next - + up - previous - contents
- Next: hb_read Read - Up: userhtml - Previous: psb_set_erraction Set -   Next: hb_write Write + Up: Utilities + Previous: Utilities +   Contents

-

- -
-Utilities -

+

+hb_read -- Read a sparse matrix from a file in the + Harwell-Boeing format +

-We have some utitlities available for input and output of -sparsematrices; the interfaces to these routines are available in the -module psb_util_mod. +

+call hb_read(a, iret, iunit, filename, b, mtitle)
+

-

- -Subsections +
+
Type:
+
Asynchronous. +
+
On Entry
+
+
+
filename
+
The name of the file to be read. +
+Type:optional. +
+Specified as: a character variable containing a valid file name, or +-, in which case the default input unit 5 (i.e. standard input +in Unix jargon) is used. Default: -. +
+
iunit
+
The Fortran file unit number. +
+Type:optional. +
+Specified as: an integer value. Only meaningful if filename is not -. +
+
- - -
+

+

+
On Return
+
+
+
a
+
the sparse matrix read from file. +
+Type:required. +
+Specified as: a structured data of type spdatapsb_spmat_type. +
+
b
+
Rigth hand side(s). +
+Type: Optional +
+An array of type real or complex, rank 2 and having the ALLOCATABLE +attribute; will be allocated and filled in if the input file contains +a right hand side, otherwise will be left in the UNALLOCATED state. +
+
mtitle
+
Matrix title. +
+Type: Optional +
+A charachter variable of length 72 holding a copy of the +matrix title as specified by the Harwell-Boeing format and contained +in the input file. +
+
iret
+
Error code. +
+Type: required +
+An integer value; 0 means no error has been detected. +
+
+ +

+

+ + +next + +up + +previous + +contents +
+ Next: hb_write Write + Up: Utilities + Previous: Utilities +   Contents + diff --git a/docs/html/node96.html b/docs/html/node96.html index badca7bd..2ad99819 100644 --- a/docs/html/node96.html +++ b/docs/html/node96.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -hb_read -- Read a sparse matrix from a file in the Harwell-Boeing format - +hb_write -- Write a sparse matrix to a file in the Harwell-Boeing format + @@ -20,45 +20,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: hb_write Write - Up: Utilities - Previous: Utilities -   Next: mm_mat_read Read + Up: Utilities + Previous: hb_read Read +   Contents

-

-hb_read -- Read a sparse matrix from a file in the - Harwell-Boeing format +

+hb_write -- Write a sparse matrix to a file + in the Harwell-Boeing format 

-call hb_read(a, iret, iunit, filename, b, mtitle)
+call hb_write(a, iret, iunit, filename, key, rhs, mtitle)

@@ -69,13 +69,29 @@ call hb_read(a, iret, iunit, filename, b, mtitle)

On Entry
+
a
+
the sparse matrix to be written. +
+Type:required. +
+Specified as: a structured data of type spdatapsb_spmat_type. +
+
b
+
Rigth hand side. +
+Type: Optional +
+An array of type real or complex, rank 1 and having the ALLOCATABLE +attribute; will be allocated and filled in if the input file contains +a right hand side. +
filename
-
The name of the file to be read. +
The name of the file to be written to.
Type:optional.
Specified as: a character variable containing a valid file name, or --, in which case the default input unit 5 (i.e. standard input +-, in which case the default output unit 6 (i.e. standard output in Unix jargon) is used. Default: -.
iunit
@@ -85,37 +101,30 @@ Type:optional.
Specified as: an integer value. Only meaningful if filename is not -. - - -

-

-
On Return
-
-
-
a
-
the sparse matrix read from file. -
-Type:required. -
-Specified as: a structured data of type spdatapsb_spmat_type. -
-
b
-
Rigth hand side(s). +
key
+
Matrix key.
Type: Optional
-An array of type real or complex, rank 2 and having the ALLOCATABLE -attribute; will be allocated and filled in if the input file contains -a right hand side, otherwise will be left in the UNALLOCATED state. +A charachter variable of length 8 holding the +matrix key as specified by the Harwell-Boeing format and to be +written to file.
mtitle
Matrix title.
Type: Optional
-A charachter variable of length 72 holding a copy of the -matrix title as specified by the Harwell-Boeing format and contained -in the input file. +A charachter variable of length 72 holding the +matrix title as specified by the Harwell-Boeing format and to be +written to file. +
+
+ +

+

+
On Return
+
iret
Error code. @@ -129,26 +138,26 @@ An integer value; 0 means no error has been detected.

- next - + up - previous - contents
- Next: hb_write Write - Up: Utilities - Previous: Utilities -   Next: mm_mat_read Read + Up: Utilities + Previous: hb_read Read +   Contents diff --git a/docs/html/node97.html b/docs/html/node97.html index 16fe819d..b29dd9c9 100644 --- a/docs/html/node97.html +++ b/docs/html/node97.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -hb_write -- Write a sparse matrix to a file in the Harwell-Boeing format - +mm_mat_read -- Read a sparse matrix from a file in the MatrixMarket format + @@ -20,45 +20,45 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: mm_mat_read Read - Up: Utilities - Previous: hb_read Read -   Next: mm_vet_read Read + Up: Utilities + Previous: hb_write Write +   Contents

-

-hb_write -- Write a sparse matrix to a file - in the Harwell-Boeing format +

+mm_mat_read -- Read a sparse matrix from a + file in the MatrixMarket format 

-call hb_write(a, iret, iunit, filename, key, rhs, mtitle)
+call mm_mat_read(a, iret, iunit, filename)

@@ -69,29 +69,13 @@ call hb_write(a, iret, iunit, filename, key, rhs, mtitle)

On Entry
-
a
-
the sparse matrix to be written. -
-Type:required. -
-Specified as: a structured data of type spdatapsb_spmat_type. -
-
b
-
Rigth hand side. -
-Type: Optional -
-An array of type real or complex, rank 1 and having the ALLOCATABLE -attribute; will be allocated and filled in if the input file contains -a right hand side. -
filename
-
The name of the file to be written to. +
The name of the file to be read.
Type:optional.
Specified as: a character variable containing a valid file name, or --, in which case the default output unit 6 (i.e. standard output +-, in which case the default input unit 5 (i.e. standard input in Unix jargon) is used. Default: -.
iunit
@@ -101,24 +85,6 @@ Type:optional.
Specified as: an integer value. Only meaningful if filename is not -. -
key
-
Matrix key. -
-Type: Optional -
-A charachter variable of length 8 holding the -matrix key as specified by the Harwell-Boeing format and to be -written to file. -
-
mtitle
-
Matrix title. -
-Type: Optional -
-A charachter variable of length 72 holding the -matrix title as specified by the Harwell-Boeing format and to be -written to file. -

@@ -126,6 +92,13 @@ written to file.

On Return
+
a
+
the sparse matrix read from file. +
+Type:required. +
+Specified as: a structured data of type spdatapsb_spmat_type. +
iret
Error code.
@@ -136,30 +109,7 @@ An integer value; 0 means no error has been detected.

-

- - -next - -up - -previous - -contents -
- Next: mm_mat_read Read - Up: Utilities - Previous: hb_read Read -   Contents - +
diff --git a/docs/html/node98.html b/docs/html/node98.html index e8def902..e9bf7fbf 100644 --- a/docs/html/node98.html +++ b/docs/html/node98.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -mm_mat_read -- Read a sparse matrix from a file in the MatrixMarket format - +mm_vet_read -- Read a dense vector from a file in the MatrixMarket format + @@ -20,45 +20,44 @@ original version by: Nikos Drakos, CBLU, University of Leeds - + - next - + up - previous - contents
- Next: mm_vet_read Read - Up: Utilities - Previous: hb_write Write -   Next: mm_mat_write Write + Up: Utilities + Previous: mm_mat_read Read +   Contents

-

-mm_mat_read -- Read a sparse matrix from a +

+mm_vet_read -- Read a dense vector from a file in the MatrixMarket format

-

-call mm_mat_read(a, iret, iunit, filename)
+call mm_vet_read(b, iret, iunit, filename)

@@ -92,12 +91,14 @@ Specified as: an integer value. Only meaningful if filename is not -On Return

-
a
-
the sparse matrix read from file. +
b
+
Rigth hand side(s).
-Type:required. +Type: required
-Specified as: a structured data of type spdatapsb_spmat_type. +An array of type real or complex, rank 2 and having the ALLOCATABLE +attribute; will be allocated and filled in if the input file contains +a right hand side, otherwise will be left in the UNALLOCATED state.
iret
Error code. diff --git a/docs/html/node99.html b/docs/html/node99.html index e4c7d672..16644100 100644 --- a/docs/html/node99.html +++ b/docs/html/node99.html @@ -7,8 +7,8 @@ original version by: Nikos Drakos, CBLU, University of Leeds Jens Lippmann, Marek Rouchal, Martin Wilck and others --> -mm_vet_read -- Read a dense vector from a file in the MatrixMarket format - +mm_mat_write -- Write a sparse matrix to a file in the MatrixMarket format + @@ -18,49 +18,46 @@ original version by: Nikos Drakos, CBLU, University of Leeds - - + - next - + up - previous - contents
- Next: mm_mat_write Write - Up: Utilities - Previous: mm_mat_read Read -   Next: Preconditioner routines + Up: Utilities + Previous: mm_vet_read Read +   Contents

-

-mm_vet_read -- Read a dense vector from a +

+mm_mat_write -- Write a sparse matrix to a file in the MatrixMarket format 

-call mm_vet_read(b, iret, iunit, filename)
+call mm_mat_write(a, mtitle, iret, iunit, filename)
- -

Type:
Asynchronous. @@ -68,13 +65,28 @@ call mm_vet_read(b, iret, iunit, filename)
On Entry
+
a
+
the sparse matrix to be written. +
+Type:required. +
+Specified as: a structured data of type spdatapsb_spmat_type. +
+
mtitle
+
Matrix title. +
+Type: required +
+A charachter variable holding a descriptive title for the matrix to be + written to file. +
filename
-
The name of the file to be read. +
The name of the file to be written to.
Type:optional.
Specified as: a character variable containing a valid file name, or --, in which case the default input unit 5 (i.e. standard input +-, in which case the default output unit 6 (i.e. standard output in Unix jargon) is used. Default: -.
iunit
@@ -91,15 +103,6 @@ Specified as: an integer value. Only meaningful if filename is not -On Return
-
b
-
Rigth hand side(s). -
-Type: required -
-An array of type real or complex, rank 2 and having the ALLOCATABLE -attribute; will be allocated and filled in if the input file contains -a right hand side, otherwise will be left in the UNALLOCATED state. -
iret
Error code.
diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html index 21e6f6b1..fc0b17cf 100644 --- a/docs/html/userhtml.html +++ b/docs/html/userhtml.html @@ -23,18 +23,18 @@ original version by: Nikos Drakos, CBLU, University of Leeds - next up previous - contents
- Next: Next: Contents -   Contents

@@ -58,296 +58,292 @@ University of Rome ``Tor Vergata'', Italy
Software version: 3.0-beta
-May 15th, 2010 +December 15th, 2011
    -
  • Contents -
  • Introduction -
  • General overview
    -
  • Data Structures
    diff --git a/docs/psblas-3.0.pdf b/docs/psblas-3.0.pdf index c00eda67..25d4ad33 100644 --- a/docs/psblas-3.0.pdf +++ b/docs/psblas-3.0.pdf @@ -79,574 +79,568 @@ endobj (3.3 Dense Vector Data Structure) endobj 57 0 obj -<< /S /GoTo /D (subsubsection.3.3.1) >> +<< /S /GoTo /D (subsection.3.4) >> endobj 60 0 obj -(3.3.1 Named Constants) +(3.4 Preconditioner data structure) endobj 61 0 obj -<< /S /GoTo /D (subsection.3.4) >> +<< /S /GoTo /D (subsection.3.5) >> endobj 64 0 obj -(3.4 Preconditioner data structure) +(3.5 Data structure query routines) endobj 65 0 obj -<< /S /GoTo /D (subsection.3.5) >> +<< /S /GoTo /D (section*.2) >> endobj 68 0 obj -(3.5 Data structure query routines) +(get\137local\137rows ) endobj 69 0 obj -<< /S /GoTo /D (section*.2) >> +<< /S /GoTo /D (section*.3) >> endobj 72 0 obj -(get\137local\137rows ) +(get\137local\137cols ) endobj 73 0 obj -<< /S /GoTo /D (section*.3) >> +<< /S /GoTo /D (section*.4) >> endobj 76 0 obj -(get\137local\137cols ) +(get\137global\137rows ) endobj 77 0 obj -<< /S /GoTo /D (section*.4) >> +<< /S /GoTo /D (section*.5) >> endobj 80 0 obj -(get\137global\137rows ) +(get\137global\137cols ) endobj 81 0 obj -<< /S /GoTo /D (section*.5) >> +<< /S /GoTo /D (section*.6) >> endobj 84 0 obj -(get\137global\137cols ) +(get\137context) endobj 85 0 obj -<< /S /GoTo /D (section*.6) >> +<< /S /GoTo /D (section*.7) >> endobj 88 0 obj -(get\137context) +(psb\137cd\137get\137large\137threshold) endobj 89 0 obj -<< /S /GoTo /D (section*.7) >> +<< /S /GoTo /D (section*.8) >> endobj 92 0 obj -(psb\137cd\137get\137large\137threshold) +(psb\137cd\137set\137large\137threshold) endobj 93 0 obj -<< /S /GoTo /D (section*.8) >> +<< /S /GoTo /D (section*.9) >> endobj 96 0 obj -(psb\137cd\137set\137large\137threshold) +(get\137nrows) endobj 97 0 obj -<< /S /GoTo /D (section*.9) >> +<< /S /GoTo /D (section*.10) >> endobj 100 0 obj -(get\137nrows) +(get\137ncols) endobj 101 0 obj -<< /S /GoTo /D (section*.10) >> +<< /S /GoTo /D (section*.11) >> endobj 104 0 obj -(get\137ncols) +(get\137nnzeros) endobj 105 0 obj -<< /S /GoTo /D (section*.11) >> +<< /S /GoTo /D (section.4) >> endobj 108 0 obj -(get\137nnzeros) +(4 Computational routines) endobj 109 0 obj -<< /S /GoTo /D (section.4) >> +<< /S /GoTo /D (section*.12) >> endobj 112 0 obj -(4 Computational routines) +(psb\137geaxpby) endobj 113 0 obj -<< /S /GoTo /D (section*.12) >> +<< /S /GoTo /D (section*.13) >> endobj 116 0 obj -(psb\137geaxpby) +(psb\137gedot) endobj 117 0 obj -<< /S /GoTo /D (section*.13) >> +<< /S /GoTo /D (section*.14) >> endobj 120 0 obj -(psb\137gedot) +(psb\137gedots) endobj 121 0 obj -<< /S /GoTo /D (section*.14) >> +<< /S /GoTo /D (section*.15) >> endobj 124 0 obj -(psb\137gedots) +(psb\137geamax) endobj 125 0 obj -<< /S /GoTo /D (section*.15) >> +<< /S /GoTo /D (section*.16) >> endobj 128 0 obj -(psb\137geamax) +(psb\137geamaxs) endobj 129 0 obj -<< /S /GoTo /D (section*.16) >> +<< /S /GoTo /D (section*.17) >> endobj 132 0 obj -(psb\137geamaxs) +(psb\137geasum) endobj 133 0 obj -<< /S /GoTo /D (section*.17) >> +<< /S /GoTo /D (section*.18) >> endobj 136 0 obj -(psb\137geasum) +(psb\137geasums) endobj 137 0 obj -<< /S /GoTo /D (section*.18) >> +<< /S /GoTo /D (section*.19) >> endobj 140 0 obj (psb\137geasums) endobj 141 0 obj -<< /S /GoTo /D (section*.19) >> +<< /S /GoTo /D (section*.20) >> endobj 144 0 obj -(psb\137geasums) +(psb\137genrm2s) endobj 145 0 obj -<< /S /GoTo /D (section*.20) >> +<< /S /GoTo /D (section*.21) >> endobj 148 0 obj -(psb\137genrm2s) +(psb\137spnrmi) endobj 149 0 obj -<< /S /GoTo /D (section*.21) >> +<< /S /GoTo /D (section*.22) >> endobj 152 0 obj -(psb\137spnrmi) +(psb\137spmm) endobj 153 0 obj -<< /S /GoTo /D (section*.22) >> +<< /S /GoTo /D (section*.23) >> endobj 156 0 obj -(psb\137spmm) +(psb\137spsm) endobj 157 0 obj -<< /S /GoTo /D (section*.23) >> +<< /S /GoTo /D (section.5) >> endobj 160 0 obj -(psb\137spsm) +(5 Communication routines) endobj 161 0 obj -<< /S /GoTo /D (section.5) >> +<< /S /GoTo /D (section*.24) >> endobj 164 0 obj -(5 Communication routines) +(psb\137halo) endobj 165 0 obj -<< /S /GoTo /D (section*.24) >> +<< /S /GoTo /D (section*.25) >> endobj 168 0 obj -(psb\137halo) +(psb\137ovrl) endobj 169 0 obj -<< /S /GoTo /D (section*.25) >> +<< /S /GoTo /D (section*.26) >> endobj 172 0 obj -(psb\137ovrl) +(psb\137gather) endobj 173 0 obj -<< /S /GoTo /D (section*.26) >> +<< /S /GoTo /D (section*.27) >> endobj 176 0 obj -(psb\137gather) +(psb\137scatter) endobj 177 0 obj -<< /S /GoTo /D (section*.27) >> +<< /S /GoTo /D (section.6) >> endobj 180 0 obj -(psb\137scatter) +(6 Data management routines) endobj 181 0 obj -<< /S /GoTo /D (section.6) >> +<< /S /GoTo /D (section*.28) >> endobj 184 0 obj -(6 Data management routines) +(psb\137cdall) endobj 185 0 obj -<< /S /GoTo /D (section*.28) >> +<< /S /GoTo /D (section*.29) >> endobj 188 0 obj -(psb\137cdall) +(psb\137cdins) endobj 189 0 obj -<< /S /GoTo /D (section*.29) >> +<< /S /GoTo /D (section*.30) >> endobj 192 0 obj -(psb\137cdins) +(psb\137cdasb) endobj 193 0 obj -<< /S /GoTo /D (section*.30) >> +<< /S /GoTo /D (section*.31) >> endobj 196 0 obj -(psb\137cdasb) +(psb\137cdcpy) endobj 197 0 obj -<< /S /GoTo /D (section*.31) >> +<< /S /GoTo /D (section*.32) >> endobj 200 0 obj -(psb\137cdcpy) +(psb\137cdfree) endobj 201 0 obj -<< /S /GoTo /D (section*.32) >> +<< /S /GoTo /D (section*.33) >> endobj 204 0 obj -(psb\137cdfree) +(psb\137cdbldext) endobj 205 0 obj -<< /S /GoTo /D (section*.33) >> +<< /S /GoTo /D (section*.34) >> endobj 208 0 obj -(psb\137cdbldext) +(psb\137spall) endobj 209 0 obj -<< /S /GoTo /D (section*.34) >> +<< /S /GoTo /D (section*.35) >> endobj 212 0 obj -(psb\137spall) +(psb\137spins) endobj 213 0 obj -<< /S /GoTo /D (section*.35) >> +<< /S /GoTo /D (section*.36) >> endobj 216 0 obj -(psb\137spins) +(psb\137spasb) endobj 217 0 obj -<< /S /GoTo /D (section*.36) >> +<< /S /GoTo /D (section*.37) >> endobj 220 0 obj -(psb\137spasb) +(psb\137spfree) 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0 0 1 175.423 471.708 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 178.412 464.015 Td [(cols)]TJ +/F8 9.9626 Tf 178.412 471.509 Td [(cols)]TJ 0 g 0 G [-863(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(17)]TJ + [-1084(15)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -40.659 -12.428 Td [(get)]TJ + -40.659 -12.703 Td [(get)]TJ ET q -1 0 0 1 151.635 451.786 cm +1 0 0 1 151.635 459.006 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 154.624 451.587 Td [(global)]TJ +/F8 9.9626 Tf 154.624 458.806 Td [(global)]TJ ET q -1 0 0 1 181.235 451.786 cm +1 0 0 1 181.235 459.006 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.224 451.587 Td [(ro)28(ws)]TJ +/F8 9.9626 Tf 184.224 458.806 Td [(ro)28(ws)]TJ 0 g 0 G 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-12.428 Td [(get)]TJ + -46.47 -12.702 Td [(get)]TJ ET q -1 0 0 1 151.635 426.93 cm +1 0 0 1 151.635 433.601 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 154.624 426.731 Td [(con)28(text)]TJ +/F8 9.9626 Tf 154.624 433.402 Td [(con)28(text)]TJ 0 g 0 G [-868(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(19)]TJ + [-1084(17)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.429 Td [(psb)]TJ + -16.87 -12.703 Td [(psb)]TJ ET q -1 0 0 1 153.351 414.502 cm +1 0 0 1 153.351 420.898 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 156.339 414.302 Td [(cd)]TJ +/F8 9.9626 Tf 156.339 420.699 Td [(cd)]TJ ET q -1 0 0 1 166.9 414.502 cm +1 0 0 1 166.9 420.898 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 169.889 414.302 Td [(get)]TJ +/F8 9.9626 Tf 169.889 420.699 Td [(get)]TJ ET q -1 0 0 1 183.77 414.502 cm +1 0 0 1 183.77 420.898 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.759 414.302 Td [(large)]TJ +/F8 9.9626 Tf 186.759 420.699 Td [(large)]TJ ET q -1 0 0 1 208.416 414.502 cm +1 0 0 1 208.416 420.898 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 211.405 414.302 Td [(threshold)]TJ +/F8 9.9626 Tf 211.405 420.699 Td [(threshold)]TJ 0 g 0 G [-549(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(20)]TJ + [-1084(17)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -73.652 -12.428 Td [(psb)]TJ + -73.652 -12.702 Td [(psb)]TJ ET q -1 0 0 1 153.351 402.073 cm +1 0 0 1 153.351 408.196 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 156.339 401.874 Td [(cd)]TJ +/F8 9.9626 Tf 156.339 407.997 Td [(cd)]TJ ET q -1 0 0 1 166.9 402.073 cm +1 0 0 1 166.9 408.196 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 169.889 401.874 Td [(set)]TJ +/F8 9.9626 Tf 169.889 407.997 Td [(set)]TJ ET q -1 0 0 1 182.718 402.073 cm +1 0 0 1 182.718 408.196 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 185.707 401.874 Td [(large)]TJ +/F8 9.9626 Tf 185.707 407.997 Td [(large)]TJ ET q -1 0 0 1 207.365 402.073 cm +1 0 0 1 207.365 408.196 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 210.354 401.874 Td [(threshold)]TJ +/F8 9.9626 Tf 210.354 407.997 Td [(threshold)]TJ 0 g 0 G [-654(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(20)]TJ + [-1084(18)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -72.601 -12.428 Td [(get)]TJ + -72.601 -12.702 Td [(get)]TJ ET q -1 0 0 1 151.635 389.645 cm +1 0 0 1 151.635 395.494 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 154.624 389.446 Td [(nro)28(ws)]TJ +/F8 9.9626 Tf 154.624 395.295 Td [(nro)28(ws)]TJ 0 g 0 G [-776(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(20)]TJ + [-1084(18)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.428 Td [(get)]TJ + -16.87 -12.703 Td [(get)]TJ ET q -1 0 0 1 151.635 377.217 cm +1 0 0 1 151.635 382.791 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 154.624 377.018 Td [(ncols)]TJ +/F8 9.9626 Tf 154.624 382.592 Td [(ncols)]TJ 0 g 0 G [-362(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(21)]TJ + [-1084(18)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.428 Td [(get)]TJ + -16.87 -12.702 Td [(get)]TJ ET q -1 0 0 1 151.635 364.789 cm +1 0 0 1 151.635 370.089 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 154.624 364.59 Td [(nnzeros)]TJ +/F8 9.9626 Tf 154.624 369.89 Td [(nnzeros)]TJ 0 g 0 G [-804(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(21)]TJ + [-1084(19)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -54.729 -22.707 Td [(4)-925(Computational)-383(r)-1(ou)1(t)-1(ines)]TJ +/F27 9.9626 Tf -54.729 -23.163 Td [(4)-925(Computational)-383(r)-1(ou)1(t)-1(ines)]TJ 0 g 0 G - [-19886(22)]TJ + [-19886(20)]TJ 0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -12.428 Td [(psb)]TJ +/F8 9.9626 Tf 14.944 -12.703 Td [(psb)]TJ ET q -1 0 0 1 130.436 329.654 cm +1 0 0 1 130.436 334.224 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 329.455 Td [(geaxpb)28(y)]TJ +/F8 9.9626 Tf 133.425 334.024 Td [(geaxpb)28(y)]TJ 0 g 0 G [-301(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(23)]TJ + [-1084(21)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.702 Td [(psb)]TJ ET q -1 0 0 1 130.436 317.226 cm +1 0 0 1 130.436 321.521 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 317.027 Td [(gedot)]TJ +/F8 9.9626 Tf 133.425 321.322 Td [(gedot)]TJ 0 g 0 G [-718(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(25)]TJ + [-1083(23)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.702 Td [(psb)]TJ ET q -1 0 0 1 130.436 304.798 cm +1 0 0 1 130.436 308.819 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 304.599 Td [(gedots)]TJ +/F8 9.9626 Tf 133.425 308.62 Td [(gedots)]TJ 0 g 0 G [-323(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(27)]TJ + [-1084(25)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.429 Td [(psb)]TJ + -18.586 -12.703 Td [(psb)]TJ ET q -1 0 0 1 130.436 292.37 cm +1 0 0 1 130.436 296.116 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 292.17 Td [(geamax)]TJ +/F8 9.9626 Tf 133.425 295.917 Td [(geamax)]TJ 0 g 0 G [-579(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(29)]TJ + [-1084(27)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.702 Td [(psb)]TJ ET q -1 0 0 1 130.436 279.941 cm +1 0 0 1 130.436 283.414 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 279.742 Td [(geamaxs)]TJ +/F8 9.9626 Tf 133.425 283.215 Td [(geamaxs)]TJ 0 g 0 G [-962(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(30)]TJ + [-1084(28)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.703 Td [(psb)]TJ ET q -1 0 0 1 130.436 267.513 cm +1 0 0 1 130.436 270.712 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 267.314 Td [(geasum)]TJ +/F8 9.9626 Tf 133.425 270.512 Td [(geasum)]TJ 0 g 0 G [-657(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(31)]TJ + [-1083(29)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.702 Td [(psb)]TJ ET q -1 0 0 1 130.436 255.085 cm +1 0 0 1 130.436 258.009 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 254.886 Td [(geasums)]TJ +/F8 9.9626 Tf 133.425 257.81 Td [(geasums)]TJ 0 g 0 G [-262(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(32)]TJ + [-1084(30)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.702 Td [(psb)]TJ ET q -1 0 0 1 130.436 242.657 cm +1 0 0 1 130.436 245.307 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 242.458 Td [(geasums)]TJ +/F8 9.9626 Tf 133.425 245.108 Td [(geasums)]TJ 0 g 0 G [-262(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(34)]TJ + [-1084(32)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.429 Td [(psb)]TJ + -18.586 -12.703 Td [(psb)]TJ ET q -1 0 0 1 130.436 230.229 cm +1 0 0 1 130.436 232.605 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 230.029 Td [(genrm2s)]TJ +/F8 9.9626 Tf 133.425 232.405 Td [(genrm2s)]TJ 0 g 0 G [-265(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(35)]TJ + [-1084(33)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.702 Td [(psb)]TJ ET q -1 0 0 1 130.436 217.8 cm +1 0 0 1 130.436 219.902 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 217.601 Td [(spnrmi)]TJ +/F8 9.9626 Tf 133.425 219.703 Td [(spnrmi)]TJ 0 g 0 G [-876(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(36)]TJ + [-1084(34)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.702 Td [(psb)]TJ ET q -1 0 0 1 130.436 205.372 cm +1 0 0 1 130.436 207.2 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 205.173 Td [(spmm)]TJ +/F8 9.9626 Tf 133.425 207.001 Td [(spmm)]TJ 0 g 0 G [-490(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(37)]TJ + [-1084(35)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.428 Td [(psb)]TJ + -18.586 -12.703 Td [(psb)]TJ ET q -1 0 0 1 130.436 192.944 cm +1 0 0 1 130.436 194.498 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 192.745 Td [(spsm)]TJ +/F8 9.9626 Tf 133.425 194.298 Td [(spsm)]TJ 0 g 0 G [-929(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(39)]TJ + [-1084(37)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -33.53 -22.707 Td [(5)-925(Comm)32(unication)-384(routines)]TJ +/F27 9.9626 Tf -33.53 -23.163 Td 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[-431(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G - [-1084(70)]TJ + [-1084(68)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(psb)]TJ @@ -1766,7 +1746,7 @@ BT 0 g 0 G [-329(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(71)]TJ + [-1084(69)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -1780,7 +1760,7 @@ BT 0 g 0 G [-934(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(72)]TJ + [-1084(70)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(psb)]TJ @@ -1794,7 +1774,7 @@ BT 0 g 0 G [-712(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(74)]TJ + [-1084(72)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -1808,7 +1788,7 @@ BT 0 g 0 G [-576(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(75)]TJ + [-1084(73)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -1822,7 +1802,7 @@ BT 0 g 0 G [-551(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(76)]TJ + [-1084(74)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(psb)]TJ @@ -1850,7 +1830,7 @@ BT 0 g 0 G [-747(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(77)]TJ + [-1083(75)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -52.879 -13.07 Td [(psb)]TJ @@ -1878,7 +1858,7 @@ BT 0 g 0 G [-748(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(79)]TJ + [-1083(77)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -47.068 -13.071 Td [(psb)]TJ @@ -1899,7 +1879,7 @@ BT 0 g 0 G [-880(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(80)]TJ + [-1084(78)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -28.869 -13.07 Td [(psb)]TJ @@ -1920,7 +1900,7 @@ BT 0 g 0 G [-746(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(81)]TJ + [-1083(79)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -49.57 -13.07 Td [(psb)]TJ @@ -1941,7 +1921,7 @@ BT 0 g 0 G [-824(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(82)]TJ + [-1084(80)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -28.869 -13.071 Td [(psb)]TJ @@ -1962,7 +1942,7 @@ BT 0 g 0 G [-691(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(83)]TJ + [-1084(81)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -42.374 -13.07 Td [(psb)]TJ @@ -1983,7 +1963,7 @@ BT 0 g 0 G [-354(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(84)]TJ + [-1083(82)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -35.456 -13.07 Td [(psb)]TJ @@ -2004,7 +1984,7 @@ BT 0 g 0 G [-605(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(85)]TJ + [-1084(83)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -35.456 -13.071 Td [(psb)]TJ @@ -2025,7 +2005,7 @@ BT 0 g 0 G [-433(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(86)]TJ + [-1084(84)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -31.637 -13.07 Td [(psb)]TJ @@ -2039,19 +2019,19 @@ BT 0 g 0 G [-740(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(88)]TJ + [-1084(86)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(Sorting)-333(utilities)]TJ 0 g 0 G [-519(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(89)]TJ + [-1083(87)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG /F27 9.9626 Tf -14.944 -23.776 Td [(7)-925(P)32(arallel)-384(en)32(vironmen)32(t)-383(routines)]TJ 0 g 0 G - [-16891(91)]TJ + [-16891(89)]TJ 0 0 1 rg 0 0 1 RG /F8 9.9626 Tf 14.944 -13.071 Td [(psb)]TJ ET @@ -2064,7 +2044,7 @@ BT 0 g 0 G [-829(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(92)]TJ + [-1083(90)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -2078,7 +2058,7 @@ BT 0 g 0 G [-690(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(93)]TJ + [-1084(91)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -2092,7 +2072,7 @@ BT 0 g 0 G [-690(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(94)]TJ + [-1084(92)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(psb)]TJ @@ -2113,7 +2093,7 @@ BT 0 g 0 G [-1024(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(95)]TJ + [-1083(93)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -35.456 -13.07 Td [(psb)]TJ @@ -2134,7 +2114,7 @@ BT 0 g 0 G [-994(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(96)]TJ + [-1083(94)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -35.456 -13.07 Td [(psb)]TJ @@ -2148,7 +2128,7 @@ BT 0 g 0 G [-440(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(97)]TJ + [-1084(95)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(psb)]TJ @@ -2162,7 +2142,7 @@ BT 0 g 0 G [-931(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G - [-1084(98)]TJ + [-1084(96)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -2176,7 +2156,7 @@ BT 0 g 0 G [-742(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(99)]TJ + [-1084(97)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(psb)]TJ @@ -2190,7 +2170,7 @@ BT 0 g 0 G [-795(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(100)]TJ + [-1084(98)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -2204,7 +2184,7 @@ BT 0 g 0 G [-545(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(101)]TJ + [-1084(99)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -2218,7 +2198,7 @@ BT 0 g 0 G [-468(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-583(102)]TJ + [-583(100)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.071 Td [(psb)]TJ @@ -2232,7 +2212,7 @@ BT 0 g 0 G [-662(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(103)]TJ + [-584(101)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -18.586 -13.07 Td [(psb)]TJ @@ -2246,7 +2226,7 @@ BT 0 g 0 G 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[<873D15B7399DBC9824362D3D17D2E286> <873D15B7399DBC9824362D3D17D2E286>] >> startxref -938075 +922100 %%EOF diff --git a/docs/src/datastruct.tex b/docs/src/datastruct.tex index fa49e64d..6ebd74c8 100644 --- a/docs/src/datastruct.tex +++ b/docs/src/datastruct.tex @@ -33,22 +33,55 @@ it is only used for the \verb|psb_sizeof| utility. All the general matrix informations and elements to be exchanged among processes are stored within a data structure of the type \hypertarget{descdata}{{\tt psb\_desc\_type}}. -Every structure of this type is associated to a sparse matrix, it -contains data about general matrix informations and elements to be -exchanged among processes. - -It is not necessary for the user to know the internal structure of -\verb|psb_desc_type|, it is set in a transparent mode by the tools -routines of Sec.~\ref{sec:toolsrout}, and its fields may be accessed -if necessary via the routines of sec.~\ref{sec:dataquery}; -nevertheless we include a description for the curious -reader: +Every structure of this type is associated with a discretization +pattern and enables data communications and other operations that are +necessary for implementing the various algorithms of interest to us. + +The data structure itself \verb|psb_desc_type| can be treated as an +opaque object handled via the tools routines of +Sec.~\ref{sec:toolsrout} and~\ref{sec:dataquery}; +nevertheless we include here a description for the curious +reader. + +First we describe the \verb|psb_indx_map| type. This is a data +structure that keeps track of a certain number of basic issues such +as: +\begin{itemize} +\item The value of the communication/MPI context; +\item The number of indices in the index space, i.e. global number of + rows and columns of a sparse matrix; +\item The local set of indices, including: +\begin{itemize} +\item The number of local indices (and local rows); +\item The number of halo indices (and therefore local columns); +\item The global indices corresponding to the local ones. +\end{itemize} +\end{itemize} +There are many different schemes for storing these data; therefore +there are a number of types extending the base one, and the descriptor +structure holds a polymorphic object whose dynamic type can be any of +the extended types. +The methods associated with this data type answer the following +queries: +\begin{itemize} +\item For a given set of local indices, find the corresponding indices + in the global numbering; +\item For a given set of global indices, find the corresponding + indices in the local numbering, if any, or return an invalid +\item Add a global index to the set of halo indices; +\item Find the process owner of each member of a set of global + indices. +\end{itemize} +All methods but the last are purely local; the last method potentially +requires communication among processes, and thus is a synchronous +method. The choice of a specific dynamic type for the index map is +made at the time the descriptor is initially allocated, according to +the mode of initialization (see also~\ref{sec:toolsrout}). + +The descriptor contents are as follows: \begin{description} -\item[{\bf matrix\_data}] includes general information about matrix and -process grid, such as the communication context, the size of the -global matrix, the size of the portion of matrix stored on the current -process, and so on. -Specified as: an allocatable integer array of dimension \verb|psb_mdata_size_|. +\item[{\bf indxmap}] A polymorphic variable of a type that is any + extension of the indx\_map type described above. \\ \item[{\bf halo\_index}] A list of the halo and boundary elements for the current process to be exchanged with other processes; for each processes with which it is necessary to communicate: @@ -88,26 +121,23 @@ ecurrent process: \item Index of a ``master'' process: \end{enumerate} Specified as: an allocatable integer array of rank two. -\item[{\bf loc\_to\_glob}] each element $i$ of this array contains -global identifier of the local variable $i$.\\ -Specified as: an allocatable integer array of rank one. -\item[{\bf glob\_to\_loc, glb\_lc, hashv}] Contain a mapping from - global to local indices. +\item [{\bf bnd\_elem}] A list of all boundary points, i.e. points + that have a connection with other processes. \end{description} -The Fortran~95 definition for \verb|psb_desc_type| structures is +The Fortran~2003 declaration for \verb|psb_desc_type| structures is as follows: \begin{figure}[h!] \begin{Sbox} \begin{minipage}[tl]{0.9\textwidth} \begin{verbatim} type psb_desc_type - integer, allocatable :: matrix_data(:), halo_index(:) - integer, allocatable :: ext_index(:) - integer, allocatable :: ovrlap_elem(:,:) - integer, allocatable :: ovrlap_index(:) - integer, allocatable :: ovr_mst_idx(:) - integer, allocatable :: loc_to_glob(:), glob_to_loc(:) - integer, allocatable :: hashv(:), glb_lc(:,:) + class(psb_indx_map), allocatable :: indxmap + integer, allocatable :: halo_index(:) + integer, allocatable :: ext_index(:) + integer, allocatable :: ovrlap_index(:) + integer, allocatable :: ovrlap_elem(:,:) + integer, allocatable :: ovr_mst_idx(:) + integer, allocatable :: bnd_elem(:) end type psb_desc_type \end{verbatim} \end{minipage} @@ -130,14 +160,7 @@ state, which can take the following values: the associated sparse matrix, such as matrix-vector products, are only possible in this state. \end{description} -The global to local index mapping may be stored in two different -formats: the first is simpler but more expensive, as it requires on -each process an amount of memory proportional to the global size of -the index space; the second is more complex, but only requires memory -proportional to the local index space size. The choice is made at the -time of the initialization according to a threshold; this threshold -may be queried and set using the functions in -sec.~\ref{sec:dataquery}. + \subsubsection{Named Constants} \label{sec:cd_constants} @@ -176,10 +199,12 @@ sec.~\ref{sec:dataquery}. \subsection{Sparse Matrix data structure} \label{sec:spmat} The \hypertarget{spdata}{{\tt psb\_spmat\_type}} data structure -contains all information about local portion of the sparse matrix and +contains all information about the local portion of the sparse matrix and its storage mode. Most of these fields are set by the tools routines when inserting a new sparse matrix; the user needs only -choose, if he/she so whishes, a specific matrix storage mode. \\ +choose, if he/she so whishes, a specific matrix storage mode. + +The \begin{description} \item[{\bf aspk}] Contains values of the local distributed sparse matrix.\\ @@ -335,153 +360,7 @@ contains all information about local portion of the sparse matrix and its storage mode. Most of these fields are set by the tools routines when inserting a new sparse matrix; the user needs only choose, if he/she so whishes, a specific matrix storage mode. \\ -\begin{description} -\item[{\bf aspk}] Contains values of the local distributed sparse -matrix.\\ -Specified as: an allocatable array of rank one of type corresponding -to matrix entries type. -\item[{\bf ia1}] Holds integer information on distributed sparse -matrix. Actual information will depend on data format used.\\ -Specified as: an allocatable integer array of rank one. -\item[{\bf ia2}] Holds integer information on distributed sparse -matrix. Actual information will depend on data format used.\\ -Specified as: an allocatable integer array of rank one. -\item[{\bf infoa}] On entry can hold auxiliary information on distributed sparse -matrix. Actual information will depend on data format used.\\ -Specified as: an integer array of length \verb|psb_ifasize_|. -\item[{\bf fida}] Defines the format of the distributed sparse matrix.\\ -Specified as: a string of length 5 -\item[{\bf descra}] Describe the characteristic of the distributed sparse matrix.\\ -Specified as: array of character of length 9. -\item[{\bf pl}] Specifies the local row permutation of distributed sparse -matrix. If pl(1) is equal to 0, then there isn't row permutation.\\ -Specified as: an allocatable integer array of dimension equal to number of local row (matrix\_data[psb\_n\_row\_\hbox{]}) -\item[{\bf pr}] Specifies the local column permutation of distributed sparse -matrix. If PR(1) is equal to 0, then there isn't columnm permutation.\\ -Specified as: an allocatable integer array of dimension equal to number of -local row (matrix\_data[psb\_n\_col\_\hbox{]}) -\item[{\bf m}] Number of rows; if row indices are stored explicitly, -as in Coordinate Storage, should be greater than or equal to the -maximum row index actually present in the sparse matrix. -Specified as: integer variable. -\item[{\bf k}] Number of columns; if column indices are stored explicitly, -as in Coordinate Storage or Compressed Sparse Rows, should be greater -than or equal to the maximum column index actually present in the sparse matrix. -Specified as: integer variable. -\end{description} -The Fortran~95 interface for distributed sparse matrices containing -double precision real entries is defined as shown in -figure~\ref{fig:spmattype}. The definitions for single precision and -complex data are identical except for the \verb|real| declaration and -for the kind type parameter. -\begin{figure}[h!] - \begin{Sbox} - \begin{minipage}[tl]{0.85\textwidth} -\begin{verbatim} -type psb_sspmat_type - integer :: m, k - character :: fida(5) - character :: descra(10) - integer :: infoa(psb_ifa_size_) - real(psb_spk_), allocatable :: aspk(:) - integer, allocatable :: ia1(:), ia2(:) - integer, allocatable :: pr(:), pl(:) -end type psb_sspmat_type -type psb_dspmat_type - integer :: m, k - character :: fida(5) - character :: descra(10) - integer :: infoa(psb_ifa_size_) - real(psb_dpk_), allocatable :: aspk(:) - integer, allocatable :: ia1(:), ia2(:) - integer, allocatable :: pr(:), pl(:) -end type psb_dspmat_type - -type psb_cspmat_type - integer :: m, k - character :: fida(5) - character :: descra(10) - integer :: infoa(psb_ifa_size_) - complex(psb_spk_), allocatable :: aspk(:) - integer, allocatable :: ia1(:), ia2(:) - integer, allocatable :: pr(:), pl(:) -end type psb_cspmat_type - -type psb_zspmat_type - integer :: m, k - character :: fida(5) - character :: descra(10) - integer :: infoa(psb_ifa_size_) - complex(psb_dpk_), allocatable :: aspk(:) - integer, allocatable :: ia1(:), ia2(:) - integer, allocatable :: pr(:), pl(:) -end type psb_zspmat_type - -\end{verbatim} - \end{minipage} - \end{Sbox} - \setlength{\fboxsep}{8pt} - \begin{center} - \fbox{\TheSbox} - \end{center} - \caption{\label{fig:spmattype} - The PSBLAS defined data type that - contains a sparse matrix.} -\end{figure} - -The following two cases are among the most commonly used: -\begin{description} -\item[fida=``CSR''] Compressed storage by rows. In this case the -following should hold: -\begin{enumerate} -\item \verb|ia2(i)| contains the index of the first element of row -\verb|i|; the last element of the sparse matrix is thus stored at -index $ia2(m+1)-1$. It should contain \verb|m+1| entries in -nondecreasing order (strictly increasing, if there are no empty rows). -\item \verb|ia1(j)| contains the column index and \verb|aspk(j)| -contains the corresponding coefficient value, for all $ia2(1) \le j -\le ia2(m+1)-1$. -\end{enumerate} -\item[fida=``COO''] Coordinate storage. In this case the following -should hold: -\begin{enumerate} -\item \verb|infoa(1)| contains the number of nonzero elements in the -matrix; -\item For all $1 \le j \le infoa(1)$, the coefficient, row index and -column index are stored into \verb|apsk(j)|, \verb|ia1(j)| and -\verb|ia2(j)| respectively. -\end{enumerate} -\end{description} -A sparse matrix has an associated state, which can take the following -values: -\begin{description} -\item[Build:] State entered after the first allocation, and before the - first assembly; in this state it is possible to add nonzero entries. -\item[Assembled:] State entered after the assembly; computations using - the sparse matrix, such as matrix-vector products, are only possible - in this state; -\item[Update:] State entered after a reinitalization; this is used to - handle applications in which the same sparsity pattern is used - multiple times with different coefficients. In this state it is only - possible to enter coefficients for already existing nonzero entries. -\end{description} -\subsubsection{Named Constants} -\label{sec:sp_constants} -\begin{description} -%% \item[psb\_nztotreq\_] Request to fetch the total number of nonzeroes -%% stored in a sparse matrix -%% \item[psb\_nzrowreq\_] Request to fetch the number of nonzeroes in a -%% given row in a sparse matrix -\item[psb\_dupl\_ovwrt\_] Duplicate coefficients should be overwritten - (i.e. ignore duplications) -\item[psb\_dupl\_add\_] Duplicate coefficients should be added; -\item[psb\_dupl\_err\_] Duplicate coefficients should trigger an error conditino -\item[psb\_upd\_dflt\_] Default update strategy for matrix coefficients; -\item[psb\_upd\_srch\_] Update strategy based on search into the data structure; -\item[psb\_upd\_perm\_] Update strategy based on additional - permutation data (see tools routine description). -\end{description} diff --git a/docs/src/figures/psblas.eps 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180 900 4425 25\001 +4 1 0 50 -1 0 12 0.0000 4 135 180 975 3525 27\001 +4 1 0 50 -1 0 12 0.0000 4 135 180 8100 3525 40\001 +4 1 0 50 -1 2 18 0.0000 4 195 300 8700 1950 P1\001 +4 1 0 50 -1 2 18 0.0000 4 195 300 8700 5850 P0\001 diff --git a/docs/src/intro.tex b/docs/src/intro.tex index b44c8d51..4c99429d 100644 --- a/docs/src/intro.tex +++ b/docs/src/intro.tex @@ -21,7 +21,11 @@ mostly in the handling of requirements for evolution and adaptation of the library to new computing architectures and integration of new algorithms. For a detailed discussion of our design see~\cite{Sparse03}; other -works tackling advanced programming in Fortran~2003 include~\cite{DesPat:11,RouXiaXu:11} +works discussing advanced programming in Fortran~2003 +include~\cite{DesPat:11,RouXiaXu:11}; sufficient support for +Fortran~2003 is now available from many compilers, including the GNU +Fortran compiler from the Free Software Foundation (as of version 4.6). + Previous approaches have been based on mixing Fortran~95, with its support for object-based design, with other languages; these have @@ -32,12 +36,7 @@ usability of the PSBLAS subroutines. In this way, the library can take care of runtime memory requirements that are quite difficult or even impossible to predict at implementation or compilation time. -In the current release we rely on the availability of the so-called -allocatable extensions, specified in TR~15581. Strictly speaking they -are outside the Fortran~95 standard; however they have been included -in the Fortran~2003 language standard, and are available in -practically all Fortran~95 compilers on the market, including the GNU -Fortran compiler from the Free Software Foundation (as of version 4.2). + The presentation of the PSBLAS library follows the general structure of the proposal for serial Sparse BLAS~\cite{sblas97,sblas02}, which in its turn is based on the @@ -84,20 +83,16 @@ influenced by the structure of the ScaLAPACK parallel library. The layered structure of the PSBLAS library is shown in figure~\ref{fig:psblas}; lower layers of the library indicate an encapsulation relationship with upper layers. The ongoing -discussion focuses on the Fortran~95 layer immediately below the +discussion focuses on the Fortran~2003 layer immediately below the application layer. The serial parts of the computation on each process are executed through -calls to the serial sparse BLAS subroutines. In a similar way, the -inter-process message exchanges are implemented through the Basic -Linear Algebra Communication Subroutines (BLACS) library~\cite{BLACS} -that guarantees a portable and efficient communication layer. The -Message Passing Interface code is encapsulated within the BLACS -layer. However, in some cases, MPI routines are directly used either -to improve efficiency or to implement communication patterns for which -the BLACS package doesn't provide any method. - -In any case we provide wrappers around the BLACS routines so that the -user does not need to delve into their details (see Sec.~\ref{sec:parenv}). +calls to the serial sparse BLAS subroutines. +In a similar way, the inter-process message exchanges are encapsulated +in an applicaiton layer that has been strongly inspired by the Basic +Linear Algebra Communication Subroutines (BLACS) library~\cite{BLACS}. +Usually there is no need to deal directly with MPI; however, in some +cases, MPI routines are used directly to improve efficiency. For +further details on our communication layer see Sec.~\ref{sec:parenv}. %% We assume that the user program has initialized a BLACS process grid %% with one column and as many rows as there are processes; the PSBLAS %% initialization routines will take the communication context for this @@ -136,10 +131,12 @@ sub-domains}. Our library supports any distribution that keeps together the coefficients of each matrix row; there are no other constraints on the variable assignment. -This choice is consistent with data distributions commonly used in -ScaLAPACK such as \verb|CYCLIC(N)| and \verb|BLOCK|, +This choice is consistent with simple data distributions +%commonly used in ScaLAPACK +such as \verb|CYCLIC(N)| and \verb|BLOCK|, as well as completely arbitrary assignments of -equation indices to processes. In particular it is consistent with the +equation indices to processes. +In particular it is consistent with the usage of graph partitioning tools commonly available in the literature, e.g. METIS~\cite{METIS}. Dense vectors conform to sparse diff --git a/docs/src/userguide.tex b/docs/src/userguide.tex index b561e217..8f1a9ded 100644 --- a/docs/src/userguide.tex +++ b/docs/src/userguide.tex @@ -100,7 +100,7 @@ by Salvatore Filippone\\ and Alfredo Buttari}\\ University of Rome ``Tor Vergata''.\\[3ex] -May 15th, 2010. +December 15th, 2011. \end{minipage}} %\addtolength{\textwidth}{\centeroffset} diff --git a/docs/src/userhtml.tex b/docs/src/userhtml.tex index 4c20cd12..5992afbb 100644 --- a/docs/src/userhtml.tex +++ b/docs/src/userhtml.tex @@ -85,7 +85,7 @@ %\today Software version: 3.0-beta\\ %\today -May 15th, 2010 +December 15th, 2011 \cleardoublepage \begingroup \renewcommand*{\thepage}{toc}