psblas3/docs/html/images.pl

# LaTeX2HTML 2018 (Released Feb 1, 2018)
# Associate images original text with physical files.


$key = q/(0dotsnp-1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img102.png"
 ALT="$(0\dots np-1)$">|; 

$key = q/(1dotsmg);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="70" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img105.png"
 ALT="$(1\dots mg)$">|; 

$key = q/(1dotsnp);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img103.png"
 ALT="$(1\dots np)$">|; 

$key = q/(i+irw-1),ja(j),val(j);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="185" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img119.png"
 ALT="$(i+irw-1),ja(j),val(j)$">|; 

$key = q/-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="24" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img88.png"
 ALT="$-1$">|; 

$key = q/-1<=root<=np-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="165" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img147.png"
 ALT="$-1&lt;= root &lt;= np-1$">|; 

$key = q/-1leiamlenp-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="139" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img141.png"
 ALT="$-1 \le iam \le np-1$">|; 

$key = q/-1lerootlenp-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="140" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img87.png"
 ALT="$-1\le root\le np-1$">|; 

$key = q/0,1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="27" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img95.png"
 ALT="$0,1$">|; 

$key = q/0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img96.png"
 ALT="$0$">|; 

$key = q/0<=dst<=np-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="145" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img152.png"
 ALT="$0&lt;= dst &lt;= np-1$">|; 

$key = q/0<=m<=size(dat,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="171" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img153.png"
 ALT="$0&lt;= m &lt;= size(dat,1)$">|; 

$key = q/0<=root<=np-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="153" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img146.png"
 ALT="$0&lt;= root &lt;= np-1$">|; 

$key = q/0<=src<=np-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="146" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img156.png"
 ALT="$0&lt;= src &lt;= np-1$">|; 

$key = q/0leiamlenp-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="127" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img142.png"
 ALT="$0 \le iam \le np-1$">|; 

$key = q/0leidlenp-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="113" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img145.png"
 ALT="$0 \le id \le np-1$">|; 

$key = q/0lepv(i)<np;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img100.png"
 ALT="$0\le pv(i) &lt; np$">|; 

$key = q/1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="13" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img122.png"
 ALT="$1$">|; 

$key = q/1dotsn;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img15.png"
 ALT="$1\dots n$">|; 

$key = q/1dotsn_{hbox{row}_i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img17.png"
 ALT="$1\dots n_{\hbox{row}_i}$">|; 

$key = q/=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img184.png"
 ALT="$=0$">|; 

$key = q/>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img126.png"
 ALT="$&gt;0$">|; 

$key = q/A;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img1.png"
 ALT="$A$">|; 

$key = q/A^T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img125.png"
 ALT="$A^T$">|; 

$key = q/CG;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="29" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img187.png"
 ALT="$CG$">|; 

$key = q/D;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img56.png"
 ALT="$D$">|; 

$key = q/FCG(1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img180.png"
 ALT="$FCG(1)$">|; 

$key = q/I;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img106.png"
 ALT="$I$">|; 

$key = q/ILU(0);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="56" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img172.png"
 ALT="$ILU(0)$">|; 

$key = q/IX;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img130.png"
 ALT="$IX$">|; 

$key = q/N_I=nl;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img107.png"
 ALT="$N_I=nl$">|; 

$key = q/O(n^2);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="33" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img139.png"
 ALT="$O(n^2)$">|; 

$key = q/O(nlogn);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img138.png"
 ALT="$O(n \log n)$">|; 

$key = q/P^T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img74.png"
 ALT="$P^T$">|; 

$key = q/P^{T};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img72.png"
 ALT="$P^{T}$">|; 

$key = q/P_a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="22" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img71.png"
 ALT="$P_a$">|; 

$key = q/P_aP^T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="34" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img75.png"
 ALT="$P_aP^T$">|; 

$key = q/Q;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="16" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img70.png"
 ALT="$Q$">|; 

$key = q/T;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img55.png"
 ALT="$T$">|; 

$key = q/X;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img129.png"
 ALT="$X$">|; 

$key = q/a;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img115.png"
 ALT="$a$">|; 

$key = q/a_{ij}ne0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img6.png"
 ALT="$a_{ij} \ne0$">|; 

$key = q/alpha;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="14" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img22.png"
 ALT="$\alpha$">|; 

$key = q/amax;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img32.png"
 ALT="$amax$">|; 

$key = q/asum;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img37.png"
 ALT="$asum$">|; 

$key = q/beta;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img23.png"
 ALT="$\beta$">|; 

$key = q/calB;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="15" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img8.png"
 ALT="$\cal B$">|; 

$key = q/calH;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img9.png"
 ALT="$\cal H$">|; 

$key = q/calI;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img7.png"
 ALT="$\cal I$">|; 

$key = q/collect;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img83.png"
 ALT="$collect$">|; 

$key = q/dat;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img149.png"
 ALT="$dat$">|; 

$key = q/dat_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="32" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img148.png"
 ALT="$dat_i$">|; 

$key = q/diag(1)=1(noscaling);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="164" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img58.png"
 ALT="$diag(1) = 1 (no scaling)$">|; 

$key = q/dot;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img26.png"
 ALT="$dot$">|; 

$key = q/dst;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img155.png"
 ALT="$dst$">|; 

$key = q/fbox{TheSbox};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="562" HEIGHT="482" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img159.png"
 ALT="\fbox{\TheSbox}">|; 

$key = q/flag=psb_sort_keep_idx_;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="184" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img136.png"
 ALT="$flag = psb\_sort\_keep\_idx\_$">|; 

$key = q/flag=psb_sort_ovw_idx_;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="180" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img131.png"
 ALT="$flag = psb\_sort\_ovw\_idx\_$">|; 

$key = q/glob_x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="46" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img80.png"
 ALT="$glob\_x$">|; 

$key = q/glob_x_{1:m,1:n};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img81.png"
 ALT="$glob\_x_{1:m,1:n}$">|; 

$key = q/i+irw-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="81" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img121.png"
 ALT="$i+irw-1$">|; 

$key = q/i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="9" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img4.png"
 ALT="$i$">|; 

$key = q/i=1,dots,nz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="91" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img117.png"
 ALT="$i=1,\dots,nz$">|; 

$key = q/i=1,nr;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="63" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img118.png"
 ALT="$i=1,nr$">|; 

$key = q/ia(i),ja(i),val(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="123" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img116.png"
 ALT="$ia(i),ja(i),val(i)$">|; 

$key = q/ia(i),ja(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img108.png"
 ALT="$ia(i),ja(i)$">|; 

$key = q/ia(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img109.png"
 ALT="$ia(i)$">|; 

$key = q/iam=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="73" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img143.png"
 ALT="$iam=-1$">|; 

$key = q/id;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img144.png"
 ALT="$id$">|; 

$key = q/iin{1dotsmg};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img92.png"
 ALT="$i\in \{1\dots mg\}$">|; 

$key = q/includegraphics[scale=0.45]{figuresslashtry8x8.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img67.png"
 ALT="\includegraphics[scale=0.45]{figures/try8x8.eps}">|; 

$key = q/includegraphics[scale=0.45]{figuresslashtry8x8};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="358" HEIGHT="313" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img68.png"
 ALT="\includegraphics[scale=0.45]{figures/try8x8}">|; 

$key = q/includegraphics[scale=0.65]{figuresslashpoints.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="318" HEIGHT="285" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img13.png"
 ALT="\includegraphics[scale=0.65]{figures/points.eps}">|; 

$key = q/includegraphics[scale=0.65]{figuresslashpsblas.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="223" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img2.png"
 ALT="\includegraphics[scale=0.65]{figures/psblas.eps}">|; 

$key = q/includegraphics[scale=0.65]{figuresslashpsblas};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="195" HEIGHT="223" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img3.png"
 ALT="\includegraphics[scale=0.65]{figures/psblas}">|; 

$key = q/includegraphics[scale=0.65]{figuresslashtry8x8_ov.eps};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="534" HEIGHT="454" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img78.png"
 ALT="\includegraphics[scale=0.65]{figures/try8x8_ov.eps}">|; 

$key = q/includegraphics[scale=0.65]{figuresslashtry8x8_ov};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="533" HEIGHT="454" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img77.png"
 ALT="\includegraphics[scale=0.65]{figures/try8x8_ov}">|; 

$key = q/irst>0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img186.png"
 ALT="$irst&gt;0$">|; 

$key = q/irw(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="47" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img124.png"
 ALT="$irw(i)$">|; 

$key = q/itmax=1000;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="99" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img181.png"
 ALT="$itmax = 1000$">|; 

$key = q/itmaxge1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img182.png"
 ALT="$itmax \ge 1$">|; 

$key = q/itrace;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="45" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img183.png"
 ALT="$itrace$">|; 

$key = q/itrace=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="87" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img185.png"
 ALT="$itrace = -1$">|; 

$key = q/ix(1:n);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="62" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img132.png"
 ALT="$ix(1:n)$">|; 

$key = q/ix(:);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="35" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img137.png"
 ALT="$ix(:)$">|; 

$key = q/ix(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="36" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img134.png"
 ALT="$ix(i)$">|; 

$key = q/ix(i)leftarrowi;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="66" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img133.png"
 ALT="$ix(i) \leftarrow
i$">|; 

$key = q/j;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="11" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img5.png"
 ALT="$j$">|; 

$key = q/j=irp(i),dots,irp(i+1)-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="201" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img120.png"
 ALT="$j=irp(i),\dots,irp(i+1)-1$">|; 

$key = q/ja(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img110.png"
 ALT="$ja(i)$">|; 

$key = q/lidx(1:nl);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="80" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img98.png"
 ALT="$lidx(1:nl)$">|; 

$key = q/loc_x_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="44" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img82.png"
 ALT="$loc\_x_i$">|; 

$key = q/m;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img151.png"
 ALT="$m$">|; 

$key = q/mg;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img104.png"
 ALT="$mg$">|; 

$key = q/n;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img16.png"
 ALT="$n$">|; 

$key = q/n_{hbox{row}_i}+1dotsn_{hbox{col}_i};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img18.png"
 ALT="$n_{\hbox{row}_i}+1\dots n_{\hbox{col}_i}$">|; 

$key = q/nlge0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img112.png"
 ALT="$nl\ge 0$">|; 

$key = q/nnz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img113.png"
 ALT="$nnz$">|; 

$key = q/np-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="49" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img173.png"
 ALT="$np-1$">|; 

$key = q/np;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img140.png"
 ALT="$np$">|; 

$key = q/nr+1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="48" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img114.png"
 ALT="$nr+1$">|; 

$key = q/nrm2;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img43.png"
 ALT="$nrm2$">|; 

$key = q/nv>1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="51" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img101.png"
 ALT="$nv&gt;1$">|; 

$key = q/nz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="21" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img111.png"
 ALT="$nz$">|; 

$key = q/nzin+nz;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img128.png"
 ALT="$nzin+nz$">|; 

$key = q/ptype;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="41" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img171.png"
 ALT="$ptype$">|; 

$key = q/r_i=b-Ax_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="90" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img178.png"
 ALT="$r_i=b-Ax_i$">|; 

$key = q/res;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img29.png"
 ALT="$res$">|; 

$key = q/root=-1;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img86.png"
 ALT="$root=-1$">|; 

$key = q/rotatebox{-90}{includegraphics[scale=0.65]{figuresslashpoints}};FSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="131" HEIGHT="2" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img12.png"
 ALT="\rotatebox{-90}{\includegraphics[scale=0.65]{figures/points}}">|; 

$key = q/row;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img127.png"
 ALT="$row$">|; 

$key = q/scatter;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="53" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img90.png"
 ALT="$scatter$">|; 

$key = q/size(dat,1);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="82" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img154.png"
 ALT="$size(dat,1)$">|; 

$key = q/slash;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img61.png"
 ALT="$/$">|; 

$key = q/src;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="26" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img157.png"
 ALT="$src$">|; 

$key = q/trans=N;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="78" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img53.png"
 ALT="$trans = N$">|; 

$key = q/unitd=U;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="76" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img57.png"
 ALT="$unitd = U$">|; 

$key = q/update_type=psb_avg_;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="166" HEIGHT="30" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img76.png"
 ALT="$update\_type = psb\_avg\_ $">|; 

$key = q/val;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img123.png"
 ALT="$val$">|; 

$key = q/vg(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="38" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img93.png"
 ALT="$vg(i)$">|; 

$key = q/vg;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="20" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img94.png"
 ALT="$vg$">|; 

$key = q/vl(1:nl);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="65" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img97.png"
 ALT="$vl(1:nl)$">|; 

$key = q/vl;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="17" HEIGHT="15" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img99.png"
 ALT="$vl$">|; 

$key = q/x(i);MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="31" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img135.png"
 ALT="$x(i)$">|; 

$key = q/x(i)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="60" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img64.png"
 ALT="$x(i) = 0$">|; 

$key = q/x;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="13" HEIGHT="14" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img20.png"
 ALT="$x$">|; 

$key = q/x_i,y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="34" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img84.png"
 ALT="$x_i, y$">|; 

$key = q/x_i;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="18" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img177.png"
 ALT="$x_i$">|; 

$key = q/x_{:,:};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="25" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img51.png"
 ALT="$x_{:, :}$">|; 

$key = q/y(i)=0;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="59" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img62.png"
 ALT="$y(i) = 0$">|; 

$key = q/y;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="12" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img21.png"
 ALT="$y$">|; 

$key = q/y_{:,:};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="23" HEIGHT="29" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img52.png"
 ALT="$y_{:, :}$">|; 

$key = q/{displaymath}<verb_mark>14<verb_mark>{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="158" HEIGHT="28" BORDER="0"
 SRC="|."$dir".q|img14.png"
 ALT="\begin{displaymath}\verb\vert psb_version_string_\vert\end{displaymath}">|; 

$key = q/{displaymath}amaxleftarrowmax_i{(|re(x_i)|+|im(x_i)|)}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="233" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img31.png"
 ALT="\begin{displaymath}amax \leftarrow \max_i {(\vert re(x_i)\vert + \vert im(x_i)\vert)}\end{displaymath}">|; 

$key = q/{displaymath}amaxleftarrowmax_i|x_i|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img30.png"
 ALT="\begin{displaymath}amax \leftarrow \max_i \vert x_i\vert\end{displaymath}">|; 

$key = q/{displaymath}asumleftarrow|re(x)|_1+|im(x)|_1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="205" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img36.png"
 ALT="\begin{displaymath}asum \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">|; 

$key = q/{displaymath}asumleftarrow|x_i|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="92" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img35.png"
 ALT="\begin{displaymath}asum \leftarrow \Vert x_i\Vert\end{displaymath}">|; 

$key = q/{displaymath}dotleftarrowx(i)y(i).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img59.png"
 ALT="\begin{displaymath}dot \leftarrow x(i) y(i).\end{displaymath}">|; 

$key = q/{displaymath}dotleftarrowx^Hy{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="75" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img25.png"
 ALT="\begin{displaymath}dot \leftarrow x^H y\end{displaymath}">|; 

$key = q/{displaymath}dotleftarrowx^Ty{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="74" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img24.png"
 ALT="\begin{displaymath}dot \leftarrow x^T y\end{displaymath}">|; 

$key = q/{displaymath}err=frac{|r_i|}{(|A||x_i|+|b|)}<eps{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="204" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img174.png"
 ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} &lt; eps \end{displaymath}">|; 

$key = q/{displaymath}err=frac{|r_i|}{|b|_2}<eps{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="121" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img175.png"
 ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} &lt; eps \end{displaymath}">|; 

$key = q/{displaymath}err=frac{|r_i|}{|r_0|_2}<eps{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="129" HEIGHT="44" BORDER="0"
 SRC="|."$dir".q|img176.png"
 ALT="\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert r_0\Vert _2} &lt; eps \end{displaymath}">|; 

$key = q/{displaymath}glob_xleftarrowcollect(loc_x_i){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="163" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img79.png"
 ALT="\begin{displaymath}glob\_x \leftarrow collect(loc\_x_i) \end{displaymath}">|; 

$key = q/{displaymath}loc_x_ileftarrowscatter(glob_x){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="168" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img89.png"
 ALT="\begin{displaymath}loc\_x_i \leftarrow scatter(glob\_x) \end{displaymath}">|; 

$key = q/{displaymath}nrm1leftarrow|A|_1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="98" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img46.png"
 ALT="\begin{displaymath}nrm1 \leftarrow \Vert A\Vert _1 \end{displaymath}">|; 

$key = q/{displaymath}nrm2leftarrowsqrt{x^Hx}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="108" HEIGHT="25" BORDER="0"
 SRC="|."$dir".q|img42.png"
 ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\end{displaymath}">|; 

$key = q/{displaymath}nrm2leftarrowsqrt{x^Tx}{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="106" HEIGHT="25" BORDER="0"
 SRC="|."$dir".q|img41.png"
 ALT="\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\end{displaymath}">|; 

$key = q/{displaymath}nrmileftarrow|A|_infty{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img47.png"
 ALT="\begin{displaymath}nrmi \leftarrow \Vert A\Vert _\infty \end{displaymath}">|; 

$key = q/{displaymath}res(i)leftarrowmax_k|x(k,i)|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="148" HEIGHT="36" BORDER="0"
 SRC="|."$dir".q|img34.png"
 ALT="\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath}">|; 

$key = q/{displaymath}res(i)leftarrowx(:,i)^Ty(:,i){displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="150" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img28.png"
 ALT="\begin{displaymath}res(i) \leftarrow x(:,i)^T y(:,i)\end{displaymath}">|; 

$key = q/{displaymath}res(i)leftarrow|re(x)|_1+|im(x)|_1{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="207" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img40.png"
 ALT="\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath}">|; 

$key = q/{displaymath}res(i)leftarrow|x(:,i)|_2{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="126" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img45.png"
 ALT="\begin{displaymath}res(i) \leftarrow \Vert x(:,i)\Vert _2 \end{displaymath}">|; 

$key = q/{displaymath}res(i)leftarrow|x_i|{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img39.png"
 ALT="\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath}">|; 

$key = q/{displaymath}res=sqrt{sum_idat_i^2},{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="119" HEIGHT="55" BORDER="0"
 SRC="|."$dir".q|img150.png"
 ALT="\begin{displaymath}res = \sqrt{\sum_i dat_i^2},\end{displaymath}">|; 

$key = q/{displaymath}slashleftarrow1slashx(i).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="77" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img63.png"
 ALT="\begin{displaymath}/ \leftarrow 1/x(i).\end{displaymath}">|; 

$key = q/{displaymath}slashleftarrowx(i)slashy(i).{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="96" HEIGHT="29" BORDER="0"
 SRC="|."$dir".q|img60.png"
 ALT="\begin{displaymath}/ \leftarrow x(i)/y(i).\end{displaymath}">|; 

$key = q/{displaymath}xleftarrowQx{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="55" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img69.png"
 ALT="\begin{displaymath}x \leftarrow Q x \end{displaymath}">|; 

$key = q/{displaymath}xleftarrowx{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="43" HEIGHT="24" BORDER="0"
 SRC="|."$dir".q|img65.png"
 ALT="\begin{displaymath}x \leftarrow x \end{displaymath}">|; 

$key = q/{displaymath}yleftarrowalpha>x+betay{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="93" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img19.png"
 ALT="\begin{displaymath}y \leftarrow \alpha\&gt; x+ \beta y \end{displaymath}">|; 

$key = q/{displaymath}yleftarrowalphaA^Hx+betay{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="114" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img50.png"
 ALT="\begin{displaymath}
y \leftarrow \alpha A^H x + \beta y
\end{displaymath}">|; 

$key = q/{displaymath}yleftarrowalphaA^Tx+betay{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="111" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img49.png"
 ALT="\begin{displaymath}
y \leftarrow \alpha A^T x + \beta y
\end{displaymath}">|; 

$key = q/{displaymath}yleftarrowalphaAx+betay{displaymath};MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="102" HEIGHT="27" BORDER="0"
 SRC="|."$dir".q|img48.png"
 ALT="\begin{displaymath}
y \leftarrow \alpha A x + \beta y
\end{displaymath}">|; 

$key = q/{eqnarraystar}y&leftarrow&alphaT^{-1}x+betayy&leftarrow&alphaDT^{-1}x+betayy&lefhaDT^{-H}x+betayy&leftarrow&alphaT^{-H}Dx+betay{eqnarraystar};MSF=1.6;TAGS=R;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="160" HEIGHT="239" BORDER="0"
 SRC="|."$dir".q|img54.png"
 ALT="\begin{eqnarray*}
y &amp;\leftarrow&amp; \alpha T^{-1} x + \beta y\\\\
y &amp;\leftarrow&amp; \al...
...-H} x + \beta y\\\\
y &amp;\leftarrow&amp; \alpha T^{-H} D x + \beta y\\\\
\end{eqnarray*}">|; 

$key = q/{lstlisting}callhb_read(a,iret,iunit,filename,b,mtitle){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="462" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img165.png"
 ALT="\begin{lstlisting}
call hb_read(a, iret, iunit, filename, b, mtitle)
\end{lstlisting}">|; 

$key = q/{lstlisting}callhb_write(a,iret,iunit,filename,key,rhs,mtitle){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="538" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img166.png"
 ALT="\begin{lstlisting}
call hb_write(a, iret, iunit, filename, key, rhs, mtitle)
\end{lstlisting}">|; 

$key = q/{lstlisting}callmm_array_read(b,iret,iunit,filename){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="414" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img168.png"
 ALT="\begin{lstlisting}
call mm_array_read(b, iret, iunit, filename)
\end{lstlisting}">|; 

$key = q/{lstlisting}callmm_array_write(b,iret,iunit,filename){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="423" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img170.png"
 ALT="\begin{lstlisting}
call mm_array_write(b, iret, iunit, filename)
\end{lstlisting}">|; 

$key = q/{lstlisting}callmm_mat_read(a,iret,iunit,filename){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="396" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img167.png"
 ALT="\begin{lstlisting}
call mm_mat_read(a, iret, iunit, filename)
\end{lstlisting}">|; 

$key = q/{lstlisting}callmm_mat_write(a,mtitle,iret,iunit,filename){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="482" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img169.png"
 ALT="\begin{lstlisting}
call mm_mat_write(a, mtitle, iret, iunit, filename)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_error(icontxt){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="213" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img162.png"
 ALT="\begin{lstlisting}
call psb_error(icontxt)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_errpush(err_c,r_name,i_err,a_err){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="424" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img161.png"
 ALT="\begin{lstlisting}
call psb_errpush(err_c, r_name, i_err, a_err)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_gather(glob_x,loc_x,desc_a,info,root)callpsb_gather(glob_x,loc_x,desc_a,info,root){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="472" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img85.png"
 ALT="\begin{lstlisting}
call psb_gather(glob_x, loc_x, desc_a, info, root)
call psb_gather(glob_x, loc_x, desc_a, info, root)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_halo(x,desc_a,info)callpsb_halo(x,desc_a,info,work,data){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="395" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img66.png"
 ALT="\begin{lstlisting}
call psb_halo(x, desc_a, info)
call psb_halo(x, desc_a, info, work, data)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_krylov(method,a,prec,b,x,eps,desc_a,info,&&itmax,iter,err,itrace,irst,istop,cond){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="483" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img179.png"
 ALT="\begin{lstlisting}
call psb_krylov(method,a,prec,b,x,eps,desc_a,info,&amp;
&amp; itmax,iter,err,itrace,irst,istop,cond)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_ovrl(x,desc_a,info)callpsb_ovrl(x,desc_a,info,update=update_type,work=work){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="577" HEIGHT="35" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img73.png"
 ALT="\begin{lstlisting}
call psb_ovrl(x, desc_a, info)
call psb_ovrl(x, desc_a, info, update=update_type, work=work)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_scatter(glob_x,loc_x,desc_a,info,root,mold){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="539" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img91.png"
 ALT="\begin{lstlisting}
call psb_scatter(glob_x, loc_x, desc_a, info, root, mold)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_set_erraction(err_act){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="290" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img164.png"
 ALT="\begin{lstlisting}
call psb_set_erraction(err_act)
\end{lstlisting}">|; 

$key = q/{lstlisting}callpsb_set_errverbosity(v){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="262" HEIGHT="16" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img163.png"
 ALT="\begin{lstlisting}
call psb_set_errverbosity(v)
\end{lstlisting}">|; 

$key = q/{lstlisting}vres(1)=psb_geamax(x1,desc_a,info,global=.false.)vres(2)=psb_geamax(eamax(x3,desc_a,info,global=.false.)callpsb_amx(ictxt,vres(1:3)){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="481" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img33.png"
 ALT="\begin{lstlisting}
vres(1) = psb_geamax(x1,desc_a,info,global=.false.)
vres(2)...
...(x3,desc_a,info,global=.false.)
call psb_amx(ictxt,vres(1:3))
\end{lstlisting}">|; 

$key = q/{lstlisting}vres(1)=psb_geasum(x1,desc_a,info,global=.false.)vres(2)=psb_geasum(easum(x3,desc_a,info,global=.false.)callpsb_sum(ictxt,vres(1:3)){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="481" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img38.png"
 ALT="\begin{lstlisting}
vres(1) = psb_geasum(x1,desc_a,info,global=.false.)
vres(2)...
...(x3,desc_a,info,global=.false.)
call psb_sum(ictxt,vres(1:3))
\end{lstlisting}">|; 

$key = q/{lstlisting}vres(1)=psb_gedot(x1,y1,desc_a,info,global=.false.)vres(2)=psb_gedotot(x3,y3,desc_a,info,global=.false.)callpsb_sum(ictxt,vres(1:3)){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="500" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img27.png"
 ALT="\begin{lstlisting}
vres(1) = psb_gedot(x1,y1,desc_a,info,global=.false.)
vres(...
...,y3,desc_a,info,global=.false.)
call psb_sum(ictxt,vres(1:3))
\end{lstlisting}">|; 

$key = q/{lstlisting}vres(1)=psb_genrm2(x1,desc_a,info,global=.false.)vres(2)=psb_genrm2(nrm2(x3,desc_a,info,global=.false.)callpsb_nrm2(ictxt,vres(1:3)){lstlisting};AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="481" HEIGHT="73" ALIGN="BOTTOM" BORDER="0"
 SRC="|."$dir".q|img44.png"
 ALT="\begin{lstlisting}
vres(1) = psb_genrm2(x1,desc_a,info,global=.false.)
vres(2)...
...x3,desc_a,info,global=.false.)
call psb_nrm2(ictxt,vres(1:3))
\end{lstlisting}">|; 

$key = q/|{calI}_i|+|{calB}_i|+|{calH}_i|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="118" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img11.png"
 ALT="$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert +\vert{\cal H}_i\vert$">|; 

$key = q/|{calI}_i|+|{calB}_i|;MSF=1.6;AAT/;
$cached_env_img{$key} = q|<IMG
 WIDTH="71" HEIGHT="31" ALIGN="MIDDLE" BORDER="0"
 SRC="|."$dir".q|img10.png"
 ALT="$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert$">|; 

1;