From 09ab7c660492d135d3ff52917d0cb825747a3428 Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Fri, 19 Oct 2007 12:32:09 +0000 Subject: [PATCH] Fixed image of PSBLAS. --- docs/pdf/datastruct.tex | 7 +- docs/pdf/figures/psblas.pdf | Bin 2177 -> 2066 bytes docs/pdf/intro.tex | 21 +- docs/pdf/toolsrout.tex | 5 +- docs/pdf/userguide.tex | 37 +- docs/userguide.pdf | 9033 ++++++++++++++++++----------------- 6 files changed, 4614 insertions(+), 4489 deletions(-) diff --git a/docs/pdf/datastruct.tex b/docs/pdf/datastruct.tex index 742fd913..f78e609c 100644 --- a/docs/pdf/datastruct.tex +++ b/docs/pdf/datastruct.tex @@ -94,7 +94,7 @@ 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. \end{description} -The Fortran95 definition for \verb|psb_desc_type| structures is +The Fortran~95 definition for \verb|psb_desc_type| structures is as follows: \begin{figure}[h!] \begin{Sbox} @@ -203,8 +203,9 @@ 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} -FORTRAN95 interface for distributed sparse matrices containing double precision -real entries is defined as in figure~\ref{fig:spmattype}. +The Fortran~95 interface for distributed sparse matrices containing +double precision real entries is defined as shown in +figure~\ref{fig:spmattype}. \begin{figure}[h!] \begin{Sbox} \begin{minipage}[tl]{0.85\textwidth} diff --git a/docs/pdf/figures/psblas.pdf b/docs/pdf/figures/psblas.pdf index 56e52047f6d45bd3901ff25db83d380f7c94aa58..5d0d1820a2d638301570ea6555bc73513bc72778 100644 GIT binary patch delta 1538 zcmZn^oFu@Z8sOrlYp7>Dk;A?|>~vnVxxn4e+BJoQ)w#4pWV_KlkXJhC~BrBO%eHM=(=9sKRnt1kr>_uni(%)i_I z=y~gpeiN=cT59(eYq>NhSUD-O*>SRe&NZB{{gi7>cUa_GZ=UewmmmJQ@xP5pvwwxz zwZn-mkJLYARa@MD+h0_@-#)%e%5|xybb$4f`ej;s|Gqt2Ci5`adt0E{l$_|P3!YCt ztpCtO+p?f&_8Xf#buSD4Th3~$jn*kYx)ifO(f`n|B|YWLjLvt($p z?nEJ3#mQ^A*hH8&URxoNvQ*{7K~4SD=k7Jo7;XHYD-ag+CN(K5%drO$GN=AV|$ z%51vq!4Y5oFmOgn`2Q*X?ip5(r#SE1?5*{L=WCoDJg!< zs<(Zo{hn#+69X3CyBsjrT~F+>?z_;_x6@TVd-qLCNDBKW-?X#RcGu_MmJj#zZ}PdP zx$e_~;Mc#qE;#ftf7}tWDR9}Esjg2GR|xDfjt-x(+lF(|oT>G)2LdM)?)YLLVALV( zdO>pco!X{FiYas5?uzvFsjTO5b9}6l?!mauZng<$pVlkJ2O_4g)V>#&Z*yJuFRL;s zA+CL)RyQd$HojmcD(8Z&f;&n;>{|H@@P_o435ui|<2)wP0i z*KN<4P?a6dpdUO}!r}C9cda_p8$4FxY_V$t7N5MpDF|ym2`*6nUQQ93)Xs!3V-m*;cmM(%yuJ7HeVz2(n7 zd+W_(-*#`~fAOo&|Nm2YcHR5ajS9!9E03MOX#V~C@!gsK3%)-MnZJn3{QcxRDtl@_ ze$ZWi=C!l#eq&YbgtSWTK3+Ay2NN&HEws;FU0FLTZb{TsU1E4)1ppd7)1!fo+ni-m4 zh#8w0Vu%5)oxGD>HQ3M`Q_jQ$=wdW;O|giXSO9|xU7exDWKIrgCZH2lIpl4>Xsag# rhg5t#U$(d}T(2QTQv*XJmJ1j(#U+VFC1Bqfnj4vNsj9mAyKw;kPBo3> delta 1736 zcmZvYe>~H99LIBHtaDmP88=(z%#ZB*o&B)Is*}}3$L?-8sW5Y-?Q&b`Qj=dphM7xS ze)L01xYVT6a)(R|n;(%|M~I6P#c)mCId_ll9`|^3?|(k;_w)6BzdrBJCvWX(n2Ejr zPTCgG6(=^?CJ6H5{!Cn3KNa}$oH5uwLdv0cTNuPNbiyZ5m`o*m`fjdG)Zq()A9E~( z`GX5(L(K!pM~j>F!yO*k^WGTx$Kwa;Ib|d57gBTq8PTn+?gL{R1*)neuMWKm-B$p~ zk6+&NyIj#6BU^sd&R)k=3vHi3E{f)5S?)h>Vuzr^1^KR4BU!$dq_PoZj6(56PB>pa zG{_OSFP{LIPPYOICom#@{I9()M>}ua2-N?gd3K+Bf7kculbdHDyi@SJ8X{%ZJZqmB zLPn1c6Z!P)OevKt;uu~nVGH;YkqTiSc3YyoI=b*!qfiVkQ5ZmG8qj5!{cvddN*`v6#|Oo;1*v zd*o%?XijuG$%nS3Q0{mjxaRZ)pV&0$K#JKM(fQi;=4@+hP>I=oJLjY=x9(Ztm6v4V zBVF2E8eZYT^?&UAT)RAN80XVT-HdD|o3Tc! zW?Bbe+_3u==)8_d3*TJS1MPfGR96JHo8@`9YB2tG2JHM7zPBhtcdw=Zcjm?g`_3)a z>EkhoW4m9NjgLlhI}l2_wB73YV@t=jRmEUNTwA01Bs!43U3_iAdNed|%X)*Y>OKv6(+L|AfW^ z{`K&!j5oB~@)r0BdGL6hR%+h0hNiW*1$y*}V(pNuMr9oI*;!U~k$J9-8{|P^-^=Q5 z1FKJZ?$RJG$0!F&dkyS<*2-0az2>p#^DG>VrV}MJP<>y&Nx)kc9So_fziBg;{DM0Z z?f7s4OGjgz972D&l4fMSA9qF5b!1q!IvfxhSsX~Gy0wf-uRrsL2G}?Wb~RR9WnK$? z0y-v4+~>7wym`hB1)iJQhb*Wib+7X|7|W(TEfLUm;fyC*_bn=SRZQ7?_Zndy>**wN zqOg!Yp*x$D-&Ix@3%|5u{J390M!;qyIBZLg{;!Q>)9}dgw)BRX0qSuKX%QIqdlmo90nv_(4Gp zn(y1IAE;cqB%z}OvEp&{uUR~1RH^)%eyOa3wzWcYsynGK>Op7(Kl@D8tpt~fr#7xn zcSP}N6aq@_PM%MawX)>xs2kgKeC7-N)Y5kTeATCj*TA$+pqmZi&3s-@I-6Yi$M2n< zTT(w75t(}#N)y?tEZA&jBB#7zz@SK&+Jpkj8JQm)V_r1s?gkbc*j2r3rR`Xqdsprc>W* zT%?lIrot9f2zBGVAL^`b5T_Isnn!xKMpN~M2tNx4qo%!1XEiQd$&xNsX&VxU@Y=11 zHLukcoGW3FK37XLbLbJAsc1^kgW*(RboE z>U?2w{Rw+DweW{^4Ar8i-SQu+jlFA`ksQ|7ytv4)!_bwC8y*8CA_3%IC+G%}B_&4A z>xdu@Nh0Gyp;!i&7siW30+L=Mz?jD6@R05j>(wHJ``Zx@4=jTOC9PBpD)k>flEln7 zM&RZM#d@t=!;9u}cCMIUc2aNvKmtIJ2omrh0a(%fxUBz|sMNQ+#m7amp#YK$1^x{r zkw9=GAlb;b3?$<4$iG!2=U+y0BCc%pSNsPOh=g|-9*38pAok99;D1a2@ST1l2`7<4 ztPRMLT8ORZU^Q&L#kCEg$A=?}li8*Lj+l2yD0Jm#zUGC+@&0}b=uUEn+S_}7LWBMZ DbhHW~ diff --git a/docs/pdf/intro.tex b/docs/pdf/intro.tex index 0d2487bd..80654b1a 100644 --- a/docs/pdf/intro.tex +++ b/docs/pdf/intro.tex @@ -11,8 +11,10 @@ dense matrix operations. The current implementation of PSBLAS addresses a distributed memory execution model operating with message passing. -The PSBLAS library is internally implemented in a mixture of -Fortran~77 and Fortran~95~\cite{metcalf} programming languages. +The PSBLAS library is internally implemented in + the Fortran~95~\cite{metcalf} programming language, with reuse and/or + adaptation of some existing Fortran~77 software, and a handful of C + routines. A similar approach has been advocated by a number of authors, e.g.~\cite{machiels}. Moreover, the Fortran~95 facilities for dynamic memory management and interface overloading greatly enhance the @@ -70,7 +72,7 @@ structures of the serial kernels is available to the parallel version. The overall design and parallelization strategy have been 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 +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 application layer. @@ -92,7 +94,7 @@ user does not need to delve into their details (see Sec.~\ref{sec:parenv}). %% grid and store internally for further use. \begin{figure}[h] \begin{center} -\includegraphics[scale=0.45]{figures/psblas} +\rotatebox{-90}{\includegraphics[scale=0.65]{figures/psblas}} \end{center} \caption{PSBLAS library components hierarchy.\label{fig:psblas}} \end{figure} @@ -173,7 +175,12 @@ another domain such that there is a boundary point which {\em depends\/} on it. Whenever performing a computational step, such as a matrix-vector product, the values associated with halo points are requested from other domains. A boundary point of a given -domain is a halo point for (at least) another domain; therefore +domain is usually a halo point for some other domain\footnote{This is + the normal situation when the pattern of the sparse matrix is + symmetric, which is equivalent to say that the interaction between + two variables is reciprocal. If the matrix pattern is non-symmetric + we may have one-way interactions, and these could cause a situation + in which a boundary point is not a halo point for its neighbour.}; therefore the cardinality of the boundary points set denotes the amount of data sent to other domains. \item[Overlap.] An overlap point is a boundary point assigned to @@ -182,8 +189,8 @@ has to be replicated for each assignment. \end{description} Overlap points do not usually exist in the basic data distribution, but they are a feature of Domain Decomposition -Schwarz preconditioners which we are in the process of including in -our distribution~\cite{PARA04,APNUM06}. +Schwarz preconditioners which we are the subject of related research +work~\cite{2007c,2007d}. We denote the sets of internal, boundary and halo points for a given subdomain by $\cal I$, $\cal B$ and $\cal H$. diff --git a/docs/pdf/toolsrout.tex b/docs/pdf/toolsrout.tex index 50dc9dad..9463b27f 100644 --- a/docs/pdf/toolsrout.tex +++ b/docs/pdf/toolsrout.tex @@ -1352,8 +1352,9 @@ position as the corresponding entries in $x$. \end{description} \section*{Usage notes} \begin{enumerate} -\item The sorting can be performed in the up/down direction; for - complex data the sorting must be done on the absolute values; +\item The sorting can be performed in the up/down direction, on the + natural or absolute values; for complex data the sorting can only + be done on the absolute values; \item 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 diff --git a/docs/pdf/userguide.tex b/docs/pdf/userguide.tex index e3d51f10..ec293b2a 100644 --- a/docs/pdf/userguide.tex +++ b/docs/pdf/userguide.tex @@ -103,11 +103,28 @@ \cleardoublepage \begin{thebibliography}{99} + +\bibitem{PARA04FOREST} +G.~Bella, S.~Filippone, A.~De Maio and M.~Testa, +{\em 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. +\bibitem{2007d} A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,\newblock +2LEV-D2P4: a package of high-performance preconditioners,\newblock +Applicable Algebra in Engineering, Communications and Computing, +Volume 18, Number 3, May, 2007, pp. 223-239 +%Published online: 13 February 2007, {\tt http://dx.doi.org/10.1007/s00200-007-0035-z} % -\bibitem{BLAS1} -Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., - Basic {L}inear {A}lgebra {S}ubprograms for {F}ortran usage, -{ACM Trans. Math. Softw.} vol.~{5}, 38--329, 1979. +\bibitem{2007c} P. D'Ambra, S. Filippone, D. Di Serafino\newblock +On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners +\newblock +Applied Numerical Mathematics, Elsevier Science, +Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196. +%published online 3 February 2007, {\tt +% http://dx.doi.org/10.1016/j.apnum.2007.01.006} + \bibitem{BLAS2} Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R., An Extended Set of {F}ortran {B}asic {L}inear {A}lgebra {S}ubprograms, @@ -122,13 +139,6 @@ A Set of level 3 Basic Linear Algebra Subprograms, %% Advances in Computational Mathematics, 1993, 1, 127-137. %% (See also {\tt http://www.mgnet.org/~douglas/ccd-codes.html}) % -\bibitem{PARA04FOREST} -G.~Bella, S.~Filippone, A.~De Maio and M.~Testa, -{\em 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. % %% \bibitem{PARA04} %% A.~Buttari, P.~D'Ambra, D.~di Serafino and S.~Filippone, @@ -215,6 +225,11 @@ Karypis, G. and Kumar, V., Minneapolis, MN 55455: University of Minnesota, Department of Computer Science, 1995. Internet Address: {\verb|http://www.cs.umn.edu/~karypis|}. +\bibitem{BLAS1} +Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., + Basic {L}inear {A}lgebra {S}ubprograms for {F}ortran usage, +{ACM Trans. Math. Softw.} vol.~{5}, 38--329, 1979. + \bibitem{machiels} {Machiels, L. and Deville, M.} {\em Fortran 90: An entry to object-oriented programming for the solution diff --git a/docs/userguide.pdf b/docs/userguide.pdf index 6cf6f8d5..f3f19d09 100644 --- a/docs/userguide.pdf +++ b/docs/userguide.pdf @@ -665,7 +665,7 @@ ET 0 g 0 G 1 0 0 1 -350.8992 -402.6932 cm BT -/F29 9.9626 Tf 355.8805 402.6932 Td[(b)32(y)-383(Sal)-1(v)64(ator)1(e)-384(Fili)-1(pp)-32(on)1(e)]TJ 12.8891 -18.5969 Td[(and)-383(A)-1(lfredo)-383(Butt)-1(ar)1(i)]TJ/F8 9.9626 Tf -131.4179 -25.2387 Td[(\134T)83(or)-333(V)83(ergata")-333(Un)1(iv)28(e)-1(r)1(s)-1(it)28(y)-333(of)-333(Rome)-1(.)-444(Octob)-27(e)-1(r)-333(18,)-333(2007)]TJ +/F29 9.9626 Tf 355.8805 402.6932 Td[(b)32(y)-383(Sal)-1(v)64(ator)1(e)-384(Fili)-1(pp)-32(on)1(e)]TJ 12.8891 -18.5969 Td[(and)-383(A)-1(lfredo)-383(Butt)-1(ar)1(i)]TJ/F8 9.9626 Tf -131.4179 -25.2387 Td[(\134T)83(or)-333(V)83(ergata")-333(Un)1(iv)28(e)-1(r)1(s)-1(it)28(y)-333(of)-333(Rome)-1(.)-444(Octob)-27(e)-1(r)-333(19,)-333(2007)]TJ ET 1 0 0 1 99.8954 90.4377 cm 0 g 0 G @@ -797,7 +797,7 @@ ET 0 g 0 G 1 0 0 1 -438.6251 -632.8697 cm BT -/F8 9.9626 Tf 438.6251 632.8697 Td[(5)]TJ +/F8 9.9626 Tf 438.6251 632.8697 Td[(4)]TJ ET 1 0 0 1 443.6065 632.8697 cm 0 g 0 G @@ -817,7 +817,7 @@ ET 0 g 0 G 1 0 0 1 -438.6251 -619.8808 cm BT -/F8 9.9626 Tf 438.6251 619.8808 Td[(6)]TJ +/F8 9.9626 Tf 438.6251 619.8808 Td[(5)]TJ ET 1 0 0 1 443.6065 619.8808 cm 0 g 0 G @@ -837,7 +837,7 @@ ET 0 g 0 G 1 0 0 1 -438.6251 -606.8919 cm BT -/F8 9.9626 Tf 438.6251 606.8919 Td[(8)]TJ +/F8 9.9626 Tf 438.6251 606.8919 Td[(7)]TJ ET 1 0 0 1 443.6065 606.8919 cm 0 g 0 G @@ -5085,7 +5085,7 @@ endobj /ProcSet [ /PDF /Text ] >> endobj 561 0 obj << -/Length 11319 +/Length 11464 >> stream 1 0 0 1 99.8954 740.9981 cm @@ -5094,91 +5094,91 @@ stream 0 g 0 G 1 0 0 1 -443.6065 -740.9981 cm BT -/F18 14.3462 Tf 99.8954 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1 409.3334 573.3639 cm 0 1 0 rg 0 1 0 RG -1 0 0 1 -172.3375 -554.3723 cm +1 0 0 1 -409.3334 -573.3639 cm BT -/F8 9.9626 Tf 172.3375 554.3723 Td[(12)]TJ +/F8 9.9626 Tf 409.3334 573.3639 Td[(14)]TJ ET -1 0 0 1 182.3001 554.3723 cm +1 0 0 1 419.2961 573.3639 cm 0 g 0 G -1 0 0 1 -182.3001 -554.3723 cm +1 0 0 1 -419.2961 -573.3639 cm BT -/F8 9.9626 Tf 182.3001 554.3723 Td[(])-362(p)1(rogr)1(am)-1(min)1(g)-362(langu)1(age)-1(s.)-529(A)-362(s)-1(i)1(m)-1(il)1(ar)-362(ap)1(proac)28(h)-362(h)1(as)-362(b)-28(ee)-1(n)-361(ad)1(-)]TJ -82.4047 -11.9552 Td[(v)28(o)-28(cate)-1(d)-391(b)28(y)-391(a)-392(n)28(u)1(m)27(b)-27(e)-1(r)-391(of)-391(auth)1(ors)-1(,)-406(e.g.)-391([)]TJ +/F8 9.9626 Tf 419.2961 573.3639 Td[(])-382(p)1(ro-)]TJ -319.4007 -11.9551 Td[(gramming)-345(lan)1(guage,)-348(w)-1(i)1(th)-345(reuse)-346(an)1(d/or)-345(ad)1(aptation)-344(of)-345(s)-1(ome)-346(existin)1(g)-346(F)84(ortr)1(an)-345(77)]TJ 0 -11.9552 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-410.9103 cm +1 0 0 1 -150.7822 -405.9916 cm BT -/F8 9.9626 Tf 249.3908 410.9103 Td[(],)-381(whi)1(c)27(h)-371(in)-372(i)1(ts)-372(turn)-371(is)-372(b)1(as)-1(ed)-372(on)-371(th)1(e)-373(p)1(rop)-27(os)-1(al)]TJ -149.4954 -11.9552 Td[(for)-333(BLAS)-333(on)-333(d)1(e)-1(n)1(s)-1(e)-333(m)-1(atr)1(ic)-1(es)-334([)]TJ +/F8 9.9626 Tf 150.7822 405.9916 Td[(],)-487(whic)28(h)-456(in)-456(its)-457(tur)1(n)-457(i)1(s)-457(base)-1(d)-456(on)-456(the)-457(p)1(rop)-27(os)-1(al)-456(for)-456(B)-1(LAS)-456(on)-456(d)1(e)-1(n)1(s)-1(e)]TJ -50.8868 -11.9552 Td[(matrice)-1(s)-333([)]TJ ET -1 0 0 1 228.469 398.9551 cm +1 0 0 1 142.5964 394.0364 cm 0 1 0 rg 0 1 0 RG -1 0 0 1 -228.469 -398.9551 cm +1 0 0 1 -142.5964 -394.0364 cm BT -/F8 9.9626 Tf 228.469 398.9551 Td[(1)]TJ +/F8 9.9626 Tf 142.5964 394.0364 Td[(12)]TJ ET -1 0 0 1 233.4504 398.9551 cm +1 0 0 1 152.5591 394.0364 cm 0 g 0 G -1 0 0 1 -233.4504 -398.9551 cm +1 0 0 1 -152.5591 -394.0364 cm BT -/F8 9.9626 Tf 233.4504 398.9551 Td[(,)]TJ +/F8 9.9626 Tf 152.5591 394.0364 Td[(,)]TJ ET -1 0 0 1 239.5386 398.9551 cm +1 0 0 1 158.6474 394.0364 cm 0 1 0 rg 0 1 0 RG -1 0 0 1 -239.5386 -398.9551 cm +1 0 0 1 -158.6474 -394.0364 cm BT -/F8 9.9626 Tf 239.5386 398.9551 Td[(2)]TJ +/F8 9.9626 Tf 158.6474 394.0364 Td[(4)]TJ ET -1 0 0 1 244.52 398.9551 cm +1 0 0 1 163.6287 394.0364 cm 0 g 0 G -1 0 0 1 -244.52 -398.9551 cm +1 0 0 1 -163.6287 -394.0364 cm BT -/F8 9.9626 Tf 244.52 398.9551 Td[(,)]TJ +/F8 9.9626 Tf 163.6287 394.0364 Td[(,)]TJ ET -1 0 0 1 250.6083 398.9551 cm +1 0 0 1 169.717 394.0364 cm 0 1 0 rg 0 1 0 RG -1 0 0 1 -250.6083 -398.9551 cm +1 0 0 1 -169.717 -394.0364 cm BT -/F8 9.9626 Tf 250.6083 398.9551 Td[(3)]TJ +/F8 9.9626 Tf 169.717 394.0364 Td[(5)]TJ ET -1 0 0 1 255.5896 398.9551 cm +1 0 0 1 174.6984 394.0364 cm 0 g 0 G -1 0 0 1 -255.5896 -398.9551 cm +1 0 0 1 -174.6984 -394.0364 cm BT -/F8 9.9626 Tf 255.5896 398.9551 Td[(].)]TJ -140.7502 -19.763 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587.0754 cm +1 0 0 1 328.1276 587.7016 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -309.6887 -587.0754 cm +1 0 0 1 -328.1276 -587.7016 cm BT -/F8 9.9626 Tf 309.6887 587.0754 Td[(1)]TJ +/F8 9.9626 Tf 328.1276 587.7016 Td[(1)]TJ ET -1 0 0 1 314.67 587.0754 cm +1 0 0 1 333.1089 587.7016 cm 0 g 0 G -1 0 0 1 -314.67 -587.0754 cm +1 0 0 1 -333.1089 -587.7016 cm BT -/F8 9.9626 Tf 318.8345 587.0754 Td[(;)-460(lo)28(w)27(er)-418(l)1(a)27(y)28(ers)-418(of)-418(th)1(e)-419(li)1(brar)1(y)-418(in)1(dicate)-418(an)]TJ -168.1296 -11.9552 Td[(encapsulati)1(on)-423(r)1(e)-1(l)1(ationshi)1(p)-422(w)-1(i)1(th)-422(upp)-27(er)-423(l)1(a)27(y)28(ers.)-712(The)-423(on)1(goin)1(g)-423(d)1(is)-1(cuss)-1(i)1(on)-422(fo)-28(cuse)-1(s)]TJ 0 -11.9552 Td[(on)-444(t)1(he)-444(F)83(ort)1(ran)-444(95)-444(la)28(y)28(er)-444(imme)-1(d)1(iately)-444(b)-27(e)-1(lo)28(w)-444(the)-444(app)1(lication)-443(la)28(y)28(e)-1(r)1(.)-777(The)-444(se)-1(ri)1(al)]TJ 0 -11.9551 Td[(par)1(ts)-475(of)-473(the)-474(c)-1(ompu)1(tation)-473(on)-474(eac)27(h)-474(p)1(ro)-28(ce)-1(ss)-475(ar)1(e)-475(exec)-1(u)1(te)-1(d)-473(throu)1(gh)-474(calls)-474(to)-474(the)]TJ 0 -11.9552 Td[(se)-1(ri)1(al)-455(spar)1(s)-1(e)-455(BLAS)-454(sub)1(rout)1(ines)-1(.)-807(In)-454(a)-455(similar)-454(w)28(a)27(y)84(,)-485(t)1(he)-455(in)29(te)-1(r)1(-)-1(p)1(ro)-28(ce)-1(ss)-455(me)-1(ss)-1(age)]TJ 0 -11.9552 Td[(exc)27(h)1(anges)-370(ar)1(e)-370(i)1(m)-1(p)1(lem)-1(en)28(ted)-369(th)1(rou)1(gh)-369(t)1(he)-369(B)-1(asic)-369(Lin)1(e)-1(ar)-368(Algebra)-368(C)-1(omm)27(u)1(ni)1(c)-1(ation)]TJ 0 -11.9551 Td[(Su)1(br)1(outin)1(e)-1(s)-353(\050BLA)27(CS)1(\051)-353(lib)1(rary)-353([)]TJ +/F8 9.9626 Tf 333.1089 587.7016 Td[(;)-470(l)1(o)27(w)28(er)-424(la)28(y)28(e)-1(rs)-424(of)-424(the)-424(lib)1(rary)-424(in)1(di)1(c)-1(ate)]TJ -182.404 -11.9552 Td[(an)-463(encapsulati)1(on)-463(relation)1(s)-1(h)1(ip)-463(with)-463(up)1(p)-27(e)-1(r)-463(la)28(y)28(ers)-1(.)-834(The)-464(on)1(goin)1(g)-464(d)1(is)-1(cussion)-463(fo-)]TJ 0 -11.9551 Td[(cuse)-1(s)-448(on)-448(th)1(e)-449(F)84(ortran)-447(95)-448(la)28(y)28(e)-1(r)-448(i)1(m)-1(me)-1(d)1(iately)-448(b)-27(e)-1(l)1(o)27(w)-448(th)1(e)-449(ap)1(plication)-447(la)28(y)28(e)-1(r)1(.)-789(The)]TJ 0 -11.9552 Td[(se)-1(ri)1(al)-399(parts)-399(of)-399(the)-399(c)-1(ompu)1(tation)-399(on)-399(eac)27(h)-399(p)1(ro)-28(ces)-1(s)-400(ar)1(e)-400(exe)-1(cuted)-399(th)1(rough)-398(c)-1(all)1(s)-400(to)]TJ 0 -11.9552 Td[(th)1(e)-311(se)-1(r)1(ial)-310(spar)1(s)-1(e)-310(BLAS)-309(s)-1(u)1(brou)1(tines.)-437(In)-309(a)-310(sim)-1(i)1(lar)-310(w)28(a)28(y)83(,)-314(th)1(e)-311(i)1(n)28(ter-pro)-27(c)-1(es)-1(s)-310(me)-1(ss)-1(age)]TJ 0 -11.9551 Td[(exc)27(h)1(anges)-370(ar)1(e)-370(i)1(m)-1(p)1(lem)-1(en)28(ted)-369(th)1(rou)1(gh)-369(t)1(he)-369(B)-1(asic)-369(Lin)1(e)-1(ar)-368(Algebra)-368(C)-1(omm)27(u)1(ni)1(c)-1(ation)]TJ 0 -11.9552 Td[(Su)1(br)1(outin)1(e)-1(s)-353(\050BLA)27(CS)1(\051)-353(lib)1(rary)-353([)]TJ ET -1 0 0 1 285.6515 515.3444 cm +1 0 0 1 285.6515 515.9706 cm 0 1 0 rg 0 1 0 RG -1 0 0 1 -285.6515 -515.3444 cm +1 0 0 1 -285.6515 -515.9706 cm BT -/F8 9.9626 Tf 285.6515 515.3444 Td[(5)]TJ +/F8 9.9626 Tf 285.6515 515.9706 Td[(6)]TJ ET -1 0 0 1 290.6329 515.3444 cm +1 0 0 1 290.6329 515.9706 cm 0 g 0 G -1 0 0 1 -290.6329 -515.3444 cm +1 0 0 1 -290.6329 -515.9706 cm BT -/F8 9.9626 Tf 290.6329 515.3444 Td[(])-353(th)1(at)-353(guar)1(an)28(te)-1(es)-354(a)-353(p)-27(ort)1(able)-353(and)-352(e)-1(\016c)-1(i)1(e)-1(n)28(t)-353(com-)]TJ -139.928 -11.9552 Td[(m)27(u)1(ni)1(c)-1(ation)-398(la)28(y)28(e)-1(r)1(.)-642(T)-1(h)1(e)-400(Mess)-1(age)-400(P)29(as)-1(sing)-399(In)28(terf)1(ac)-1(e)-399(c)-1(o)-28(d)1(e)-400(is)-399(e)-1(n)1(c)-1(ap)1(s)-1(u)1(late)-1(d)-398(w)-1(i)1(thin)]TJ 0 -11.9552 Td[(th)1(e)-386(BLA)27(CS)-384(la)28(y)28(e)-1(r)1(.)-600(Ho)28(w)27(ev)28(er,)-398(in)-384(s)-1(ome)-386(case)-1(s,)-398(MP)1(I)-385(routi)1(nes)-386(are)-385(di)1(re)-1(ctly)-384(use)-1(d)-385(ei-)]TJ 0 -11.9551 Td[(th)1(e)-1(r)-403(to)-404(i)1(m)-1(p)1(ro)28(v)28(e)-404(e)-1(\016c)-1(i)1(e)-1(n)1(c)-1(y)-403(or)-403(to)-404(impl)1(e)-1(me)-1(n)29(t)-404(com)-1(m)28(un)1(ic)-1(at)1(ion)-403(pattern)1(s)-404(for)-403(w)-1(h)1(ic)27(h)]TJ 0 -11.9552 Td[(th)1(e)-334(B)-1(LA)28(CS)-333(p)1(ac)27(k)56(age)-334(do)-27(e)-1(sn't)-333(pr)1(o)28(vide)-333(an)28(y)-333(m)-1(eth)1(o)-28(d.)]TJ 14.9439 -12.8102 Td[(In)-416(an)29(y)-416(c)-1(ase)-417(w)28(e)-416(pro)28(vi)1(de)-416(w)-1(r)1(app)-27(e)-1(r)1(s)-417(ar)1(oun)1(d)-416(th)1(e)-417(BLA)28(C)-1(S)-415(rou)1(tines)-416(s)-1(o)-416(th)1(at)-416(the)]TJ -14.9439 -11.9552 Td[(user)-333(do)-28(es)-334(not)-333(n)1(e)-1(ed)-333(to)-333(delv)28(e)-334(in)29(to)-334(th)1(e)-1(i)1(r)-333(details)-334(\050see)-334(Sec)-1(.)]TJ +/F8 9.9626 Tf 290.6329 515.9706 Td[(])-353(th)1(at)-353(guar)1(an)28(te)-1(es)-354(a)-353(p)-27(ort)1(able)-353(and)-352(e)-1(\016c)-1(i)1(e)-1(n)28(t)-353(com-)]TJ -139.928 -11.9552 Td[(m)27(u)1(ni)1(c)-1(ation)-398(la)28(y)28(e)-1(r)1(.)-642(T)-1(h)1(e)-400(Mess)-1(age)-400(P)29(as)-1(sing)-399(In)28(terf)1(ac)-1(e)-399(c)-1(o)-28(d)1(e)-400(is)-399(e)-1(n)1(c)-1(ap)1(s)-1(u)1(late)-1(d)-398(w)-1(i)1(thin)]TJ 0 -11.9551 Td[(th)1(e)-386(BLA)27(CS)-384(la)28(y)28(e)-1(r)1(.)-600(Ho)28(w)27(ev)28(er,)-398(in)-384(s)-1(ome)-386(case)-1(s,)-398(MP)1(I)-385(routi)1(nes)-386(are)-385(di)1(re)-1(ctly)-384(use)-1(d)-385(ei-)]TJ 0 -11.9552 Td[(th)1(e)-1(r)-403(to)-404(i)1(m)-1(p)1(ro)28(v)28(e)-404(e)-1(\016c)-1(i)1(e)-1(n)1(c)-1(y)-403(or)-403(to)-404(impl)1(e)-1(me)-1(n)29(t)-404(com)-1(m)28(un)1(ic)-1(at)1(ion)-403(pattern)1(s)-404(for)-403(w)-1(h)1(ic)27(h)]TJ 0 -11.9552 Td[(th)1(e)-334(B)-1(LA)28(CS)-333(p)1(ac)27(k)56(age)-334(do)-27(e)-1(sn't)-333(pr)1(o)28(vide)-333(an)28(y)-333(m)-1(eth)1(o)-28(d.)]TJ 14.9439 -12.4736 Td[(In)-416(an)29(y)-416(c)-1(ase)-417(w)28(e)-416(pro)28(vi)1(de)-416(w)-1(r)1(app)-27(e)-1(r)1(s)-417(ar)1(oun)1(d)-416(th)1(e)-417(BLA)28(C)-1(S)-415(rou)1(tines)-416(s)-1(o)-416(th)1(at)-416(the)]TJ -14.9439 -11.9552 Td[(user)-333(do)-28(es)-334(not)-333(n)1(e)-1(ed)-333(to)-333(delv)28(e)-334(in)29(to)-334(th)1(e)-1(i)1(r)-333(details)-334(\050see)-334(Sec)-1(.)]TJ ET -1 0 0 1 388.9783 442.7583 cm +1 0 0 1 388.9783 443.7211 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -388.9783 -442.7583 cm +1 0 0 1 -388.9783 -443.7211 cm BT -/F8 9.9626 Tf 388.9783 442.7583 Td[(7)]TJ +/F8 9.9626 Tf 388.9783 443.7211 Td[(7)]TJ ET -1 0 0 1 393.9596 442.7583 cm +1 0 0 1 393.9596 443.7211 cm 0 g 0 G -1 0 0 1 -393.9596 -442.7583 cm +1 0 0 1 -393.9596 -443.7211 cm BT -/F8 9.9626 Tf 393.9596 442.7583 Td[(\051.)]TJ -228.3108 -12.8101 Td[(The)-439(t)28(yp)-27(e)-439(of)-438(li)1(near)-438(s)-1(ystem)-439(m)-1(at)1(rice)-1(s)-439(t)1(hat)-438(w)27(e)-439(ad)1(dr)1(e)-1(ss)-439(t)28(ypi)1(c)-1(all)1(y)-439(ar)1(is)-1(e)-438(in)-438(the)]TJ -14.9439 -11.9552 Td[(n)28(u)1(m)-1(erical)-428(soluti)1(on)-428(of)-428(P)1(DEs;)-475(in)-428(suc)28(h)-428(a)-428(c)-1(on)29(te)-1(x)1(t,)-452(it)-428(i)1(s)-429(n)1(e)-1(ce)-1(ss)-1(ar)1(y)-428(to)-428(pa)28(y)-428(sp)-28(ec)-1(i)1(al)]TJ 0 -11.9552 Td[(atten)28(tion)-295(to)-296(t)1(he)-296(s)-1(t)1(ructur)1(e)-296(of)-296(th)1(e)-296(prob)1(lem)-296(from)-296(wh)1(ic)27(h)-295(the)-296(ap)1(pli)1(c)-1(ati)1(on)-296(or)1(iginat)1(e)-1(s.)]TJ 0 -11.9551 Td[(The)-322(non)1(z)-1(ero)-322(pat)1(te)-1(r)1(n)-322(of)-322(a)-322(matr)1(ix)-322(arisin)1(g)-322(from)-322(th)1(e)-323(d)1(is)-1(cretization)-322(of)-321(a)-322(PDE)-321(is)-322(in-)]TJ 0 -11.9552 Td[(\015u)1(e)-1(n)1(c)-1(ed)-332(b)29(y)-332(v)55(ar)1(ious)-332(factors,)-332(s)-1(u)1(c)27(h)-332(as)-332(the)-332(s)-1(h)1(ap)-28(e)-332(of)-332(th)1(e)-333(domain)1(,)-332(the)-332(disc)-1(r)1(e)-1(ti)1(z)-1(ation)]TJ 0 -11.9552 Td[(strategy)83(,)-396(an)1(d)-383(the)-383(e)-1(qu)1(ation)1(/unk)1(no)28(wn)-383(orderi)1(ng.)-595(Th)1(e)-384(m)-1(atr)1(ix)-383(itse)-1(lf)-383(can)-383(b)-27(e)-384(in)28(ter-)]TJ 0 -11.9551 Td[(pr)1(e)-1(ted)-358(as)-358(the)-358(adj)1(ac)-1(ency)-358(matrix)-358(of)-357(the)-358(grap)1(h)-358(ass)-1(o)-28(ciated)-358(with)-357(the)-358(disc)-1(r)1(e)-1(ti)1(z)-1(ation)]TJ 0 -11.9552 Td[(me)-1(sh.)]TJ 14.9439 -12.8102 Td[(The)-241(d)1(is)-1(t)1(ribu)1(tion)-240(of)-240(the)-241(co)-28(e\016)-1(cien)28(t)-240(m)-1(atr)1(ix)-241(f)1(or)-240(the)-241(li)1(near)-241(syste)-1(m)-241(i)1(s)-241(base)-1(d)-240(on)-240(the)]TJ -14.9439 -11.9551 Td[(\134o)28(wner)-247(c)-1(ompu)1(tes)-1(")-247(ru)1(le:)-402(t)1(he)-248(v)56(ar)1(iable)-247(as)-1(so)-28(ciated)-247(to)-247(eac)27(h)-247(me)-1(sh)-247(p)-27(oin)28(t)-247(i)1(s)-248(ass)-1(ign)1(e)-1(d)-246(to)]TJ 0 -11.9552 Td[(a)-307(pro)-27(c)-1(es)-1(s)-308(th)1(at)-308(wil)1(l)-308(o)28(wn)-307(the)-307(c)-1(orr)1(e)-1(sp)-27(ondi)1(ng)-307(ro)28(w)-308(in)-307(th)1(e)-308(c)-1(o)-27(e)-1(\016c)-1(i)1(e)-1(n)28(t)-307(matrix)-307(and)-307(wil)1(l)]TJ 0 -11.9552 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136.7572 616.5862 Td[(\017)]TJ ET -1 0 0 1 141.7385 488.2519 cm +1 0 0 1 141.7385 616.5862 cm 0 g 0 G -1 0 0 1 -141.7385 -488.2519 cm +1 0 0 1 -141.7385 -616.5862 cm BT -/F8 9.9626 Tf 146.7198 488.2519 Td[(Dense)-334(and)-333(spar)1(s)-1(e)-333(m)-1(atr)1(ix)-333(bu)1(ild)-333(an)1(d)-333(up)-27(date;)]TJ +/F8 9.9626 Tf 146.7198 616.5862 Td[(Dense)-334(and)-333(spar)1(s)-1(e)-333(m)-1(atr)1(ix)-333(bu)1(ild)-333(an)1(d)-333(up)-27(date;)]TJ ET -1 0 0 1 124.802 473.2132 cm +1 0 0 1 124.802 600.3786 cm 0 g 0 G -1 0 0 1 -124.802 -473.2132 cm +1 0 0 1 -124.802 -600.3786 cm BT -/F14 9.9626 Tf 136.7572 473.2132 Td[(\017)]TJ +/F14 9.9626 Tf 136.7572 600.3786 Td[(\017)]TJ ET -1 0 0 1 141.7385 473.2132 cm +1 0 0 1 141.7385 600.3786 cm 0 g 0 G -1 0 0 1 -141.7385 -473.2132 cm +1 0 0 1 -141.7385 -600.3786 cm BT -/F8 9.9626 Tf 146.7198 473.2132 Td[(Sp)1(arse)-334(matrix)-333(an)1(d)-333(data)-333(di)1(s)-1(tr)1(ibu)1(tion)-333(p)1(re)-1(p)1(ro)-28(ces)-1(sing.)]TJ +/F8 9.9626 Tf 146.7198 600.3786 Td[(Sp)1(arse)-334(matrix)-333(an)1(d)-333(data)-333(di)1(s)-1(tr)1(ibu)1(tion)-333(p)1(re)-1(p)1(ro)-28(ces)-1(sing.)]TJ ET -1 0 0 1 94.9141 454.1895 cm +1 0 0 1 94.9141 579.9187 cm 0 g 0 G -1 0 0 1 -94.9141 -454.1895 cm +1 0 0 1 -94.9141 -579.9187 cm BT -/F29 9.9626 Tf 99.8954 454.1895 Td[(Preconditi)-1(oner)-383(r)1(outi)-1(nes)]TJ +/F29 9.9626 Tf 99.8954 579.9187 Td[(Preconditi)-1(oner)-383(r)1(outi)-1(nes)]TJ ET -1 0 0 1 218.5346 454.1895 cm +1 0 0 1 218.5346 579.9187 cm 0 g 0 G -1 0 0 1 -123.6205 -19.0237 cm +1 0 0 1 -123.6205 -20.46 cm 0 g 0 G -1 0 0 1 -94.9141 -435.1658 cm +1 0 0 1 -94.9141 -559.4587 cm BT -/F29 9.9626 Tf 99.8954 435.1658 Td[(Iterati)-1(v)32(e)-383(me)-1(tho)-32(d)1(s)]TJ +/F29 9.9626 Tf 99.8954 559.4587 Td[(Iterati)-1(v)32(e)-383(me)-1(tho)-32(d)1(s)]TJ ET -1 0 0 1 189.2211 435.1658 cm +1 0 0 1 189.2211 559.4587 cm 0 g 0 G -1 0 0 1 -189.2211 -435.1658 cm +1 0 0 1 -189.2211 -559.4587 cm BT -/F8 9.9626 Tf 194.2024 435.1658 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cm +1 0 0 1 99.8954 506.8509 cm 0 g 0 G -1 0 0 1 -99.8954 -386.9664 cm +1 0 0 1 -99.8954 -506.8509 cm BT -/F14 9.9626 Tf 114.8394 386.9664 Td[(\017)]TJ +/F14 9.9626 Tf 114.8394 506.8509 Td[(\017)]TJ ET -1 0 0 1 119.8207 386.9664 cm +1 0 0 1 119.8207 506.8509 cm 0 g 0 G -1 0 0 1 -119.8207 -386.9664 cm +1 0 0 1 -119.8207 -506.8509 cm BT -/F8 9.9626 Tf 124.802 386.9664 Td[(all)-275(t)1(he)-275(s)-1(ym)28(b)-27(ols)-276(\050i)1(.e)-1(.)-424(s)-1(u)1(brou)1(tin)1(e)-276(n)1(am)-1(es,)-287(d)1(ata)-275(t)28(yp)-27(e)-1(s...\051)-425(ar)1(e)-276(p)1(re\014xed)-275(b)29(y)]TJ/F32 9.9626 Tf 297.8831 0 Td[(psb_)]TJ +/F8 9.9626 Tf 124.802 506.8509 Td[(all)-275(t)1(he)-275(s)-1(ym)28(b)-27(ols)-276(\050i)1(.e)-1(.)-424(s)-1(u)1(brou)1(tin)1(e)-276(n)1(am)-1(es,)-287(d)1(ata)-275(t)28(yp)-27(e)-1(s...\051)-425(ar)1(e)-276(p)1(re\014xed)-275(b)29(y)]TJ/F32 9.9626 Tf 297.8831 0 Td[(psb_)]TJ ET -1 0 0 1 99.8954 367.9426 cm +1 0 0 1 99.8954 486.391 cm 0 g 0 G -1 0 0 1 -99.8954 -367.9426 cm +1 0 0 1 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Td[(:)-444(the)-333(routi)1(ne)-334(i)1(s)-334(related)-333(to)-334(d)1(e)-1(n)1(s)-1(e)-333(data,)]TJ ET -1 0 0 1 124.802 283.8777 cm +1 0 0 1 124.802 396.8483 cm 0 g 0 G -1 0 0 1 -124.802 -283.8777 cm +1 0 0 1 -124.802 -396.8483 cm BT -/F29 9.9626 Tf 136.01 283.8777 Td[({)]TJ +/F29 9.9626 Tf 136.01 396.8483 Td[({)]TJ ET -1 0 0 1 141.7385 283.8777 cm +1 0 0 1 141.7385 396.8483 cm 0 g 0 G -1 0 0 1 -141.7385 -283.8777 cm +1 0 0 1 -141.7385 -396.8483 cm BT -/F32 9.9626 Tf 146.7198 283.8777 Td[(sp)]TJ/F8 9.9626 Tf 10.4607 0 Td[(:)-444(the)-333(routi)1(ne)-334(i)1(s)-334(related)-333(to)-334(spar)1(s)-1(e)-334(d)1(ata,)]TJ +/F32 9.9626 Tf 146.7198 396.8483 Td[(sp)]TJ/F8 9.9626 Tf 10.4607 0 Td[(:)-444(the)-333(routi)1(ne)-334(i)1(s)-334(related)-333(to)-334(spar)1(s)-1(e)-334(d)1(ata,)]TJ ET -1 0 0 1 124.802 268.839 cm +1 0 0 1 124.802 380.6408 cm 0 g 0 G -1 0 0 1 -124.802 -268.839 cm +1 0 0 1 -124.802 -380.6408 cm BT -/F29 9.9626 Tf 136.01 268.839 Td[({)]TJ +/F29 9.9626 Tf 136.01 380.6408 Td[({)]TJ ET -1 0 0 1 141.7385 268.839 cm +1 0 0 1 141.7385 380.6408 cm 0 g 0 G -1 0 0 1 -141.7385 -268.839 cm +1 0 0 1 -141.7385 -380.6408 cm BT -/F32 9.9626 Tf 146.7198 268.839 Td[(cd)]TJ/F8 9.9626 Tf 10.4607 0 Td[(:)-444(the)-333(routi)1(ne)-334(i)1(s)-334(related)-333(to)-334(comm)27(un)1(ication)-333(d)1(e)-1(sc)-1(r)1(iptor)-333(\050see)]TJ +/F32 9.9626 Tf 146.7198 380.6408 Td[(cd)]TJ/F8 9.9626 Tf 10.4607 0 Td[(:)-444(the)-333(routi)1(ne)-334(i)1(s)-334(related)-333(to)-334(comm)27(un)1(ication)-333(d)1(e)-1(sc)-1(r)1(iptor)-333(\050see)]TJ ET -1 0 0 1 407.3539 268.839 cm +1 0 0 1 407.3539 380.6408 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -407.3539 -268.839 cm +1 0 0 1 -407.3539 -380.6408 cm BT -/F8 9.9626 Tf 407.3539 268.839 Td[(3)]TJ +/F8 9.9626 Tf 407.3539 380.6408 Td[(3)]TJ ET -1 0 0 1 412.3352 268.839 cm +1 0 0 1 412.3352 380.6408 cm 0 g 0 G -1 0 0 1 -412.3352 -268.839 cm +1 0 0 1 -412.3352 -380.6408 cm BT -/F8 9.9626 Tf 412.3352 268.839 Td[(\051.)]TJ -287.5332 -19.0237 Td[(F)84(or)-276(example)-276(th)1(e)]TJ/F32 9.9626 Tf 72.3296 0 Td[(psb_geins)]TJ/F8 9.9626 Tf 47.073 0 Td[(,)]TJ/F32 9.9626 Tf 5.628 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 49.8186 0 Td[(and)]TJ/F32 9.9626 Tf 18.7964 0 Td[(psb_cdins)]TJ/F8 9.9626 Tf 49.8186 0 Td[(p)-27(e)-1(r)1(form)-276(t)1(he)-276(s)-1(ame)]TJ -243.4642 -11.9552 Td[(action)-342(\050s)-1(ee)]TJ +/F8 9.9626 Tf 412.3352 380.6408 Td[(\051.)]TJ -287.5332 -20.46 Td[(F)84(or)-276(example)-276(th)1(e)]TJ/F32 9.9626 Tf 72.3296 0 Td[(psb_geins)]TJ/F8 9.9626 Tf 47.073 0 Td[(,)]TJ/F32 9.9626 Tf 5.628 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 49.8186 0 Td[(and)]TJ/F32 9.9626 Tf 18.7964 0 Td[(psb_cdins)]TJ/F8 9.9626 Tf 49.8186 0 Td[(p)-27(e)-1(r)1(form)-276(t)1(he)-276(s)-1(ame)]TJ -243.4642 -11.9552 Td[(action)-342(\050s)-1(ee)]TJ ET -1 0 0 1 174.8595 237.8601 cm +1 0 0 1 174.8595 348.2256 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -174.8595 -237.8601 cm +1 0 0 1 -174.8595 -348.2256 cm BT -/F8 9.9626 Tf 174.8595 237.8601 Td[(6)]TJ +/F8 9.9626 Tf 174.8595 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Td[(will)-338(h)1(a)27(v)28(e)-338(de\014n)1(e)-1(d)-338(a)-338(se)-1(t)-338(of)-338(\134h)1(alo")-338(\050or)-338(\134ghost"\051)-338(in)1(dice)-1(s)]TJ/F11 9.9626 Tf -114.4896 -11.9551 Td[(n)]TJ/F8 9.9626 Tf 5.9799 -1.4944 Td[(ro)28(w)]TJ/F9 4.9813 Tf 15.8019 -0.9963 Td[(i)]TJ/F8 9.9626 Tf 5.9852 2.4907 Td[(+)-234(1)]TJ/F11 9.9626 Tf 16.7216 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 -3.487 Td[(col)]TJ/F9 4.9813 Tf 12.1766 -0.9962 Td[(i)]TJ/F8 9.9626 Tf 3.6541 4.4832 Td[(,)-355(denoti)1(ng)-351(ele)-1(men)28(ts)-352(of)-350(the)-351(in)1(dex)-351(space)-352(th)1(at)-351(are)]TJ/F19 9.9626 Tf 209.5968 0 Td[(not)]TJ/F8 9.9626 Tf 18.4447 0 Td[(ass)-1(ign)1(e)-1(d)]TJ -307.6241 -11.9552 Td[(to)-284(p)1(ro)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 45.9205 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(;)-300(ho)28(w)28(e)-1(v)28(er)-284(th)1(e)-284(v)55(ar)1(iabl)1(e)-1(s)-284(as)-1(so)-28(ciated)-284(with)-283(th)1(e)-1(m)-284(are)-284(n)1(e)-1(eded)-284(to)-283(c)-1(omplete)]TJ -49.3528 -11.9552 Td[(com)-1(p)1(utati)1(ons)-410(ass)-1(o)-28(ciated)-409(w)-1(i)1(th)-409(the)-410(spar)1(s)-1(e)-410(matri)1(x)]TJ/F11 9.9626 Tf 216.3159 0 Td[(A)]TJ/F8 9.9626 Tf 7.472 0 Td[(,)-428(and)-409(th)28(u)1(s)-410(they)-409(ha)28(v)28(e)-410(to)-410(b)-27(e)]TJ -223.7879 -11.9551 Td[(fetc)27(h)1(e)-1(d)-463(f)1(rom)-464(\050n)1(e)-1(igh)29(b)-28(ou)1(rin)1(g\051)-464(p)1(ro)-28(ce)-1(ss)-1(es)-1(.)-835(The)-464(d)1(e)-1(sc)-1(r)1(ipt)1(or)-464(of)-463(th)1(e)-465(i)1(nd)1(e)-1(x)-463(s)-1(p)1(ac)-1(e)-464(is)]TJ 0 -11.9552 Td[(bu)1(ilt)-393(e)-1(xactly)-393(for)-394(t)1(he)-394(pu)1(rp)-27(os)-1(e)-394(of)-394(p)1(rop)-27(e)-1(r)1(ly)-394(se)-1(q)1(ue)-1(n)1(c)-1(i)1(ng)-394(th)1(e)-395(comm)27(u)1(nication)-393(s)-1(teps)]TJ 0 -11.9552 Td[(requ)1(ired)-333(to)-333(ac)27(hi)1(e)-1(v)28(e)-334(th)1(is)-334(ob)-55(j)1(e)-1(ctiv)28(e.)]TJ 14.944 -12.1686 Td[(A)-306(simple)-306(app)1(lication)-305(s)-1(tr)1(uctur)1(e)-307(wil)1(l)-306(w)28(alk)-306(th)1(rou)1(gh)-306(th)1(e)-307(i)1(ndex)-306(space)-306(allo)-28(cation)1(,)]TJ -14.944 -11.9552 Td[(matrix)1(/v)28(e)-1(ctor)-333(c)-1(r)1(e)-1(ati)1(on)-333(and)-333(li)1(near)-333(s)-1(ystem)-334(s)-1(ol)1(ution)-332(as)-334(foll)1(o)27(ws:)]TJ +/F8 9.9626 Tf 150.7049 706.1289 Td[(to)-277(the)-278(ad)1(jace)-1(n)1(c)-1(y)-277(grap)1(h)-277(im)-1(p)-27(ose)-1(d)-277(on)-277(th)1(e)-278(disc)-1(r)1(e)-1(ti)1(z)-1(ation)-277(mes)-1(h)-277(b)28(y)-277(th)1(e)-278(disc)-1(r)1(e)-1(ti)1(z)-1(ation)]TJ 0 -11.9552 Td[(ste)-1(n)1(c)-1(il)1(.)]TJ 14.9439 -12.0478 Td[(Th)28(us)-408(the)-409(\014)1(rst)-409(or)1(der)-408(of)-408(bu)1(s)-1(in)1(e)-1(ss)-409(is)-408(to)-409(es)-1(tab)1(lish)-408(an)-408(in)1(dex)-408(s)-1(p)1(ac)-1(e,)-427(and)-408(th)1(is)-409(is)]TJ -14.9439 -11.9552 Td[(don)1(e)-371(w)-1(i)1(th)-371(a)-371(call)-371(to)]TJ/F32 9.9626 Tf 87.1086 0 Td[(psb_cdall)]TJ/F8 9.9626 Tf 50.7685 0 Td[(in)-370(whic)28(h)-371(w)28(e)-372(sp)-28(ecify)-371(t)1(he)-371(s)-1(ize)-371(of)-371(th)1(e)-372(i)1(ndex)-371(space)]TJ/F11 9.9626 Tf -137.8771 -11.9552 Td[(n)]TJ/F8 9.9626 Tf 9.1424 0 Td[(and)-317(t)1(he)-318(all)1(o)-28(c)-1(ati)1(on)-317(of)-317(the)-318(elem)-1(en)28(ts)-318(of)-317(th)1(e)-318(in)1(dex)-318(space)-318(to)-317(the)-318(v)56(ari)1(ous)-318(p)1(ro)-28(ce)-1(ss)-1(es)]TJ -9.1424 -11.9551 Td[(makin)1(g)-334(u)1(p)-333(the)-333(MPI)-333(\050vir)1(tual\051)-333(p)1(arallel)-333(mac)27(hi)1(ne.)]TJ 14.9439 -12.0479 Td[(The)-309(i)1(ndex)-308(s)-1(p)1(ac)-1(e)-308(is)-309(par)1(tition)1(e)-1(d)-308(amon)1(g)-309(p)1(ro)-28(ce)-1(ss)-1(es,)-314(an)1(d)-308(thi)1(s)-309(c)-1(r)1(e)-1(ates)-309(a)-308(m)-1(ap)1(pin)1(g)]TJ -14.9439 -11.9552 Td[(fr)1(om)-250(t)1(he)-250(\134gl)1(obal")-249(n)29(um)27(b)-27(erin)1(g)-249(1)]TJ/F11 9.9626 Tf 132.8519 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 21.7442 0 Td[(to)-249(a)-249(n)28(u)1(m)27(b)-27(e)-1(r)1(ing)-249(\134l)1(o)-28(c)-1(al)1(")-249(to)-249(e)-1(ac)27(h)-248(pr)1(o)-28(c)-1(ess)-1(;)-277(eac)27(h)]TJ -154.5961 -11.9551 Td[(pr)1(o)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 33.7713 0 Td[(i)]TJ/F8 9.9626 Tf 5.7936 0 Td[(will)-237(o)28(wn)-237(a)-237(ce)-1(r)1(tain)-236(s)-1(u)1(bse)-1(t)-237(1)]TJ/F11 9.9626 Tf 113.5085 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 -1.4944 Td[(ro)28(w)]TJ/F9 4.9813 Tf 15.8019 -0.9963 Td[(i)]TJ/F8 9.9626 Tf 3.6541 2.4907 Td[(,)-256(e)-1(ac)28(h)-237(elem)-1(en)28(t)-237(of)-236(w)-1(h)1(ic)27(h)-236(c)-1(or)1(re)-1(sp)-27(ond)1(s)]TJ -191.7927 -11.9552 Td[(to)-390(a)-389(c)-1(ertai)1(n)-390(elem)-1(en)28(t)-389(of)-389(1)]TJ/F11 9.9626 Tf 111.3133 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 0 Td[(.)-613(The)-390(u)1(s)-1(er)-390(d)1(o)-28(es)-390(not)-390(set)-390(expli)1(c)-1(it)1(ly)-390(t)1(his)-390(mapp)1(ing;)]TJ -130.5766 -11.9552 Td[(when)-392(the)-392(app)1(lication)-392(needs)-393(to)-392(in)1(dicate)-393(to)-392(whi)1(c)27(h)-392(ele)-1(men)28(t)-392(of)-392(the)-392(ind)1(e)-1(x)-392(space)-393(a)]TJ 0 -11.9551 Td[(ce)-1(rt)1(ain)-273(it)1(e)-1(m)-273(is)-273(relate)-1(d)1(,)-285(suc)27(h)-272(as)-273(the)-273(ro)28(w)-273(and)-272(c)-1(olu)1(m)-1(n)-272(in)1(dex)-273(of)-273(a)-273(matr)1(ix)-273(co)-28(e)-1(\016cie)-1(n)29(t,)]TJ 0 -11.9552 Td[(it)-448(do)-28(es)-449(s)-1(o)-448(in)-448(the)-449(\134glob)1(al")-449(n)29(um)28(b)-28(erin)1(g,)-477(and)-448(the)-449(li)1(brar)1(y)-449(wil)1(l)-449(tr)1(anslate)-449(in)28(to)-448(the)]TJ 0 -11.9552 Td[(app)1(rop)1(riate)-333(\134lo)-28(cal")-334(n)29(um)27(b)-27(erin)1(g.)]TJ 14.944 -12.0478 Td[(F)84(or)-274(a)-274(gi)1(v)28(e)-1(n)-273(in)1(dex)-274(space)-274(1)]TJ/F11 9.9626 Tf 109.3313 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 21.9902 0 Td[(th)1(e)-1(re)-274(ar)1(e)-275(man)28(y)-273(p)-28(ossible)-274(ass)-1(o)-27(c)-1(iat)1(e)-1(d)-273(top)-27(ologies)-1(,)]TJ -146.2655 -11.9552 Td[(i.e.)-418(man)28(y)-254(d)1(i\013)-1(eren)28(t)-254(di)1(s)-1(cretization)-254(ste)-1(n)1(c)-1(i)1(ls)-1(;)-280(th)28(u)1(s)-255(th)1(e)-255(d)1(e)-1(sc)-1(r)1(ipti)1(on)-254(of)-254(th)1(e)-255(in)1(dex)-254(s)-1(p)1(ac)-1(e)]TJ 0 -11.9551 Td[(is)-355(not)-355(com)-1(p)1(lete)-1(d)-354(un)28(ti)1(l)-355(the)-355(use)-1(r)-355(h)1(as)-356(d)1(e)-1(\014)1(ned)-355(a)-355(sparsit)28(y)-355(p)1(atte)-1(r)1(n,)-360(e)-1(i)1(ther)-355(e)-1(x)1(pli)1(c)-1(itl)1(y)]TJ 0 -11.9552 Td[(th)1(rough)]TJ/F32 9.9626 Tf 36.9305 0 Td[(psb_cdins)]TJ/F8 9.9626 Tf 49.6601 0 Td[(or)-259(implicitl)1(y)-260(th)1(rough)]TJ/F32 9.9626 Tf 92.2223 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 47.073 0 Td[(.)-420(Th)1(e)-261(d)1(e)-1(scrip)1(tor)-260(i)1(s)-261(\014)1(nali)1(z)-1(ed)]TJ -225.8859 -11.9552 Td[(with)-354(a)-354(c)-1(al)1(l)-354(to)]TJ/F32 9.9626 Tf 62.2736 0 Td[(psb_cdasb)]TJ/F8 9.9626 Tf 50.6033 0 Td[(and)-353(a)-355(spar)1(s)-1(e)-355(matri)1(x)-355(wit)1(h)-354(a)-355(call)-354(to)]TJ/F32 9.9626 Tf 153.2175 0 Td[(psb_spasb)]TJ/F8 9.9626 Tf 47.0731 0 Td[(.)-507(After)]TJ/F32 9.9626 Tf -313.1675 -11.9551 Td[(psb_cdasb)]TJ/F8 9.9626 Tf 50.4428 0 Td[(eac)27(h)-338(p)1(ro)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 57.2447 0 Td[(i)]TJ/F8 9.9626 Tf 6.8021 0 Td[(will)-338(h)1(a)27(v)28(e)-338(de\014n)1(e)-1(d)-338(a)-338(se)-1(t)-338(of)-338(\134h)1(alo")-338(\050or)-338(\134ghost"\051)-338(in)1(dice)-1(s)]TJ/F11 9.9626 Tf -114.4896 -11.9552 Td[(n)]TJ/F8 9.9626 Tf 5.9799 -1.4944 Td[(ro)28(w)]TJ/F9 4.9813 Tf 15.8019 -0.9962 Td[(i)]TJ/F8 9.9626 Tf 5.9852 2.4906 Td[(+)-234(1)]TJ/F11 9.9626 Tf 16.7216 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 -3.4869 Td[(col)]TJ/F9 4.9813 Tf 12.1766 -0.9963 Td[(i)]TJ/F8 9.9626 Tf 3.6541 4.4832 Td[(,)-355(denoti)1(ng)-351(ele)-1(men)28(ts)-352(of)-350(the)-351(in)1(dex)-351(space)-352(th)1(at)-351(are)]TJ/F19 9.9626 Tf 209.5968 0 Td[(not)]TJ/F8 9.9626 Tf 18.4447 0 Td[(ass)-1(ign)1(e)-1(d)]TJ -307.6241 -11.9552 Td[(to)-284(p)1(ro)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 45.9205 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(;)-300(ho)28(w)28(e)-1(v)28(er)-284(th)1(e)-284(v)55(ar)1(iabl)1(e)-1(s)-284(as)-1(so)-28(ciated)-284(with)-283(th)1(e)-1(m)-284(are)-284(n)1(e)-1(eded)-284(to)-283(c)-1(omplete)]TJ -49.3528 -11.9551 Td[(com)-1(p)1(utati)1(ons)-410(ass)-1(o)-28(ciated)-409(w)-1(i)1(th)-409(the)-410(spar)1(s)-1(e)-410(matri)1(x)]TJ/F11 9.9626 Tf 216.3159 0 Td[(A)]TJ/F8 9.9626 Tf 7.472 0 Td[(,)-428(and)-409(th)28(u)1(s)-410(they)-409(ha)28(v)28(e)-410(to)-410(b)-27(e)]TJ -223.7879 -11.9552 Td[(fetc)27(h)1(e)-1(d)-463(f)1(rom)-464(\050n)1(e)-1(igh)29(b)-28(ou)1(rin)1(g\051)-464(p)1(ro)-28(ce)-1(ss)-1(es)-1(.)-835(The)-464(d)1(e)-1(sc)-1(r)1(ipt)1(or)-464(of)-463(th)1(e)-465(i)1(nd)1(e)-1(x)-463(s)-1(p)1(ac)-1(e)-464(is)]TJ 0 -11.9552 Td[(bu)1(ilt)-393(e)-1(xactly)-393(for)-394(t)1(he)-394(pu)1(rp)-27(os)-1(e)-394(of)-394(p)1(rop)-27(e)-1(r)1(ly)-394(se)-1(q)1(ue)-1(n)1(c)-1(i)1(ng)-394(th)1(e)-395(comm)27(u)1(nication)-393(s)-1(teps)]TJ 0 -11.9551 Td[(requ)1(ired)-333(to)-333(ac)27(hi)1(e)-1(v)28(e)-334(th)1(is)-334(ob)-55(j)1(e)-1(ctiv)28(e.)]TJ 14.944 -12.0479 Td[(A)-306(simple)-306(app)1(lication)-305(s)-1(tr)1(uctur)1(e)-307(wil)1(l)-306(w)28(alk)-306(th)1(rou)1(gh)-306(th)1(e)-307(i)1(ndex)-306(space)-306(allo)-28(cation)1(,)]TJ -14.944 -11.9551 Td[(matrix)1(/v)28(e)-1(ctor)-333(c)-1(r)1(e)-1(ati)1(on)-333(and)-333(li)1(near)-333(s)-1(ystem)-334(s)-1(ol)1(ution)-332(as)-334(foll)1(o)27(ws:)]TJ +ET +1 0 0 1 150.7049 362.7653 cm +0 g 0 G +1 0 0 1 -150.7049 -362.7653 cm +BT +/F8 9.9626 Tf 162.8814 362.7653 Td[(1.)]TJ +ET +1 0 0 1 170.6302 362.7653 cm +0 g 0 G +1 0 0 1 -170.6302 -362.7653 cm +BT +/F8 9.9626 Tf 175.6115 362.7653 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436.2836 Td[(\050a\051)]TJ +/F8 9.9626 Tf 129.0084 573.8369 Td[(\050a\051)]TJ ET -1 0 0 1 141.7385 436.2836 cm +1 0 0 1 141.7385 573.8369 cm 0 g 0 G -1 0 0 1 -141.7385 -436.2836 cm +1 0 0 1 -141.7385 -573.8369 cm BT -/F8 9.9626 Tf 146.7198 436.2836 Td[(If)-339(after)-339(\014rst)-340(t)1(im)-1(e)-340(step,)-341(r)1(e)-1(in)1(itial)1(iz)-1(e)-340(th)1(e)-340(s)-1(p)1(arse)-340(m)-1(atr)1(ix)-339(w)-1(i)1(th)]TJ/F32 9.9626 Tf 252.2765 0 Td[(psb_sprn)]TJ/F8 9.9626 Tf 41.8428 0 Td[(;)]TJ -294.1193 -11.9552 Td[(also)-334(zero)-333(out)-333(the)-333(dense)-334(v)28(e)-1(ctors;)]TJ +/F8 9.9626 Tf 146.7198 573.8369 Td[(If)-339(after)-339(\014rst)-340(t)1(im)-1(e)-340(step,)-341(r)1(e)-1(in)1(itial)1(iz)-1(e)-340(th)1(e)-340(s)-1(p)1(arse)-340(m)-1(atr)1(ix)-339(w)-1(i)1(th)]TJ/F32 9.9626 Tf 252.2765 0 Td[(psb_sprn)]TJ/F8 9.9626 Tf 41.8428 0 Td[(;)]TJ -294.1193 -11.9552 Td[(also)-334(zero)-333(out)-333(the)-333(dense)-334(v)28(e)-1(ctors;)]TJ ET -1 0 0 1 124.802 405.9484 cm +1 0 0 1 124.802 545.8761 cm 0 g 0 G -1 0 0 1 -124.802 -405.9484 cm +1 0 0 1 -124.802 -545.8761 cm BT -/F8 9.9626 Tf 128.455 405.9484 Td[(\050b)1(\051)]TJ +/F8 9.9626 Tf 128.455 545.8761 Td[(\050b)1(\051)]TJ ET -1 0 0 1 141.7385 405.9484 cm +1 0 0 1 141.7385 545.8761 cm 0 g 0 G -1 0 0 1 -141.7385 -405.9484 cm +1 0 0 1 -141.7385 -545.8761 cm BT -/F8 9.9626 Tf 146.7198 405.9484 Td[(Lo)-28(op)-252(o)28(v)28(e)-1(r)-252(th)1(e)-253(me)-1(sh,)-268(ge)-1(n)1(e)-1(rat)1(e)-253(the)-253(co)-28(e\016)-1(cien)28(ts)-253(and)-252(in)1(s)-1(ert/u)1(p)-27(date)-253(th)1(e)-1(m)]TJ 0 -11.9552 Td[(with)]TJ/F32 9.9626 Tf 22.6927 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 50.394 0 Td[(and)]TJ/F32 9.9626 Tf 19.3718 0 Td[(psb_geins)]TJ +/F8 9.9626 Tf 146.7198 545.8761 Td[(Lo)-28(op)-252(o)28(v)28(e)-1(r)-252(th)1(e)-253(me)-1(sh,)-268(ge)-1(n)1(e)-1(rat)1(e)-253(the)-253(co)-28(e\016)-1(cien)28(ts)-253(and)-252(in)1(s)-1(ert/u)1(p)-27(date)-253(th)1(e)-1(m)]TJ 0 -11.9552 Td[(with)]TJ/F32 9.9626 Tf 22.6927 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 50.394 0 Td[(and)]TJ/F32 9.9626 Tf 19.3718 0 Td[(psb_geins)]TJ ET -1 0 0 1 124.802 375.6132 cm +1 0 0 1 124.802 517.9153 cm 0 g 0 G -1 0 0 1 -124.802 -375.6132 cm +1 0 0 1 -124.802 -517.9153 cm BT -/F8 9.9626 Tf 129.5619 375.6132 Td[(\050c\051)]TJ +/F8 9.9626 Tf 129.5619 517.9153 Td[(\050c\051)]TJ ET -1 0 0 1 141.7385 375.6132 cm +1 0 0 1 141.7385 517.9153 cm 0 g 0 G -1 0 0 1 -141.7385 -375.6132 cm +1 0 0 1 -141.7385 -517.9153 cm BT -/F8 9.9626 Tf 146.7198 375.6132 Td[(Ass)-1(em)27(b)1(le)-334(with)]TJ/F32 9.9626 Tf 66.5284 0 Td[(psb_spasb)]TJ/F8 9.9626 Tf 50.3939 0 Td[(and)]TJ/F32 9.9626 Tf 19.3719 0 Td[(psb_geasb)]TJ +/F8 9.9626 Tf 146.7198 517.9153 Td[(Ass)-1(em)27(b)1(le)-334(with)]TJ/F32 9.9626 Tf 66.5284 0 Td[(psb_spasb)]TJ/F8 9.9626 Tf 50.3939 0 Td[(and)]TJ/F32 9.9626 Tf 19.3719 0 Td[(psb_geasb)]TJ ET -1 0 0 1 124.802 357.2331 cm +1 0 0 1 124.802 501.9096 cm 0 g 0 G -1 0 0 1 -124.802 -357.2331 cm +1 0 0 1 -124.802 -501.9096 cm BT -/F8 9.9626 Tf 128.455 357.2331 Td[(\050d)1(\051)]TJ +/F8 9.9626 Tf 128.455 501.9096 Td[(\050d)1(\051)]TJ ET -1 0 0 1 141.7385 357.2331 cm +1 0 0 1 141.7385 501.9096 cm 0 g 0 G -1 0 0 1 -141.7385 -357.2331 cm +1 0 0 1 -141.7385 -501.9096 cm BT -/F8 9.9626 Tf 146.7198 357.2331 Td[(Cho)-28(ose)-223(an)1(d)-222(bu)1(ild)-221(prec)-1(on)1(dit)1(ioner)-222(with)]TJ/F32 9.9626 Tf 162.5574 0 Td[(psb_precset)]TJ/F8 9.9626 Tf 59.7477 0 Td[(and)]TJ/F32 9.9626 Tf 18.2649 0 Td[(psb_precbld)]TJ +/F8 9.9626 Tf 146.7198 501.9096 Td[(Cho)-28(ose)-223(an)1(d)-222(bu)1(ild)-221(prec)-1(on)1(dit)1(ioner)-222(with)]TJ/F32 9.9626 Tf 162.5574 0 Td[(psb_precset)]TJ/F8 9.9626 Tf 59.7477 0 Td[(and)]TJ/F32 9.9626 Tf 18.2649 0 Td[(psb_precbld)]TJ ET -1 0 0 1 124.802 338.8531 cm +1 0 0 1 124.802 485.904 cm 0 g 0 G -1 0 0 1 -124.802 -338.8531 cm +1 0 0 1 -124.802 -485.904 cm BT -/F8 9.9626 Tf 129.5619 338.8531 Td[(\050e\051)]TJ +/F8 9.9626 Tf 129.5619 485.904 Td[(\050e\051)]TJ ET -1 0 0 1 141.7385 338.8531 cm +1 0 0 1 141.7385 485.904 cm 0 g 0 G -1 0 0 1 -141.7385 -338.8531 cm +1 0 0 1 -141.7385 -485.904 cm BT -/F8 9.9626 Tf 146.7198 338.8531 Td[(Call)-333(the)-333(iterativ)28(e)-334(metho)-28(d)-333(of)-332(c)27(hoi)1(c)-1(e,)-333(e)-1(.g.)]TJ/F32 9.9626 Tf 176.8649 0 Td[(psb_bicgstab)]TJ/F8 9.9626 Tf -223.6893 -24.805 Td[(The)-370(insertion)-369(rou)1(tines)-371(wil)1(l)-370(b)-27(e)-371(called)-370(as)-370(m)-1(an)29(y)-370(time)-1(s)-370(as)-370(nee)-1(d)1(e)-1(d)1(;)-388(they)-370(onl)1(y)-370(nee)-1(d)]TJ 0 -11.9551 Td[(to)-404(b)-27(e)-404(c)-1(al)1(le)-1(d)-403(on)-403(the)-404(d)1(ata)-404(th)1(at)-404(is)-404(actual)1(ly)-404(all)1(o)-28(c)-1(at)1(e)-1(d)-403(to)-404(th)1(e)-404(c)-1(u)1(rren)28(t)-403(pro)-27(c)-1(es)-1(s,)-421(i.e.)]TJ 0 -11.9552 Td[(eac)27(h)-333(pr)1(o)-28(ce)-1(ss)-334(ge)-1(n)1(e)-1(r)1(ate)-1(s)-333(its)-334(o)28(wn)-333(data.)]TJ 14.944 -13.1751 Td[(In)-326(pr)1(incip)1(le)-327(th)1(e)-1(r)1(e)-327(is)-327(n)1(o)-326(s)-1(p)-27(e)-1(ci\014)1(c)-327(ord)1(e)-1(r)-326(in)-325(the)-327(calls)-326(to)]TJ/F32 9.9626 Tf 225.8783 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 47.0731 0 Td[(,)-327(nor)-326(is)-327(t)1(here)]TJ -287.8954 -11.9552 Td[(a)-393(requir)1(e)-1(me)-1(n)29(t)-394(t)1(o)-394(b)1(uil)1(d)-393(a)-394(matri)1(x)-394(r)1(o)27(w)-393(in)-393(its)-393(e)-1(n)28(t)1(iret)28(y)-394(b)-27(efore)-393(c)-1(all)1(ing)-393(the)-393(routi)1(ne;)]TJ 0 -11.9551 Td[(th)1(is)-289(all)1(o)27(ws)-288(the)-288(app)1(lication)-288(p)1(rogr)1(am)-1(me)-1(r)-287(to)-288(w)27(alk)-287(thr)1(ough)-288(th)1(e)-289(d)1(isc)-1(r)1(e)-1(tization)-287(m)-1(es)-1(h)]TJ 0 -11.9552 Td[(ele)-1(men)28(t)-401(b)28(y)-401(e)-1(l)1(e)-1(me)-1(n)29(t,)-418(ge)-1(n)1(e)-1(r)1(ating)-401(th)1(e)-402(main)-401(par)1(t)-401(of)-401(a)-401(giv)28(e)-1(n)-401(matr)1(ix)-401(ro)28(w)-402(b)1(ut)-401(also)]TJ 0 -11.9552 Td[(con)28(trib)1(uti)1(ons)-334(to)-333(th)1(e)-334(ro)28(ws)-334(co)-1(r)1(res)-1(p)-27(ond)1(ing)-333(to)-333(neigh)28(b)-27(our)1(ing)-333(ele)-1(men)28(ts.)]TJ 14.944 -13.175 Td[(F)84(rom)-411(a)-410(f)1(un)1(c)-1(ti)1(onal)-410(p)-27(oin)28(t)-410(of)-410(v)1(ie)-1(w)-410(it)-410(i)1(s)-411(ev)28(e)-1(n)-410(p)-27(oss)-1(ib)1(le)-410(to)-411(exec)-1(u)1(te)-411(on)1(e)-411(call)-410(f)1(or)]TJ -14.944 -11.9552 Td[(eac)27(h)-372(n)1(onze)-1(r)1(o)-372(c)-1(o)-27(e)-1(\016c)-1(i)1(e)-1(n)28(t;)-391(h)1(o)28(w)27(ev)28(e)-1(r)-371(this)-372(w)28(ould)-371(ha)28(v)28(e)-372(a)-372(s)-1(u)1(bstan)28(tial)-371(c)-1(ompu)1(tation)1(al)]TJ 0 -11.9552 Td[(o)28(v)28(e)-1(r)1(head.)-412(It)-235(is)-237(t)1(here)-1(f)1(ore)-236(adv)1(is)-1(ab)1(le)-236(to)-236(pac)28(k)-236(a)-236(ce)-1(r)1(tain)-235(am)-1(ou)1(n)28(t)-236(of)-235(dat)1(a)-236(in)28(to)-236(eac)27(h)-235(c)-1(al)1(l)]TJ 0 -11.9551 Td[(to)-307(the)-308(in)1(s)-1(erti)1(on)-308(r)1(outi)1(ne,)-313(sa)27(y)-307(tou)1(c)27(hi)1(ng)-308(on)-307(a)-307(few)-308(tens)-308(of)-307(ro)28(ws)-1(;)-315(the)-308(b)-27(e)-1(st)-308(p)-27(erfor)1(m)-1(n)1(g)]TJ 0 -11.9552 Td[(v)56(alue)-385(w)27(ou)1(ld)-385(dep)-28(end)-385(on)-384(b)-28(oth)-385(th)1(e)-386(arc)28(hitecture)-385(of)-385(the)-386(computer)-385(b)-27(e)-1(in)1(g)-386(u)1(s)-1(ed)-385(and)]TJ 0 -11.9552 Td[(on)-449(the)-450(pr)1(oblem)-451(stru)1(c)-1(t)1(ure.)-794(A)28(t)-450(th)1(e)-451(op)1(p)-28(osite)-450(e)-1(x)1(trem)-1(e,)-479(it)-450(w)28(oul)1(d)-450(b)-27(e)-451(p)-27(oss)-1(ib)1(le)-450(to)]TJ 0 -11.9551 Td[(generate)-311(th)1(e)-311(en)28(tire)-310(part)-310(of)-310(a)-310(co)-28(e)-1(\016cie)-1(n)29(t)-311(matri)1(x)-310(re)-1(sid)1(ing)-310(on)-310(a)-310(pr)1(o)-28(c)-1(ess)-311(and)-310(p)1(as)-1(s)-310(it)]TJ 0 -11.9552 Td[(in)-308(a)-310(sin)1(gle)-310(call)-309(to)]TJ/F32 9.9626 Tf 76.8891 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 47.0731 0 Td[(;)-317(th)1(is)-1(,)-313(ho)28(w)27(ev)28(er,)-314(w)28(ould)-308(e)-1(n)28(t)1(ail)-309(a)-309(dou)1(bli)1(ng)-309(of)-309(me)-1(mory)]TJ -123.9622 -11.9552 Td[(o)-28(cc)-1(u)1(pati)1(on,)-333(and)-333(t)1(h)28(us)-334(w)28(oul)1(d)-333(b)-28(e)-333(alm)-1(ost)-333(alw)28(a)27(y)1(s)-334(far)-333(f)1(rom)-334(op)1(timal.)]TJ +/F8 9.9626 Tf 146.7198 485.904 Td[(Call)-333(the)-333(iterativ)28(e)-334(metho)-28(d)-333(of)-332(c)27(hoi)1(c)-1(e,)-333(e)-1(.g.)]TJ/F32 9.9626 Tf 176.8649 0 Td[(psb_bicgstab)]TJ/F8 9.9626 Tf -223.6893 -20.0561 Td[(The)-370(insertion)-369(rou)1(tines)-371(wil)1(l)-370(b)-27(e)-371(called)-370(as)-370(m)-1(an)29(y)-370(time)-1(s)-370(as)-370(nee)-1(d)1(e)-1(d)1(;)-388(they)-370(onl)1(y)-370(nee)-1(d)]TJ 0 -11.9552 Td[(to)-404(b)-27(e)-404(c)-1(al)1(le)-1(d)-403(on)-403(the)-404(d)1(ata)-404(th)1(at)-404(is)-404(actual)1(ly)-404(all)1(o)-28(c)-1(at)1(e)-1(d)-403(to)-404(th)1(e)-404(c)-1(u)1(rren)28(t)-403(pro)-27(c)-1(es)-1(s,)-421(i.e.)]TJ 0 -11.9552 Td[(eac)27(h)-333(pr)1(o)-28(ce)-1(ss)-334(ge)-1(n)1(e)-1(r)1(ate)-1(s)-333(its)-334(o)28(wn)-333(data.)]TJ 14.944 -11.9878 Td[(In)-326(pr)1(incip)1(le)-327(th)1(e)-1(r)1(e)-327(is)-327(n)1(o)-326(s)-1(p)-27(e)-1(ci\014)1(c)-327(ord)1(e)-1(r)-326(in)-325(the)-327(calls)-326(to)]TJ/F32 9.9626 Tf 225.8783 0 Td[(psb_spins)]TJ/F8 9.9626 Tf 47.0731 0 Td[(,)-327(nor)-326(is)-327(t)1(here)]TJ -287.8954 -11.9552 Td[(a)-393(requir)1(e)-1(me)-1(n)29(t)-394(t)1(o)-394(b)1(uil)1(d)-393(a)-394(matri)1(x)-394(r)1(o)27(w)-393(in)-393(its)-393(e)-1(n)28(t)1(iret)28(y)-394(b)-27(efore)-393(c)-1(all)1(ing)-393(the)-393(routi)1(ne;)]TJ 0 -11.9552 Td[(th)1(is)-289(all)1(o)27(ws)-288(the)-288(app)1(lication)-288(p)1(rogr)1(am)-1(me)-1(r)-287(to)-288(w)27(alk)-287(thr)1(ough)-288(th)1(e)-289(d)1(isc)-1(r)1(e)-1(tization)-287(m)-1(es)-1(h)]TJ 0 -11.9551 Td[(ele)-1(men)28(t)-401(b)28(y)-401(e)-1(l)1(e)-1(me)-1(n)29(t,)-418(ge)-1(n)1(e)-1(r)1(ating)-401(th)1(e)-402(main)-401(par)1(t)-401(of)-401(a)-401(giv)28(e)-1(n)-401(matr)1(ix)-401(ro)28(w)-402(b)1(ut)-401(also)]TJ 0 -11.9552 Td[(con)28(trib)1(uti)1(ons)-334(to)-333(th)1(e)-334(ro)28(ws)-334(co)-1(r)1(res)-1(p)-27(ond)1(ing)-333(to)-333(neigh)28(b)-27(our)1(ing)-333(ele)-1(men)28(ts.)]TJ 14.944 -11.9879 Td[(F)84(rom)-411(a)-410(f)1(un)1(c)-1(ti)1(onal)-410(p)-27(oin)28(t)-410(of)-410(v)1(ie)-1(w)-410(it)-410(i)1(s)-411(ev)28(e)-1(n)-410(p)-27(oss)-1(ib)1(le)-410(to)-411(exec)-1(u)1(te)-411(on)1(e)-411(call)-410(f)1(or)]TJ -14.944 -11.9552 Td[(eac)27(h)-372(n)1(onze)-1(r)1(o)-372(c)-1(o)-27(e)-1(\016c)-1(i)1(e)-1(n)28(t;)-391(h)1(o)28(w)27(ev)28(e)-1(r)-371(this)-372(w)28(ould)-371(ha)28(v)28(e)-372(a)-372(s)-1(u)1(bstan)28(tial)-371(c)-1(ompu)1(tation)1(al)]TJ 0 -11.9551 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Td[(th)1(e)-1(n)-252(the)-253(en)28(tri)1(e)-1(s)-253(in)]TJ/F11 9.9626 Tf 80.1688 0 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\0501)-278(:)]TJ/F11 9.9626 Tf 17.1578 0 Td[(n)]TJ/F8 9.9626 Tf 5.9799 0 Td[(\051)-253(wh)1(e)-1(r)1(e)]TJ/F11 9.9626 Tf 34.3974 0 Td[(n)]TJ/F8 9.9626 Tf 8.4975 0 Td[(is)-253(th)1(e)-254(size)]TJ -277.6823 -11.9551 Td[(of)]TJ/F11 9.9626 Tf 11.9104 0 Td[(x)]TJ/F8 9.9626 Tf 9.5788 0 Td[(are)-390(in)1(itiali)1(z)-1(ed)-390(to)]TJ/F11 9.9626 Tf 76.4397 0 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8743 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(\051)]TJ/F14 9.9626 Tf 7.5817 0 Td[(\040)]TJ/F11 9.9626 Tf 13.67 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(;)-418(th)28(u)1(s)-1(,)-404(u)1(p)-27(on)-390(retur)1(n)-390(f)1(rom)-390(the)-390(s)-1(u)1(br)1(outin)1(e)-1(,)]TJ -139.0457 -11.9552 Td[(for)-332(e)-1(ac)27(h)-332(ind)1(e)-1(x)]TJ/F11 9.9626 Tf 64.5045 0 Td[(i)]TJ/F8 9.9626 Tf 6.7519 0 Td[(w)28(e)-334(ha)28(v)28(e)-334(i)1(n)]TJ/F11 9.9626 Tf 49.2561 0 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(\051)-333(the)-333(p)-28(ositi)1(on)-333(that)-333(th)1(e)-334(item)]TJ/F11 9.9626 Tf 123.751 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(\051)-333(o)-28(cc)-1(u)1(pied)]TJ -273.697 -11.9552 Td[(in)-333(th)1(e)-334(ori)1(ginal)-333(d)1(ata)-334(sequence)-1(;)]TJ +/F8 9.9626 Tf 297.9662 452.1093 Td[(th)1(e)-1(n)-252(the)-253(en)28(tri)1(e)-1(s)-253(in)]TJ/F11 9.9626 Tf 80.1688 0 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\0501)-278(:)]TJ/F11 9.9626 Tf 17.1578 0 Td[(n)]TJ/F8 9.9626 Tf 5.9799 0 Td[(\051)-253(wh)1(e)-1(r)1(e)]TJ/F11 9.9626 Tf 34.3974 0 Td[(n)]TJ/F8 9.9626 Tf 8.4975 0 Td[(is)-253(th)1(e)-254(size)]TJ -277.6823 -11.9552 Td[(of)]TJ/F11 9.9626 Tf 11.9104 0 Td[(x)]TJ/F8 9.9626 Tf 9.5788 0 Td[(are)-390(in)1(itiali)1(z)-1(ed)-390(to)]TJ/F11 9.9626 Tf 76.4397 0 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8743 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(\051)]TJ/F14 9.9626 Tf 7.5817 0 Td[(\040)]TJ/F11 9.9626 Tf 13.67 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(;)-418(th)28(u)1(s)-1(,)-404(u)1(p)-27(on)-390(retur)1(n)-390(f)1(rom)-390(the)-390(s)-1(u)1(br)1(outin)1(e)-1(,)]TJ -139.0457 -11.9551 Td[(for)-332(e)-1(ac)27(h)-332(ind)1(e)-1(x)]TJ/F11 9.9626 Tf 64.5045 0 Td[(i)]TJ/F8 9.9626 Tf 6.7519 0 Td[(w)28(e)-334(ha)28(v)28(e)-334(i)1(n)]TJ/F11 9.9626 Tf 49.2561 0 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(\051)-333(the)-333(p)-28(ositi)1(on)-333(that)-333(th)1(e)-334(item)]TJ/F11 9.9626 Tf 123.751 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(\051)-333(o)-28(cc)-1(u)1(pied)]TJ -273.697 -11.9552 Td[(in)-333(th)1(e)-334(ori)1(ginal)-333(d)1(ata)-334(sequence)-1(;)]TJ ET -1 0 0 1 150.7049 408.2737 cm +1 0 0 1 150.7049 396.3185 cm 0 g 0 G -1 0 0 1 -150.7049 -408.2737 cm +1 0 0 1 -150.7049 -396.3185 cm BT -/F8 9.9626 Tf 162.8814 408.2737 Td[(4.)]TJ +/F8 9.9626 Tf 162.8814 396.3185 Td[(4.)]TJ ET -1 0 0 1 170.6302 408.2737 cm +1 0 0 1 170.6302 396.3185 cm 0 g 0 G -1 0 0 1 -170.6302 -408.2737 cm +1 0 0 1 -170.6302 -396.3185 cm BT -/F8 9.9626 Tf 175.6115 408.2737 Td[(If)]TJ/F11 9.9626 Tf 10.6736 0 Td[(f)-107(l)-20(ag)]TJ/F8 9.9626 Tf 23.4464 0 Td[(=)]TJ/F11 9.9626 Tf 11.701 0 Td[(psb)]TJ +/F8 9.9626 Tf 175.6115 396.3185 Td[(If)]TJ/F11 9.9626 Tf 10.6736 0 Td[(f)-107(l)-20(ag)]TJ/F8 9.9626 Tf 23.4464 0 Td[(=)]TJ/F11 9.9626 Tf 11.701 0 Td[(psb)]TJ ET -1 0 0 1 235.9883 408.2737 cm +1 0 0 1 235.9883 396.3185 cm q []0 d 0 J @@ -25682,11 +25752,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -235.9883 -408.2737 cm +1 0 0 1 -235.9883 -396.3185 cm BT -/F11 9.9626 Tf 238.9771 408.2737 Td[(so)1(r)-28(t)]TJ +/F11 9.9626 Tf 238.9771 396.3185 Td[(so)1(r)-28(t)]TJ ET -1 0 0 1 257.443 408.2737 cm +1 0 0 1 257.443 396.3185 cm q []0 d 0 J @@ -25695,11 +25765,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -257.443 -408.2737 cm +1 0 0 1 -257.443 -396.3185 cm BT -/F11 9.9626 Tf 260.4319 408.2737 Td[(k)-31(ee)1(p)]TJ +/F11 9.9626 Tf 260.4319 396.3185 Td[(k)-31(ee)1(p)]TJ ET -1 0 0 1 280.82 408.2737 cm +1 0 0 1 280.82 396.3185 cm q []0 d 0 J @@ -25708,11 +25778,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -280.82 -408.2737 cm +1 0 0 1 -280.82 -396.3185 cm BT -/F11 9.9626 Tf 283.8088 408.2737 Td[(idx)]TJ +/F11 9.9626 Tf 283.8088 396.3185 Td[(idx)]TJ ET -1 0 0 1 298.7182 408.2737 cm +1 0 0 1 298.7182 396.3185 cm q []0 d 0 J @@ -25721,57 +25791,57 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -298.7182 -408.2737 cm +1 0 0 1 -298.7182 -396.3185 cm BT -/F8 9.9626 Tf 305.7388 408.2737 Td[(th)1(e)-406(r)1(outi)1(ne)-405(will)-404(as)-1(sume)-405(that)-404(the)-405(en)28(tries)-405(in)]TJ/F11 9.9626 Tf -130.1273 -11.9552 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\050:\051)-333(h)1(a)27(v)28(e)-333(already)-333(b)-27(e)-1(en)-333(in)1(itialized)-333(b)28(y)-333(the)-333(use)-1(r;)]TJ +/F8 9.9626 Tf 305.7388 396.3185 Td[(th)1(e)-406(r)1(outi)1(ne)-405(will)-404(as)-1(sume)-405(that)-404(the)-405(en)28(tries)-405(in)]TJ/F11 9.9626 Tf -130.1273 -11.9552 Td[(ix)]TJ/F8 9.9626 Tf 9.1262 0 Td[(\050:\051)-333(h)1(a)27(v)28(e)-333(already)-333(b)-27(e)-1(en)-333(in)1(itialized)-333(b)28(y)-333(the)-333(use)-1(r;)]TJ ET -1 0 0 1 150.7049 376.3932 cm +1 0 0 1 150.7049 364.438 cm 0 g 0 G -1 0 0 1 -150.7049 -376.3932 cm +1 0 0 1 -150.7049 -364.438 cm BT -/F8 9.9626 Tf 162.8814 376.3932 Td[(5.)]TJ +/F8 9.9626 Tf 162.8814 364.438 Td[(5.)]TJ ET -1 0 0 1 170.6302 376.3932 cm +1 0 0 1 170.6302 364.438 cm 0 g 0 G -1 0 0 1 -170.6302 -376.3932 cm +1 0 0 1 -170.6302 -364.438 cm BT -/F8 9.9626 Tf 175.6115 376.3932 Td[(The)-376(th)1(ree)-377(sorti)1(ng)-376(al)1(gorith)1(m)-1(s)-376(h)1(a)27(v)28(e)-376(a)-375(s)-1(imilar)]TJ/F11 9.9626 Tf 195.5648 0 Td[(O)]TJ/F8 9.9626 Tf 7.876 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(n)]TJ/F8 9.9626 Tf 7.6403 0 Td[(log)]TJ/F11 9.9626 Tf 14.5288 0 Td[(n)]TJ/F8 9.9626 Tf 5.9799 0 Td[(\051)-376(exp)-27(e)-1(cted)-376(r)1(un)1(nin)1(g)]TJ -235.4642 -11.9552 Td[(time;)-349(in)-343(th)1(e)-344(a)28(v)28(e)-1(rage)-344(case)-344(quic)28(ksort)-344(wil)1(l)-344(b)-27(e)-344(th)1(e)-344(fas)-1(t)1(e)-1(st)-344(an)1(d)-343(m)-1(erge-)-1(sort)-343(the)]TJ 0 -11.9551 Td[(slo)28(w)27(es)-1(t.)-444(Ho)28(w)27(ev)28(er)-333(note)-334(th)1(at:)]TJ +/F8 9.9626 Tf 175.6115 364.438 Td[(The)-376(th)1(ree)-377(sorti)1(ng)-376(al)1(gorith)1(m)-1(s)-376(h)1(a)27(v)28(e)-376(a)-375(s)-1(imilar)]TJ/F11 9.9626 Tf 195.5648 0 Td[(O)]TJ/F8 9.9626 Tf 7.876 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(n)]TJ/F8 9.9626 Tf 7.6403 0 Td[(log)]TJ/F11 9.9626 Tf 14.5288 0 Td[(n)]TJ/F8 9.9626 Tf 5.9799 0 Td[(\051)-376(exp)-27(e)-1(cted)-376(r)1(un)1(nin)1(g)]TJ -235.4642 -11.9551 Td[(time;)-349(in)-343(th)1(e)-344(a)28(v)28(e)-1(rage)-344(case)-344(quic)28(ksort)-344(wil)1(l)-344(b)-27(e)-344(th)1(e)-344(fas)-1(t)1(e)-1(st)-344(an)1(d)-343(m)-1(erge-)-1(sort)-343(the)]TJ 0 -11.9552 Td[(slo)28(w)27(es)-1(t.)-444(Ho)28(w)27(ev)28(er)-333(note)-334(th)1(at:)]TJ ET -1 0 0 1 175.6115 332.5576 cm +1 0 0 1 175.6115 320.6024 cm 0 g 0 G -1 0 0 1 -175.6115 -332.5576 cm +1 0 0 1 -175.6115 -320.6024 cm BT -/F8 9.9626 Tf 179.8179 332.5576 Td[(\050a\051)]TJ +/F8 9.9626 Tf 179.8179 320.6024 Td[(\050a\051)]TJ ET -1 0 0 1 192.548 332.5576 cm +1 0 0 1 192.548 320.6024 cm 0 g 0 G -1 0 0 1 -192.548 -332.5576 cm +1 0 0 1 -192.548 -320.6024 cm BT -/F8 9.9626 Tf 197.5293 332.5576 Td[(The)-419(w)28(ors)-1(t)-418(c)-1(ase)-419(ru)1(nni)1(ng)-419(ti)1(m)-1(e)-419(f)1(or)-419(qu)1(ic)27(k)1(s)-1(or)1(t)-419(is)]TJ/F11 9.9626 Tf 203.3472 0 Td[(O)]TJ/F8 9.9626 Tf 7.876 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(n)]TJ/F7 6.9738 Tf 5.9799 3.6154 Td[(2)]TJ/F8 9.9626 Tf 4.4694 -3.6154 Td[(\051;)-461(the)-419(algor)1(ith)1(m)]TJ -225.5469 -11.9552 Td[(impl)1(e)-1(me)-1(n)29(te)-1(d)-318(here)-319(follo)28(ws)-319(the)-319(w)27(ell-kn)1(o)27(wn)-318(m)-1(edian)1(-of-thr)1(e)-1(e)-319(heuri)1(s)-1(ti)1(c)-1(s,)]TJ 0 -11.9551 Td[(bu)1(t)-333(the)-334(w)28(orst)-333(c)-1(ase)-334(ma)27(y)-333(still)-333(ap)1(ply)1(;)]TJ +/F8 9.9626 Tf 197.5293 320.6024 Td[(The)-419(w)28(ors)-1(t)-418(c)-1(ase)-419(ru)1(nni)1(ng)-419(ti)1(m)-1(e)-419(f)1(or)-419(qu)1(ic)27(k)1(s)-1(or)1(t)-419(is)]TJ/F11 9.9626 Tf 203.3472 0 Td[(O)]TJ/F8 9.9626 Tf 7.876 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(n)]TJ/F7 6.9738 Tf 5.9799 3.6154 Td[(2)]TJ/F8 9.9626 Tf 4.4694 -3.6154 Td[(\051;)-461(the)-419(algor)1(ith)1(m)]TJ -225.5469 -11.9552 Td[(impl)1(e)-1(me)-1(n)29(te)-1(d)-318(here)-319(follo)28(ws)-319(the)-319(w)27(ell-kn)1(o)27(wn)-318(m)-1(edian)1(-of-thr)1(e)-1(e)-319(heuri)1(s)-1(ti)1(c)-1(s,)]TJ 0 -11.9551 Td[(bu)1(t)-333(the)-334(w)28(orst)-333(c)-1(ase)-334(ma)27(y)-333(still)-333(ap)1(ply)1(;)]TJ ET -1 0 0 1 175.6115 292.707 cm +1 0 0 1 175.6115 280.7519 cm 0 g 0 G -1 0 0 1 -175.6115 -292.707 cm +1 0 0 1 -175.6115 -280.7519 cm BT -/F8 9.9626 Tf 179.2644 292.707 Td[(\050b)1(\051)]TJ +/F8 9.9626 Tf 179.2644 280.7519 Td[(\050b)1(\051)]TJ ET -1 0 0 1 192.548 292.707 cm +1 0 0 1 192.548 280.7519 cm 0 g 0 G -1 0 0 1 -192.548 -292.707 cm +1 0 0 1 -192.548 -280.7519 cm BT -/F8 9.9626 Tf 197.5293 292.707 Td[(The)-222(w)27(orst)-222(c)-1(ase)-223(r)1(un)1(nin)1(g)-223(t)1(im)-1(e)-222(for)-222(me)-1(r)1(ge)-1(-sort)-222(and)-222(h)1(e)-1(ap)1(-s)-1(ort)-222(i)1(s)]TJ/F11 9.9626 Tf 255.0439 0 Td[(O)]TJ/F8 9.9626 Tf 7.876 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(n)]TJ/F8 9.9626 Tf 7.6403 0 Td[(log)]TJ/F11 9.9626 Tf 14.5288 0 Td[(n)]TJ/F8 9.9626 Tf 5.98 0 Td[(\051)]TJ -294.9434 -11.9551 Td[(as)-334(th)1(e)-334(a)28(v)28(e)-1(r)1(age)-334(c)-1(ase;)]TJ +/F8 9.9626 Tf 197.5293 280.7519 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/Descent -194 -/FontName /FANUMM+CMSY7 +/FontName /LZILKO+CMSY7 /ItalicAngle -14.035 /StemV 93 /XHeight 431 /FontBBox [-15 -951 1252 782] /Flags 4 /CharSet (/minus/infinity) -/FontFile 884 0 R +/FontFile 891 0 R >> endobj -1543 0 obj +1550 0 obj [893 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1139 ] endobj -1542 0 obj << +1549 0 obj << /Type /Encoding /Differences [ 0 /minus 1/.notdef 49/infinity 50/.notdef] >> endobj -722 0 obj << +729 0 obj << /Length1 1306 /Length2 5708 /Length3 532 @@ -32445,7 +32545,7 @@ stream /ItalicAngle 0 def /isFixedPitch true def end readonly def -/FontName /HTJQFP+CMTT9 def +/FontName /INRSCM+CMTT9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -32512,37 +32612,37 @@ qܖ cleartomark endstream endobj -723 0 obj << +730 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1544 0 R +/Encoding 1551 0 R /FirstChar 39 /LastChar 122 -/Widths 1545 0 R -/BaseFont /HTJQFP+CMTT9 -/FontDescriptor 721 0 R +/Widths 1552 0 R +/BaseFont /INRSCM+CMTT9 +/FontDescriptor 728 0 R >> endobj -721 0 obj << +728 0 obj << /Ascent 611 /CapHeight 611 /Descent -222 -/FontName /HTJQFP+CMTT9 +/FontName /INRSCM+CMTT9 /ItalicAngle 0 /StemV 74 /XHeight 431 /FontBBox [-6 -233 542 698] /Flags 4 /CharSet (/quoteright/parenleft/parenright/comma/period/zero/one/two/nine/colon/equal/underscore/a/b/c/d/e/f/g/h/i/k/l/m/n/o/p/q/r/s/t/u/v/x/y/z) -/FontFile 722 0 R +/FontFile 729 0 R >> endobj -1545 0 obj +1552 0 obj [525 525 525 0 0 525 0 525 0 525 525 525 0 0 0 0 0 0 525 525 0 0 525 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 525 0 525 525 525 525 525 525 525 525 525 0 525 525 525 525 525 525 525 525 525 525 525 525 0 525 525 525 ] endobj -1544 0 obj << +1551 0 obj << /Type /Encoding /Differences [ 0 /.notdef 39/quoteright/parenleft/parenright 42/.notdef 44/comma 45/.notdef 46/period 47/.notdef 48/zero/one/two 51/.notdef 57/nine/colon 59/.notdef 61/equal 62/.notdef 95/underscore 96/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 107/k/l/m/n/o/p/q/r/s/t/u/v 119/.notdef 120/x/y/z 123/.notdef] >> endobj -642 0 obj << +649 0 obj << /Length1 745 /Length2 1242 /Length3 532 @@ -32562,7 +32662,7 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /NGREMF+CMMI5 def +/FontName /PHIQVH+CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -32588,243 +32688,41 @@ currentfile eexec cleartomark endstream endobj -643 0 obj << +650 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1546 0 R +/Encoding 1553 0 R /FirstChar 105 /LastChar 105 -/Widths 1547 0 R -/BaseFont /NGREMF+CMMI5 -/FontDescriptor 641 0 R +/Widths 1554 0 R +/BaseFont /PHIQVH+CMMI5 +/FontDescriptor 648 0 R >> endobj -641 0 obj << +648 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /NGREMF+CMMI5 +/FontName /PHIQVH+CMMI5 /ItalicAngle -14.04 /StemV 90 /XHeight 431 /FontBBox [37 -250 1349 750] /Flags 4 /CharSet (/i) -/FontFile 642 0 R +/FontFile 649 0 R >> endobj -1547 0 obj +1554 0 obj [534 ] endobj -1546 0 obj << +1553 0 obj << /Type /Encoding /Differences [ 0 /.notdef 105/i 106/.notdef] >> endobj -616 0 obj << -/Length1 1050 -/Length2 2900 -/Length3 532 -/Length 4482 ->> -stream -%!PS-AdobeFont-1.1: CMSY10 1.0 -%%CreationDate: 1991 Aug 15 07:20:57 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.0) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMSY10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.035 def -/isFixedPitch false def -end readonly def -/FontName /LNBNXK+CMSY10 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 0 /minus put -dup 15 /bullet put -dup 20 /lessequal put -dup 21 /greaterequal put -dup 32 /arrowleft put -dup 50 /element put -dup 54 /negationslash put -dup 66 /B put -dup 72 /H put -dup 73 /I put -dup 102 /braceleft put -dup 103 /braceright put -dup 106 /bar put -dup 107 /bardbl put -dup 112 /radical put -dup 120 /section put -readonly def -/FontBBox{-29 -960 1116 775}readonly def -currentdict end -currentfile eexec -oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨y=cLIPsF'f> ba -]fv+QAwdO[x"%Sx~{p҈덡|O -BÄ/GL3h+Ng03jU1~akDzq=U}.KY碌 ֻ1?C N2Muh/4Gm |Q] -OaFދp4/rY\ ۑM GR5j<uvyƻD$/y^z $j1 -}Ɲa756,7 -i7.X5$< ƏV띱ٍ(FOFM>Es}8UJR?Ldg4"LLKt|#.djVMKf6 wCŰ~]4|dͮOSz܄D]dL#g!TMtmvFr4aڻ}ظ}FExy- C2"tvM񪩟ЀvB6F}w@f5 `Cߍ -g'"̢Ryk8S2WQF܎ *~5ނp6U⢨w,ż4y|\^dϰH[+W9rWT|/& :0d@\D\[UjrDcQ0~-$ELmQ6j׀ V~uύN W_(~P/3Bbֵ -i,ewr3gŲ0srVIJzG7R 1K1ߺ]0Uv>mkYWN0`s@T'=4.>M[CB˽pnv)~Uo[I<7`^? _u{yKŷCޮ;ӈ˽\'}eq!l͟_>#b/EQ>+r/kFZ 2ۨ~+oJو֌#i󿈻ja.N=-rc`"A7z< \дV@1m؝3MU4c>2@UߓݩDNd |83ALDR?nW A͕8'Z2KS˗~/Ĥ(Pcq:q/Vko=Һ~w&iZ -R,L& pa 7iBl#cǏogd- u@xbVac*tacD: -Ƽ?jbh,zלDcBVL|3%[By>ݟ)]}mo| H#e2RsF1' kEΐDPB(7EaʘR^2aS1XҘ6\Ey >VyMmީr;'8v3CN6wl$zI,$po"^ƾ2X}Z!>P7f.*8Qb+]/u[ -k. vCo/> endobj -615 0 obj << -/Ascent 750 -/CapHeight 683 -/Descent -194 -/FontName /LNBNXK+CMSY10 -/ItalicAngle -14.035 -/StemV 85 -/XHeight 431 -/FontBBox [-29 -960 1116 775] -/Flags 4 -/CharSet (/minus/bullet/lessequal/greaterequal/arrowleft/element/negationslash/B/H/I/braceleft/braceright/bar/bardbl/radical/section) -/FontFile 616 0 R ->> endobj -1549 0 obj -[778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 0 778 778 0 0 0 0 0 0 0 0 0 0 1000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 657 0 0 0 0 0 845 545 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 500 0 0 278 500 0 0 0 0 833 0 0 0 0 0 0 0 444 ] -endobj -1548 0 obj << -/Type /Encoding -/Differences [ 0 /minus 1/.notdef 15/bullet 16/.notdef 20/lessequal/greaterequal 22/.notdef 32/arrowleft 33/.notdef 50/element 51/.notdef 54/negationslash 55/.notdef 66/B 67/.notdef 72/H/I 74/.notdef 102/braceleft/braceright 104/.notdef 106/bar/bardbl 108/.notdef 112/radical 113/.notdef 120/section 121/.notdef] ->> endobj -613 0 obj << -/Length1 907 -/Length2 3553 +620 0 obj << +/Length1 1462 +/Length2 8120 /Length3 532 -/Length 4992 ->> -stream -%!PS-AdobeFont-1.1: CMMI7 1.100 -%%CreationDate: 1996 Jul 23 07:53:53 -% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. -11 dict begin -/FontInfo 7 dict dup begin -/version (1.100) readonly def -/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI7) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def -end readonly def -/FontName /XHNIDC+CMMI7 def -/PaintType 0 def -/FontType 1 def -/FontMatrix [0.001 0 0 0.001 0 0] readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 59 /comma put -dup 72 /H put -dup 73 /I put -dup 84 /T put -dup 97 /a put -dup 99 /c put -dup 105 /i put -dup 106 /j put -dup 107 /k put -dup 109 /m put -dup 110 /n put -dup 114 /r put -readonly def -/FontBBox{0 -250 1171 750}readonly def -currentdict end -currentfile eexec -oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# -]LeVߐGoo٥\k 9Mv92#:iQ?.n>%jzGm >NjS])7uևUQh4)-×p#z{8YаGP9 )"Pƣ3ГzYYZgp_PC߬CܔDC'<|(Rl/IxXMYzntԟlAv)|*iQP3|TxL" ʃ?Aw·pҋ:r)6,N{?JoA剳Js(0T9$ն''0j%&4LwQcKHpY Bֶ6$bZXZmX>B#9xҥ6IUJeG#݆>@P1o(ߋUcCо"[D.)>;@Ly±P4Ֆ>qc# AhwTfM15*=<giT˞pˠCvSq@5tVǑ- $F')"o Ҵ NYNsQZ-C&mR^RWI%Tnv ( -d> Q='CA>l`F.廊s=WEq̼p1³j{bm4 i \q4NbwbM7 N6REHn9gN'=#$.dƚP:$Ab왏Zh0 nͭ_eYUv*;5@_aPM]߮p1|"KIS\۹(xmj6.M[DZ)Z&iiOi~ _R_mX~~if-..sEj6(upE}er5!/; 8xю(V#0}r"Rz0.I2_bX"rq}\'<*:ak/ 3N!s jUµDQE4'8%drO9QT":t{EގDcCh%sf:s[#:`+ AѺ}~Z[1kyI|K|` :H\\ojf? 4¹k/=~)}Z>=?HNF RLZ> ms Cv^lʝFJ=1x|{ORƲ?~t 5/QpxyhXiswԡcj`Am#ɔtU}PPxP;/8>JZquf/q-FG23yA~8)rVt -Hw -um'Wߍ -8-[~YS;<íi{I*H.(_-{Ւkg=j-p I^NcRYϡN9OrBGU39H9*,^IE U)DLsM?f] cjpMwjՈK^:,yJ,rV!!;gbEQMyO|0L`2/<ŮCH "˫hd}w1m| ]NA,jXu:j0LQˮA'.R*+ -ZC^{#3y8)*cRSvy))}>C9>'Z#7 I?||9?B/#DQn+MW= }6/(NJY|M!͒+҂Nu tl@[CҠJw S%3&Xh|I]|ɮL6S? -Nؕ -7l޵`\U(:F'Nۿ*,#Ð|TZN`Ίlxer3bӭ{ã$=üf}mi\i}Hib{=3l#/Ί0P>.Hg`\wiSN*1~^6#4ޯq[( Dh^<(SEKՒ|s#q% :`Xz$RN#;m|ϒRb'n@]ZcBS7rNڇ 2\0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark -endstream -endobj -614 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 1550 0 R -/FirstChar 59 -/LastChar 114 -/Widths 1551 0 R -/BaseFont /XHNIDC+CMMI7 -/FontDescriptor 612 0 R ->> endobj -612 0 obj << -/Ascent 694 -/CapHeight 683 -/Descent -194 -/FontName /XHNIDC+CMMI7 -/ItalicAngle -14.04 -/StemV 81 -/XHeight 431 -/FontBBox [0 -250 1171 750] -/Flags 4 -/CharSet (/comma/H/I/T/a/c/i/j/k/m/n/r) -/FontFile 613 0 R ->> endobj -1551 0 obj -[339 0 0 0 0 0 0 0 0 0 0 0 0 936 506 0 0 0 0 0 0 0 0 0 0 675 0 0 0 0 0 0 0 0 0 0 0 0 620 0 511 0 0 0 0 0 404 473 607 0 1014 706 0 0 0 530 ] -endobj -1550 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 59/comma 60/.notdef 72/H/I 74/.notdef 84/T 85/.notdef 97/a 98/.notdef 99/c 100/.notdef 105/i/j/k 108/.notdef 109/m/n 111/.notdef 114/r 115/.notdef] ->> endobj -603 0 obj << -/Length1 1385 -/Length2 7327 -/Length3 532 -/Length 9244 +/Length 10114 >> stream %!PS-AdobeFont-1.1: CMR8 1.0 @@ -32840,7 +32738,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /ZIEWDR+CMR8 def +/FontName /LRJVHJ+CMR8 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -32848,6 +32746,7 @@ end readonly def 0 1 255 {1 index exch /.notdef put} for dup 40 /parenleft put dup 41 /parenright put +dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put @@ -32870,9 +32769,11 @@ dup 80 /P put dup 84 /T put dup 88 /X put dup 97 /a put +dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put +dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put @@ -32881,12 +32782,14 @@ dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put +dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put +dup 120 /x put dup 121 /y put readonly def /FontBBox{-36 -250 1070 750}readonly def @@ -32898,34 +32801,30 @@ currentfile eexec ۊ31S\DKZW` P^3 eێ 8`2?l;Ȋ!eXxh Df@=$*IBXԏ!Wx-b1 C; p}hQi=HXbgbmǣR,>_Q! Z؞Ar]< Qjt8?B,mN3v լǵ+K6 t{AJcQ%r?v60RmXsŤ+pǸi:Us)kPW\~; 7T.N }.&:D~zp0C_HOzCByAOve1k`G|f28'j0&®uk6sw, I5&{oP}p2d -CA!8Z⓪٦ǎaBLebǖs=k㍁bny#`h N7VE shG%J4쨲e?cxc>ޙyg[ 5×hՒ{^#E6=a}|vj1h]k71[[;L?H*LjssUyKCDg|AR chãYDieirvZ+Y$> $ ccQ ӡqH_BW, ,im8ѷ55&KD%^XH\@*/]UYeh87q3[!AcJATux.2@lh|+xXq C1D 6t#K6غ'd,E+҆$ĝNMH|&0viI$ n۬{\xBmC8G4}7[q#KX4D#ŀTpkHO|a֟]Oaċ*N7,v5Sr% :-,ݚ0v -c?=Qtgo]T3kl%P\D Ak&uڂ0@G!;H7%@͖uu+bP;J3k6S{n!i]f$ -s6m #gD -=45Or3eH߶Cw`3K.iex=-Ou՚P,;dZh>amp1Eq7*I"2ק}8܆]iIUbvȇH9*|_ W` ^(*NӨ(9^iӡtZOːԥa[73wŅw_C4=`Ș48x7>lhwm(gVxcM" S=0 -ӴS*#o~% 2pO+`Ke*e f "ڠlTL/QpgVn}˧h&а^Ha,Iܛ<1!lK|yGA}''u^E+J;FJo"M,1\Xwfzq CW^v"1В5y^F` (U.wpq?T߭o]+WPqFޔVyJ"0=.^Ny -yg(u?=IHYl<<-0ߵH 3?![bWԝ(7AjljidT#h~$ypTیG_S -;֝9@kc[Y`7Oaiө)lѴozj]Ƴ֚mCq7~R; - ;E!|o6W#4n93F<$V}Ƃ` j3k!kݺ YpQ} JPVg#H^y>ց`:ԧAt2V%k1mwkG vrќ?IM)/:FK=I|E̓F\bku}dR2܇2r"=D"A{C&Kh^F>r6#šVfȹI{*{ T -MpWvcܘv cc|%>;A쵳mør!qxÖ <2xG^L@v`w*R2Zi ]a–TUtEBlU] -īW]Rw,}Qc>".U1B Tcxn MW.eثi'䓩- ed$ 1#wdU l_m0ErtIPO`%z]d/LiagR= s8 )dK.)e -҉P%eps\l rU Y}x[SsKnj|: -` Gۊc{ӕCQJ@F:tW;̀1P}~y .Ķ(6o;evo<9uCo:N!EԼOr@#ohbC'lƏ'C(^6%-݌P]$ l7ѿvf7|U؟@e7B[\Md}vJI -r/V[t'Iƃ&ף+QjܶzY/WnvfqⷄT]:h!0qI$f :g'?+$wxǚGܖ0zIS3=жdcJ~٭4|NL2ѷ SgyxETLҀ5SP:!Ԣxp@NQ׆p𳦢-Ҋ O rչXrlIv >I!K+% /F -NF[,i. t{\ wfܽqLG66E|-=DՁ:$L3&ֲhNLW(N}=b49'`8PPv#MRb`6c&)> 9-`+آI3a]yJq+ДfЄZ'$ -M׎* {ߵ-]n`mPt'͊A1 '1N)}h -92*oI3D訚wC T+5z,'D9]HU]hlB_qx$1T2CNW.1̄;tB"]Fi-js*m4'~)=uv!Z֍uX=IWL@ UY۪ç|,pAZxӚxeA:(گaX{6vdH6)z/^wIzeҒALb5L|u1D\%j[I:DB9%FS -- 0K57*Ntש*9#51syi;PC__]\Py͊gn ʪ|ZjqHað6w/;`~2+TͺQfֽCRkHLBw>150eǝ+dUVi9GY6y?AÓFYYF?Ҍ0L(Ffae[{lL)h i6:F -GzD)*ӳH!]6S[/#}&:Hr+Է0=z -YzyV}d[aDT${79[5 +u~H4=.mf -h<6i4/yV3p]Ӹ׬M¯1׏0}6Ô$K.}]kѣ+ީvVgffu$Ax|Iˆ#MΟ֖^f`>Ớgqr5g٨@ {,СsWHEfaɅY`x1}G)Wf,/*Ц~ J<^e:IjY$.2~G##@t?ݒ$DQЎZzY'%8*=ZV,[.2C~*r! K{\;A1iZ(2aX:12ե1_g{gJW%k;[O/^pALr_S達LpaLb ܋3%^l;<G8"8:a4W>0QF23lMOo̶84 |e!?C./Eq׈{vWjT}nnR6-byJMH/N9&ځ_o"4D}\@ɦv!ZKw^Z'Ϣ -첶מ;lϯ_ }ٽ'y\؞/l :VhQy@\k~}k vI8&7qP05u9QjjKR9%qZқ6nNmИx"_V/QatXD^,20+~.x?E+Nay~ʣ8n,c6Oj6|w%r k< wL^N)V5:q2m9ؠgܨkBP=B.{)WjJTvW:Nf&HEN u="KKILRw+@39 OyǺg=XHb@@V^jkhp隶gH.?Ug 7ܪlٶID#i2ΞQ\6E!jgT4g6]pUsA:5Pg -Ӿ+n![2A[d63].왫cZ"ocć@wE~9&"W#Y8 J,zd<}D{ʎ|@m:.ЖzU~oz@ς}Av 3,*>dp /P]arsy5hcy?*JCГa -0ΦR}Os,K (1ܯT&bwM~Ǩ5ku~zGjcF#x]Dty NVO»Tjsz`K@%u#g{/gAE~y`&jMFvs{vBz!dMfMϬ$ʓ%pqoJT 롚8l}{DNV*; hx/㈒EKuy8.8|f8"fr Et{0eJ@gQW,JqK82!B7BJ5u7z\$+&7LJ -0W)WcDeiVo?ca;ggfL[j)Еm+GXb4'.#aRY':]{gf&$aذL'%VoAЉ?Sr_aNJOQu@\}| l> -bΎ6,b#x)2 -MC?聁UAt8ڀ -?25 -sBb &\\d*2.߃! @W7/DSĆx'ZkMes-N/IG  g#됭mJm@Q~oN_f İ`-tCcWACŬ=<%N:;띣`Wſ9R5t*M3:\b(!!O2Vݍnj<΃ ?BO{E`d lǏ^CRsok=[L@j|AA-ƀ*Ai ;[B_H~4]f]auMQD~7<7ä'>?C 2\swf5{dxf j/`>cdϕ)?83"_5oڳkVЎDl{i ,xh(+qTL+qI .=+?0&PcԒ-5OZd"p\6>Ϯ$cZ)|ף홏z$4 w0000000000000000000000000000000000000000000000000000000000000000 +CA!8Z⓪٦ǎaBLeb̞s }{A>*~(qi  XIw<_-N^0nQ5`WZ+Z BPeCق ]X|jlOnPBRAp-g+GO k܃d>7Y+À4B4nTV ;=bDzUXEGWAVah1^+?Im'SrFIYfcĪFBRcf֔'8(R?x5o ﻍ¡['XdjJF{quᆱQED7q+~RDFeCuKr,їR jO>HUelEE8TUEZà׶3 jYN=iG.h}D P̘}B-4,Hc:YD2ňл/S0 ^_SUqnqcK.sH;\mz8Yy +9OBsD͹yf,3+|ON|!,N萵.]l7h)j+BAVq'}N>1'$G:pq7 ij `[/7-"5ڵl?LYbD8-_ u›6HqtmraI€|,yN%н8s#=\\bD1`V_B +b@~dɨeiGw"R*{{:,np/.:kcDx{;iO9S+ިi>+fǹd7"0EcY#yr Ȗ嘹 g\JuC״NF )ӿ -UA;SF{N_YHD jZdVf&<ď!Bzdxs@MV܊Sǽ WDzCqFlvUZJsѩy*v6ǧ տIprGW"׭oP,<Jlݽiy95=Yɺ^6p#ha{Le霣Rx +阯Dƅ&I-bJϬɞMRR5xC :8mz˘ħ!7Si3NRL]'͵w$/%Hbm.,nb'Kz}`B? {(L,"ټL~DplZV~UA >\c8yS_T^,}b"b,CSzn?ܗETdOã[Uo]wy$p>sb,Jg8ŒPTi}by+ =`<̼H/kRF*]иxd60#G ?C.fv +=)?=~2c1ԑbM1?!&js ` C2>_aٚ%v fYwP~Cn|x"e{nW9d=sVQ*ʼMCĭM8ZsQKLҦl)r6+2"P2)v8v%y9^W5Y0b?Cdx3N.$"\e2y2!;eڎu~c%ߤ/e5͊f+W'E "TmbGO*Nu ZؾjSɖAEsrhĵ"V3^? F z+bsl\r%aISPJ?2I^@4AsYL$DtMGoфNp3U]٨xz߾; RI,i`,AE!KGvH1ǻm*7xWexlpuwfI"ɀ)ɳ, >/ +3$U`Od' C6sS#05-b{/ʗCDYk_&GIw3&+nBw5NcEl6;$HW3j ?iT,( aL@&NZƔԄ3oZT >^8Hgj;ѐ|C3V Am'%j6#by 0 & lNhi ㈿'9("x&什w=ۅ<OK, +PaȆe&-u7K[,[?@ 'ϾR#Cd:{7%kt>lEVmܚ'M_׌D.TyL46E: N"Kgߋd"#M)˺\-R7I0M +n$αmc̃+}J1+'tU'7%%R?xm?OK79+Aԕ 9E͗zz/gwY+/e-b>m7NҐ_zGw-;&0V) Kʳv%5%ayXpPcλ ?f9rJ<} ~xv{g^RHIv[N,o{JW?c@h0 aHyt^pC[EM%17pw8.z+bv3||,V9 E183fZۤ4$q9ZOZ]VG Whghލץ^<5Lh`Ѭ} MoaU[7" }2d޿]]; g(E֔HA`<+R,Tg$w7`C*>;6Oз@ӄDӼ:'sk%좘M{}͝/HA"44}۹ait,ܢۻ[݇mT.h5I[;4d.Xbu#$)v#|@Yw1熔xG '@Y%ˊZfe +Ki(Q_ZV~l>$q.{vtӌDL7RzTXFҡǽ{~kBH(py.P*W{XRo-rTaR.@w&Eq_6XgPP{LU/@iС +^^fq}Y{z:Օ <'UHJ+ɘl}8+c_Ҿ @fn?6(r<[Bc;;\fW3Up:~Se\,l gBM$QW1eZ֐._Ǘo_Xh0ry~wgr>2eP1W'0?re\??M}QyLGd+MD[*,<TRo&;f[ʴ?sD,G({/[X=8[:ݳ3]YhyPs=]6:4yI+EH(ދB>S0: '4^^ +4w4n]{s,r/Lˤ/S.$Vi+WJv*96\u>tG'3 (h[Wu:=bAB涌Mawr,˿OS2 ?3w;/nJ0R}CpS^:z3|8Vgá`~17[|~9dy_*zUIJ@{tVK;SmH$X`W窝>:8E43 w>0MovLxyrbQU0_tu'I^m]*ʗ:\ xKgDٳ=I8ҏ-vx`%QӢ8E+@eXn"V"ɁeS:wS%d9#`ԒղmMBePnpbܓ^mbK0m1R\&e{b"W{u)W2x c9|課#ᎹJH1Tڳvn-F `5*G1}Yω?dUf o.nIfDg/'@T|>1U.By.Ʀ25m;sylf9k z<# S>"zQN<)Wni};!@e W&=FX1.8.vi. &SӬ74RPQCNj8qkYDX4ֱHt7 Azd5Z㿾)05N$H=RK+h`PT3'/(#+U5A-T0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 @@ -32936,41 +32835,41 @@ h cleartomark endstream endobj -604 0 obj << +621 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1552 0 R +/Encoding 1555 0 R /FirstChar 40 /LastChar 121 -/Widths 1553 0 R -/BaseFont /ZIEWDR+CMR8 -/FontDescriptor 602 0 R +/Widths 1556 0 R +/BaseFont /LRJVHJ+CMR8 +/FontDescriptor 619 0 R >> endobj -602 0 obj << +619 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /ZIEWDR+CMR8 +/FontName /LRJVHJ+CMR8 /ItalicAngle 0 /StemV 76 /XHeight 431 /FontBBox [-36 -250 1070 750] /Flags 4 -/CharSet (/parenleft/parenright/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/B/G/I/L/O/P/T/X/a/c/d/e/g/h/i/l/m/n/o/p/r/s/t/u/v/w/y) -/FontFile 603 0 R +/CharSet (/parenleft/parenright/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/B/G/I/L/O/P/T/X/a/b/c/d/e/f/g/h/i/l/m/n/o/p/q/r/s/t/u/v/w/x/y) +/FontFile 620 0 R >> endobj -1553 0 obj -[413 413 0 0 0 354 295 531 531 531 531 531 531 531 531 531 531 531 0 0 0 0 0 0 0 0 752 0 0 0 0 834 0 383 0 0 664 0 0 826 723 0 0 0 767 0 0 0 796 0 0 0 0 0 0 0 0 531 0 472 590 472 0 531 590 295 0 0 295 885 590 531 590 0 414 419 413 590 561 767 0 561 ] +1556 0 obj +[413 413 0 0 295 354 295 531 531 531 531 531 531 531 531 531 531 531 0 0 0 0 0 0 0 0 752 0 0 0 0 834 0 383 0 0 664 0 0 826 723 0 0 0 767 0 0 0 796 0 0 0 0 0 0 0 0 531 590 472 590 472 325 531 590 295 0 0 295 885 590 531 590 561 414 419 413 590 561 767 561 561 ] endobj -1552 0 obj << +1555 0 obj << /Type /Encoding -/Differences [ 0 /.notdef 40/parenleft/parenright 42/.notdef 45/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine 58/.notdef 66/B 67/.notdef 71/G 72/.notdef 73/I 74/.notdef 76/L 77/.notdef 79/O/P 81/.notdef 84/T 85/.notdef 88/X 89/.notdef 97/a 98/.notdef 99/c/d/e 102/.notdef 103/g/h/i 106/.notdef 108/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w 120/.notdef 121/y 122/.notdef] +/Differences [ 0 /.notdef 40/parenleft/parenright 42/.notdef 44/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine 58/.notdef 66/B 67/.notdef 71/G 72/.notdef 73/I 74/.notdef 76/L 77/.notdef 79/O/P 81/.notdef 84/T 85/.notdef 88/X 89/.notdef 97/a/b/c/d/e/f/g/h/i 106/.notdef 108/l/m/n/o/p/q/r/s/t/u/v/w/x/y 122/.notdef] >> endobj -599 0 obj << -/Length1 751 -/Length2 1212 +616 0 obj << +/Length1 769 +/Length2 1408 /Length3 532 -/Length 2495 +/Length 2709 >> stream %!PS-AdobeFont-1.1: CMR6 1.0 @@ -32986,7 +32885,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /PEVRUV+CMR6 def +/FontName /GKQPMI+CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -32994,6 +32893,7 @@ end readonly def 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put +dup 51 /three put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end @@ -33001,8 +32901,10 @@ currentfile eexec oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\@[6]nhmlhaH+4/?3&n=a6E#|~.ԅˡ}_B$~\|"4Pxҍ>P% ~ߏ4q.C3s蛼q翈by?Z72z6LpHC1D"28s B ~ OPQ O\O}';Pǂ;߉~ I;^קg U51&:MgRXcO`BM vJxv𒋣&$æθwzFMqGkȖfho/m)Z k@p;~9V0͛E}Aêp+_Y:Q_i> oӯÑj0k?+6,݉"1UnM/ &mӿȶ{۾DX w4 h@$6o`P3D8 7yPmAzqb-#> -*s-KR{CDywjY;Rg|ʿA3xpqY mfI 5q[ T}(W3ڟtߥqZ2dgxAX'dUYxfxZ'|\&b)hi0000000000000000000000000000000000000000000000000000000000000000 +1T\E#k3i(-Ќ9hծ;Y-kC O;5q\yv~wSՏ1>';Pǂ;߉~ I;^ק`F*'nu/&o+\z~ 3M#8Z cD%aiV{t ++ ++s)l^mMV6</ 5L8Y1jA!UiMwLi>$d4ntLHm%4Cs>=wtm}qq%ı ˾3edD,d}tD `KBoŹaC!hK ^Qft>P[ &G%s[{ zF$j-Lݷ‚Ղnin:,CHoԹN/OEnxYS7]޴ &W}+u!Q:|&1C6{Ӑk2|ytIkٮ1ku"L+½a+YEo0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 @@ -33013,41 +32915,243 @@ currentfile eexec cleartomark endstream endobj -600 0 obj << +617 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1554 0 R +/Encoding 1557 0 R /FirstChar 49 -/LastChar 50 -/Widths 1555 0 R -/BaseFont /PEVRUV+CMR6 -/FontDescriptor 598 0 R +/LastChar 51 +/Widths 1558 0 R +/BaseFont /GKQPMI+CMR6 +/FontDescriptor 615 0 R >> endobj -598 0 obj << +615 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /PEVRUV+CMR6 +/FontName /GKQPMI+CMR6 /ItalicAngle 0 /StemV 83 /XHeight 431 /FontBBox [-20 -250 1193 750] /Flags 4 -/CharSet (/one/two) -/FontFile 599 0 R +/CharSet (/one/two/three) +/FontFile 616 0 R >> endobj -1555 0 obj -[611 611 ] +1558 0 obj +[611 611 611 ] endobj -1554 0 obj << +1557 0 obj << /Type /Encoding -/Differences [ 0 /.notdef 49/one/two 51/.notdef] +/Differences [ 0 /.notdef 49/one/two/three 52/.notdef] >> endobj -596 0 obj << -/Length1 769 -/Length2 1298 +612 0 obj << +/Length1 1050 +/Length2 2900 +/Length3 532 +/Length 4482 +>> +stream +%!PS-AdobeFont-1.1: CMSY10 1.0 +%%CreationDate: 1991 Aug 15 07:20:57 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.0) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMSY10) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.035 def +/isFixedPitch false def +end readonly def +/FontName /ASGKDG+CMSY10 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 0 /minus put +dup 15 /bullet put +dup 20 /lessequal put +dup 21 /greaterequal put +dup 32 /arrowleft put +dup 50 /element put +dup 54 /negationslash put +dup 66 /B put +dup 72 /H put +dup 73 /I put +dup 102 /braceleft put +dup 103 /braceright put +dup 106 /bar put +dup 107 /bardbl put +dup 112 /radical put +dup 120 /section put +readonly def +/FontBBox{-29 -960 1116 775}readonly def +currentdict end +currentfile eexec +oc;j~EЪ/ ȭX~id}S5Q!gtⵎkJc;rN^X5.Sy +'IqV:r㚉#,# dBZ *R*"7٨y=cLIPsF'f> ba +]fv+QAwdO[x"%Sx~{p҈덡|O +BÄ/GL3h+Ng03jU1~akDzq=U}.KY碌 ֻ1?C N2Muh/4Gm |Q] +OaFދp4/rY\ ۑM GR5j<uvyƻD$/y^z $j1 +}Ɲa756,7 +i7.X5$< ƏV띱ٍ(FOFM>Es}8UJR?Ldg4"LLKt|#.djVMKf6 wCŰ~]4|dͮOSz܄D]dL#g!TMtmvFr4aڻ}ظ}FExy- C2"tvM񪩟ЀvB6F}w@f5 `Cߍ +g'"̢Ryk8S2WQF܎ *~5ނp6U⢨w,ż4y|\^dϰH[+W9rWT|/& :0d@\D\[UjrDcQ0~-$ELmQ6j׀ V~uύN W_(~P/3Bbֵ +i,ewr3gŲ0srVIJzG7R 1K1ߺ]0Uv>mkYWN0`s@T'=4.>M[CB˽pnv)~Uo[I<7`^? _u{yKŷCޮ;ӈ˽\'}eq!l͟_>#b/EQ>+r/kFZ 2ۨ~+oJو֌#i󿈻ja.N=-rc`"A7z< \дV@1m؝3MU4c>2@UߓݩDNd |83ALDR?nW A͕8'Z2KS˗~/Ĥ(Pcq:q/Vko=Һ~w&iZ +R,L& pa 7iBl#cǏogd- u@xbVac*tacD: +Ƽ?jbh,zלDcBVL|3%[By>ݟ)]}mo| H#e2RsF1' kEΐDPB(7EaʘR^2aS1XҘ6\Ey >VyMmީr;'8v3CN6wl$zI,$po"^ƾ2X}Z!>P7f.*8Qb+]/u[ +k. vCo/> endobj +611 0 obj << +/Ascent 750 +/CapHeight 683 +/Descent -194 +/FontName /ASGKDG+CMSY10 +/ItalicAngle -14.035 +/StemV 85 +/XHeight 431 +/FontBBox [-29 -960 1116 775] +/Flags 4 +/CharSet (/minus/bullet/lessequal/greaterequal/arrowleft/element/negationslash/B/H/I/braceleft/braceright/bar/bardbl/radical/section) +/FontFile 612 0 R +>> endobj +1560 0 obj +[778 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 0 778 778 0 0 0 0 0 0 0 0 0 0 1000 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 667 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 657 0 0 0 0 0 845 545 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 500 0 0 278 500 0 0 0 0 833 0 0 0 0 0 0 0 444 ] +endobj +1559 0 obj << +/Type /Encoding +/Differences [ 0 /minus 1/.notdef 15/bullet 16/.notdef 20/lessequal/greaterequal 22/.notdef 32/arrowleft 33/.notdef 50/element 51/.notdef 54/negationslash 55/.notdef 66/B 67/.notdef 72/H/I 74/.notdef 102/braceleft/braceright 104/.notdef 106/bar/bardbl 108/.notdef 112/radical 113/.notdef 120/section 121/.notdef] +>> endobj +609 0 obj << +/Length1 907 +/Length2 3553 +/Length3 532 +/Length 4992 +>> +stream +%!PS-AdobeFont-1.1: CMMI7 1.100 +%%CreationDate: 1996 Jul 23 07:53:53 +% Copyright (C) 1997 American Mathematical Society. All Rights Reserved. +11 dict begin +/FontInfo 7 dict dup begin +/version (1.100) readonly def +/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def +/FullName (CMMI7) readonly def +/FamilyName (Computer Modern) readonly def +/Weight (Medium) readonly def +/ItalicAngle -14.04 def +/isFixedPitch false def +end readonly def +/FontName /MEBLRX+CMMI7 def +/PaintType 0 def +/FontType 1 def +/FontMatrix [0.001 0 0 0.001 0 0] readonly def +/Encoding 256 array +0 1 255 {1 index exch /.notdef put} for +dup 59 /comma put +dup 72 /H put +dup 73 /I put +dup 84 /T put +dup 97 /a put +dup 99 /c put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 109 /m put +dup 110 /n put +dup 114 /r put +readonly def +/FontBBox{0 -250 1171 750}readonly def +currentdict end +currentfile eexec +oc;j~EЪ)s̾;.;rTejiK/df5A|{S/ )Sc\^ȟmp+#vL17~k d# +]LeVߐGoo٥\k 9Mv92#:iQ?.n>%jzGm >NjS])7uևUQh4)-×p#z{8YаGP9 )"Pƣ3ГzYYZgp_PC߬CܔDC'<|(Rl/IxXMYzntԟlAv)|*iQP3|TxL" ʃ?Aw·pҋ:r)6,N{?JoA剳Js(0T9$ն''0j%&4LwQcKHpY Bֶ6$bZXZmX>B#9xҥ6IUJeG#݆>@P1o(ߋUcCо"[D.)>;@Ly±P4Ֆ>qc# AhwTfM15*=<giT˞pˠCvSq@5tVǑ- $F')"o Ҵ NYNsQZ-C&mR^RWI%Tnv ( +d> Q='CA>l`F.廊s=WEq̼p1³j{bm4 i \q4NbwbM7 N6REHn9gN'=#$.dƚP:$Ab왏Zh0 nͭ_eYUv*;5@_aPM]߮p1|"KIS\۹(xmj6.M[DZ)Z&iiOi~ _R_mX~~if-..sEj6(upE}er5!/; 8xю(V#0}r"Rz0.I2_bX"rq}\'<*:ak/ 3N!s jUµDQE4'8%drO9QT":t{EގDcCh%sf:s[#:`+ AѺ}~Z[1kyI|K|` :H\\ojf? 4¹k/=~)}Z>=?HNF RLZ> ms Cv^lʝFJ=1x|{ORƲ?~t 5/QpxyhXiswԡcj`Am#ɔtU}PPxP;/8>JZquf/q-FG23yA~8)rVt +Hw +um'Wߍ +8-[~YS;<íi{I*H.(_-{Ւkg=j-p I^NcRYϡN9OrBGU39H9*,^IE U)DLsM?f] cjpMwjՈK^:,yJ,rV!!;gbEQMyO|0L`2/<ŮCH "˫hd}w1m| ]NA,jXu:j0LQˮA'.R*+ +ZC^{#3y8)*cRSvy))}>C9>'Z#7 I?||9?B/#DQn+MW= }6/(NJY|M!͒+҂Nu tl@[CҠJw S%3&Xh|I]|ɮL6S? +Nؕ +7l޵`\U(:F'Nۿ*,#Ð|TZN`Ίlxer3bӭ{ã$=üf}mi\i}Hib{=3l#/Ί0P>.Hg`\wiSN*1~^6#4ޯq[( Dh^<(SEKՒ|s#q% :`Xz$RN#;m|ϒRb'n@]ZcBS7rNڇ 2\0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +0000000000000000000000000000000000000000000000000000000000000000 +cleartomark +endstream +endobj +610 0 obj << +/Type /Font +/Subtype /Type1 +/Encoding 1561 0 R +/FirstChar 59 +/LastChar 114 +/Widths 1562 0 R +/BaseFont /MEBLRX+CMMI7 +/FontDescriptor 608 0 R +>> endobj +608 0 obj << +/Ascent 694 +/CapHeight 683 +/Descent -194 +/FontName /MEBLRX+CMMI7 +/ItalicAngle -14.04 +/StemV 81 +/XHeight 431 +/FontBBox [0 -250 1171 750] +/Flags 4 +/CharSet (/comma/H/I/T/a/c/i/j/k/m/n/r) +/FontFile 609 0 R +>> endobj +1562 0 obj +[339 0 0 0 0 0 0 0 0 0 0 0 0 936 506 0 0 0 0 0 0 0 0 0 0 675 0 0 0 0 0 0 0 0 0 0 0 0 620 0 511 0 0 0 0 0 404 473 607 0 1014 706 0 0 0 530 ] +endobj +1561 0 obj << +/Type /Encoding +/Differences [ 0 /.notdef 59/comma 60/.notdef 72/H/I 74/.notdef 84/T 85/.notdef 97/a 98/.notdef 99/c 100/.notdef 105/i/j/k 108/.notdef 109/m/n 111/.notdef 114/r 115/.notdef] +>> endobj +606 0 obj << +/Length1 787 +/Length2 1497 /Length3 532 -/Length 2599 +/Length 2816 >> stream %!PS-AdobeFont-1.1: CMR7 1.0 @@ -33063,7 +33167,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /BENDPP+CMR7 def +/FontName /NVCORV+CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33071,6 +33175,7 @@ end readonly def 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put +dup 51 /three put dup 58 /colon put readonly def /FontBBox{-27 -250 1122 750}readonly def @@ -33079,7 +33184,11 @@ currentfile eexec oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\ʻl24`}IRB s\pzEGAۋa4_p0uAEG)Q|8B*dGWj'0Vix#(=@'qIT5i (Ѵt` ?E)4E^yҴF+$8&G"Yl?eYjt+TI2! nXKt`˱~h]{>Qaiσ\mFU#Gvh2un8W;R4Ej1B4b ;b9y[lV:P񕈇9g`\J~ O>%V0 ݬ;cJԺjYrt6yql4Qo٫~o_=6xqw,",kϷo -#vI7_ fz!y(3)5*кYb#aM?3G%wG*KzF*呭0I99O"}w'[Fn,WWI(P3c;X8#{9GYuWK?}l] v#!=,H/"efh+dʈp&c(2TdnX0je\;p5SLT] 8X2#f|ŪꅍYtMԭܳtRt|ഄq=cCZ5)'m/e x  t u 'X%S,օ1D Yd`. B1,wQã UȲܗG'^Xf=-[76R޳Nt>垖c=D{ݏSܡ:8aJxXV%THF-n$ u貾,v'QR B_z0񙗓 i/i{H]3%huOEi} ]7Lنuwd.0000000000000000000000000000000000000000000000000000000000000000 +#vI7_ fz!y(3)5*кYb#aM?3G%wG*Jx,N +R k +v`5eMT$lޅzpH{R~# 9afA@텀gAIKN| ˰2p!/xVTWw V88΄QvJ5mz}6,'Uye X@g4qGagkKݓ=-B{E +bx}Һzs7')8-XTG`9?Pe: ^3~hcxbk1!o^KWki7ݱ=3O |0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 @@ -33090,37 +33199,37 @@ _2 cleartomark endstream endobj -597 0 obj << +607 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1556 0 R +/Encoding 1563 0 R /FirstChar 49 /LastChar 58 -/Widths 1557 0 R -/BaseFont /BENDPP+CMR7 -/FontDescriptor 595 0 R +/Widths 1564 0 R +/BaseFont /NVCORV+CMR7 +/FontDescriptor 605 0 R >> endobj -595 0 obj << +605 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /BENDPP+CMR7 +/FontName /NVCORV+CMR7 /ItalicAngle 0 /StemV 79 /XHeight 431 /FontBBox [-27 -250 1122 750] /Flags 4 -/CharSet (/one/two/colon) -/FontFile 596 0 R +/CharSet (/one/two/three/colon) +/FontFile 606 0 R >> endobj -1557 0 obj -[569 569 0 0 0 0 0 0 0 323 ] +1564 0 obj +[569 569 569 0 0 0 0 0 0 323 ] endobj -1556 0 obj << +1563 0 obj << /Type /Encoding -/Differences [ 0 /.notdef 49/one/two 51/.notdef 58/colon 59/.notdef] +/Differences [ 0 /.notdef 49/one/two/three 52/.notdef 58/colon 59/.notdef] >> endobj -591 0 obj << +601 0 obj << /Length1 1719 /Length2 10393 /Length3 532 @@ -33140,7 +33249,7 @@ stream /ItalicAngle 0 def /isFixedPitch true def end readonly def -/FontName /GXISJL+CMTT10 def +/FontName /MRECRN+CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33260,33 +33369,33 @@ b cleartomark endstream endobj -592 0 obj << +602 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1558 0 R +/Encoding 1565 0 R /FirstChar 40 /LastChar 126 -/Widths 1559 0 R -/BaseFont /GXISJL+CMTT10 -/FontDescriptor 590 0 R +/Widths 1566 0 R +/BaseFont /MRECRN+CMTT10 +/FontDescriptor 600 0 R >> endobj -590 0 obj << +600 0 obj << /Ascent 611 /CapHeight 611 /Descent -222 -/FontName /GXISJL+CMTT10 +/FontName /MRECRN+CMTT10 /ItalicAngle 0 /StemV 69 /XHeight 431 /FontBBox [-4 -235 731 800] /Flags 4 /CharSet (/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/nine/colon/equal/A/B/C/E/F/I/K/L/N/O/P/S/T/W/Y/backslash/underscore/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/asciitilde) -/FontFile 591 0 R +/FontFile 601 0 R >> endobj -1559 0 obj +1566 0 obj [525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 525 525 0 0 525 0 0 0 525 525 525 0 525 525 0 0 525 0 525 525 0 525 525 525 0 0 525 525 0 0 525 0 525 0 0 525 0 0 525 0 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 525 0 0 0 525 ] endobj -1558 0 obj << +1565 0 obj << /Type /Encoding /Differences [ 0 /.notdef 40/parenleft/parenright/asterisk/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six 55/.notdef 57/nine/colon 59/.notdef 61/equal 62/.notdef 65/A/B/C 68/.notdef 69/E/F 71/.notdef 73/I 74/.notdef 75/K/L 77/.notdef 78/N/O/P 81/.notdef 83/S/T 85/.notdef 87/W 88/.notdef 89/Y 90/.notdef 92/backslash 93/.notdef 95/underscore 96/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef 126/asciitilde 127/.notdef] >> endobj @@ -33310,7 +33419,7 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /XQUKOV+CMMI10 def +/FontName /FTOEAW+CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33412,18 +33521,18 @@ endobj 586 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1560 0 R +/Encoding 1567 0 R /FirstChar 11 /LastChar 122 -/Widths 1561 0 R -/BaseFont /XQUKOV+CMMI10 +/Widths 1568 0 R +/BaseFont /FTOEAW+CMMI10 /FontDescriptor 584 0 R >> endobj 584 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /XQUKOV+CMMI10 +/FontName /FTOEAW+CMMI10 /ItalicAngle -14.04 /StemV 72 /XHeight 431 @@ -33432,10 +33541,10 @@ endobj /CharSet (/alpha/beta/period/comma/less/greater/A/D/I/L/N/O/P/Q/T/U/X/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/r/s/t/u/v/w/x/y/z) /FontFile 585 0 R >> endobj -1561 0 obj +1568 0 obj [640 566 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 278 278 778 0 778 0 0 750 0 0 828 0 0 0 0 440 0 0 681 0 803 763 642 791 0 0 584 683 0 0 828 0 0 0 0 0 0 0 0 529 429 433 520 466 490 477 576 345 412 521 298 878 600 485 503 0 451 469 361 572 485 716 572 490 465 ] endobj -1560 0 obj << +1567 0 obj << /Type /Encoding /Differences [ 0 /.notdef 11/alpha/beta 13/.notdef 58/period/comma/less 61/.notdef 62/greater 63/.notdef 65/A 66/.notdef 68/D 69/.notdef 73/I 74/.notdef 76/L 77/.notdef 78/N/O/P/Q 82/.notdef 84/T/U 86/.notdef 88/X 89/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p 113/.notdef 114/r/s/t/u/v/w/x/y/z 123/.notdef] >> endobj @@ -33459,7 +33568,7 @@ stream /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /BMAEFM+CMTI10 def +/FontName /HNLSFN+CMTI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33610,18 +33719,18 @@ endobj 571 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1562 0 R +/Encoding 1569 0 R /FirstChar 11 /LastChar 122 -/Widths 1563 0 R -/BaseFont /BMAEFM+CMTI10 +/Widths 1570 0 R +/BaseFont /HNLSFN+CMTI10 /FontDescriptor 569 0 R >> endobj 569 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /BMAEFM+CMTI10 +/FontName /HNLSFN+CMTI10 /ItalicAngle -14.04 /StemV 68 /XHeight 431 @@ -33630,10 +33739,10 @@ endobj /CharSet (/ff/fi/fl/quoteright/comma/hyphen/period/slash/zero/one/two/three/five/nine/colon/equal/A/B/C/D/E/F/G/I/L/M/N/O/P/R/S/T/U/V/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z) /FontFile 570 0 R >> endobj -1563 0 obj +1570 0 obj [613 562 588 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 307 0 0 0 0 307 358 307 511 511 511 511 511 0 511 0 0 0 511 307 0 0 767 0 0 0 743 704 716 755 678 653 774 0 386 0 0 627 897 743 767 678 0 729 562 716 743 743 0 0 0 0 0 0 0 0 0 0 511 460 460 511 460 307 460 511 307 307 460 256 818 562 511 511 460 422 409 332 537 460 664 464 486 409 ] endobj -1562 0 obj << +1569 0 obj << /Type /Encoding /Differences [ 0 /.notdef 11/ff/fi/fl 14/.notdef 39/quoteright 40/.notdef 44/comma/hyphen/period/slash/zero/one/two/three 52/.notdef 53/five 54/.notdef 57/nine/colon 59/.notdef 61/equal 62/.notdef 65/A/B/C/D/E/F/G 72/.notdef 73/I 74/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S/T/U/V 87/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z 123/.notdef] >> endobj @@ -33657,7 +33766,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /TMOLKN+CMR10 def +/FontName /HEDAZU+CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33810,18 +33919,18 @@ endobj 434 0 obj << /Type /Font /Subtype /Type1 -/Encoding 1564 0 R +/Encoding 1571 0 R /FirstChar 11 /LastChar 123 -/Widths 1565 0 R -/BaseFont /TMOLKN+CMR10 +/Widths 1572 0 R +/BaseFont /HEDAZU+CMR10 /FontDescriptor 432 0 R >> endobj 432 0 obj << /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /TMOLKN+CMR10 +/FontName /HEDAZU+CMR10 /ItalicAngle 0 /StemV 69 /XHeight 431 @@ -33830,18 +33939,18 @@ endobj /CharSet (/ff/fi/fl/ffi/quotedblright/ampersand/quoteright/parenleft/parenright/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon/equal/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/bracketleft/quotedblleft/bracketright/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash) /FontFile 433 0 R >> endobj -1565 0 obj +1572 0 obj [583 556 556 833 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 500 0 0 0 778 278 389 389 0 778 278 333 278 500 500 500 500 500 500 500 500 500 500 500 278 278 0 778 0 0 0 750 708 722 764 681 653 785 750 361 514 778 625 917 750 778 681 0 736 556 722 750 750 1028 0 0 0 278 500 278 0 0 0 500 556 444 556 444 306 500 556 278 306 528 278 833 556 500 556 528 392 394 389 556 528 722 528 528 444 500 ] endobj -1564 0 obj << +1571 0 obj << /Type /Encoding /Differences [ 0 /.notdef 11/ff/fi/fl/ffi 15/.notdef 34/quotedblright 35/.notdef 38/ampersand/quoteright/parenleft/parenright 42/.notdef 43/plus/comma/hyphen/period/slash/zero/one/two/three/four/five/six/seven/eight/nine/colon/semicolon 60/.notdef 61/equal 62/.notdef 65/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P 81/.notdef 82/R/S/T/U/V/W 88/.notdef 91/bracketleft/quotedblleft/bracketright 94/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash 124/.notdef] >> endobj 430 0 obj << -/Length1 1783 -/Length2 12373 +/Length1 1762 +/Length2 12194 /Length3 532 -/Length 14688 +/Length 14488 >> stream %!PS-AdobeFont-1.1: CMBX10 1.00B @@ -33857,7 +33966,7 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /RIMMUN+CMBX10 def +/FontName /LTOUKE+CMBX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -33881,7 +33990,6 @@ dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 61 /equal put -dup 63 /question put dup 65 /A put dup 66 /B put dup 67 /C put @@ -33944,57 +34052,43 @@ S ?] FxºzDL_>bTvʻbp'au&zM7nGkhj֔a#SfS/+  5&`81?{p~w~5(frEh]^bfhǑX;/%oOvٚc9rXo$ݒ-#z}fSUϻy;͔>r^0~;:6]:SS(x:bNPc i:(O>EQ@q;yʨ؅Fn<&S^υ',5:8 N :U6HSKL M7 AoKr;pzYHbЫF&/ԋ㊞5;O*';h2˸2*aK2GA`Onr!Ll>%h.rYaSC-嵵bEshmbT/E nHҍ.iURf -SK2,M݅Sv; -t8X e!ad3|SCLڇ<{8 [qЬ:ȌoXz2y<7݅671\T";;߻_.Ǯ"Nd_ug޴Ҟ`8NH2aĨ{KJ X?X*$//6n/یzo=ǔ;+^4'4b!OZ- -)BfJ 3E/@g %&U6!<Zd攍!qju|?8tN6hEnG)? 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endobj -1566 0 obj << +1573 0 obj << /Type /Encoding -/Differences [ 0 /.notdef 12/fi/fl 14/.notdef 34/quotedblright 35/.notdef 39/quoteright 40/.notdef 44/comma 45/.notdef 46/period 47/.notdef 48/zero/one/two/three/four/five/six/seven/eight/nine/colon 59/.notdef 61/equal 62/.notdef 63/question 64/.notdef 65/A/B/C/D/E/F/G/H/I/J 75/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S/T/U/V 87/.notdef 92/quotedblleft 93/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash 124/.notdef] +/Differences [ 0 /.notdef 12/fi/fl 14/.notdef 34/quotedblright 35/.notdef 39/quoteright 40/.notdef 44/comma 45/.notdef 46/period 47/.notdef 48/zero/one/two/three/four/five/six/seven/eight/nine/colon 59/.notdef 61/equal 62/.notdef 65/A/B/C/D/E/F/G/H/I/J 75/.notdef 76/L/M/N/O/P 81/.notdef 82/R/S/T/U/V 87/.notdef 92/quotedblleft 93/.notdef 97/a/b/c/d/e/f/g/h/i/j/k/l/m/n/o/p/q/r/s/t/u/v/w/x/y/z/endash 124/.notdef] >> endobj 427 0 obj << /Length1 1067 @@ -34055,7 +34149,7 @@ stream /ItalicAngle -14.04 def 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