From b888d66e985b3ffb4eb1af14a3409321a654519a Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Tue, 27 May 2008 11:33:31 +0000 Subject: [PATCH] psblas: docs/pdf/commrout.tex docs/pdf/datastruct.tex docs/pdf/methods.tex docs/pdf/penv.tex docs/pdf/psbrout.tex docs/pdf/title.tex docs/pdf/toolsrout.tex docs/userguide.pdf Updated docs with single precision. --- docs/pdf/commrout.tex | 11 + docs/pdf/datastruct.tex | 76 +- docs/pdf/methods.tex | 20 +- docs/pdf/penv.tex | 28 +- docs/pdf/psbrout.tex | 60 +- docs/pdf/title.tex | 4 +- docs/pdf/toolsrout.tex | 5 +- docs/userguide.pdf | 38677 ++++++++++++-------------------------- 8 files changed, 12200 insertions(+), 26681 deletions(-) diff --git a/docs/pdf/commrout.tex b/docs/pdf/commrout.tex index dff67886..74ecd37d 100644 --- a/docs/pdf/commrout.tex +++ b/docs/pdf/commrout.tex @@ -25,7 +25,10 @@ where: \hline $\alpha$, $x$ & {\bf Subroutine}\\ \hline +Integer & psb\_halo \\ +Short Precision Real & psb\_halo \\ Long Precision Real & psb\_halo \\ +Short Precision Complex & psb\_halo \\ Long Precision Complex & psb\_halo \\ \hline \end{tabular} @@ -174,7 +177,9 @@ operators $ P_a$ and $ P^{T}$. \hline $x$ & {\bf Subroutine}\\ \hline +Short Precision Real & psb\_ovrl \\ Long Precision Real & psb\_ovrl \\ +Short Precision Complex & psb\_ovrl \\ Long Precision Complex & psb\_ovrl \\ \hline \end{tabular} @@ -359,7 +364,10 @@ process $i$. \hline $x_i, y$ & {\bf Subroutine}\\ \hline +Integer & psb\_gather \\ +Short Precision Real & psb\_gather \\ Long Precision Real & psb\_gather \\ +Short Precision Complex & psb\_gather \\ Long Precision Complex & psb\_gather \\ \hline \end{tabular} @@ -454,7 +462,10 @@ process $i$. \hline $x_i, y$ & {\bf Subroutine}\\ \hline +Integer & psb\_scatter \\ +Short Precision Real & psb\_scatter \\ Long Precision Real & psb\_scatter \\ +Short Precision Complex & psb\_scatter \\ Long Precision Complex & psb\_scatter \\ \hline \end{tabular} diff --git a/docs/pdf/datastruct.tex b/docs/pdf/datastruct.tex index 16dbb29f..a86555d0 100644 --- a/docs/pdf/datastruct.tex +++ b/docs/pdf/datastruct.tex @@ -15,6 +15,9 @@ user subroutine that makes use of the library. Real and complex data types are parametrized with a kind type defined in the library as follows: \begin{description} +\item[psb\_spk\_] Kind parameter for short precision real and complex + data; corresponds to a \verb|REAL| declaration and is + normally 4 bytes. \item[psb\_dpk\_] Kind parameter for long precision real and complex data; corresponds to a \verb|DOUBLE PRECISION| declaration and is normally 8 bytes. @@ -226,11 +229,23 @@ Specified as: integer variable. \end{description} The Fortran~95 interface for distributed sparse matrices containing double precision real entries is defined as shown in -figure~\ref{fig:spmattype}. +figure~\ref{fig:spmattype}. The definitions for single precision and +complex data are identical except for the \verb|real| declaration and +for the kind type parameter. \begin{figure}[h!] \begin{Sbox} \begin{minipage}[tl]{0.85\textwidth} \begin{verbatim} +type psb_sspmat_type + integer :: m, k + character :: fida(5) + character :: descra(10) + integer :: infoa(psb_ifa_size_) + real(psb_spk_), allocatable :: aspk(:) + integer, allocatable :: ia1(:), ia2(:) + integer, allocatable :: pr(:), pl(:) +end type psb_sspmat_type + type psb_dspmat_type integer :: m, k character :: fida(5) @@ -240,6 +255,27 @@ type psb_dspmat_type integer, allocatable :: ia1(:), ia2(:) integer, allocatable :: pr(:), pl(:) end type psb_dspmat_type + +type psb_cspmat_type + integer :: m, k + character :: fida(5) + character :: descra(10) + integer :: infoa(psb_ifa_size_) + complex(psb_spk_), allocatable :: aspk(:) + integer, allocatable :: ia1(:), ia2(:) + integer, allocatable :: pr(:), pl(:) +end type psb_cspmat_type + +type psb_zspmat_type + integer :: m, k + character :: fida(5) + character :: descra(10) + integer :: infoa(psb_ifa_size_) + complex(psb_dpk_), allocatable :: aspk(:) + integer, allocatable :: ia1(:), ia2(:) + integer, allocatable :: pr(:), pl(:) +end type psb_zspmat_type + \end{verbatim} \end{minipage} \end{Sbox} @@ -330,10 +366,10 @@ associated communication descriptor.%% which may be different than the %% This data structure wants to be flexible enough to easily allow the %% implementation of new kind of preconditioners. The values contained in -the \verb|iprcparm| and \verb|dprcparm| define tha type of +the \verb|iprcparm| and \verb|rprcparm| define tha type of preconditioner along with all the parameters related to it; thus, -\verb|iprcparm| and \verb|dprcparm| define how the other records have -to be interpreted. This data structure is the basis of ore complex +\verb|iprcparm| and \verb|rprcparm| define how the other records have +to be interpreted. This data structure is the basis of more complex preconditioning strategies, which are the subject of further research. \begin{figure}[h!] @@ -342,16 +378,46 @@ research. \begin{minipage}[tl]{0.9\textwidth} \begin{verbatim} + type psb_sprec_type + type(psb_sspmat_type), allocatable :: av(:) + real(psb_spk_), allocatable :: d(:) + type(psb_desc_type) :: desc_data + integer, allocatable :: iprcparm(:) + real(psb_spk_), allocatable :: rprcparm(:) + integer, allocatable :: perm(:), invperm(:) + integer :: prec, base_prec + end type psb_sprec_type + type psb_dprec_type type(psb_dspmat_type), allocatable :: av(:) real(psb_dpk_), allocatable :: d(:) type(psb_desc_type) :: desc_data integer, allocatable :: iprcparm(:) - real(psb_dpk_), allocatable :: dprcparm(:) + real(psb_dpk_), allocatable :: rprcparm(:) integer, allocatable :: perm(:), invperm(:) integer :: prec, base_prec end type psb_dprec_type + type psb_cprec_type + type(psb_cspmat_type), allocatable :: av(:) + complex(psb_spk_), allocatable :: d(:) + type(psb_desc_type) :: desc_data + integer, allocatable :: iprcparm(:) + real(psb_spk_), allocatable :: rprcparm(:) + integer, allocatable :: perm(:), invperm(:) + integer :: prec, base_prec + end type psb_cprec_type + + type psb_zprec_type + type(psb_zspmat_type), allocatable :: av(:) + complex(psb_dpk_), allocatable :: d(:) + type(psb_desc_type) :: desc_data + integer, allocatable :: iprcparm(:) + real(psb_dpk_), allocatable :: rprcparm(:) + integer, allocatable :: perm(:), invperm(:) + integer :: prec, base_prec + end type psb_zprec_type + \end{verbatim} \end{minipage} \end{Sbox} diff --git a/docs/pdf/methods.tex b/docs/pdf/methods.tex index 438ec201..e1120ef0 100644 --- a/docs/pdf/methods.tex +++ b/docs/pdf/methods.tex @@ -26,7 +26,7 @@ later). In the above formulae, $x_i$ is the tentative solution and $r_i=b-Ax_i$ the corresponding residual at the $i$-th iteration. -\syntax{call psb\_krylov}{method,a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} +\syntax{call psb\_krylov}{method,a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop,cond} \begin{description} \item[Type:] Synchronous. @@ -34,13 +34,13 @@ $r_i=b-Ax_i$ the corresponding residual at the $i$-th iteration. \item[method] a string that defines the iterative method to be used. Supported values are: \begin{description} - \item[CG]: the Conjugate Gradient method; - \item[CGS]:the Conjugate Gradient Stabilized method; + \item[CG:] the Conjugate Gradient method; + \item[CGS:] the Conjugate Gradient Stabilized method; - \item[BICG]: the Bi-Conjugate Gradient method; - \item[BICGSTAB]: the Bi-Conjugate Gradient Stabilized method; - \item[BICGSTABL]: the Bi-Conjugate Gradient Stabilized method with restarting; - \item[RGMRES]: the Generalized Minimal Residual method with restarting. + \item[BICG:] the Bi-Conjugate Gradient method; + \item[BICGSTAB:] the Bi-Conjugate Gradient Stabilized method; + \item[BICGSTABL:] the Bi-Conjugate Gradient Stabilized method with restarting; + \item[RGMRES:] the Generalized Minimal Residual method with restarting. \end{description} \item[a] the local portion of global sparse matrix $A$. \\ @@ -113,6 +113,12 @@ Scope: {\bf global} \\ Type: {\bf optional}\\ Intent: {\bf out}.\\ Returned as: a real number. +\item[cond] An estimate of the condition number of matrix $A$; only + available with the $CG$ method.\\ +Scope: {\bf global} \\ +Type: {\bf optional}\\ +Intent: {\bf out}.\\ +Returned as: a real number. \item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ diff --git a/docs/pdf/penv.tex b/docs/pdf/penv.tex index 970b4d10..9394a2fd 100644 --- a/docs/pdf/penv.tex +++ b/docs/pdf/penv.tex @@ -255,7 +255,7 @@ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array, or a character or logical variable, which may be a scalar or rank 1 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \item[root] Root process holding data to be broadcast.\\ Scope: {\bf global}.\\ Type: {\bf optional}.\\ @@ -272,7 +272,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array, or a character or logical scalar. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \end{description} @@ -297,7 +297,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \item[root] Process to hold the final sum, or $-1$ to make it available on all processes.\\ Scope: {\bf global}.\\ @@ -315,7 +315,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array. \\ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \end{description} \section*{Notes} @@ -348,7 +348,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer or real variable, which may be a scalar, or a rank 1 or 2 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \item[root] Process to hold the final maximum, or $-1$ to make it available on all processes.\\ Scope: {\bf global}.\\ @@ -366,7 +366,7 @@ Type: {\bf required}.\\ Intent: {\bf in}.\\ Specified as: an integer or real variable, which may be a scalar, or a rank 1 or 2 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \end{description} @@ -398,7 +398,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer or real variable, which may be a scalar, or a rank 1 or 2 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \item[root] Process to hold the final value, or $-1$ to make it available on all processes.\\ Scope: {\bf global}.\\ @@ -416,7 +416,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer or real variable, which may be a scalar, or a rank 1 or 2 array. \\ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \end{description} @@ -448,7 +448,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \item[root] Process to hold the final value, or $-1$ to make it available on all processes.\\ Scope: {\bf global}.\\ @@ -466,7 +466,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \end{description} @@ -498,7 +498,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array. \ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \item[root] Process to hold the final value, or $-1$ to make it available on all processes.\\ Scope: {\bf global}.\\ @@ -516,7 +516,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array. \\ -Type, rank and size must agree on all processes. +Type, kind, rank and size must agree on all processes. \end{description} @@ -548,7 +548,7 @@ Type: {\bf required}.\\ Intent: {\bf in}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array, or a character or logical scalar. \ -Type and rank must agree on sender and receiver process; if $m$ is +Type, kind and rank must agree on sender and receiver process; if $m$ is not specified, size must agree as well. \item[dst] Destination process.\\ Scope: {\bf global}.\\ @@ -615,7 +615,7 @@ Type: {\bf required}.\\ Intent: {\bf inout}.\\ Specified as: an integer, real or complex variable, which may be a scalar, or a rank 1 or 2 array, or a character or logical scalar. \ -Type and rank must agree on sender and receiver process; if $m$ is +Type, kind and rank must agree on sender and receiver process; if $m$ is not specified, size must agree as well. \end{description} diff --git a/docs/pdf/psbrout.tex b/docs/pdf/psbrout.tex index 4d77b135..c864256a 100644 --- a/docs/pdf/psbrout.tex +++ b/docs/pdf/psbrout.tex @@ -26,7 +26,9 @@ dense matrix sum: \hline $x$, $y$, $\alpha$, $\beta$ & {\bf Subroutine}\\ \hline +Short Precision Real & psb\_geaxpby \\ Long Precision Real & psb\_geaxpby \\ +Short Precision Complex & psb\_geaxpby \\ Long Precision Complex & psb\_geaxpby \\ \hline \end{tabular} @@ -113,10 +115,10 @@ An integer value; 0 means no error has been detected. This function computes dot product between two vectors $x$ and $y$.\\ -If $x$ and $y$ are double precision real vectors -computes dot-product as: +If $x$ and $y$ are real vectors +it computes dot-product as: \[dot \leftarrow x^T y\] -Else if $x$ and $y$ are double precision complex vectors then computes dot-product as: +Else if $x$ and $y$ are complex vectors then it computes dot-product as: \[dot \leftarrow x^H y\] %% where: %% \begin{description} @@ -132,7 +134,9 @@ Else if $x$ and $y$ are double precision complex vectors then computes dot-produ \hline $dot$, $x$, $y$ & {\bf Function}\\ \hline +Short Precision Real & psb\_gedot \\ Long Precision Real & psb\_gedot \\ +Short Precision Complex & psb\_gedot \\ Long Precision Complex & psb\_gedot \\ \hline \end{tabular} @@ -213,7 +217,9 @@ is a rank one array. \hline $res$, $x$, $y$ & {\bf Subroutine}\\ \hline +Short Precision Real & psb\_gedots \\ Long Precision Real & psb\_gedots \\ +Short Precision Complex & psb\_gedots \\ Long Precision Complex & psb\_gedots \\ \hline \end{tabular} @@ -269,10 +275,10 @@ An integer value; 0 means no error has been detected. This function computes the infinity-norm of a vector $x$.\\ -If $x$ is a double precision real vector -computes infinity norm as: +If $x$ is a real vector +it computes infinity norm as: \[ amax \leftarrow \max_i |x_i|\] -else if $x$ is a double precision complex vector then computes infinity-norm as: +else if $x$ is a complex vector then it computes infinity-norm as: \[ amax \leftarrow \max_i {(|re(x_i)| + |im(x_i)|)}\] %% where: %% \begin{description} @@ -288,7 +294,9 @@ else if $x$ is a double precision complex vector then computes infinity-norm as \hline $amax$ & $x$ & {\bf Function}\\ \hline +Short Precision Real& Short Precision Real & psb\_geamax \\ Long Precision Real&Long Precision Real & psb\_geamax \\ +Short Precision Real&Short Precision Complex & psb\_geamax \\ Long Precision Real&Long Precision Complex & psb\_geamax \\ \hline \end{tabular} @@ -351,7 +359,9 @@ a dense matrix $x$: \hline $res$& $x$& {\bf Subroutine}\\ \hline +Short Precision Real &Short Precision Real & psb\_geamaxs\\ Long Precision Real &Long Precision Real & psb\_geamaxs\\ +Short Precision Real &Short Precision Complex & psb\_geamaxs\\ Long Precision Real &Long Precision Complex & psb\_geamaxs\\ \hline \end{tabular} @@ -397,10 +407,10 @@ An integer value; 0 means no error has been detected. \subroutine{psb\_geasum}{1-Norm of Vector} This function computes the 1-norm of a vector $x$.\\ -If $x$ is a double precision real vector -computes 1-norm as: +If $x$ is a real vector +it computes 1-norm as: \[ asum \leftarrow \|x_i\|\] -else if $x$ is double precision complex vector then computes 1-norm as: +else if $x$ is a vector then it computes 1-norm as: \[ asum \leftarrow \|re(x)\|_1 + \|im(x)\|_1\] @@ -412,7 +422,9 @@ else if $x$ is double precision complex vector then computes 1-norm as: \hline $asum$ & $x$ & {\bf Function}\\ \hline +Short Precision Real&Short Precision Real & psb\_geasum \\ Long Precision Real&Long Precision Real & psb\_geasum \\ +Short Precision Real&Short Precision Complex & psb\_geasum \\ Long Precision Real&Long Precision Complex & psb\_geasum \\ \hline \end{tabular} @@ -457,10 +469,10 @@ This subroutine computes a series of 1-norms on the columns of a dense matrix $x$: \[ res(i) \leftarrow \max_k |x(k,i)| \] This function computes the 1-norm of a vector $x$.\\ -If $x$ is a double precision real vector -computes 1-norm as: +If $x$ is a real vector +it computes 1-norm as: \[ res(i) \leftarrow \|x_i\|\] -else if $x$ is double precision complex vector then computes 1-norm as: +else if $x$ is a complex vector then it computes 1-norm as: \[ res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1\] @@ -472,7 +484,9 @@ else if $x$ is double precision complex vector then computes 1-norm as: \hline $res$ & $x$ & {\bf Subroutine}\\ \hline +Short Precision Real&Short Precision Real & psb\_geasums \\ Long Precision Real&Long Precision Real & psb\_geasums \\ +Short Precision Real&Short Precision Complex & psb\_geasums \\ Long Precision Real&Long Precision Complex & psb\_geasums \\ \hline \end{tabular} @@ -503,6 +517,7 @@ Specified as: a structured data of type \descdata. \item[res] contains the 1-norm of (the columns of) $x$.\\ Scope: {\bf global} \\ Intent: {\bf out}.\\ +Short as: a long precision real number. Specified as: a long precision real number. \item[info] Error code.\\ Scope: {\bf local} \\ @@ -523,9 +538,9 @@ An integer value; 0 means no error has been detected. This function computes the 2-norm of a vector $x$.\\ If $x$ is a double precision real vector -computes 2-norm as: +it computes 2-norm as: \[ nrm2 \leftarrow \sqrt{x^T x}\] -else if $x$ is double precision complex vector then computes 2-norm as: +else if $x$ is double precision complex vector then it computes 2-norm as: \[ nrm2 \leftarrow \sqrt{x^H x}\] %% where: %% \begin{description} @@ -538,7 +553,9 @@ else if $x$ is double precision complex vector then computes 2-norm as: \hline $nrm2$ & $x$ & {\bf Function}\\ \hline +Short Precision Real&Short Precision Real & psb\_genrm2 \\ Long Precision Real&Long Precision Real & psb\_genrm2 \\ +Short Precision Real&Short Precision Complex & psb\_genrm2 \\ Long Precision Real&Long Precision Complex & psb\_genrm2 \\ \hline \end{tabular} @@ -593,11 +610,10 @@ This subroutine computes a series of 1-norms on the columns of a dense matrix $x$: \[ res(i) \leftarrow \max_k |x(k,i)| \] This function computes the 1-norm of a vector $x$.\\ -If $x$ is a double precision real vector -computes 1-norm as: +If $x$ is a real vector +it computes 1-norm as: \[ res(i) \leftarrow \sqrt{x^T x}\] - -else if $x$ is double precision complex vector then computes 1-norm as: +else if $x$ is a complex vector then it computes 1-norm as: \[ res(i) \leftarrow \sqrt{x^H x}\] @@ -609,7 +625,9 @@ else if $x$ is double precision complex vector then computes 1-norm as: \hline $res$ & $x$ & {\bf Subroutine}\\ \hline +Short Precision Real&Short Precision Real & psb\_genrm2s \\ Long Precision Real&Long Precision Real & psb\_genrm2s \\ +Short Precision Real&Short Precision Complex & psb\_genrm2s \\ Long Precision Real&Long Precision Complex & psb\_genrm2s \\ \hline \end{tabular} @@ -673,7 +691,9 @@ where: \hline $A$ & {\bf Function}\\ \hline +Short Precision Real & psb\_spnrmi \\ Long Precision Real & psb\_spnrmi \\ +Short Precision Complex & psb\_spnrmi \\ Long Precision Complex & psb\_spnrmi \\ \hline \end{tabular} @@ -747,7 +767,9 @@ where: \hline $A$, $x$, $y$, $\alpha$, $\beta$ & {\bf Subroutine}\\ \hline +Short Precision Real & psb\_spmm \\ Long Precision Real & psb\_spmm \\ +Short Precision Complex & psb\_spmm \\ Long Precision Complex & psb\_spmm \\ \hline \end{tabular} @@ -900,7 +922,9 @@ trans, unit, choice, diag, work} \hline $T$, $x$, $y$, $D$, $\alpha$, $\beta$ & {\bf Subroutine}\\ \hline +Short Precision Real & psb\_spsm \\ Long Precision Real & psb\_spsm \\ +Short Precision Complex & psb\_spsm \\ Long Precision Complex & psb\_spsm \\ \hline \end{tabular} diff --git a/docs/pdf/title.tex b/docs/pdf/title.tex index 0651770a..0cc16df0 100644 --- a/docs/pdf/title.tex +++ b/docs/pdf/title.tex @@ -5,7 +5,7 @@ \ifx\pdfoutput\undefined % We're not running pdftex \else -\pdfbookmark{PSBLAS-v2.2 User's Guide}{title} +\pdfbookmark{PSBLAS-v2.3 User's Guide}{title} \fi \newlength{\centeroffset} \setlength{\centeroffset}{-0.5\oddsidemargin} @@ -15,7 +15,7 @@ \vspace*{\stretch{1}} \noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth} \flushright -{\Huge\bfseries PSBLAS-2.2 User's guide +{\Huge\bfseries PSBLAS 2.3 User's guide } \noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex] \hfill\emph{\Large A reference guide for the Parallel Sparse BLAS library} diff --git a/docs/pdf/toolsrout.tex b/docs/pdf/toolsrout.tex index 886dee87..592b0d83 100644 --- a/docs/pdf/toolsrout.tex +++ b/docs/pdf/toolsrout.tex @@ -509,7 +509,8 @@ Specified as: an integer array of size $nz$. Scope:{\bf local}.\\ Type:{\bf required}.\\ Intent: {\bf in}.\\ -Specified as: an array of size $nz$. +Specified as: an array of size $nz$. Must be of the same type and kind +of the \verb|aspk| component of the sparse matrix $a$. \item[desc\_a] The communication descriptor.\\ Scope: {\bf local}. \\ Type: {\bf required}.\\ @@ -1544,7 +1545,7 @@ position as the corresponding entries in $x$. output difference is the handling of ties (i.e. items with an equal value) in the original input. With the merge-sort algorithm ties are preserved in the same order as they had in the original - sequence, while this is not guaranteed for quicksort; + sequence, while this is not guaranteed for quicksort or heapsort; \item If $flag = psb\_sort\_ovw\_idx\_$ then the entries in $ix(1:n)$ where $n$ is the size of $x$ are initialized to $ix(i) \leftarrow i$; thus, upon return from the subroutine, for each diff --git a/docs/userguide.pdf b/docs/userguide.pdf index f76eef93..de42e050 100644 --- a/docs/userguide.pdf +++ b/docs/userguide.pdf @@ -1,9 +1,10 @@ %PDF-1.4 +%ÐÔÅØ 5 0 obj << /S /GoTo /D (title.0) >> endobj 8 0 obj -(PSBLAS-v2.2 User's Guide) +(PSBLAS-v2.3 User's Guide) endobj 9 0 obj << /S /GoTo /D (section.1) >> @@ -645,16201 +646,9074 @@ endobj << /S /GoTo /D [434 0 R /Fit ] >> endobj 436 0 obj << -/Length 1187 +/Length 683 >> stream -1 0 0 1 99.8954 740.9981 cm 0 g 0 G -1 0 0 1 343.7111 0 cm 0 g 0 G -1 0 0 1 -343.7111 -24.9066 cm 0 g 0 G -1 g 1 G 0 g 0 G -1 g 1 G 0 g 0 G -0 g 0 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Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 433.6438 492.329 cm + [-385(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -492.329 cm -BT -/F8 9.9626 Tf 433.6438 492.329 Td[(14)]TJ -ET -1 0 0 1 443.6065 492.329 cm + [-1084(14)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9888 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -479.3402 cm -BT -/F8 9.9626 Tf 137.7535 479.3402 Td[(psb)]TJ + -72.794 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 479.3402 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 479.539 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -479.3402 cm BT -/F8 9.9626 Tf 156.3394 479.3402 Td[(cd)]TJ +/F8 9.9626 Tf 156.339 479.34 Td [(cd)]TJ ET -1 0 0 1 166.8998 479.3402 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.9 479.539 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.8998 -479.3402 cm BT -/F8 9.9626 Tf 169.8886 479.3402 Td[(get)]TJ +/F8 9.9626 Tf 169.889 479.34 Td [(get)]TJ ET -1 0 0 1 183.7699 479.3402 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.77 479.539 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.7699 -479.3402 cm BT -/F8 9.9626 Tf 186.7587 479.3402 Td[(lo)-28(cal)]TJ +/F8 9.9626 Tf 186.759 479.34 Td [(lo)-28(cal)]TJ ET -1 0 0 1 207.5585 479.3402 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 207.559 479.539 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -207.5585 -479.3402 cm BT -/F8 9.9626 Tf 210.5473 479.3402 Td[(cols)]TJ -ET -1 0 0 1 226.6536 479.3402 cm +/F8 9.9626 Tf 210.547 479.34 Td [(cols)]TJ 0 g 0 G -1 0 0 1 -226.6536 -479.3402 cm -BT -/F8 9.9626 Tf 234.1123 479.3402 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 433.6438 479.3402 cm + [-749(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -479.3402 cm -BT -/F8 9.9626 Tf 433.6438 479.3402 Td[(14)]TJ -ET -1 0 0 1 443.6065 479.3402 cm + [-1084(15)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -466.3513 cm -BT -/F8 9.9626 Tf 137.7535 466.3513 Td[(psb)]TJ + -72.794 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 466.3513 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 466.551 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -466.3513 cm BT -/F8 9.9626 Tf 156.3394 466.3513 Td[(cd)]TJ +/F8 9.9626 Tf 156.339 466.351 Td [(cd)]TJ ET -1 0 0 1 166.8998 466.3513 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.9 466.551 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.8998 -466.3513 cm BT -/F8 9.9626 Tf 169.8886 466.3513 Td[(get)]TJ +/F8 9.9626 Tf 169.889 466.351 Td [(get)]TJ ET -1 0 0 1 183.7699 466.3513 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.77 466.551 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.7699 -466.3513 cm BT -/F8 9.9626 Tf 186.7587 466.3513 Td[(glob)1(al)]TJ +/F8 9.9626 Tf 186.759 466.351 Td [(global)]TJ ET -1 0 0 1 213.3701 466.3513 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 213.37 466.551 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -213.3701 -466.3513 cm BT -/F8 9.9626 Tf 216.3589 466.3513 Td[(ro)28(ws)]TJ -ET -1 0 0 1 236.0905 466.3513 cm +/F8 9.9626 Tf 216.359 466.351 Td [(ro)28(ws)]TJ 0 g 0 G -1 0 0 1 -236.0905 -466.3513 cm -BT -/F8 9.9626 Tf 241.8609 466.3513 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 466.3513 cm + [-579(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -466.3513 cm -BT -/F8 9.9626 Tf 433.6438 466.3513 Td[(15)]TJ -ET -1 0 0 1 443.6065 466.3513 cm + [-1084(16)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -453.3624 cm -BT -/F8 9.9626 Tf 137.7535 453.3624 Td[(psb)]TJ + -78.605 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 453.3624 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 453.562 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -453.3624 cm BT -/F8 9.9626 Tf 156.3394 453.3624 Td[(cd)]TJ +/F8 9.9626 Tf 156.339 453.362 Td [(cd)]TJ ET -1 0 0 1 166.8998 453.3624 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.9 453.562 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.8998 -453.3624 cm BT -/F8 9.9626 Tf 169.8886 453.3624 Td[(get)]TJ +/F8 9.9626 Tf 169.889 453.362 Td [(get)]TJ ET -1 0 0 1 183.7699 453.3624 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.77 453.562 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.7699 -453.3624 cm BT -/F8 9.9626 Tf 186.7587 453.3624 Td[(glob)1(al)]TJ +/F8 9.9626 Tf 186.759 453.362 Td [(global)]TJ ET -1 0 0 1 213.3701 453.3624 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 213.37 453.562 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -213.3701 -453.3624 cm BT -/F8 9.9626 Tf 216.3589 453.3624 Td[(cols)]TJ -ET -1 0 0 1 232.4652 453.3624 cm +/F8 9.9626 Tf 216.359 453.362 Td [(cols)]TJ 0 g 0 G -1 0 0 1 -232.4652 -453.3624 cm -BT -/F8 9.9626 Tf 241.8609 453.3624 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 453.3624 cm + [-943(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -453.3624 cm -BT -/F8 9.9626 Tf 433.6438 453.3624 Td[(15)]TJ -ET -1 0 0 1 443.6065 453.3624 cm + [-1084(16)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -440.3735 cm -BT -/F8 9.9626 Tf 137.7535 440.3735 Td[(psb)]TJ + -78.605 -12.988 Td [(psb)]TJ ET -1 0 0 1 153.3506 440.3735 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 440.573 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -440.3735 cm BT -/F8 9.9626 Tf 156.3394 440.3735 Td[(cd)]TJ +/F8 9.9626 Tf 156.339 440.374 Td [(cd)]TJ ET -1 0 0 1 166.8998 440.3735 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.9 440.573 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.8998 -440.3735 cm BT -/F8 9.9626 Tf 169.8886 440.3735 Td[(get)]TJ +/F8 9.9626 Tf 169.889 440.374 Td [(get)]TJ ET -1 0 0 1 183.7699 440.3735 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.77 440.573 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.7699 -440.3735 cm BT -/F8 9.9626 Tf 186.7587 440.3735 Td[(con)28(te)-1(x)1(t)]TJ -ET -1 0 0 1 218.8606 440.3735 cm +/F8 9.9626 Tf 186.759 440.374 Td [(con)28(text)]TJ 0 g 0 G -1 0 0 1 -218.8606 -440.3735 cm -BT -/F8 9.9626 Tf 226.3637 440.3735 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 433.6438 440.3735 cm + [-753(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -440.3735 cm -BT -/F8 9.9626 Tf 433.6438 440.3735 Td[(16)]TJ -ET -1 0 0 1 443.6065 440.3735 cm + [-1083(17)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -427.3846 cm -BT -/F8 9.9626 Tf 137.7535 427.3846 Td[(psb)]TJ + -49.005 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 427.3846 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 427.584 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -427.3846 cm BT -/F8 9.9626 Tf 156.3394 427.3846 Td[(cd)]TJ +/F8 9.9626 Tf 156.339 427.385 Td [(cd)]TJ ET -1 0 0 1 166.8998 427.3846 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.9 427.584 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.8998 -427.3846 cm BT -/F8 9.9626 Tf 169.8886 427.3846 Td[(get)]TJ +/F8 9.9626 Tf 169.889 427.385 Td [(get)]TJ ET -1 0 0 1 183.7699 427.3846 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.77 427.584 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.7699 -427.3846 cm BT -/F8 9.9626 Tf 186.7587 427.3846 Td[(lar)1(ge)]TJ +/F8 9.9626 Tf 186.759 427.385 Td [(large)]TJ ET -1 0 0 1 208.4164 427.3846 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 208.416 427.584 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -208.4164 -427.3846 cm BT -/F8 9.9626 Tf 211.4052 427.3846 Td[(th)1(re)-1(shol)1(d)]TJ -ET -1 0 0 1 251.8924 427.3846 cm +/F8 9.9626 Tf 211.405 427.385 Td [(threshold)]TJ 0 g 0 G -1 0 0 1 -251.8924 -427.3846 cm -BT -/F8 9.9626 Tf 257.3581 427.3846 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 433.6438 427.3846 cm + [-549(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -427.3846 cm -BT -/F8 9.9626 Tf 433.6438 427.3846 Td[(16)]TJ -ET -1 0 0 1 443.6065 427.3846 cm + [-1084(17)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -414.3958 cm -BT -/F8 9.9626 Tf 137.7535 414.3958 Td[(psb)]TJ + -73.652 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 414.3958 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 414.595 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -414.3958 cm BT -/F8 9.9626 Tf 156.3394 414.3958 Td[(cd)]TJ +/F8 9.9626 Tf 156.339 414.396 Td [(cd)]TJ ET -1 0 0 1 166.8998 414.3958 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.9 414.595 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.8998 -414.3958 cm BT -/F8 9.9626 Tf 169.8886 414.3958 Td[(se)-1(t)]TJ +/F8 9.9626 Tf 169.889 414.396 Td [(set)]TJ ET -1 0 0 1 182.7183 414.3958 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 182.718 414.595 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -182.7183 -414.3958 cm BT -/F8 9.9626 Tf 185.7071 414.3958 Td[(lar)1(ge)]TJ +/F8 9.9626 Tf 185.707 414.396 Td [(large)]TJ ET -1 0 0 1 207.3648 414.3958 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 207.365 414.595 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -207.3648 -414.3958 cm BT -/F8 9.9626 Tf 210.3536 414.3958 Td[(th)1(re)-1(shol)1(d)]TJ -ET -1 0 0 1 250.8407 414.3958 cm +/F8 9.9626 Tf 210.354 414.396 Td [(threshold)]TJ 0 g 0 G -1 0 0 1 -250.8407 -414.3958 cm -BT -/F8 9.9626 Tf 257.3581 414.3958 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 433.6438 414.3958 cm + [-654(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -414.3958 cm -BT -/F8 9.9626 Tf 433.6438 414.3958 Td[(17)]TJ -ET -1 0 0 1 443.6065 414.3958 cm + [-1084(18)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -401.4069 cm -BT -/F8 9.9626 Tf 137.7535 401.4069 Td[(psb)]TJ + -72.601 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 401.4069 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 401.606 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -401.4069 cm BT -/F8 9.9626 Tf 156.3394 401.4069 Td[(sp)]TJ +/F8 9.9626 Tf 156.339 401.407 Td [(sp)]TJ ET -1 0 0 1 166.4017 401.4069 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.402 401.606 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.4017 -401.4069 cm BT -/F8 9.9626 Tf 169.3905 401.4069 Td[(get)]TJ +/F8 9.9626 Tf 169.39 401.407 Td [(get)]TJ ET -1 0 0 1 183.2718 401.4069 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.272 401.606 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.2718 -401.4069 cm BT -/F8 9.9626 Tf 186.2606 401.4069 Td[(nr)1(o)28(w)-1(s)]TJ -ET -1 0 0 1 211.527 401.4069 cm +/F8 9.9626 Tf 186.261 401.407 Td [(nro)28(ws)]TJ 0 g 0 G -1 0 0 1 -211.527 -401.4069 cm -BT -/F8 9.9626 Tf 218.6151 401.4069 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 401.4069 cm + [-712(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -401.4069 cm -BT -/F8 9.9626 Tf 433.6438 401.4069 Td[(17)]TJ -ET -1 0 0 1 443.6065 401.4069 cm + [-1084(18)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -388.418 cm -BT -/F8 9.9626 Tf 137.7535 388.418 Td[(psb)]TJ + -48.508 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 388.418 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 388.617 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -388.418 cm BT -/F8 9.9626 Tf 156.3394 388.418 Td[(sp)]TJ +/F8 9.9626 Tf 156.339 388.418 Td [(sp)]TJ ET -1 0 0 1 166.4017 388.418 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.402 388.617 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.4017 -388.418 cm BT -/F8 9.9626 Tf 169.3905 388.418 Td[(get)]TJ +/F8 9.9626 Tf 169.39 388.418 Td [(get)]TJ ET -1 0 0 1 183.2718 388.418 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.272 388.617 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.2718 -388.418 cm BT -/F8 9.9626 Tf 186.2606 388.418 Td[(ncols)]TJ -ET -1 0 0 1 207.9017 388.418 cm +/F8 9.9626 Tf 186.261 388.418 Td [(ncols)]TJ 0 g 0 G -1 0 0 1 -207.9017 -388.418 cm -BT -/F8 9.9626 Tf 210.8665 388.418 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 388.418 cm + [-298(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -388.418 cm -BT -/F8 9.9626 Tf 433.6438 388.418 Td[(18)]TJ -ET -1 0 0 1 443.6065 388.418 cm + [-1084(19)]TJ 0 g 0 G -1 0 0 1 -305.853 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -137.7535 -375.4291 cm -BT -/F8 9.9626 Tf 137.7535 375.4291 Td[(psb)]TJ + -48.508 -12.989 Td [(psb)]TJ ET -1 0 0 1 153.3506 375.4291 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 153.351 375.628 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -153.3506 -375.4291 cm BT -/F8 9.9626 Tf 156.3394 375.4291 Td[(sp)]TJ +/F8 9.9626 Tf 156.339 375.429 Td [(sp)]TJ ET -1 0 0 1 166.4017 375.4291 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 166.402 375.628 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -166.4017 -375.4291 cm BT -/F8 9.9626 Tf 169.3905 375.4291 Td[(get)]TJ +/F8 9.9626 Tf 169.39 375.429 Td [(get)]TJ ET -1 0 0 1 183.2718 375.4291 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 183.272 375.628 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -183.2718 -375.4291 cm BT -/F8 9.9626 Tf 186.2606 375.4291 Td[(nn)1(z)-1(eros)]TJ -ET -1 0 0 1 218.999 375.4291 cm +/F8 9.9626 Tf 186.261 375.429 Td [(nnzeros)]TJ 0 g 0 G -1 0 0 1 -218.999 -375.4291 cm -BT -/F8 9.9626 Tf 226.3637 375.4291 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 433.6438 375.4291 cm + [-739(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -375.4291 cm -BT -/F8 9.9626 Tf 433.6438 375.4291 Td[(18)]TJ -ET -1 0 0 1 443.6065 375.4291 cm + [-1084(19)]TJ 0 g 0 G -1 0 0 1 -343.7111 -23.6407 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -99.8954 -351.7884 cm -BT -/F29 9.9626 Tf 99.8954 351.7884 Td[(4)-925(Computati)-1(on)1(al)-384(routines)]TJ -ET -1 0 0 1 234.032 351.7884 cm +/F27 9.9626 Tf -86.366 -23.641 Td [(4)-925(Computational)-383(r)-1(ou)1(t)-1(ines)]TJ 0 g 0 G -1 0 0 1 -234.032 -351.7884 cm -BT -/F29 9.9626 Tf 432.1495 351.7884 Td[(19)]TJ -ET -1 0 0 1 114.8394 338.7995 cm + [-19886(20)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -338.7995 cm -BT -/F8 9.9626 Tf 114.8394 338.7995 Td[(psb)]TJ +/F8 9.9626 Tf 14.944 -12.988 Td [(psb)]TJ ET -1 0 0 1 130.4364 338.7995 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 130.436 338.999 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -130.4364 -338.7995 cm BT -/F8 9.9626 Tf 133.4253 338.7995 Td[(geaxpb)28(y)]TJ -ET -1 0 0 1 169.1248 338.7995 cm +/F8 9.9626 Tf 133.425 338.8 Td [(geaxpb)28(y)]TJ 0 g 0 G -1 0 0 1 -169.1248 -338.7995 cm -BT -/F8 9.9626 Tf 172.1235 338.7995 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 338.7995 cm + [-301(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -338.7995 cm -BT -/F8 9.9626 Tf 433.6438 338.7995 Td[(20)]TJ -ET -1 0 0 1 443.6065 338.7995 cm + [-1084(21)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.9888 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -325.8107 cm -BT -/F8 9.9626 Tf 114.8394 325.8107 Td[(psb)]TJ + -18.586 -12.989 Td [(psb)]TJ ET -1 0 0 1 130.4364 325.8107 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 130.436 326.01 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -130.4364 -325.8107 cm BT -/F8 9.9626 Tf 133.4253 325.8107 Td[(gedot)]TJ -ET -1 0 0 1 157.225 325.8107 cm +/F8 9.9626 Tf 133.425 325.811 Td [(gedot)]TJ 0 g 0 G -1 0 0 1 -157.225 -325.8107 cm -BT -/F8 9.9626 Tf 164.3749 325.8107 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 433.6438 325.8107 cm + [-718(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -325.8107 cm -BT -/F8 9.9626 Tf 433.6438 325.8107 Td[(22)]TJ -ET -1 0 0 1 443.6065 325.8107 cm + [-1083(23)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -312.8218 cm -BT -/F8 9.9626 Tf 114.8394 312.8218 Td[(psb)]TJ + -18.586 -12.989 Td [(psb)]TJ ET -1 0 0 1 130.4364 312.8218 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 130.436 313.021 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -130.4364 -312.8218 cm BT -/F8 9.9626 Tf 133.4253 312.8218 Td[(gedots)]TJ -ET -1 0 0 1 161.1547 312.8218 cm +/F8 9.9626 Tf 133.425 312.822 Td [(gedots)]TJ 0 g 0 G -1 0 0 1 -161.1547 -312.8218 cm -BT -/F8 9.9626 Tf 164.3749 312.8218 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 433.6438 312.8218 cm + [-323(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -312.8218 cm -BT -/F8 9.9626 Tf 433.6438 312.8218 Td[(24)]TJ -ET -1 0 0 1 443.6065 312.8218 cm + [-1084(25)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -299.8329 cm -BT -/F8 9.9626 Tf 114.8394 299.8329 Td[(psb)]TJ + -18.586 -12.989 Td [(psb)]TJ ET -1 0 0 1 130.4364 299.8329 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 130.436 300.032 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -130.4364 -299.8329 cm BT -/F8 9.9626 Tf 133.4253 299.8329 Td[(geam)-1(ax)]TJ -ET -1 0 0 1 166.3574 299.8329 cm +/F8 9.9626 Tf 133.425 299.833 Td [(geamax)]TJ 0 g 0 G -1 0 0 1 -166.3574 -299.8329 cm -BT -/F8 9.9626 Tf 172.1235 299.8329 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 299.8329 cm + [-579(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -299.8329 cm -BT -/F8 9.9626 Tf 433.6438 299.8329 Td[(26)]TJ -ET -1 0 0 1 443.6065 299.8329 cm + [-1084(27)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -286.844 cm -BT -/F8 9.9626 Tf 114.8394 286.844 Td[(psb)]TJ + -18.586 -12.989 Td [(psb)]TJ ET -1 0 0 1 130.4364 286.844 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 130.436 287.043 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -130.4364 -286.844 cm BT -/F8 9.9626 Tf 133.4253 286.844 Td[(geam)-1(axs)]TJ -ET -1 0 0 1 170.2871 286.844 cm +/F8 9.9626 Tf 133.425 286.844 Td [(geamaxs)]TJ 0 g 0 G -1 0 0 1 -170.2871 -286.844 cm -BT -/F8 9.9626 Tf 179.8721 286.844 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 286.844 cm + [-962(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -433.6438 -286.844 cm -BT -/F8 9.9626 Tf 433.6438 286.844 Td[(27)]TJ -ET -1 0 0 1 443.6065 286.844 cm + [-1084(29)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.9889 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -273.8551 cm -BT -/F8 9.9626 Tf 114.8394 273.8551 Td[(psb)]TJ + -18.586 -12.989 Td [(psb)]TJ ET -1 0 0 1 130.4364 273.8551 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 130.436 274.054 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -130.4364 -273.8551 cm BT -/F8 9.9626 Tf 133.4253 273.8551 Td[(geas)-1(u)1(m)]TJ -ET -1 0 0 1 165.5825 273.8551 cm +/F8 9.9626 Tf 133.425 273.855 Td [(geasum)]TJ 0 g 0 G -1 0 0 1 -165.5825 -273.8551 cm -BT -/F8 9.9626 Tf 172.1235 273.8551 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 433.6438 273.8551 cm + 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Tf 165.6488 632.6422 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 632.6422 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 632.841 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -632.6422 cm BT -/F8 9.9626 Tf 184.2347 632.6422 Td[(cdbl)1(dext)]TJ -ET -1 0 0 1 221.5947 632.6422 cm +/F8 9.9626 Tf 184.235 632.642 Td [(cdbldext)]TJ 0 g 0 G -1 0 0 1 -221.5947 -632.6422 cm -BT -/F8 9.9626 Tf 230.6815 632.6422 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 484.4533 632.6422 cm + [-912(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -632.6422 cm -BT -/F8 9.9626 Tf 484.4533 632.6422 Td[(64)]TJ -ET -1 0 0 1 494.4159 632.6422 cm + [-1084(67)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -620.3944 cm -BT -/F8 9.9626 Tf 165.6488 620.3944 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 620.3944 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 620.594 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -620.3944 cm BT -/F8 9.9626 Tf 184.2347 620.3944 Td[(spall)]TJ -ET -1 0 0 1 204.2154 620.3944 cm +/F8 9.9626 Tf 184.235 620.394 Td [(spall)]TJ 0 g 0 G -1 0 0 1 -204.2154 -620.3944 cm -BT -/F8 9.9626 Tf 207.4357 620.3944 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 620.3944 cm + [-323(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -620.3944 cm -BT -/F8 9.9626 Tf 484.4533 620.3944 Td[(66)]TJ -ET -1 0 0 1 494.4159 620.3944 cm + [-1084(69)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -608.1466 cm -BT -/F8 9.9626 Tf 165.6488 608.1466 Td[(psb)]TJ + -18.586 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 608.1466 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 608.346 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -608.1466 cm BT -/F8 9.9626 Tf 184.2347 608.1466 Td[(spin)1(s)]TJ -ET -1 0 0 1 205.9312 608.1466 cm +/F8 9.9626 Tf 184.235 608.147 Td [(spins)]TJ 0 g 0 G -1 0 0 1 -205.9312 -608.1466 cm -BT -/F8 9.9626 Tf 215.1843 608.1466 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 608.1466 cm + [-929(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -608.1466 cm -BT -/F8 9.9626 Tf 484.4533 608.1466 Td[(67)]TJ -ET -1 0 0 1 494.4159 608.1466 cm + [-1084(70)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -595.8988 cm -BT -/F8 9.9626 Tf 165.6488 595.8988 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 595.8988 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 596.098 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -595.8988 cm BT -/F8 9.9626 Tf 184.2347 595.8988 Td[(spasb)]TJ -ET -1 0 0 1 208.1451 595.8988 cm +/F8 9.9626 Tf 184.235 595.899 Td [(spasb)]TJ 0 g 0 G -1 0 0 1 -208.1451 -595.8988 cm -BT -/F8 9.9626 Tf 215.1843 595.8988 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 595.8988 cm + [-707(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -595.8988 cm -BT -/F8 9.9626 Tf 484.4533 595.8988 Td[(69)]TJ -ET -1 0 0 1 494.4159 595.8988 cm + [-1083(72)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -583.6511 cm -BT -/F8 9.9626 Tf 165.6488 583.6511 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 583.6511 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 583.85 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -583.6511 cm BT -/F8 9.9626 Tf 184.2347 583.6511 Td[(spfr)1(e)-1(e)]TJ -ET -1 0 0 1 209.5011 583.6511 cm +/F8 9.9626 Tf 184.235 583.651 Td [(spfree)]TJ 0 g 0 G -1 0 0 1 -209.5011 -583.6511 cm -BT -/F8 9.9626 Tf 215.1843 583.6511 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 583.6511 cm + [-570(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -583.6511 cm -BT -/F8 9.9626 Tf 484.4533 583.6511 Td[(71)]TJ -ET -1 0 0 1 494.4159 583.6511 cm + [-1084(74)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -571.4033 cm -BT -/F8 9.9626 Tf 165.6488 571.4033 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 571.4033 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 571.603 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -571.4033 cm BT -/F8 9.9626 Tf 184.2347 571.4033 Td[(sprn)]TJ -ET -1 0 0 1 203.1361 571.4033 cm +/F8 9.9626 Tf 184.235 571.403 Td [(sprn)]TJ 0 g 0 G -1 0 0 1 -203.1361 -571.4033 cm -BT -/F8 9.9626 Tf 207.4357 571.4033 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 571.4033 cm + [-431(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -571.4033 cm -BT -/F8 9.9626 Tf 484.4533 571.4033 Td[(72)]TJ -ET -1 0 0 1 494.4159 571.4033 cm + [-1084(75)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -559.1555 cm -BT -/F8 9.9626 Tf 165.6488 559.1555 Td[(psb)]TJ + -18.586 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 559.1555 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 559.355 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -559.1555 cm BT -/F8 9.9626 Tf 184.2347 559.1555 Td[(geall)]TJ -ET -1 0 0 1 204.1601 559.1555 cm +/F8 9.9626 Tf 184.235 559.156 Td [(geall)]TJ 0 g 0 G -1 0 0 1 -204.1601 -559.1555 cm -BT -/F8 9.9626 Tf 207.4357 559.1555 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 559.1555 cm + [-329(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -559.1555 cm -BT -/F8 9.9626 Tf 484.4533 559.1555 Td[(73)]TJ -ET -1 0 0 1 494.4159 559.1555 cm + [-1084(76)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -546.9077 cm -BT -/F8 9.9626 Tf 165.6488 546.9077 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 546.9077 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 547.107 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -546.9077 cm BT -/F8 9.9626 Tf 184.2347 546.9077 Td[(geins)]TJ -ET -1 0 0 1 205.8758 546.9077 cm +/F8 9.9626 Tf 184.235 546.908 Td [(geins)]TJ 0 g 0 G -1 0 0 1 -205.8758 -546.9077 cm -BT -/F8 9.9626 Tf 215.1843 546.9077 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 546.9077 cm + [-934(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -546.9077 cm -BT -/F8 9.9626 Tf 484.4533 546.9077 Td[(74)]TJ -ET -1 0 0 1 494.4159 546.9077 cm + [-1084(77)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -534.66 cm -BT -/F8 9.9626 Tf 165.6488 534.66 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 534.66 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 534.859 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -534.66 cm BT -/F8 9.9626 Tf 184.2347 534.66 Td[(geas)-1(b)]TJ -ET -1 0 0 1 208.0898 534.66 cm +/F8 9.9626 Tf 184.235 534.66 Td [(geasb)]TJ 0 g 0 G -1 0 0 1 -208.0898 -534.66 cm -BT -/F8 9.9626 Tf 215.1843 534.66 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 534.66 cm + [-712(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -534.66 cm -BT -/F8 9.9626 Tf 484.4533 534.66 Td[(76)]TJ -ET -1 0 0 1 494.4159 534.66 cm + [-1084(79)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -522.4122 cm -BT -/F8 9.9626 Tf 165.6488 522.4122 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 522.4122 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 522.611 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -522.4122 cm BT -/F8 9.9626 Tf 184.2347 522.4122 Td[(gefree)]TJ -ET -1 0 0 1 209.4458 522.4122 cm +/F8 9.9626 Tf 184.235 522.412 Td [(gefree)]TJ 0 g 0 G -1 0 0 1 -209.4458 -522.4122 cm -BT -/F8 9.9626 Tf 215.1843 522.4122 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 522.4122 cm + [-576(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -522.4122 cm -BT -/F8 9.9626 Tf 484.4533 522.4122 Td[(77)]TJ -ET -1 0 0 1 494.4159 522.4122 cm + [-1084(80)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -510.1644 cm -BT -/F8 9.9626 Tf 165.6488 510.1644 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 510.1644 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 510.364 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -510.1644 cm BT -/F8 9.9626 Tf 184.2347 510.1644 Td[(gelp)]TJ -ET -1 0 0 1 201.9461 510.1644 cm +/F8 9.9626 Tf 184.235 510.164 Td [(gelp)]TJ 0 g 0 G -1 0 0 1 -201.9461 -510.1644 cm -BT -/F8 9.9626 Tf 207.4357 510.1644 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 510.1644 cm + [-551(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -510.1644 cm -BT -/F8 9.9626 Tf 484.4533 510.1644 Td[(78)]TJ -ET -1 0 0 1 494.4159 510.1644 cm + [-1084(81)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -497.9166 cm -BT -/F8 9.9626 Tf 165.6488 497.9166 Td[(psb)]TJ + -18.586 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 497.9166 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 498.116 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -497.9166 cm BT -/F8 9.9626 Tf 184.2347 497.9166 Td[(glob)]TJ +/F8 9.9626 Tf 184.235 497.917 Td [(glob)]TJ ET -1 0 0 1 203.0974 497.9166 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 203.097 498.116 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -203.0974 -497.9166 cm BT -/F8 9.9626 Tf 206.0862 497.9166 Td[(to)]TJ +/F8 9.9626 Tf 206.086 497.917 Td [(to)]TJ ET -1 0 0 1 215.5396 497.9166 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 215.54 498.116 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -215.5396 -497.9166 cm BT -/F8 9.9626 Tf 218.5284 497.9166 Td[(lo)-28(c)]TJ -ET -1 0 0 1 230.9818 497.9166 cm +/F8 9.9626 Tf 218.528 497.917 Td [(lo)-28(c)]TJ 0 g 0 G -1 0 0 1 -230.9818 -497.9166 cm -BT -/F8 9.9626 Tf 238.4301 497.9166 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 497.9166 cm + [-747(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -497.9166 cm -BT -/F8 9.9626 Tf 484.4533 497.9166 Td[(79)]TJ -ET -1 0 0 1 494.4159 497.9166 cm + [-1083(82)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -485.6688 cm -BT -/F8 9.9626 Tf 165.6488 485.6688 Td[(psb)]TJ + -52.879 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 485.6688 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 485.868 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -485.6688 cm BT -/F8 9.9626 Tf 184.2347 485.6688 Td[(lo)-28(c)]TJ +/F8 9.9626 Tf 184.235 485.669 Td [(lo)-28(c)]TJ ET -1 0 0 1 197.2858 485.6688 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 197.286 485.868 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -197.2858 -485.6688 cm BT -/F8 9.9626 Tf 200.2746 485.6688 Td[(to)]TJ +/F8 9.9626 Tf 200.275 485.669 Td [(to)]TJ ET -1 0 0 1 209.7281 485.6688 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 209.728 485.868 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -209.7281 -485.6688 cm BT -/F8 9.9626 Tf 212.7169 485.6688 Td[(glob)]TJ -ET -1 0 0 1 230.9818 485.6688 cm +/F8 9.9626 Tf 212.717 485.669 Td [(glob)]TJ 0 g 0 G -1 0 0 1 -230.9818 -485.6688 cm -BT -/F8 9.9626 Tf 238.4301 485.6688 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 485.6688 cm + [-748(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -485.6688 cm -BT -/F8 9.9626 Tf 484.4533 485.6688 Td[(81)]TJ -ET -1 0 0 1 494.4159 485.6688 cm + [-1083(84)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -473.4211 cm -BT -/F8 9.9626 Tf 165.6488 473.4211 Td[(psb)]TJ + -47.068 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 473.4211 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 473.62 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -473.4211 cm BT -/F8 9.9626 Tf 184.2347 473.4211 Td[(is)]TJ +/F8 9.9626 Tf 184.235 473.421 Td [(is)]TJ ET -1 0 0 1 191.5296 473.4211 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 191.53 473.62 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -191.5296 -473.4211 cm BT -/F8 9.9626 Tf 194.5184 473.4211 Td[(o)28(wned)]TJ -ET -1 0 0 1 221.9157 473.4211 cm +/F8 9.9626 Tf 194.518 473.421 Td [(o)28(wned)]TJ 0 g 0 G -1 0 0 1 -221.9157 -473.4211 cm -BT -/F8 9.9626 Tf 230.6815 473.4211 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 484.4533 473.4211 cm + [-880(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -473.4211 cm -BT -/F8 9.9626 Tf 484.4533 473.4211 Td[(82)]TJ -ET -1 0 0 1 494.4159 473.4211 cm + [-1084(85)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -461.1733 cm -BT -/F8 9.9626 Tf 165.6488 461.1733 Td[(psb)]TJ + -28.869 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 461.1733 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 461.373 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -461.1733 cm BT -/F8 9.9626 Tf 184.2347 461.1733 Td[(o)28(wned)]TJ +/F8 9.9626 Tf 184.235 461.173 Td [(o)28(wned)]TJ ET -1 0 0 1 212.2298 461.1733 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 212.23 461.373 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -212.2298 -461.1733 cm BT -/F8 9.9626 Tf 215.2186 461.1733 Td[(in)1(dex)]TJ -ET -1 0 0 1 238.7416 461.1733 cm +/F8 9.9626 Tf 215.219 461.173 Td [(index)]TJ 0 g 0 G -1 0 0 1 -238.7416 -461.1733 cm -BT -/F8 9.9626 Tf 246.1787 461.1733 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 461.1733 cm + [-746(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -461.1733 cm -BT -/F8 9.9626 Tf 484.4533 461.1733 Td[(83)]TJ -ET -1 0 0 1 494.4159 461.1733 cm + [-1083(86)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -448.9255 cm -BT -/F8 9.9626 Tf 165.6488 448.9255 Td[(psb)]TJ + -49.57 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 448.9255 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 449.125 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -448.9255 cm BT -/F8 9.9626 Tf 184.2347 448.9255 Td[(is)]TJ +/F8 9.9626 Tf 184.235 448.926 Td [(is)]TJ ET -1 0 0 1 191.5296 448.9255 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 191.53 449.125 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -191.5296 -448.9255 cm BT -/F8 9.9626 Tf 194.5184 448.9255 Td[(lo)-28(cal)]TJ -ET -1 0 0 1 214.7205 448.9255 cm +/F8 9.9626 Tf 194.518 448.926 Td [(lo)-28(cal)]TJ 0 g 0 G -1 0 0 1 -214.7205 -448.9255 cm -BT -/F8 9.9626 Tf 222.9329 448.9255 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 484.4533 448.9255 cm + [-824(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -448.9255 cm -BT -/F8 9.9626 Tf 484.4533 448.9255 Td[(84)]TJ -ET -1 0 0 1 494.4159 448.9255 cm + [-1084(87)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -436.6777 cm -BT -/F8 9.9626 Tf 165.6488 436.6777 Td[(psb)]TJ + -28.869 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 436.6777 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 436.877 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -436.6777 cm BT -/F8 9.9626 Tf 184.2347 436.6777 Td[(lo)-28(cal)]TJ +/F8 9.9626 Tf 184.235 436.678 Td [(lo)-28(cal)]TJ ET -1 0 0 1 205.0345 436.6777 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 205.035 436.877 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -205.0345 -436.6777 cm BT -/F8 9.9626 Tf 208.0234 436.6777 Td[(in)1(dex)]TJ -ET -1 0 0 1 231.5463 436.6777 cm +/F8 9.9626 Tf 208.023 436.678 Td [(index)]TJ 0 g 0 G -1 0 0 1 -231.5463 -436.6777 cm -BT -/F8 9.9626 Tf 238.4301 436.6777 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 436.6777 cm + [-691(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -436.6777 cm -BT -/F8 9.9626 Tf 484.4533 436.6777 Td[(85)]TJ -ET -1 0 0 1 494.4159 436.6777 cm + [-1084(88)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -424.43 cm -BT -/F8 9.9626 Tf 165.6488 424.43 Td[(psb)]TJ + -42.374 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 424.43 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 424.629 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -424.43 cm BT -/F8 9.9626 Tf 184.2347 424.43 Td[(get)]TJ +/F8 9.9626 Tf 184.235 424.43 Td [(get)]TJ ET -1 0 0 1 198.116 424.43 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 198.116 424.629 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -198.116 -424.43 cm BT -/F8 9.9626 Tf 201.1048 424.43 Td[(b)-27(oun)1(dary)]TJ -ET -1 0 0 1 242.6436 424.43 cm +/F8 9.9626 Tf 201.105 424.43 Td [(b)-28(oundary)]TJ 0 g 0 G -1 0 0 1 -242.6436 -424.43 cm -BT -/F8 9.9626 Tf 246.1787 424.43 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 424.43 cm + [-354(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -424.43 cm -BT -/F8 9.9626 Tf 484.4533 424.43 Td[(86)]TJ -ET -1 0 0 1 494.4159 424.43 cm + [-1083(89)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -412.1822 cm -BT -/F8 9.9626 Tf 165.6488 412.1822 Td[(psb)]TJ + -35.456 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 412.1822 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 412.381 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -412.1822 cm BT -/F8 9.9626 Tf 184.2347 412.1822 Td[(get)]TJ +/F8 9.9626 Tf 184.235 412.182 Td [(get)]TJ ET -1 0 0 1 198.116 412.1822 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 198.116 412.381 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -198.116 -412.1822 cm BT -/F8 9.9626 Tf 201.1048 412.1822 Td[(o)28(v)28(e)-1(r)1(lap)]TJ -ET -1 0 0 1 232.4042 412.1822 cm +/F8 9.9626 Tf 201.105 412.182 Td [(o)28(v)28(erlap)]TJ 0 g 0 G -1 0 0 1 -232.4042 -412.1822 cm -BT -/F8 9.9626 Tf 238.4301 412.1822 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 412.1822 cm + [-605(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -412.1822 cm -BT -/F8 9.9626 Tf 484.4533 412.1822 Td[(87)]TJ -ET -1 0 0 1 494.4159 412.1822 cm + [-1084(90)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -399.9344 cm -BT -/F8 9.9626 Tf 165.6488 399.9344 Td[(psb)]TJ + -35.456 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 399.9344 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 400.134 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -399.9344 cm BT -/F8 9.9626 Tf 184.2347 399.9344 Td[(sp)]TJ +/F8 9.9626 Tf 184.235 399.934 Td [(sp)]TJ ET -1 0 0 1 194.297 399.9344 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 194.297 400.134 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -194.297 -399.9344 cm BT -/F8 9.9626 Tf 197.2858 399.9344 Td[(getro)28(w)]TJ -ET -1 0 0 1 226.3712 399.9344 cm +/F8 9.9626 Tf 197.286 399.934 Td [(getro)28(w)]TJ 0 g 0 G -1 0 0 1 -226.3712 -399.9344 cm -BT -/F8 9.9626 Tf 230.6815 399.9344 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 484.4533 399.9344 cm + [-433(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -399.9344 cm -BT -/F8 9.9626 Tf 484.4533 399.9344 Td[(88)]TJ -ET -1 0 0 1 494.4159 399.9344 cm + [-1084(91)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -387.6866 cm -BT -/F8 9.9626 Tf 165.6488 387.6866 Td[(psb)]TJ + -31.637 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 387.6866 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 387.886 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -387.6866 cm BT -/F8 9.9626 Tf 184.2347 387.6866 Td[(siz)-1(eof)]TJ -ET -1 0 0 1 207.813 387.6866 cm +/F8 9.9626 Tf 184.235 387.687 Td [(sizeof)]TJ 0 g 0 G -1 0 0 1 -207.813 -387.6866 cm -BT -/F8 9.9626 Tf 215.1843 387.6866 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 387.6866 cm + [-740(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -387.6866 cm -BT -/F8 9.9626 Tf 484.4533 387.6866 Td[(90)]TJ -ET -1 0 0 1 494.4159 387.6866 cm + [-1084(93)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -375.4389 cm -BT -/F8 9.9626 Tf 165.6488 375.4389 Td[(Sor)1(tin)1(g)-334(u)1(tilit)1(ie)-1(s)]TJ -ET -1 0 0 1 233.2566 375.4389 cm + -18.586 -12.248 Td [(Sorting)-333(utilities)]TJ 0 g 0 G -1 0 0 1 -233.2566 -375.4389 cm -BT -/F8 9.9626 Tf 238.4301 375.4389 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 375.4389 cm + [-519(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -375.4389 cm -BT -/F8 9.9626 Tf 484.4533 375.4389 Td[(91)]TJ -ET -1 0 0 1 494.4159 375.4389 cm + [-1083(94)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -363.1911 cm -BT -/F8 9.9626 Tf 165.6488 363.1911 Td[(psb)]TJ + 0 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 363.1911 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 363.39 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -363.1911 cm BT -/F8 9.9626 Tf 184.2347 363.1911 Td[(ms)-1(or)1(t)]TJ -ET -1 0 0 1 209.2244 363.1911 cm +/F8 9.9626 Tf 184.235 363.191 Td [(msort)]TJ 0 g 0 G -1 0 0 1 -209.2244 -363.1911 cm -BT -/F8 9.9626 Tf 215.1843 363.1911 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 363.1911 cm + [-598(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -363.1911 cm -BT -/F8 9.9626 Tf 484.4533 363.1911 Td[(91)]TJ -ET -1 0 0 1 494.4159 363.1911 cm + [-1084(94)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -350.9433 cm -BT -/F8 9.9626 Tf 165.6488 350.9433 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 350.9433 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 351.143 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -350.9433 cm BT -/F8 9.9626 Tf 184.2347 350.9433 Td[(qsort)]TJ -ET -1 0 0 1 206.1803 350.9433 cm +/F8 9.9626 Tf 184.235 350.943 Td [(qsort)]TJ 0 g 0 G -1 0 0 1 -206.1803 -350.9433 cm -BT -/F8 9.9626 Tf 215.1843 350.9433 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 350.9433 cm + [-904(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -350.9433 cm -BT -/F8 9.9626 Tf 484.4533 350.9433 Td[(91)]TJ -ET -1 0 0 1 494.4159 350.9433 cm + [-1084(94)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -338.6955 cm -BT -/F8 9.9626 Tf 165.6488 338.6955 Td[(psb)]TJ + -18.586 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 338.6955 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 338.895 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -338.6955 cm BT -/F8 9.9626 Tf 184.2347 338.6955 Td[(hsort)]TJ -ET -1 0 0 1 206.457 338.6955 cm +/F8 9.9626 Tf 184.235 338.696 Td [(hsort)]TJ 0 g 0 G -1 0 0 1 -206.457 -338.6955 cm -BT -/F8 9.9626 Tf 215.1843 338.6955 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 338.6955 cm + [-876(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -338.6955 cm -BT -/F8 9.9626 Tf 484.4533 338.6955 Td[(91)]TJ -ET -1 0 0 1 494.4159 338.6955 cm + [-1084(94)]TJ 0 g 0 G -1 0 0 1 -343.7111 -22.4055 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -150.7048 -316.29 cm -BT -/F29 9.9626 Tf 150.7048 316.29 Td[(7)-925(P)32(arall)-1(el)-384(en)32(viron)1(m)-1(en)32(t)-383(routi)-1(n)1(e)-1(s)]TJ -ET -1 0 0 1 314.6808 316.29 cm +/F27 9.9626 Tf -33.53 -22.406 Td [(7)-925(P)32(arallel)-384(en)32(vironmen)32(t)-383(routines)]TJ 0 g 0 G -1 0 0 1 -314.6808 -316.29 cm -BT -/F29 9.9626 Tf 482.959 316.29 Td[(93)]TJ -ET -1 0 0 1 165.6488 304.0422 cm + [-16891(96)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -304.0422 cm -BT -/F8 9.9626 Tf 165.6488 304.0422 Td[(psb)]TJ +/F8 9.9626 Tf 14.944 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 304.0422 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 304.242 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -304.0422 cm BT -/F8 9.9626 Tf 184.2347 304.0422 Td[(in)1(it)]TJ -ET -1 0 0 1 199.1787 304.0422 cm +/F8 9.9626 Tf 184.235 304.042 Td [(init)]TJ 0 g 0 G -1 0 0 1 -199.1787 -304.0422 cm -BT -/F8 9.9626 Tf 207.4357 304.0422 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 304.0422 cm + [-829(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -304.0422 cm -BT -/F8 9.9626 Tf 484.4533 304.0422 Td[(94)]TJ -ET -1 0 0 1 494.4159 304.0422 cm + [-1083(97)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -291.7945 cm -BT -/F8 9.9626 Tf 165.6488 291.7945 Td[(psb)]TJ + -18.586 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 291.7945 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 291.994 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -291.7945 cm BT -/F8 9.9626 Tf 184.2347 291.7945 Td[(in)1(fo)]TJ -ET -1 0 0 1 200.5625 291.7945 cm +/F8 9.9626 Tf 184.235 291.795 Td [(info)]TJ 0 g 0 G -1 0 0 1 -200.5625 -291.7945 cm -BT -/F8 9.9626 Tf 207.4357 291.7945 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 291.7945 cm + [-690(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -291.7945 cm -BT -/F8 9.9626 Tf 484.4533 291.7945 Td[(95)]TJ -ET -1 0 0 1 494.4159 291.7945 cm + [-1084(98)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -279.5467 cm -BT -/F8 9.9626 Tf 165.6488 279.5467 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 279.5467 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 279.746 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -279.5467 cm BT -/F8 9.9626 Tf 184.2347 279.5467 Td[(exit)]TJ -ET -1 0 0 1 200.5624 279.5467 cm +/F8 9.9626 Tf 184.235 279.547 Td [(exit)]TJ 0 g 0 G -1 0 0 1 -200.5624 -279.5467 cm -BT -/F8 9.9626 Tf 207.4357 279.5467 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 484.4533 279.5467 cm + [-690(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -279.5467 cm -BT -/F8 9.9626 Tf 484.4533 279.5467 Td[(96)]TJ -ET -1 0 0 1 494.4159 279.5467 cm + [-1084(99)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -267.2989 cm -BT -/F8 9.9626 Tf 165.6488 267.2989 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 267.2989 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 267.498 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -267.2989 cm BT -/F8 9.9626 Tf 184.2347 267.2989 Td[(get)]TJ +/F8 9.9626 Tf 184.235 267.299 Td [(get)]TJ ET -1 0 0 1 198.116 267.2989 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 198.116 267.498 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -198.116 -267.2989 cm BT -/F8 9.9626 Tf 201.1048 267.2989 Td[(mpicomm)]TJ -ET -1 0 0 1 243.7229 267.2989 cm +/F8 9.9626 Tf 201.105 267.299 Td [(mpicomm)]TJ 0 g 0 G -1 0 0 1 -243.7229 -267.2989 cm -BT -/F8 9.9626 Tf 253.9274 267.2989 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 484.4533 267.2989 cm + [-1024(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -267.2989 cm -BT -/F8 9.9626 Tf 484.4533 267.2989 Td[(97)]TJ -ET -1 0 0 1 494.4159 267.2989 cm + [-583(100)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -255.0511 cm -BT -/F8 9.9626 Tf 165.6488 255.0511 Td[(psb)]TJ + -35.456 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 255.0511 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 255.25 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -255.0511 cm BT -/F8 9.9626 Tf 184.2347 255.0511 Td[(get)]TJ +/F8 9.9626 Tf 184.235 255.051 Td [(get)]TJ ET -1 0 0 1 198.116 255.0511 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 198.116 255.25 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -198.116 -255.0511 cm BT -/F8 9.9626 Tf 201.1048 255.0511 Td[(ran)1(k)]TJ -ET -1 0 0 1 220.7811 255.0511 cm +/F8 9.9626 Tf 201.105 255.051 Td [(rank)]TJ 0 g 0 G -1 0 0 1 -220.7811 -255.0511 cm -BT -/F8 9.9626 Tf 230.6815 255.0511 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ -ET -1 0 0 1 484.4533 255.0511 cm + [-994(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -255.0511 cm -BT -/F8 9.9626 Tf 484.4533 255.0511 Td[(98)]TJ -ET -1 0 0 1 494.4159 255.0511 cm + [-583(101)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2477 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -242.8034 cm -BT -/F8 9.9626 Tf 165.6488 242.8034 Td[(psb)]TJ + -35.456 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 242.8034 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 243.003 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -242.8034 cm BT -/F8 9.9626 Tf 184.2347 242.8034 Td[(wtime)]TJ -ET -1 0 0 1 210.8018 242.8034 cm +/F8 9.9626 Tf 184.235 242.803 Td [(wtime)]TJ 0 g 0 G -1 0 0 1 -210.8018 -242.8034 cm -BT -/F8 9.9626 Tf 215.1843 242.8034 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 484.4533 242.8034 cm + [-440(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -484.4533 -242.8034 cm -BT -/F8 9.9626 Tf 484.4533 242.8034 Td[(99)]TJ -ET -1 0 0 1 494.4159 242.8034 cm + [-584(102)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -230.5556 cm -BT -/F8 9.9626 Tf 165.6488 230.5556 Td[(psb)]TJ + -18.586 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 230.5556 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 230.755 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -230.5556 cm BT -/F8 9.9626 Tf 184.2347 230.5556 Td[(bar)1(rier)]TJ -ET -1 0 0 1 213.6522 230.5556 cm +/F8 9.9626 Tf 184.235 230.556 Td [(barrier)]TJ 0 g 0 G -1 0 0 1 -213.6522 -230.5556 cm -BT -/F8 9.9626 Tf 222.9329 230.5556 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -ET -1 0 0 1 479.4719 230.5556 cm + [-931(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -479.4719 -230.5556 cm -BT -/F8 9.9626 Tf 479.4719 230.5556 Td[(100)]TJ -ET -1 0 0 1 494.4159 230.5556 cm + [-584(103)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -218.3078 cm -BT -/F8 9.9626 Tf 165.6488 218.3078 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 218.3078 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 218.507 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -218.3078 cm BT -/F8 9.9626 Tf 184.2347 218.3078 Td[(ab)-27(ort)]TJ -ET -1 0 0 1 207.7854 218.3078 cm +/F8 9.9626 Tf 184.235 218.308 Td [(ab)-28(ort)]TJ 0 g 0 G -1 0 0 1 -207.7854 -218.3078 cm -BT -/F8 9.9626 Tf 215.1843 218.3078 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 479.4719 218.3078 cm + [-742(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -479.4719 -218.3078 cm -BT -/F8 9.9626 Tf 479.4719 218.3078 Td[(101)]TJ -ET -1 0 0 1 494.4159 218.3078 cm + [-584(104)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -206.06 cm -BT -/F8 9.9626 Tf 165.6488 206.06 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 206.06 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 206.259 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -206.06 cm BT -/F8 9.9626 Tf 184.2347 206.06 Td[(b)-27(c)-1(ast)]TJ -ET -1 0 0 1 207.2596 206.06 cm +/F8 9.9626 Tf 184.235 206.06 Td [(b)-28(cast)]TJ 0 g 0 G -1 0 0 1 -207.2596 -206.06 cm -BT -/F8 9.9626 Tf 215.1843 206.06 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ -ET -1 0 0 1 479.4719 206.06 cm + [-795(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -479.4719 -206.06 cm -BT -/F8 9.9626 Tf 479.4719 206.06 Td[(102)]TJ -ET -1 0 0 1 494.4159 206.06 cm + [-584(105)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -193.8123 cm -BT -/F8 9.9626 Tf 165.6488 193.8123 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 193.8123 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 194.012 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -193.8123 cm BT -/F8 9.9626 Tf 184.2347 193.8123 Td[(sum)]TJ -ET -1 0 0 1 202.0015 193.8123 cm +/F8 9.9626 Tf 184.235 193.812 Td [(sum)]TJ 0 g 0 G -1 0 0 1 -202.0015 -193.8123 cm -BT -/F8 9.9626 Tf 207.4357 193.8123 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 479.4719 193.8123 cm + [-545(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -479.4719 -193.8123 cm -BT -/F8 9.9626 Tf 479.4719 193.8123 Td[(103)]TJ -ET -1 0 0 1 494.4159 193.8123 cm + [-584(106)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -181.5645 cm -BT -/F8 9.9626 Tf 165.6488 181.5645 Td[(psb)]TJ + -18.586 -12.247 Td [(psb)]TJ ET -1 0 0 1 181.2459 181.5645 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 181.764 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -181.5645 cm BT -/F8 9.9626 Tf 184.2347 181.5645 Td[(max)]TJ -ET -1 0 0 1 202.7764 181.5645 cm +/F8 9.9626 Tf 184.235 181.565 Td [(max)]TJ 0 g 0 G -1 0 0 1 -202.7764 -181.5645 cm -BT -/F8 9.9626 Tf 207.4357 181.5645 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 479.4719 181.5645 cm + [-468(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -1 0 0 1 -479.4719 -181.5645 cm -BT -/F8 9.9626 Tf 479.4719 181.5645 Td[(104)]TJ -ET -1 0 0 1 494.4159 181.5645 cm + [-583(107)]TJ 0 g 0 G -1 0 0 1 -328.7671 -12.2478 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -169.3167 cm -BT -/F8 9.9626 Tf 165.6488 169.3167 Td[(psb)]TJ + -18.586 -12.248 Td [(psb)]TJ ET -1 0 0 1 181.2459 169.3167 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 181.246 169.516 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -181.2459 -169.3167 cm BT -/F8 9.9626 Tf 184.2347 169.3167 Td[(min)]TJ -ET -1 0 0 1 200.8392 169.3167 cm +/F8 9.9626 Tf 184.235 169.317 Td [(min)]TJ 0 g 0 G -1 0 0 1 -200.8392 -169.3167 cm -BT -/F8 9.9626 Tf 207.4357 169.3167 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ -ET -1 0 0 1 479.4719 169.3167 cm + [-662(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 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14.3462 Tf 99.895 706.129 Td [(1)-1125(In)31(tro)-31(duction)]TJ/F8 9.9626 Tf 0 -31.775 Td [(The)-316(PSBLAS)-316(library)84(,)-319(dev)27(elop)-27(e)-1(d)-315(with)-316(the)-316(aim)-316(to)-316(facilitate)-315(the)-316(parallelization)-316(of)]TJ 0 -11.955 Td [(computationally)-324(in)28(tensiv)28(e)-324(s)-1(cien)28(ti\014c)-324(applications,)-326(is)-324(designed)-324(to)-324(address)-324(parallel)]TJ 0 -11.955 Td [(implemen)28(tation)-427(of)-428(iterativ)28(e)-427(solv)28(ers)-428(for)-427(sparse)-427(linear)-427(systems)-428(thr)1(ough)-428(the)-427(dis-)]TJ 0 -11.956 Td [(tributed)-284(memory)-285(paradigm.)-428(It)-284(includes)-284(routines)-285(f)1(o)-1(r)-284(m)28(ultiplying)-284(sparse)-285(matrices)]TJ 0 -11.955 Td [(b)28(y)-343(dense)-343(matrices,)-345(solving)-343(blo)-28(c)28(k)-343(diagonal)-342(syste)-1(ms)-342(with)-343(triangular)-343(diagonal)-343(en-)]TJ 0 -11.955 Td [(tries,)-350(prepro)-28(cessing)-346(sparse)-347(matrices,)-350(an)1(d)-347(con)28(tains)-347(addition)1(al)-347(routines)-346(for)-347(dense)]TJ 0 -11.955 Td [(matrix)-439(op)-28(erations.)-763(The)-439(curren)28(t)-440(implemen)28(tation)-439(of)-440(PSBLAS)-439(addresses)-439(a)-440(dis-)]TJ 0 -11.955 Td [(tributed)-333(memory)-334(execution)-333(mo)-28(del)-333(op)-28(erating)-333(with)-333(me)-1(ssage)-333(passing.)]TJ 14.944 -17.304 Td [(The)-382(PSBLAS)-382(lib)1(rary)-382(is)-382(in)28(ternally)-382(implemen)28(ted)-382(in)-382(the)-382(F)84(ortran)-382(95)-382([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -409.3334 -573.3639 cm -BT -/F8 9.9626 Tf 409.3334 573.3639 Td[(14)]TJ -ET -1 0 0 1 419.2961 573.3639 cm + [(14)]TJ 0 g 0 G -1 0 0 1 -419.2961 -573.3639 cm -BT -/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 Td[(soft)28(w)27(ar)1(e)-1(,)-352(an)1(d)-348(a)-349(han)1(df)1(ul)-348(of)-348(C)-349(rou)1(tin)1(e)-1(s.)-490(A)-349(similar)-348(app)1(roac)28(h)-349(h)1(as)-349(b)-27(e)-1(en)-348(adv)28(o)-28(cate)-1(d)]TJ 0 -11.9552 Td[(b)28(y)-248(a)-248(n)28(u)1(m)27(b)-27(e)-1(r)-247(of)-248(aut)1(hors,)-265(e)-1(.)1(g.)-248([)]TJ -ET -1 0 0 1 224.5974 537.4984 cm + [(])-382(pro-)]TJ -14.944 -11.955 Td [(gramming)-345(language,)-348(with)-346(reuse)-345(and/or)-345(adaptation)-345(of)-345(som)-1(e)-345(existing)-345(F)83(ortran)-345(77)]TJ 0 -11.955 Td [(soft)28(w)27(ar)1(e)-1(,)-352(and)-348(a)-349(handful)-348(of)-349(C)-348(routines.)-490(A)-349(similar)-348(approac)28(h)-349(has)-348(b)-28(een)-349(adv)28(o)-28(cated)]TJ 0 -11.956 Td [(b)28(y)-248(a)-248(n)27(um)28(b)-28(er)-248(of)-248(authors,)-265(e.g.)-248([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -224.5974 -537.4984 cm -BT -/F8 9.9626 Tf 224.5974 537.4984 Td[(13)]TJ -ET -1 0 0 1 234.5601 537.4984 cm + [(13)]TJ 0 g 0 G -1 0 0 1 -234.5601 -537.4984 cm -BT -/F8 9.9626 Tf 234.5601 537.4984 Td[(].)-416(M)1(oreo)27(v)28(er,)-265(th)1(e)-249(F)84(ortr)1(an)-248(95)-248(facilit)1(ie)-1(s)-248(for)-248(d)1(ynamic)]TJ -134.6647 -11.9551 Td[(me)-1(mory)-297(managem)-1(en)28(t)-297(and)-297(in)28(terf)1(ac)-1(e)-298(o)28(v)28(erload)1(ing)-297(greatly)-297(e)-1(n)1(han)1(c)-1(e)-298(th)1(e)-298(usabil)1(it)28(y)-298(of)]TJ 0 -11.9552 Td[(th)1(e)-458(P)1(SBLAS)-457(sub)1(rou)1(tines)-1(.)-815(In)-456(thi)1(s)-458(w)28(a)28(y)83(,)-487(the)-457(lib)1(rary)-456(c)-1(an)-456(tak)28(e)-458(care)-457(of)-457(r)1(un)28(ti)1(m)-1(e)]TJ 0 -11.9552 Td[(me)-1(mory)-403(requi)1(rem)-1(en)28(ts)-404(th)1(at)-404(ar)1(e)-404(quit)1(e)-404(di\016c)-1(u)1(lt)-403(or)-403(e)-1(v)28(en)-403(im)-1(p)-27(oss)-1(ib)1(le)-404(to)-403(predi)1(c)-1(t)-403(at)]TJ 0 -11.9551 Td[(impl)1(e)-1(me)-1(n)29(tation)-285(or)-284(c)-1(ompi)1(lation)-285(t)1(im)-1(e.)-428(In)-285(th)1(e)-286(cur)1(re)-1(n)29(t)-285(rele)-1(ase)-286(w)28(e)-285(re)-1(l)1(y)-285(on)-285(th)1(e)-286(a)28(v)56(ail-)]TJ 0 -11.9552 Td[(abi)1(lit)28(y)-405(of)-404(the)-405(s)-1(o-called)-405(allo)-27(c)-1(atab)1(le)-405(e)-1(xtension)1(s)-1(,)-422(s)-1(p)-27(e)-1(ci\014)1(e)-1(d)-404(in)-405(TR)-405(15581.)-659(Str)1(ic)-1(tl)1(y)]TJ 0 -11.9552 Td[(sp)-28(eakin)1(g)-330(th)1(e)-1(y)-329(are)-330(ou)1(ts)-1(i)1(de)-330(th)1(e)-330(F)83(or)1(tran)-329(95)-330(stand)1(ard)1(;)-331(h)1(o)27(w)28(e)-1(v)28(er)-329(they)-329(ha)28(v)28(e)-330(b)-27(e)-1(en)-329(in-)]TJ 0 -11.9551 Td[(clud)1(e)-1(d)-367(in)-366(the)-368(F)84(ortr)1(an)-367(2003)-368(lan)1(guage)-368(stand)1(ard)1(,)-376(and)-367(ar)1(e)-368(a)28(v)56(ailabl)1(e)-368(in)-367(pr)1(ac)-1(ti)1(c)-1(all)1(y)]TJ 0 -11.9552 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[(the)-457(PSBLAS)-457(subroutines.)-815(In)-457(this)-457(w)28(a)28(y)83(,)-488(th)1(e)-457(library)-457(can)-457(tak)28(e)-457(care)-457(of)-457(run)28(time)]TJ 0 -11.955 Td [(memory)-404(requiremen)28(ts)-403(that)-404(are)-403(quite)-404(di\016cult)-403(or)-404(ev)28(en)-404(imp)-27(os)-1(sibl)1(e)-404(to)-404(predict)-403(at)]TJ 0 -11.955 Td [(implemen)28(tation)-285(or)-285(compilation)-285(time.)-429(In)-285(the)-285(curren)28(t)-285(release)-285(w)28(e)-285(rely)-285(on)-285(the)-286(a)28(v)56(ail-)]TJ 0 -11.955 Td [(abilit)28(y)-405(of)-405(the)-405(so-called)-405(allo)-28(catable)-405(extensions,)-423(sp)-28(eci\014ed)-405(in)-405(TR)-405(15581.)-659(Strictly)]TJ 0 -11.956 Td [(sp)-28(eaking)-329(they)-330(are)-329(outside)-330(the)-329(F)83(ortran)-329(95)-330(standard;)-331(ho)28(w)28(ev)28(er)-330(they)-329(ha)27(v)28(e)-329(b)-28(een)-330(in-)]TJ 0 -11.955 Td [(cluded)-367(in)-368(the)-367(F)83(ortran)-367(2003)-367(language)-368(standard,)-376(and)-367(are)-367(a)27(v)56(ailable)-367(in)-368(practically)]TJ 0 -11.955 Td [(all)-412(F)83(ortran)-412(95)-411(c)-1(ompil)1(e)-1(rs)-412(on)-411(the)-412(mark)27(et,)-431(including)-412(the)-412(GNU)-412(F)83(ortran)-412(compiler)]TJ 0 -11.955 Td [(from)-335(the)-335(F)83(ree)-335(Soft)28(w)28(are)-336(F)84(oundation)-335(\050as)-335(of)-335(v)27(ersion)-335(4.2\051.)-449(The)-336(presen)28(tation)-335(of)-335(the)]TJ 0 -11.955 Td [(PSBLAS)-370(library)-370(follo)28(ws)-371(the)-370(general)-370(structure)-370(of)-370(the)-371(p)1(rop)-28(osal)-370(for)-371(serial)-370(Sparse)]TJ 0 -11.955 Td [(BLAS)-457([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -133.5026 -405.9916 cm -BT -/F8 9.9626 Tf 133.5026 405.9916 Td[(7)]TJ -ET -1 0 0 1 138.484 405.9916 cm + [(7)]TJ 0 g 0 G -1 0 0 1 -138.484 -405.9916 cm -BT -/F8 9.9626 Tf 138.484 405.9916 Td[(,)]TJ -ET -1 0 0 1 145.8008 405.9916 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -145.8008 -405.9916 cm -BT -/F8 9.9626 Tf 145.8008 405.9916 Td[(8)]TJ -ET -1 0 0 1 150.7822 405.9916 cm + [-456(8)]TJ 0 g 0 G -1 0 0 1 -150.7822 -405.9916 cm -BT -/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 1 142.5964 394.0364 cm + [(],)-488(whic)28(h)-457(in)-456(its)-457(turn)-456(is)-457(based)-457(on)-456(the)-457(prop)-28(osal)-456(for)-457(BLAS)-456(on)-457(dense)]TJ 0 -11.956 Td [(matrices)-333([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -142.5964 -394.0364 cm -BT -/F8 9.9626 Tf 142.5964 394.0364 Td[(12)]TJ -ET -1 0 0 1 152.5591 394.0364 cm + [(12)]TJ 0 g 0 G -1 0 0 1 -152.5591 -394.0364 cm -BT -/F8 9.9626 Tf 152.5591 394.0364 Td[(,)]TJ -ET -1 0 0 1 158.6474 394.0364 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -158.6474 -394.0364 cm -BT -/F8 9.9626 Tf 158.6474 394.0364 Td[(4)]TJ -ET -1 0 0 1 163.6287 394.0364 cm + [-334(4)]TJ 0 g 0 G -1 0 0 1 -163.6287 -394.0364 cm -BT -/F8 9.9626 Tf 163.6287 394.0364 Td[(,)]TJ -ET -1 0 0 1 169.717 394.0364 cm + [(,)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -169.717 -394.0364 cm -BT -/F8 9.9626 Tf 169.717 394.0364 Td[(5)]TJ -ET -1 0 0 1 174.6984 394.0364 cm + [-333(5)]TJ 0 g 0 G -1 0 0 1 -174.6984 -394.0364 cm -BT -/F8 9.9626 Tf 174.6984 394.0364 Td[(].)]TJ -59.859 -17.3037 Td[(The)-403(app)1(licabili)1(t)28(y)-403(of)-403(sparse)-403(ite)-1(r)1(ativ)28(e)-403(s)-1(olv)28(ers)-403(to)-403(m)-1(an)29(y)-403(di\013eren)28(t)-403(areas)-404(cause)-1(s)]TJ -14.944 -11.9552 Td[(som)-1(e)-317(termin)1(ology)-316(pr)1(oblem)-1(s)-316(b)-28(ec)-1(au)1(s)-1(e)-316(the)-317(sam)-1(e)-316(c)-1(on)1(c)-1(ept)-316(ma)27(y)-316(b)-27(e)-317(denot)1(e)-1(d)-316(th)1(rough)]TJ 0 -11.9551 Td[(di)1(\013)-1(eren)28(t)-342(n)1(am)-1(es)-342(dep)-28(end)1(ing)-342(on)-341(the)-342(ap)1(plication)-341(area.)-470(The)-342(PS)1(B)-1(LAS)-341(featur)1(e)-1(s)-342(pr)1(e)-1(-)]TJ 0 -11.9552 Td[(se)-1(n)28(ted)-450(i)1(n)-450(th)1(is)-451(d)1(o)-28(cume)-1(n)29(t)-450(w)-1(i)1(ll)-450(b)-27(e)-451(d)1(isc)-1(u)1(s)-1(se)-1(d)-449(re)-1(f)1(e)-1(r)1(rin)1(g)-450(to)-450(a)-450(\014n)1(ite)-450(di\013ere)-1(n)1(c)-1(e)-450(di)1(s)-1(-)]TJ 0 -11.9552 Td[(cre)-1(t)1(iz)-1(ati)1(on)-329(of)-329(a)-329(P)28(art)1(ial)-329(Di\013e)-1(r)1(e)-1(n)28(t)1(ial)-329(Equ)1(ation)-329(\050P)1(DE\051)1(.)-329(Ho)27(w)28(e)-1(v)28(er,)-329(the)-330(scop)-28(e)-329(of)-329(the)]TJ 0 -11.9551 Td[(lib)1(rar)1(y)-345(is)-345(wid)1(e)-1(r)-344(th)1(an)-345(th)1(at:)-467(f)1(or)-345(example,)-347(it)-345(can)-344(b)-27(e)-346(ap)1(pl)1(ie)-1(d)-344(to)-344(\014ni)1(te)-345(e)-1(l)1(e)-1(me)-1(n)29(t)-345(di)1(s)-1(-)]TJ 0 -11.9552 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Td[(par)1(ticular)-344(it)-345(is)-345(c)-1(on)1(s)-1(i)1(s)-1(ten)28(t)-345(with)-344(the)-345(usage)-345(of)-345(grap)1(h)-345(p)1(arti)1(tionin)1(g)-345(to)-28(ol)1(s)-346(com)-1(monl)1(y)]TJ 0 -11.9552 Td[(a)28(v)56(ailabl)1(e)-396(i)1(n)-395(t)1(he)-395(literatu)1(re,)-410(e)-1(.)1(g.)-629(M)1(ETIS)-395([)]TJ -ET -1 0 0 1 278.9271 574.622 cm +/F8 9.9626 Tf 99.895 706.129 Td [(mesh.)]TJ 14.944 -11.955 Td [(The)-241(distribut)1(ion)-241(of)-241(the)-240(co)-28(e\016cien)28(t)-241(matrix)-240(for)-241(the)-241(linear)-240(system)-241(is)-240(base)-1(d)-240(on)-241(the)]TJ -14.944 -11.955 Td [(\134o)28(wner)-247(computes")-248(ru)1(le:)-402(the)-247(v)56(ariable)-247(asso)-28(ciated)-247(to)-247(eac)27(h)-247(mesh)-247(p)-28(oin)28(t)-247(is)-247(assigned)-247(to)]TJ 0 -11.956 Td [(a)-308(p)1(ro)-28(cess)-308(that)-307(will)-308(o)28(wn)-307(the)-308(corresp)-28(onding)-307(ro)28(w)-308(in)-307(the)-308(co)-27(e)-1(\016cien)28(t)-307(matrix)-308(and)-307(will)]TJ 0 -11.955 Td [(carry)-378(out)-378(al)1(l)-378(related)-378(computations.)-578(This)-378(all)1(o)-28(cation)-378(strategy)-378(is)-378(equiv)56(alen)28(t)-378(to)-378(a)]TJ 0 -11.955 Td [(partition)-293(of)-293(the)-293(discretization)-293(mesh)-293(in)27(to)]TJ/F17 9.9626 Tf 174.875 0 Td [(sub-domains)]TJ/F8 9.9626 Tf 53.72 0 Td [(.)-431(Our)-293(library)-293(supp)-28(orts)-293(an)28(y)]TJ -228.595 -11.955 Td [(distribution)-278(that)-278(k)28(eeps)-278(together)-278(the)-279(co)-27(e\016cie)-1(n)28(ts)-278(of)-278(eac)28(h)-278(matrix)-278(ro)28(w)-1(;)-296(there)-278(are)-278(no)]TJ 0 -11.955 Td [(other)-261(constrain)28(ts)-261(on)-261(the)-261(v)55(ariable)-261(assignmen)28(t.)-420(This)-261(c)27(h)1(oic)-1(e)-261(is)-261(consisten)28(t)-261(with)-261(data)]TJ 0 -11.956 Td [(distributions)-308(c)-1(ommonly)-308(used)-309(in)-308(ScaLAP)83(A)28(CK)-309(suc)28(h)-309(as)]TJ/F30 9.9626 Tf 233.534 0 Td [(CYCLIC\050N\051)]TJ/F8 9.9626 Tf 50.147 0 Td [(and)]TJ/F30 9.9626 Tf 19.126 0 Td [(BLOCK)]TJ/F8 9.9626 Tf 26.151 0 Td [(,)-309(as)]TJ -328.958 -11.955 Td [(w)28(ell)-422(as)-421(completely)-421(arbitrary)-421(assignme)-1(n)28(ts)-421(of)-421(equation)-422(i)1(ndices)-422(to)-421(pro)-28(cesses.)-708(In)]TJ 0 -11.955 Td [(particular)-345(it)-345(is)-345(consisten)28(t)-345(with)-345(the)-345(usage)-345(of)-345(graph)-345(par)1(titioning)-345(to)-28(ols)-345(commonly)]TJ 0 -11.955 Td [(a)28(v)55(ailable)-394(in)-395(the)-395(literature,)-410(e.g.)-628(METIS)-395([)]TJ 0 1 0 rg 0 1 0 RG -1 0 0 1 -278.9271 -574.622 cm -BT -/F8 9.9626 Tf 278.9271 574.622 Td[(11)]TJ -ET -1 0 0 1 288.8898 574.622 cm + [(11)]TJ 0 g 0 G -1 0 0 1 -288.8898 -574.622 cm -BT -/F8 9.9626 Tf 288.8898 574.622 Td[(].)-628(Dense)-396(v)28(ec)-1(t)1(ors)-395(c)-1(on)1(form)-395(t)1(o)-395(s)-1(p)1(arse)]TJ -188.9944 -11.9552 Td[(matrice)-1(s,)-497(th)1(at)-464(is,)-497(the)-464(e)-1(n)29(tries)-465(of)-464(a)-464(v)28(ec)-1(tor)-464(f)1(ollo)28(w)-464(the)-464(s)-1(ame)-465(d)1(is)-1(t)1(rib)1(ution)-463(of)-464(the)]TJ 0 -11.9551 Td[(matrix)-333(r)1(o)27(ws.)]TJ 14.944 -11.9552 Td[(W)84(e)-414(ass)-1(u)1(m)-1(e)-413(th)1(at)-413(the)-413(sparse)-414(matr)1(ix)-413(is)-413(bu)1(ilt)-413(i)1(n)-413(p)1(arallel,)-432(w)-1(h)1(e)-1(r)1(e)-414(eac)27(h)-412(pro)-27(c)-1(es)-1(s)]TJ -14.944 -11.9552 Td[(generates)-322(it)1(s)-322(o)28(wn)-321(p)-27(ort)1(ion.)-440(W)84(e)-322(n)1(e)-1(v)28(er)-320(re)-1(q)1(uir)1(e)-322(th)1(at)-321(th)1(e)-322(en)28(ti)1(re)-321(m)-1(atr)1(ix)-321(b)-27(e)-321(a)27(v)56(ail)1(able)]TJ 0 -11.9551 Td[(on)-279(a)-279(singl)1(e)-280(n)1(o)-28(de.)-426(Ho)27(w)28(ev)28(e)-1(r,)-289(it)-279(is)-279(p)-28(oss)-1(i)1(ble)-279(to)-279(hold)-278(the)-279(e)-1(n)29(tire)-279(m)-1(at)1(rix)-279(in)-278(one)-279(pro)-27(c)-1(es)-1(s)]TJ 0 -11.9552 Td[(and)-368(distri)1(but)1(e)-370(it)-369(e)-1(x)1(pli)1(c)-1(itl)1(y)]TJ -ET -1 0 0 1 215.6221 502.891 cm + [(].)-628(De)-1(n)1(s)-1(e)-394(v)28(e)-1(ctors)-394(conform)-395(to)-395(sparse)]TJ 0 -11.955 Td [(matrices,)-497(that)-464(is,)-497(the)-464(en)27(tr)1(ies)-465(of)-464(a)-464(v)28(ector)-465(fol)1(lo)27(w)-464(the)-464(same)-464(distribution)-464(of)-465(the)]TJ 0 -11.955 Td [(matrix)-333(ro)27(ws.)]TJ 14.944 -11.956 Td [(W)83(e)-413(assume)-413(that)-413(the)-412(s)-1(par)1(s)-1(e)-412(m)-1(atr)1(ix)-413(is)-413(built)-413(in)-413(parallel,)-433(where)-413(eac)28(h)-413(pro)-28(cess)]TJ -14.944 -11.955 Td [(generates)-321(its)-321(o)28(wn)-321(p)-28(ortion.)-440(W)84(e)-321(nev)28(e)-1(r)-320(require)-321(that)-321(the)-321(en)28(tire)-321(matrix)-321(b)-27(e)-321(a)28(v)55(ailable)]TJ 0 -11.955 Td [(on)-279(a)-279(single)-279(no)-28(de.)-426(Ho)27(w)28(ev)28(er,)-290(it)-279(is)-279(p)-28(ossible)-279(to)-279(hold)-279(the)-279(en)28(tire)-279(m)-1(atr)1(ix)-280(in)-279(one)-279(pro)-27(ces)-1(s)]TJ 0 -11.955 Td [(and)-369(distribute)-369(it)-370(expl)1(ic)-1(i)1(tly)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -215.6221 -502.891 cm -BT -/F7 6.9738 Tf 215.6221 506.5064 Td[(1)]TJ -ET -1 0 0 1 220.0914 502.891 cm +/F7 6.9738 Tf 115.727 3.615 Td [(1)]TJ 0 g 0 G -1 0 0 1 -220.0914 -502.891 cm -BT -/F8 9.9626 Tf 220.0914 502.891 Td[(,)-378(ev)28(e)-1(n)-369(th)1(ough)-368(the)-370(r)1(e)-1(sult)1(ing)-369(b)-27(ottlenec)27(k)-369(w)28(ould)-369(mak)28(e)]TJ -120.196 -11.9552 Td[(th)1(is)-334(opt)1(ion)-333(un)1(attractiv)28(e)-334(i)1(n)-333(m)-1(ost)-333(c)-1(ase)-1(s.)]TJ/F18 11.9552 Tf 0 -27.4046 Td[(2.)-1(1)-1125(Basic)-375(No)-1(mencl)-1(atur)-1(e)]TJ/F8 9.9626 Tf 0 -18.3893 Td[(Ou)1(r)-377(c)-1(ompu)1(tation)1(al)-377(m)-1(o)-27(del)-378(i)1(m)-1(p)1(lies)-378(th)1(at)-378(t)1(he)-378(d)1(ata)-377(allo)-28(cation)-377(on)-377(t)1(he)-378(p)1(arallel)-377(di)1(s)-1(-)]TJ 0 -11.9552 Td[(tri)1(bu)1(te)-1(d)-302(me)-1(mory)-302(m)-1(ac)28(hin)1(e)-303(is)-303(guid)1(e)-1(d)-302(b)28(y)-302(the)-303(structu)1(re)-303(of)-303(t)1(he)-303(ph)29(ys)-1(i)1(c)-1(al)-302(m)-1(o)-28(d)1(e)-1(l)1(,)-309(and)]TJ 0 -11.9552 Td[(sp)-28(ec)-1(i)1(\014cally)-333(b)28(y)-333(th)1(e)-334(discre)-1(t)1(iz)-1(ati)1(on)-333(m)-1(es)-1(h)-332(of)-333(the)-334(P)1(DE.)]TJ 14.944 -11.9551 Td[(Eac)28(h)-470(p)-28(oin)29(t)-471(of)-470(the)-471(d)1(is)-1(cretization)-470(m)-1(esh)-471(will)-470(ha)28(v)28(e)-471(\050at)-470(le)-1(ast\051)-471(on)1(e)-471(as)-1(so)-28(ciate)-1(d)]TJ -14.944 -11.9552 Td[(equati)1(on/v)56(ariab)1(le,)-466(and)-439(therefor)1(e)-441(on)1(e)-440(ind)1(e)-1(x)1(.)-763(W)83(e)-440(sa)27(y)-439(th)1(at)-440(p)-27(oin)28(t)]TJ/F11 9.9626 Tf 286.5782 0 Td[(i)]TJ/F19 9.9626 Tf 7.8121 0 Td[(dep)51(ends)]TJ/F8 9.9626 Tf 38.8046 0 Td[(on)]TJ -333.1949 -11.9552 Td[(p)-27(oin)28(t)]TJ/F11 9.9626 Tf 26.99 0 Td[(j)]TJ/F8 9.9626 Tf 8.9703 0 Td[(if)-431(th)1(e)-432(equati)1(on)-431(for)-431(a)-431(v)56(ariab)1(le)-432(ass)-1(o)-28(ciated)-431(with)]TJ/F11 9.9626 Tf 205.8468 0 Td[(i)]TJ/F8 9.9626 Tf 7.7295 0 Td[(con)28(tain)1(s)-432(a)-432(t)1(e)-1(rm)-431(in)]TJ/F11 9.9626 Tf 86.7341 0 Td[(j)]TJ/F8 9.9626 Tf 4.673 0 Td[(,)]TJ -340.9437 -11.9551 Td[(or)-408(equ)1(iv)56(ale)-1(n)29(tly)-408(i)1(f)]TJ/F11 9.9626 Tf 78.9119 0 Td[(a)]TJ/F10 6.9738 Tf 5.2662 -1.4944 Td[(ij)]TJ/F14 9.9626 Tf 11.0211 1.4944 Td[(6)]TJ/F8 9.9626 Tf 0 0 Td[(=)-402(0.)-668(Af)1(ter)-408(th)1(e)-409(p)1(artit)1(ion)-408(of)-407(the)-408(d)1(is)-1(cretization)-407(m)-1(es)-1(h)-407(in)28(t)1(o)]TJ/F19 9.9626 Tf -95.1992 -11.9552 Td[(sub-)1(do)-1(m)1(ains)]TJ/F8 9.9626 Tf 57.6275 0 Td[(ass)-1(ign)1(e)-1(d)-309(to)-310(the)-310(paral)1(le)-1(l)-309(pro)-27(c)-1(es)-1(se)-1(s,)-315(w)28(e)-311(class)-1(i)1(fy)-310(th)1(e)-311(p)-27(oin)28(ts)-310(of)-310(a)-310(giv)28(en)]TJ -57.6275 -11.9552 Td[(sub-d)1(om)-1(ain)-332(as)-334(foll)1(o)27(win)1(g.)]TJ -ET -1 0 0 1 94.9141 331.8229 cm +/F8 9.9626 Tf 4.469 -3.615 Td [(,)-378(ev)28(e)-1(n)-369(though)-369(the)-369(resulting)-369(b)-28(ottlenec)28(k)-369(w)27(ould)-369(mak)28(e)]TJ -120.196 -11.955 Td [(this)-333(option)-334(un)1(a)-1(t)1(trac)-1(t)1(iv)27(e)-333(in)-333(most)-334(cases.)]TJ/F16 11.9552 Tf 0 -27.405 Td [(2.1)-1125(Basic)-375(Nomenclature)]TJ/F8 9.9626 Tf 0 -18.389 Td [(Our)-377(computational)-377(mo)-28(del)-377(implies)-378(that)-377(the)-377(data)-377(allo)-28(cation)-377(on)-378(the)-377(parallel)-377(dis-)]TJ 0 -11.955 Td [(tributed)-303(memory)-302(mac)27(hine)-302(is)-303(guided)-303(b)28(y)-303(the)-302(structure)-303(of)-303(the)-303(p)1(h)27(ysical)-302(mo)-28(del,)-309(and)]TJ 0 -11.956 Td [(sp)-28(eci\014cally)-333(b)28(y)-334(the)-333(discretization)-333(mesh)-334(of)-333(the)-333(PDE.)]TJ 14.944 -11.955 Td [(Eac)28(h)-471(p)-28(oin)28(t)-471(of)-470(the)-471(discretization)-471(mesh)-470(will)-471(ha)28(v)28(e)-471(\050at)-471(least\051)-471(one)-470(asso)-28(ciated)]TJ -14.944 -11.955 Td [(equation/v)56(ariable,)-467(an)1(d)-440(therefore)-440(one)-439(index.)-764(W)84(e)-440(sa)28(y)-440(that)-439(p)-28(oin)28(t)]TJ/F11 9.9626 Tf 286.579 0 Td [(i)]TJ/F17 9.9626 Tf 7.812 0 Td [(dep)51(ends)]TJ/F8 9.9626 Tf 38.804 0 Td [(on)]TJ -333.195 -11.955 Td [(p)-28(oin)28(t)]TJ/F11 9.9626 Tf 26.99 0 Td [(j)]TJ/F8 9.9626 Tf 8.971 0 Td [(if)-431(the)-432(equation)-431(for)-431(a)-431(v)55(ariable)-431(asso)-28(ciated)-431(with)]TJ/F11 9.9626 Tf 205.846 0 Td [(i)]TJ/F8 9.9626 Tf 7.73 0 Td [(con)28(tains)-432(a)-431(term)-431(in)]TJ/F11 9.9626 Tf 86.734 0 Td [(j)]TJ/F8 9.9626 Tf 4.673 0 Td [(,)]TJ -340.944 -11.955 Td [(or)-408(equiv)56(alen)28(tly)-408(if)]TJ/F11 9.9626 Tf 78.912 0 Td [(a)]TJ/F10 6.9738 Tf 5.266 -1.495 Td [(ij)]TJ/F14 9.9626 Tf 11.021 1.495 Td [(6)]TJ/F8 9.9626 Tf 0 0 Td [(=)-402(0.)-668(After)-408(the)-408(partition)-407(of)-408(the)-408(discretization)-408(mesh)-408(in)28(to)]TJ/F17 9.9626 Tf -95.199 -11.955 Td [(sub-domains)]TJ/F8 9.9626 Tf 57.628 0 Td [(assigned)-310(to)-310(the)-310(parallel)-310(pro)-28(cesses,)-315(w)28(e)-310(classify)-310(the)-311(p)-27(oin)28(ts)-311(of)-310(a)-310(giv)28(en)]TJ -57.628 -11.956 Td [(sub-domain)-333(as)-334(follo)28(wing.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -331.8229 cm -BT -/F29 9.9626 Tf 99.8954 331.8229 Td[(In)32(ternal.)]TJ -ET -1 0 0 1 143.0113 331.8229 cm +/F27 9.9626 Tf 0 -17.677 Td [(In)32(ternal.)]TJ 0 g 0 G -1 0 0 1 -143.0113 -331.8229 cm -BT -/F8 9.9626 Tf 147.9926 331.8229 Td[(An)-396(in)28(ternal)-396(p)-28(oi)1(n)28(t)-397(of)-396(a)-397(giv)28(e)-1(n)-396(domain)]TJ/F19 9.9626 Tf 164.6933 0 Td[(dep)51(ends)]TJ/F8 9.9626 Tf 37.5612 0 Td[(onl)1(y)-397(on)-396(p)-28(oin)29(ts)-398(of)-396(the)]TJ -225.4451 -11.9552 Td[(sam)-1(e)-288(domain.)-429(If)-287(all)-288(p)-27(oin)28(ts)-288(of)-288(a)-288(domain)-287(are)-289(assigned)-288(to)-288(on)1(e)-289(p)1(ro)-28(ce)-1(ss)-1(,)-297(t)1(hen)-288(a)]TJ 0 -11.9552 Td[(com)-1(p)1(utati)1(onal)-342(ste)-1(p)-341(\050e)-1(.)1(g.,)-344(a)-342(matrix-v)28(ec)-1(tor)-341(pro)-27(duct\051)-342(of)-341(the)-342(e)-1(qu)1(ation)1(s)-343(ass)-1(o-)]TJ 0 -11.9551 Td[(ciate)-1(d)-301(w)-1(i)1(th)-302(the)-302(in)28(tern)1(al)-302(p)-28(oin)29(ts)-303(requ)1(ires)-303(no)-302(d)1(ata)-303(i)1(te)-1(ms)-303(f)1(rom)-303(ot)1(her)-302(domains)]TJ 0 -11.9552 Td[(and)-332(no)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ -ET -1 0 0 1 94.9141 265.2007 cm +/F8 9.9626 Tf 48.097 0 Td [(An)-397(in)28(ternal)-397(p)-28(oin)28(t)-397(of)-397(a)-396(giv)27(en)-397(domain)]TJ/F17 9.9626 Tf 164.694 0 Td [(dep)51(ends)]TJ/F8 9.9626 Tf 37.561 0 Td [(only)-397(on)-397(p)-27(oin)27(ts)-397(of)-396(the)]TJ -225.445 -11.955 Td 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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 +/F8 9.9626 Tf 150.705 706.129 Td [(to)-278(t)1(he)-278(adjacency)-278(grap)1(h)-278(imp)-28(osed)-277(on)-278(the)-277(discretization)-278(mesh)-277(b)27(y)-277(the)-278(discretization)]TJ 0 -11.955 Td [(stencil.)]TJ 14.944 -12.048 Td [(Th)28(us)-409(the)-408(\014rst)-408(order)-409(of)-408(business)-408(is)-409(to)-408(establish)-409(an)-408(index)-408(space,)-427(and)-409(this)-408(is)]TJ -14.944 -11.955 Td [(done)-371(with)-371(a)-371(call)-371(to)]TJ/F30 9.9626 Tf 87.109 0 Td [(psb_cdall)]TJ/F8 9.9626 Tf 50.768 0 Td [(in)-371(whic)28(h)-371(w)28(e)-371(sp)-28(ecify)-371(the)-371(size)-371(of)-371(the)-371(index)-371(space)]TJ/F11 9.9626 Tf -137.877 -11.955 Td [(n)]TJ/F8 9.9626 Tf 9.142 0 Td [(and)-317(the)-318(allo)-28(cation)-317(of)-317(the)-318(elemen)28(ts)-318(of)-317(the)-317(index)-318(space)-317(to)-318(the)-317(v)55(arious)-317(pro)-28(cesses)]TJ -9.142 -11.956 Td [(making)-333(up)-334(th)1(e)-334(MPI)-333(\050virtual\051)-333(parallel)-334(mac)28(hine.)]TJ 14.944 -12.047 Td [(The)-308(index)-309(space)-308(is)-309(parti)1(tioned)-309(among)-308(pro)-28(cesses,)-314(an)1(d)-309(this)-308(creates)-309(a)-308(mapping)]TJ -14.944 -11.956 Td [(from)-249(the)-249(\134global")-249(n)28(um)28(b)-28(ering)-249(1)]TJ/F11 9.9626 Tf 132.852 0 Td [(:)-167(:)-166(:)-167(n)]TJ/F8 9.9626 Tf 21.744 0 Td [(to)-249(a)-249(n)28(um)28(b)-28(ering)-249(\134lo)-28(cal")-249(to)-249(eac)28(h)-249(pro)-28(cess;)-277(eac)27(h)]TJ -154.596 -11.955 Td [(pro)-28(cess)]TJ/F11 9.9626 Tf 33.771 0 Td [(i)]TJ/F8 9.9626 Tf 5.794 0 Td [(will)-237(o)28(wn)-237(a)-237(certain)-237(subset)-237(1)]TJ/F11 9.9626 Tf 113.508 0 Td [(:)-167(:)-166(:)-167(n)]TJ/F8 9.9626 Tf 19.264 -1.494 Td [(ro)28(w)]TJ/F9 4.9813 Tf 15.801 -0.996 Td [(i)]TJ/F8 9.9626 Tf 3.655 2.49 Td [(,)-256(eac)27(h)-237(elemen)28(t)-237(of)-237(whic)28(h)-237(corresp)-28(onds)]TJ -191.793 -11.955 Td [(to)-390(a)-389(certain)-390(elemen)28(t)-390(of)-389(1)]TJ/F11 9.9626 Tf 111.313 0 Td [(:)-167(:)-166(:)-167(n)]TJ/F8 9.9626 Tf 19.264 0 Td [(.)-613(The)-390(user)-389(do)-28(es)-390(not)-389(s)-1(et)-389(explicitly)-390(this)-389(mapping;)]TJ -130.577 -11.955 Td [(when)-392(the)-393(appl)1(ic)-1(ati)1(on)-393(needs)-392(to)-392(indicate)-393(to)-392(whic)28(h)-392(e)-1(lemen)28(t)-392(of)-392(the)-393(index)-392(space)-392(a)]TJ 0 -11.955 Td [(certain)-273(item)-273(is)-273(related,)-285(suc)28(h)-273(as)-273(the)-273(ro)28(w)-273(and)-273(column)-273(index)-273(of)-273(a)-273(matrix)-273(co)-27(e\016c)-1(ien)28(t,)]TJ 0 -11.956 Td [(it)-449(do)-27(es)-449(so)-449(in)-448(the)-449(\134global")-449(n)28(um)28(b)-28(ering,)-477(and)-449(the)-448(library)-449(will)-448(translate)-449(in)28(to)-449(the)]TJ 0 -11.955 Td [(appropriate)-333(\134lo)-28(cal")-333(n)28(um)27(b)-27(ering.)]TJ 14.944 -12.048 Td [(F)83(or)-273(a)-274(giv)28(en)-274(index)-274(space)-273(1)]TJ/F11 9.9626 Tf 109.331 0 Td [(:)-167(:)-166(:)-167(n)]TJ/F8 9.9626 Tf 21.99 0 Td [(there)-274(are)-273(m)-1(an)28(y)-273(p)-28(ossible)-274(asso)-28(ciated)-274(top)-27(ologies,)]TJ -146.265 -11.955 Td [(i.e.)-418(man)28(y)-254(di\013eren)27(t)-254(discretization)-254(stencils;)-281(th)28(us)-254(the)-254(description)-254(of)-254(the)-254(index)-255(space)]TJ 0 -11.955 Td [(is)-355(not)-355(completed)-355(un)28(til)-356(th)1(e)-356(user)-355(has)-355(de\014ned)-355(a)-355(sparsit)28(y)-355(pattern,)-361(either)-355(explicitly)]TJ 0 -11.955 Td [(through)]TJ/F30 9.9626 Tf 36.93 0 Td [(psb_cdins)]TJ/F8 9.9626 Tf 49.661 0 Td [(or)-260(implicitly)-259(through)]TJ/F30 9.9626 Tf 92.222 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 47.073 0 Td [(.)-420(The)-260(descriptor)-259(is)-260(\014nalized)]TJ -225.886 -11.955 Td [(with)-354(a)-355(call)-354(to)]TJ/F30 9.9626 Tf 62.274 0 Td [(psb_cdasb)]TJ/F8 9.9626 Tf 50.603 0 Td [(and)-354(a)-355(sparse)-354(matrix)-354(with)-355(a)-354(call)-354(to)]TJ/F30 9.9626 Tf 153.217 0 Td [(psb_spasb)]TJ/F8 9.9626 Tf 47.073 0 Td [(.)-508(Af)1(te)-1(r)]TJ/F30 9.9626 Tf -313.167 -11.955 Td [(psb_cdasb)]TJ/F8 9.9626 Tf 50.443 0 Td [(eac)28(h)-338(pro)-28(cess)]TJ/F11 9.9626 Tf 57.244 0 Td [(i)]TJ/F8 9.9626 Tf 6.803 0 Td [(will)-338(ha)28(v)27(e)-338(de\014ned)-338(a)-338(set)-339(of)-338(\134halo")-338(\050or)-338(\134ghost"\051)-338(indices)]TJ/F11 9.9626 Tf -114.49 -11.956 Td [(n)]TJ/F8 9.9626 Tf 5.98 -1.494 Td [(ro)28(w)]TJ/F9 4.9813 Tf 15.802 -0.996 Td [(i)]TJ/F8 9.9626 Tf 5.985 2.49 Td [(+)-234(1)]TJ/F11 9.9626 Tf 16.722 0 Td [(:)-167(:)-166(:)-167(n)]TJ/F8 9.9626 Tf 19.263 -3.487 Td [(col)]TJ/F9 4.9813 Tf 12.177 -0.996 Td [(i)]TJ/F8 9.9626 Tf 3.654 4.483 Td [(,)-355(denoting)-351(elemen)27(ts)-351(of)-351(th)1(e)-351(index)-351(space)-351(that)-351(are)]TJ/F17 9.9626 Tf 209.596 0 Td [(not)]TJ/F8 9.9626 Tf 18.445 0 Td [(assigned)]TJ -307.624 -11.955 Td [(to)-284(pro)-28(cess)]TJ/F11 9.9626 Tf 45.921 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(;)-300(ho)28(w)27(ev)28(er)-284(the)-284(v)56(ariables)-284(asso)-28(ciated)-283(with)-284(them)-284(are)-284(needed)-284(to)-283(c)-1(omplete)]TJ -49.353 -11.955 Td [(computations)-410(asso)-27(ciated)-410(with)-409(the)-410(sparse)-409(m)-1(atri)1(x)]TJ/F11 9.9626 Tf 216.316 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(,)-429(an)1(d)-410(th)28(us)-410(they)-409(ha)28(v)27(e)-409(to)-410(b)-27(e)]TJ -223.788 -11.955 Td [(fetc)28(hed)-464(from)-464(\050)1(ne)-1(i)1(gh)27(b)-27(ouring\051)-464(pro)-28(cesses.)-835(The)-464(descriptor)-464(of)-463(the)-464(index)-463(space)-464(is)]TJ 0 -11.955 Td [(built)-394(exactly)-394(for)-393(the)-394(purp)-28(ose)-394(of)-394(prop)-27(e)-1(r)1(ly)-394(sequencing)-394(the)-394(comm)28(unication)-394(steps)]TJ 0 -11.956 Td [(required)-333(to)-334(ac)28(hiev)28(e)-333(this)-334(ob)-55(jectiv)28(e)-1(.)]TJ 14.944 -12.047 Td [(A)-306(simple)-306(application)-305(structure)-306(will)-306(w)28(alk)-306(through)-306(the)-306(in)1(dex)-306(space)-306(allo)-28(cation,)]TJ -14.944 -11.956 Td [(matrix/v)28(ector)-334(creation)-333(and)-333(linear)-333(syste)-1(m)-333(solution)-333(as)-334(f)1(o)-1(l)1(lo)27(ws:)]TJ 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 + 12.177 -20.203 Td [(1.)]TJ 0 g 0 G -1 0 0 1 -170.6302 -362.7653 cm -BT -/F8 9.9626 Tf 175.6115 362.7653 Td[(Ini)1(tialize)-334(p)1(arallel)-333(e)-1(n)29(viron)1(m)-1(en)28(t)-333(with)]TJ/F32 9.9626 Tf 156.6905 0 Td[(psb_init)]TJ -ET -1 0 0 1 150.7049 342.4693 cm + [-500(Initialize)-333(parallel)-334(en)28(vironmen)28(t)-333(with)]TJ/F30 9.9626 Tf 169.42 0 Td [(psb_init)]TJ 0 g 0 G -1 0 0 1 -150.7049 -342.4693 cm -BT -/F8 9.9626 Tf 162.8814 342.4693 Td[(2.)]TJ -ET -1 0 0 1 170.6302 342.4693 cm +/F8 9.9626 Tf -169.42 -20.296 Td [(2.)]TJ 0 g 0 G -1 0 0 1 -170.6302 -342.4693 cm -BT -/F8 9.9626 Tf 175.6115 342.4693 Td[(Ini)1(tialize)-334(in)1(dex)-333(s)-1(p)1(ac)-1(e)-334(wit)1(h)]TJ/F32 9.9626 Tf 117.3933 0 Td[(psb_cdall)]TJ -ET -1 0 0 1 150.7049 322.1733 cm + [-500(Initialize)-333(index)-334(space)-333(with)]TJ/F30 9.9626 Tf 130.123 0 Td [(psb_cdall)]TJ 0 g 0 G -1 0 0 1 -150.7049 -322.1733 cm -BT -/F8 9.9626 Tf 162.8814 322.1733 Td[(3.)]TJ -ET -1 0 0 1 170.6302 322.1733 cm +/F8 9.9626 Tf -130.123 -20.296 Td [(3.)]TJ 0 g 0 G -1 0 0 1 -170.6302 -322.1733 cm -BT -/F8 9.9626 Tf 175.6115 322.1733 Td[(Allo)-27(c)-1(ate)-302(spar)1(s)-1(e)-302(matri)1(x)-302(an)1(d)-301(dense)-302(v)28(e)-1(ctors)-302(with)]TJ/F32 9.9626 Tf 202.5989 0 Td[(psb_spall)]TJ/F8 9.9626 Tf 50.0773 0 Td[(and)]TJ/F32 9.9626 Tf 19.0552 0 Td[(psb_geall)]TJ -ET -1 0 0 1 150.7049 301.8774 cm + [-500(Allo)-28(cate)-301(sparse)-302(matrix)-301(and)-302(dense)-302(v)28(ectors)-301(with)]TJ/F30 9.9626 Tf 215.329 0 Td [(psb_spall)]TJ/F8 9.9626 Tf 50.077 0 Td [(and)]TJ/F30 9.9626 Tf 19.055 0 Td [(psb_geall)]TJ 0 g 0 G -1 0 0 1 -150.7049 -301.8774 cm -BT -/F8 9.9626 Tf 162.8814 301.8774 Td[(4.)]TJ -ET -1 0 0 1 170.6302 301.8774 cm +/F8 9.9626 Tf -284.461 -20.296 Td [(4.)]TJ 0 g 0 G -1 0 0 1 -170.6302 -301.8774 cm -BT -/F8 9.9626 Tf 175.6115 301.8774 Td[(Lo)-28(op)-410(o)27(v)28(er)-411(all)-411(l)1(o)-28(c)-1(al)-410(ro)28(w)-1(s,)-430(ge)-1(n)1(e)-1(r)1(ate)-412(matrix)-411(an)1(d)-411(v)28(ec)-1(tor)-410(e)-1(n)28(t)1(ries)-1(,)-430(and)-410(inse)-1(r)1(t)]TJ 0 -11.9552 Td[(th)1(e)-1(m)-334(wit)1(h)]TJ/F32 9.9626 Tf 48.1528 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 1 150.7049 269.6262 cm 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[(generate)-310(the)-311(en)28(tire)-310(part)-310(of)-311(a)-310(co)-28(e\016cien)28(t)-311(matrix)-310(residing)-310(on)-310(a)-311(pro)-27(ces)-1(s)-310(and)-310(pass)-310(it)]TJ 0 -11.955 Td [(in)-309(a)-309(single)-309(call)-309(to)]TJ/F30 9.9626 Tf 76.89 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 47.073 0 Td [(;)-317(this,)-314(ho)28(w)28(e)-1(v)28(er,)-314(w)28(ould)-309(en)28(tail)-309(a)-309(doubling)-309(of)-309(memory)]TJ -123.963 -11.955 Td [(o)-28(ccupation,)-333(and)-333(th)27(u)1(s)-334(w)28(ould)-333(b)-28(e)-333(almos)-1(t)-333(alw)28(a)28(ys)-334(far)-333(from)-333(optimal.)]TJ/F16 11.9552 Tf 0 -28.062 Td [(2.4)-1125(Programming)-375(mo)-31(del)]TJ/F8 9.9626 Tf 0 -18.451 Td [(The)-325(PSBLAS)-324(librarary)-325(is)-325(based)-325(on)-324(the)-325(Single)-325(Program)-324(Multiple)-325(Data)-325(\050SPMD\051)]TJ 0 -11.955 Td [(programming)-413(mo)-28(del:)-603(eac)27(h)-413(pro)-27(cess)-413(participating)-413(in)-413(the)-413(computation)-413(p)-28(erforms)]TJ 0 -11.955 Td 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ET -1 0 0 1 361.7069 460.3995 cm -0 g 0 G -1 0 0 1 -361.7069 -460.3995 cm +q +1 0 0 1 383.433 479.858 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q BT -/F8 9.9626 Tf 361.7069 460.3995 Td[(,)-307(and)-300(its)-301(\014)1(e)-1(ld)1(s)-301(m)-1(a)28(y)]TJ -261.8115 -11.9552 Td[(b)-27(e)-388(acc)-1(es)-1(sed)-387(if)-386(nec)-1(es)-1(sary)-387(vi)1(a)-387(the)-387(rou)1(tines)-388(of)-386(s)-1(ec)-1(.)]TJ -ET -1 0 0 1 312.9298 448.4444 cm +/F30 9.9626 Tf 386.571 479.659 Td [(type)]TJ/F8 9.9626 Tf 20.922 0 Td [(.)-803(Ev)28(ery)]TJ -307.598 -11.955 Td [(structure)-392(of)-392(this)-392(t)28(yp)-28(e)-392(is)-392(asso)-28(ciated)-392(to)-392(a)-392(sparse)-392(matrix,)-407(it)-392(con)28(tains)-392(data)-392(ab)-28(out)]TJ 0 -11.955 Td [(general)-333(matrix)-334(informations)-333(and)-333(elemen)28(ts)-334(to)-333(b)-28(e)-333(exc)27(hanged)-333(among)-333(pro)-28(cesses.)]TJ 14.944 -11.955 Td [(It)-222(is)-223(n)1(ot)-223(necessary)-222(for)-222(the)-222(user)-223(to)-222(kno)28(w)-222(the)-223(i)1(n)27(ternal)-222(structure)-222(of)]TJ/F30 9.9626 Tf 268.051 0 Td [(psb_desc_type)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ -350.989 -11.956 Td [(it)-301(is)-301(set)-300(in)-301(a)-301(transparen)28(t)-301(mo)-28(de)-300(b)28(y)-301(the)-301(to)-28(ols)-301(rou)1(tines)-301(of)-301(Sec.)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -312.9298 -448.4444 cm -BT -/F8 9.9626 Tf 312.9298 448.4444 Td[(3.4)]TJ -ET -1 0 0 1 325.6599 448.4444 cm + [-301(6)]TJ 0 g 0 G -1 0 0 1 -325.6599 -448.4444 cm -BT -/F8 9.9626 Tf 325.6599 448.4444 Td[(;)-414(n)1(e)-1(v)28(erth)1(e)-1(l)1(e)-1(ss)-388(w)28(e)-388(in)1(c)-1(l)1(ud)1(e)-388(a)]TJ -225.7645 -11.9552 Td[(desc)-1(ri)1(ption)-332(for)-333(th)1(e)-334(c)-1(u)1(riou)1(s)-334(reader:)]TJ -ET -1 0 0 1 94.9141 416.1071 cm + [(,)-307(and)-301(its)-300(\014elds)-301(ma)28(y)]TJ 0 -11.955 Td [(b)-28(e)-387(accessed)-387(if)-387(necessary)-387(via)-387(the)-387(routines)-387(of)-387(sec.)]TJ +0 0 1 rg 0 0 1 RG + [-387(3.4)]TJ 0 g 0 G -1 0 0 1 -94.9141 -416.1071 cm -BT -/F29 9.9626 Tf 99.8954 416.1071 Td[(mat)-1(r)1(i)-1(x)]TJ + [(;)-414(nev)28(e)-1(r)1(thele)-1(ss)-387(w)28(e)-387(include)-387(a)]TJ 0 -11.955 Td [(description)-333(for)-334(the)-333(curious)-333(reader:)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -19.324 Td [(matrix)]TJ ET -1 0 0 1 134.1027 416.1071 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 134.103 388.803 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -134.1027 -416.1071 cm BT -/F29 9.9626 Tf 137.5398 416.1071 Td[(data)]TJ -ET -1 0 0 1 159.499 416.1071 cm +/F27 9.9626 Tf 137.54 388.604 Td [(data)]TJ 0 g 0 G -1 0 0 1 -159.499 -416.1071 cm -BT -/F8 9.9626 Tf 164.4803 416.1071 Td[(in)1(c)-1(lu)1(des)-271(general)-270(inf)1(ormation)-270(ab)-27(out)-270(matrix)-270(an)1(d)-270(pr)1(o)-28(c)-1(es)-1(s)-270(grid)1(,)-283(s)-1(u)1(c)27(h)]TJ -39.6783 -11.9552 Td[(as)-403(the)-403(c)-1(omm)28(uni)1(c)-1(ati)1(on)-403(con)28(text,)-420(the)-403(siz)-1(e)-403(of)-402(the)-403(global)-402(m)-1(at)1(rix,)-420(th)1(e)-404(size)-404(of)]TJ 0 -11.9551 Td[(th)1(e)-347(p)-27(ortion)-346(of)-345(m)-1(atr)1(ix)-346(stored)-346(on)-346(th)1(e)-347(curr)1(e)-1(n)28(t)-346(p)1(ro)-28(ce)-1(ss,)-350(an)1(d)-346(so)-347(on)1(.)-483(Sp)-27(ec)-1(i\014)1(e)-1(d)]TJ 0 -11.9552 Td[(as:)-445(an)-333(al)1(lo)-28(catable)-333(in)28(tege)-1(r)-333(ar)1(ra)28(y)-333(of)-333(dimension)]TJ/F32 9.9626 Tf 197.5097 0 Td[(psb_mdata_size_)]TJ/F8 9.9626 Tf 78.4551 0 Td[(.)]TJ -ET -1 0 0 1 94.9141 359.7073 cm +/F8 9.9626 Tf 26.94 0 Td [(includes)-270(general)-271(information)-270(ab)-28(out)-270(matrix)-270(and)-271(pro)-27(ces)-1(s)-270(grid,)-283(suc)28(h)]TJ -39.678 -11.955 Td [(as)-403(the)-403(comm)28(unication)-403(con)28(text,)-420(the)-403(size)-403(of)-403(the)-403(global)-403(matrix,)-420(the)-403(size)-403(of)]TJ 0 -11.955 Td 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Td[(A)-384(list)-384(of)-384(th)1(e)-385(hal)1(o)-385(an)1(d)-384(b)-27(oun)1(dary)-384(elem)-1(en)28(ts)-385(f)1(or)-384(th)1(e)-385(curr)1(e)-1(n)28(t)-384(p)1(ro)-28(ce)-1(ss)]TJ -32.2548 -11.9552 Td[(to)-347(b)-27(e)-348(exc)27(h)1(anged)-347(with)-347(ot)1(her)-347(pr)1(o)-28(c)-1(es)-1(ses)-1(;)-354(f)1(or)-347(e)-1(ac)28(h)-347(p)1(ro)-28(ce)-1(ss)-1(es)-348(with)-346(whic)28(h)-347(it)-347(is)]TJ 0 -11.9552 Td[(nece)-1(ss)-1(ar)1(y)-334(t)1(o)-334(com)-1(m)28(un)1(icate)-1(:)]TJ -ET -1 0 0 1 124.802 315.2626 cm +/F8 9.9626 Tf 32.192 0 Td [(A)-384(list)-384(of)-385(th)1(e)-385(halo)-384(and)-384(b)-28(oundary)-384(elemen)28(ts)-384(for)-385(th)1(e)-385(curren)28(t)-384(pro)-28(cess)]TJ -32.255 -11.955 Td [(to)-347(b)-28(e)-347(exc)28(hanged)-347(with)-347(other)-347(pro)-28(cesses;)-354(for)-347(ea)-1(c)28(h)-347(pro)-28(cesses)-347(with)-347(whic)28(h)-347(it)-347(is)]TJ 0 -11.955 Td [(necessary)-333(to)-334(comm)28(unicate:)]TJ 0 g 0 G -1 0 0 1 -124.802 -315.2626 cm -BT -/F8 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Td[(Ind)1(ice)-1(s)-334(of)-333(p)-27(oin)29(ts)-334(to)-333(b)-28(e)-333(re)-1(ceiv)28(e)-1(d)1(;)]TJ -ET -1 0 0 1 124.802 266.5284 cm + [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(receiv)27(ed;)]TJ 0 g 0 G -1 0 0 1 -124.802 -266.5284 cm -BT -/F8 9.9626 Tf 133.9898 266.5284 Td[(4.)]TJ -ET -1 0 0 1 141.7385 266.5284 cm + 0 -15.64 Td [(4.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -266.5284 cm -BT -/F8 9.9626 Tf 146.7198 266.5284 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(p)-27(oin)28(ts)-333(to)-334(b)-27(e)-334(se)-1(n)29(t;)]TJ -ET -1 0 0 1 124.802 250.2836 cm + [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)28(ts)-334(to)-333(b)-28(e)-333(sen)27(t;)]TJ 0 g 0 G -1 0 0 1 -124.802 -250.2836 cm -BT -/F8 9.9626 Tf 133.9898 250.2836 Td[(5.)]TJ -ET -1 0 0 1 141.7385 250.2836 cm + 0 -15.64 Td [(5.)]TJ 0 g 0 G -1 0 0 1 -141.7385 -250.2836 cm -BT -/F8 9.9626 Tf 146.7198 250.2836 Td[(Ind)1(ice)-1(s)-334(of)-333(p)-27(oin)29(ts)-334(to)-333(b)-28(e)-333(s)-1(en)28(t;)]TJ -21.9178 -20.5343 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142.8017 515.8222 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 142.802 516.022 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -146.2388 -515.8222 cm BT -/F8 9.9626 Tf 151.2201 515.8222 Td[(F)84(e)-1(tc)28(h)-333(halo)-333(ele)-1(men)28(ts)-334(f)1(rom)-334(n)1(e)-1(igh)29(b)-28(ou)1(rin)1(g)-334(p)1(ro)-28(ce)-1(sse)-1(s;)]TJ -ET -1 0 0 1 94.9141 495.3334 cm +/F8 9.9626 Tf 151.22 515.822 Td [(F)83(etc)28(h)-333(halo)-334(elemen)28(ts)-333(from)-334(neigh)28(b)-27(ouring)-334(pro)-27(ces)-1(ses;)]TJ 0 g 0 G -1 0 0 1 -94.9141 -495.3334 cm -BT -/F29 9.9626 Tf 99.8954 495.3334 Td[(ps)1(b)]TJ +/F27 9.9626 Tf -51.325 -20.489 Td [(psb)]TJ ET -1 0 0 1 117.8319 495.3334 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 117.832 495.533 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -117.8319 -495.3334 cm BT -/F29 9.9626 Tf 121.269 495.3334 Td[(su)1(m)]TJ +/F27 9.9626 Tf 121.269 495.333 Td [(sum)]TJ ET -1 0 0 1 142.388 495.3334 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 142.388 495.533 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -145.8251 -495.3334 cm BT -/F8 9.9626 Tf 150.8064 495.3334 Td[(Su)1(m)-334(o)28(v)28(erlap)1(p)-28(ed)-333(e)-1(l)1(e)-1(me)-1(n)29(ts)]TJ -ET -1 0 0 1 94.9141 474.8446 cm +/F8 9.9626 Tf 150.806 495.333 Td [(Sum)-333(o)27(v)28(erlapp)-27(e)-1(d)-333(elemen)28(ts)]TJ 0 g 0 G -1 0 0 1 -94.9141 -474.8446 cm -BT -/F29 9.9626 Tf 99.8954 474.8446 Td[(ps)1(b)]TJ +/F27 9.9626 Tf -50.911 -20.488 Td [(psb)]TJ ET -1 0 0 1 117.8319 474.8446 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 117.832 475.044 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -117.8319 -474.8446 cm BT -/F29 9.9626 Tf 121.269 474.8446 Td[(a)32(vg)]TJ +/F27 9.9626 Tf 121.269 474.845 Td [(a)32(vg)]TJ ET -1 0 0 1 138.9827 474.8446 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 138.983 475.044 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -142.4198 -474.8446 cm BT -/F8 9.9626 Tf 147.4011 474.8446 Td[(Av)28(erage)-334(o)28(v)28(e)-1(r)1(lapp)-27(ed)-333(e)-1(l)1(e)-1(me)-1(n)28(t)1(s)]TJ -ET -1 0 0 1 94.9141 454.3558 cm +/F8 9.9626 Tf 147.401 474.845 Td [(Av)28(erage)-334(o)28(v)28(erlapp)-28(ed)-333(elemen)28(ts)]TJ 0 g 0 G -1 0 0 1 -94.9141 -454.3558 cm -BT -/F29 9.9626 Tf 99.8954 454.3558 Td[(ps)1(b)]TJ +/F27 9.9626 Tf -47.506 -20.489 Td [(psb)]TJ ET -1 0 0 1 117.8319 454.3558 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 117.832 454.555 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -117.8319 -454.3558 cm BT -/F29 9.9626 Tf 121.269 454.3558 Td[(comm)]TJ +/F27 9.9626 Tf 121.269 454.356 Td [(comm)]TJ ET -1 0 0 1 151.8718 454.3558 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 151.872 454.555 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -151.8718 -454.3558 cm BT -/F29 9.9626 Tf 155.3089 454.3558 Td[(halo)]TJ +/F27 9.9626 Tf 155.309 454.356 Td [(halo)]TJ ET -1 0 0 1 176.8416 454.3558 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 176.842 454.555 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -180.2787 -454.3558 cm BT -/F8 9.9626 Tf 185.2601 454.3558 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(halo_index)]TJ/F8 9.9626 Tf 55.6242 0 Td[(list;)]TJ -ET -1 0 0 1 94.9141 433.867 cm +/F8 9.9626 Tf 185.26 454.356 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.387 0 Td [(halo_index)]TJ/F8 9.9626 Tf 55.625 0 Td [(list;)]TJ 0 g 0 G -1 0 0 1 -94.9141 -433.867 cm -BT -/F29 9.9626 Tf 99.8954 433.867 Td[(ps)1(b)]TJ +/F27 9.9626 Tf -267.377 -20.489 Td [(psb)]TJ ET -1 0 0 1 117.8319 433.867 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 117.832 434.066 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -117.8319 -433.867 cm BT -/F29 9.9626 Tf 121.269 433.867 Td[(comm)]TJ +/F27 9.9626 Tf 121.269 433.867 Td [(comm)]TJ ET -1 0 0 1 151.8718 433.867 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 151.872 434.066 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -151.8718 -433.867 cm BT -/F29 9.9626 Tf 155.3089 433.867 Td[(ext)]TJ +/F27 9.9626 Tf 155.309 433.867 Td [(ext)]TJ ET -1 0 0 1 171.7497 433.867 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 171.75 434.066 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -175.1868 -433.867 cm BT -/F8 9.9626 Tf 180.1681 433.867 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(ext_index)]TJ/F8 9.9626 Tf 50.3939 0 Td[(list;)]TJ -ET -1 0 0 1 94.9141 413.3782 cm +/F8 9.9626 Tf 180.168 433.867 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.387 0 Td [(ext_index)]TJ/F8 9.9626 Tf 50.394 0 Td [(list;)]TJ 0 g 0 G -1 0 0 1 -94.9141 -413.3782 cm -BT -/F29 9.9626 Tf 99.8954 413.3782 Td[(ps)1(b)]TJ +/F27 9.9626 Tf -257.054 -20.489 Td [(psb)]TJ ET -1 0 0 1 117.8319 413.3782 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 117.832 413.577 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -117.8319 -413.3782 cm BT -/F29 9.9626 Tf 121.269 413.3782 Td[(comm)]TJ +/F27 9.9626 Tf 121.269 413.378 Td [(comm)]TJ ET -1 0 0 1 151.8718 413.3782 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 151.872 413.577 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -151.8718 -413.3782 cm BT -/F29 9.9626 Tf 155.3089 413.3782 Td[(o)32(vr)]TJ +/F27 9.9626 Tf 155.309 413.378 Td [(o)32(vr)]TJ ET -1 0 0 1 172.1717 413.3782 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 172.172 413.577 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -175.6088 -413.3782 cm BT -/F8 9.9626 Tf 180.5901 413.3782 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(ovrlap_index)]TJ/F8 9.9626 Tf 66.085 0 Td[(list;)]TJ -ET -1 0 0 1 94.9141 392.8894 cm +/F8 9.9626 Tf 180.59 413.378 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.387 0 Td [(ovrlap_index)]TJ/F8 9.9626 Tf 66.085 0 Td [(list;)]TJ 0 g 0 G -1 0 0 1 -94.9141 -392.8894 cm -BT -/F29 9.9626 Tf 99.8954 392.8894 Td[(ps)1(b)]TJ +/F27 9.9626 Tf -273.167 -20.489 Td [(psb)]TJ ET -1 0 0 1 117.8319 392.8894 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 117.832 393.089 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -117.8319 -392.8894 cm BT -/F29 9.9626 Tf 121.269 392.8894 Td[(comm)]TJ +/F27 9.9626 Tf 121.269 392.889 Td [(comm)]TJ ET -1 0 0 1 151.8718 392.8894 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 151.872 393.089 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -151.8718 -392.8894 cm BT -/F29 9.9626 Tf 155.3089 392.8894 Td[(mo)32(v)]TJ +/F27 9.9626 Tf 155.309 392.889 Td [(mo)32(v)]TJ ET -1 0 0 1 177.0008 392.8894 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 177.001 393.089 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -180.4379 -392.8894 cm BT -/F8 9.9626 Tf 185.4192 392.8894 Td[(Ex)1(c)27(han)1(ge)-334(d)1(ata)-334(b)1(as)-1(ed)-333(on)-333(th)1(e)]TJ/F32 9.9626 Tf 126.3874 0 Td[(ovr_mst_idx)]TJ/F8 9.9626 Tf 60.8546 0 Td[(list;)]TJ/F18 11.9552 Tf -272.7658 -28.6359 Td[(3.)-1(2)-1125(Spar)-1(se)-375(Matr)-1(ix)-375(dat)-1(a)-374(st)-1(ruct)-1(ure)]TJ/F8 9.9626 Tf 0 -18.6516 Td[(The)]TJ/F32 9.9626 Tf 19.7465 0 Td[(psb)]TJ +/F8 9.9626 Tf 185.419 392.889 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.388 0 Td [(ovr_mst_idx)]TJ/F8 9.9626 Tf 60.854 0 Td [(list;)]TJ/F16 11.9552 Tf -272.766 -28.635 Td [(3.2)-1125(Sparse)-375(Matrix)-375(data)-375(structure)]TJ/F8 9.9626 Tf 0 -18.652 Td [(The)]TJ/F30 9.9626 Tf 19.747 0 Td [(psb)]TJ ET -1 0 0 1 135.9605 345.602 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 135.96 345.801 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -135.9605 -345.602 cm BT -/F32 9.9626 Tf 139.0987 345.602 Td[(spmat)]TJ +/F30 9.9626 Tf 139.099 345.602 Td [(spmat)]TJ ET -1 0 0 1 165.878 345.602 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 165.878 345.801 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -165.878 -345.602 cm BT -/F32 9.9626 Tf 169.0162 345.602 Td[(type)]TJ/F8 9.9626 Tf 23.51 0 Td[(dat)1(a)-260(s)-1(tr)1(uctur)1(e)-261(con)28(tain)1(s)-260(all)-260(in)1(for)1(m)-1(ati)1(on)-260(ab)-27(out)-259(lo)-28(cal)-260(p)-27(ortion)]TJ -92.6308 -11.9552 Td[(of)-374(th)1(e)-375(spar)1(s)-1(e)-375(matr)1(ix)-374(and)-374(i)1(ts)-375(storage)-374(m)-1(o)-28(d)1(e)-1(.)-566(Most)-375(of)-373(thes)-1(e)-374(\014elds)-374(are)-375(set)-374(b)28(y)-374(the)]TJ 0 -11.9552 Td[(to)-28(ol)1(s)-350(r)1(outi)1(nes)-350(wh)1(e)-1(n)-348(in)1(s)-1(ertin)1(g)-349(a)-348(new)-349(s)-1(p)1(arse)-350(matri)1(x;)-356(the)-349(u)1(s)-1(er)-349(n)1(e)-1(eds)-349(on)1(ly)-348(c)27(ho)-27(os)-1(e,)]TJ 0 -11.9551 Td[(if)-333(h)1(e)-1(/she)-333(s)-1(o)-333(whishes)-1(,)-333(a)-333(s)-1(p)-27(ec)-1(i\014)1(c)-334(matrix)-333(storage)-334(mo)-28(d)1(e)-1(.)]TJ -ET -1 0 0 1 94.9141 277.4334 cm +/F30 9.9626 Tf 169.016 345.602 Td [(type)]TJ/F8 9.9626 Tf 23.51 0 Td [(data)-260(structure)-260(con)28(tains)-260(all)-259(information)-260(ab)-28(out)-260(lo)-27(cal)-260(p)-28(ortion)]TJ -92.631 -11.955 Td [(of)-374(the)-374(sparse)-375(matrix)-374(and)-374(its)-374(storage)-374(mo)-28(de.)-567(Most)-374(of)-374(these)-375(\014elds)-374(are)-374(set)-374(b)28(y)-375(the)]TJ 0 -11.955 Td [(to)-28(ols)-349(r)1(outines)-349(when)-349(inserting)-348(a)-349(new)-349(sparse)-348(matrix;)-357(the)-348(user)-349(needs)-349(only)-348(c)27(ho)-27(ose,)]TJ 0 -11.956 Td [(if)-333(he/she)-334(so)-333(whishes,)-333(a)-334(sp)-28(eci\014c)-333(matrix)-333(storage)-334(mo)-27(de.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -277.4334 cm -BT -/F29 9.9626 Tf 99.8954 277.4334 Td[(aspk)]TJ -ET -1 0 0 1 122.3956 277.4334 cm +/F27 9.9626 Tf 0 -32.303 Td [(aspk)]TJ 0 g 0 G -1 0 0 1 -122.3956 -277.4334 cm -BT -/F8 9.9626 Tf 127.3769 277.4334 Td[(Con)28(tain)1(s)-334(v)56(alues)-334(of)-333(th)1(e)-334(lo)-27(c)-1(al)-333(di)1(s)-1(tr)1(ibu)1(te)-1(d)-333(spar)1(s)-1(e)-333(m)-1(atr)1(ix.)]TJ -2.5749 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-430(as:)-639(an)-431(all)1(o)-28(c)-1(atab)1(le)-431(arr)1(a)27(y)-430(of)-431(r)1(ank)-430(one)-431(of)-430(t)27(y)1(p)-28(e)-431(corres)-1(p)-27(ond)1(in)1(g)-431(to)]TJ 0 -11.9552 Td[(matrix)-333(en)28(tri)1(e)-1(s)-334(t)28(y)1(p)-28(e.)]TJ -ET -1 0 0 1 94.9141 233.0342 cm +/F8 9.9626 Tf 27.482 0 Td [(Con)28(tains)-334(v)56(alues)-333(of)-334(the)-333(lo)-28(cal)-333(distributed)-333(sparse)-334(matrix.)]TJ -2.575 -11.955 Td [(Sp)-28(eci\014ed)-431(as:)-639(an)-431(allo)-27(catable)-431(arra)28(y)-431(of)-431(rank)-431(one)-430(of)-431(t)28(yp)-28(e)-431(corresp)-28(onding)-430(to)]TJ 0 -11.955 Td [(matrix)-333(en)27(tr)1(ie)-1(s)-333(t)28(yp)-28(e.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -233.0342 cm -BT -/F29 9.9626 Tf 99.8954 233.0342 Td[(ia1)]TJ -ET -1 0 0 1 114.3757 233.0342 cm +/F27 9.9626 Tf -24.907 -20.489 Td [(ia1)]TJ 0 g 0 G -1 0 0 1 -114.3757 -233.0342 cm -BT -/F8 9.9626 Tf 119.357 233.0342 Td[(Hold)1(s)-267(in)28(t)1(e)-1(ger)-266(inf)1(ormation)-266(on)-265(distri)1(bu)1(te)-1(d)-266(spar)1(s)-1(e)-266(m)-1(atr)1(ix.)-422(Actual)-266(i)1(nf)1(ormation)]TJ 5.445 -11.9551 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(dat)1(a)-334(f)1(ormat)-334(u)1(s)-1(ed.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ -ET -1 0 0 1 94.9141 188.6351 cm +/F8 9.9626 Tf 19.462 0 Td [(Holds)-266(in)28(teger)-267(inf)1(ormation)-267(on)-266(distributed)-266(sparse)-266(matrix.)-422(Actual)-266(information)]TJ 5.445 -11.955 Td [(will)-333(dep)-28(end)-333(on)-334(data)-333(format)-333(used.)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(allo)-28(catable)-333(in)28(teger)-333(arra)27(y)-333(of)-333(rank)-334(on)1(e)-1(.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -188.6351 cm -BT -/F29 9.9626 Tf 99.8954 188.6351 Td[(ia2)]TJ -ET -1 0 0 1 114.3757 188.6351 cm +/F27 9.9626 Tf -24.907 -20.489 Td [(ia2)]TJ 0 g 0 G -1 0 0 1 -114.3757 -188.6351 cm -BT -/F8 9.9626 Tf 119.357 188.6351 Td[(Hold)1(s)-267(in)28(t)1(e)-1(ger)-266(inf)1(ormation)-266(on)-265(distri)1(bu)1(te)-1(d)-266(spar)1(s)-1(e)-266(m)-1(atr)1(ix.)-422(Actual)-266(i)1(nf)1(ormation)]TJ 5.445 -11.9552 Td[(will)-333(d)1(e)-1(p)-27(e)-1(n)1(d)-333(on)-333(dat)1(a)-334(f)1(ormat)-334(u)1(s)-1(ed.)]TJ 0 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(allo)-27(c)-1(atab)1(le)-334(in)29(te)-1(ger)-333(arra)28(y)-333(of)-333(r)1(ank)-333(one.)]TJ -ET -1 0 0 1 94.9141 144.236 cm +/F8 9.9626 Tf 19.462 0 Td [(Holds)-266(in)28(teger)-267(inf)1(ormation)-267(on)-266(distributed)-266(sparse)-266(matrix.)-422(Actual)-266(information)]TJ 5.445 -11.955 Td [(will)-333(dep)-28(end)-333(on)-334(data)-333(format)-333(used.)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(allo)-28(catable)-333(in)28(teger)-333(arra)27(y)-333(of)-333(rank)-334(on)1(e)-1(.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -144.236 cm -BT -/F29 9.9626 Tf 99.8954 144.236 Td[(inf)-1(oa)]TJ -ET -1 0 0 1 124.2414 144.236 cm +/F27 9.9626 Tf -24.907 -20.489 Td [(infoa)]TJ 0 g 0 G -1 0 0 1 -124.2414 -144.236 cm -BT -/F8 9.9626 Tf 129.2228 144.236 Td[(On)-434(en)28(try)-434(c)-1(an)-434(h)1(old)-434(auxi)1(liary)-434(in)1(formation)-434(on)-434(di)1(s)-1(tr)1(ibu)1(te)-1(d)-434(sparse)-435(matrix.)]TJ -4.4208 -11.9552 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Td [(are)-333(complex)-334(v)28(ectors)-333(then)-334(it)-333(computes)-333(dot-pro)-28(duct)-333(as:)]TJ/F11 9.9626 Tf 80.747 -21.053 Td [(dot)]TJ/F14 9.9626 Tf 16.38 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F10 6.9738 Tf 5.693 4.114 Td [(H)]TJ/F11 9.9626 Tf 7.557 -4.114 Td [(y)]TJ/F16 14.3462 Tf -190.415 -41.894 Td [(Syn)31(tax)]TJ/F8 9.9626 Tf 108.523 -21.821 Td [(psb)]TJ ET -1 0 0 1 274.8246 511.0362 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 224.015 513.189 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -274.8246 -511.0362 cm BT -/F8 9.9626 Tf 277.8134 511.0362 Td[(gedot)-333(\050)]TJ/F19 9.9626 Tf 30.995 0 Td[(x,)-357(y,)-357(desc)]TJ +/F8 9.9626 Tf 227.004 512.99 Td [(gedot)-333(\050)]TJ/F17 9.9626 Tf 30.995 0 Td [(x,)-358(y,)-357(desc)]TJ ET -1 0 0 1 350.4486 511.0362 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.0552 0.1992 l -S +1 0 0 1 299.639 513.189 cm +[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S Q -1 0 0 1 -350.4486 -511.0362 cm BT -/F19 9.9626 Tf 353.5038 511.0362 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ -ET -1 0 0 1 150.7049 484.7309 cm +/F17 9.9626 Tf 302.694 512.99 Td [(a,)-358(info)]TJ/F8 9.9626 Tf 28.515 0 Td [(\051)]TJ 0 g 0 G -1 0 0 1 79.8395 -21.0211 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.9813 20.6226 cm +ET q -[]0 d -0 J -0.3985 w -0 0.1992 m -174.0695 0.1992 l -S +1 0 0 1 183.665 486.736 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S Q -1 0 0 1 -235.5257 -484.3324 cm BT -/F11 9.9626 Tf 241.5033 475.9639 Td[(dot)]TJ/F8 9.9626 Tf 13.6122 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(y)]TJ/F29 9.9626 Tf 86.8239 0 Td[(F)96(unction)]TJ +/F11 9.9626 Tf 189.642 478.168 Td [(dot)]TJ/F8 9.9626 Tf 13.612 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F27 9.9626 Tf 88.927 0 Td [(F)96(unction)]TJ ET -1 0 0 1 235.5257 471.9788 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -174.0695 0.1992 l -S +1 0 0 1 183.665 474.382 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S Q -1 0 0 1 -235.5257 -471.9788 cm BT -/F8 9.9626 Tf 241.5033 463.6102 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-3103(psb)]TJ +/F8 9.9626 Tf 189.642 465.814 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ ET -1 0 0 1 375.407 463.6102 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 325.649 466.013 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -375.407 -463.6102 cm BT -/F8 9.9626 Tf 378.3958 463.6102 Td[(gedot)]TJ -136.8925 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 328.638 465.814 Td [(gedot)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ ET -1 0 0 1 375.407 451.655 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 325.649 454.058 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -375.407 -451.655 cm BT -/F8 9.9626 Tf 378.3958 451.655 Td[(gedot)]TJ +/F8 9.9626 Tf 328.638 453.859 Td [(gedot)]TJ -138.996 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ ET -1 0 0 1 235.5257 447.6699 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -174.0695 0.1992 l -S +1 0 0 1 325.649 442.103 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 43.3513 -27.84 cm -0 g 0 G -1 0 0 1 -278.877 -419.8299 cm BT -/F8 9.9626 Tf 278.877 419.8299 Td[(T)83(ab)1(le)-334(2:)-444(Data)-333(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 328.638 441.904 Td [(gedot)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ ET -1 0 0 1 366.2439 419.8299 cm -0 g 0 G -1 0 0 1 -215.539 -1.9372 cm -0 g 0 G -1 0 0 1 -4.9813 -31.0471 cm -0 g 0 G -1 0 0 1 -145.7236 -386.8456 cm +q +1 0 0 1 325.649 430.148 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q BT -/F29 9.9626 Tf 150.7049 386.8456 Td[(T)32(yp)-32(e:)]TJ +/F8 9.9626 Tf 328.638 429.949 Td [(gedot)]TJ ET -1 0 0 1 179.5203 386.8456 cm +q +1 0 0 1 183.665 426.163 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S +Q 0 g 0 G -1 0 0 1 -179.5203 -386.8456 cm BT -/F8 9.9626 Tf 184.5016 386.8456 Td[(Sy)1(nc)27(h)1(ron)1(ous.)]TJ -ET -1 0 0 1 145.7236 367.0161 cm +/F8 9.9626 Tf 228.067 398.124 Td [(T)83(able)-333(2:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G -1 0 0 1 -145.7236 -367.0161 cm -BT -/F29 9.9626 Tf 150.7049 367.0161 Td[(On)-383(En)32(tr)1(y)]TJ -ET -1 0 0 1 198.2901 367.0161 cm 0 g 0 G -1 0 0 1 -52.5665 -19.8296 cm 0 g 0 G -1 0 0 1 -145.7236 -347.1865 cm -BT -/F29 9.9626 Tf 150.7049 347.1865 Td[(x)]TJ -ET -1 0 0 1 156.7516 347.1865 cm +/F27 9.9626 Tf -128.172 -32.109 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -1 0 0 1 -156.7516 -347.1865 cm -BT -/F8 9.9626 Tf 161.7329 347.1865 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -167.933 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-474(as:)-727(an)-474(arr)1(a)27(y)-474(of)-474(ran)1(k)-475(on)1(e)-475(or)-474(t)27(w)28(o)-475(con)28(tai)1(nin)1(g)-475(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-474(t)27(y)1(p)-28(e)]TJ 0 -11.9551 Td[(sp)-28(ec)-1(i)1(\014ed)-333(in)-333(T)83(ab)1(le)]TJ -ET -1 0 0 1 254.8146 287.4107 cm +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.579 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.579 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-474(of)-475(rank)-475(on)1(e)-475(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -254.8146 -287.4107 cm -BT -/F8 9.9626 Tf 254.8146 287.4107 Td[(2)]TJ -ET -1 0 0 1 259.7959 287.4107 cm + [-333(2)]TJ 0 g 0 G -1 0 0 1 -259.7959 -287.4107 cm -BT -/F8 9.9626 Tf 259.7959 287.4107 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.9626 Tf 62.0176 0 Td[(x)]TJ/F8 9.9626 Tf 9.0148 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.9626 Tf 91.7117 0 Td[(y)]TJ/F8 9.9626 Tf 5.242 0 Td[(.)]TJ -ET -1 0 0 1 145.7235 267.5812 cm + [(.)-445(The)-333(rank)-333(of)]TJ/F11 9.9626 Tf 146.202 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(m)28(ust)-334(b)-27(e)-334(the)-333(same)-333(of)]TJ/F11 9.9626 Tf 91.712 0 Td [(y)]TJ/F8 9.9626 Tf 5.241 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -267.5812 cm -BT -/F29 9.9626 Tf 150.7049 267.5812 Td[(y)]TJ -ET -1 0 0 1 156.7516 267.5812 cm +/F27 9.9626 Tf -277.077 -19.58 Td [(y)]TJ 0 g 0 G -1 0 0 1 -156.7516 -267.5812 cm -BT -/F8 9.9626 Tf 161.7329 267.5812 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(y)]TJ/F8 9.9626 Tf 5.242 0 Td[(.)]TJ -167.4811 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-474(as:)-727(an)-474(arr)1(a)27(y)-474(of)-474(ran)1(k)-475(on)1(e)-475(or)-474(t)27(w)28(o)-475(con)28(tai)1(nin)1(g)-475(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-474(t)27(y)1(p)-28(e)]TJ 0 -11.9552 Td[(sp)-28(ec)-1(i)1(\014ed)-333(in)-333(T)83(ab)1(le)]TJ -ET -1 0 0 1 254.8146 207.8053 cm +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-474(of)-475(rank)-475(on)1(e)-475(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -254.8146 -207.8053 cm -BT -/F8 9.9626 Tf 254.8146 207.8053 Td[(2)]TJ -ET -1 0 0 1 259.7959 207.8053 cm + [-333(2)]TJ 0 g 0 G -1 0 0 1 -259.7959 -207.8053 cm -BT -/F8 9.9626 Tf 259.7959 207.8053 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.9626 Tf 62.0176 0 Td[(y)]TJ/F8 9.9626 Tf 8.5628 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.9626 Tf 91.7118 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -ET -1 0 0 1 145.7235 187.9758 cm + [(.)-445(The)-333(rank)-333(of)]TJ/F11 9.9626 Tf 146.202 0 Td [(y)]TJ/F8 9.9626 Tf 8.563 0 Td [(m)28(ust)-334(b)-27(e)-334(the)-333(same)-333(of)]TJ/F11 9.9626 Tf 91.712 0 Td [(x)]TJ/F8 9.9626 Tf 5.693 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -187.9758 cm -BT -/F29 9.9626 Tf 150.7049 187.9758 Td[(desc)]TJ +/F27 9.9626 Tf -277.077 -19.58 Td [(desc)]TJ ET -1 0 0 1 172.6195 187.9758 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 121.81 168.346 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -172.6195 -187.9758 cm BT -/F29 9.9626 Tf 176.0566 187.9758 Td[(a)]TJ -ET -1 0 0 1 181.6259 187.9758 cm +/F27 9.9626 Tf 125.247 168.146 Td [(a)]TJ 0 g 0 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9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -346.5264 -140.1551 cm -BT -/F32 9.9626 Tf 346.5264 140.1551 Td[(psb)]TJ +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET -1 0 0 1 362.8451 140.1551 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 312.036 120.525 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -362.8451 -140.1551 cm BT -/F32 9.9626 Tf 365.9833 140.1551 Td[(desc)]TJ +/F30 9.9626 Tf 315.174 120.326 Td [(desc)]TJ ET -1 0 0 1 387.5322 140.1551 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 336.723 120.525 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -387.5322 -140.1551 cm -BT -/F32 9.9626 Tf 390.6705 140.1551 Td[(type)]TJ -ET -1 0 0 1 411.5918 140.1551 cm -0 g 0 G -1 0 0 1 -411.5918 -140.1551 cm BT -/F8 9.9626 Tf 411.5918 140.1551 Td[(.)]TJ -ET -1 0 0 1 145.7235 120.3256 cm +/F30 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Td[(th)1(e)-334(global)-333(p)-27(orti)1(on)-333(of)-333(the)-333(s)-1(p)1(ars)-1(e)-333(m)-1(atr)1(ix)]TJ/F11 9.9626 Tf 172.6031 0 Td[(T)]TJ/F8 9.9626 Tf 7.2056 0 Td[(.)]TJ -164.3389 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(t)28(yp)-27(e)-334(sp)-28(eci\014ed)-333(in)]TJ/F14 9.9626 Tf 211.3744 0 Td[(x)]TJ -ET -1 0 0 1 394.7346 590.8943 cm +/F8 9.9626 Tf 9.437 0 Td [(the)-333(global)-334(p)-27(ortion)-334(of)-333(the)-333(sparse)-334(matrix)]TJ/F11 9.9626 Tf 172.603 0 Td [(T)]TJ/F8 9.9626 Tf 7.206 0 Td [(.)]TJ -164.339 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(t)27(yp)-27(e)-334(sp)-28(eci\014ed)-333(in)]TJ/F14 9.9626 Tf 211.374 0 Td [(x)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -394.7346 -590.8943 cm -BT -/F8 9.9626 Tf 394.7346 590.8943 Td[(3)]TJ -ET -1 0 0 1 399.7159 590.8943 cm +/F8 9.9626 Tf 7.749 0 Td [(3)]TJ 0 g 0 G -1 0 0 1 -399.7159 -590.8943 cm -BT -/F8 9.9626 Tf 399.7159 590.8943 Td[(.)]TJ -ET -1 0 0 1 145.7235 571.3011 cm + [(.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -571.3011 cm -BT -/F29 9.9626 Tf 150.7049 571.3011 Td[(x)]TJ -ET -1 0 0 1 156.7516 571.3011 cm +/F27 9.9626 Tf -244.03 -19.593 Td [(x)]TJ 0 g 0 G -1 0 0 1 -156.7516 -571.3011 cm -BT -/F8 9.9626 Tf 161.7329 571.3011 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -167.933 -11.9551 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-289(as:)-423(a)-289(ran)1(k)-290(on)1(e)-290(or)-290(t)28(w)28(o)-290(arr)1(a)28(y)-290(con)28(tain)1(ing)-289(n)28(um)28(b)-27(e)-1(rs)-290(of)-289(t)28(yp)-27(e)-290(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)]TJ 0 -11.9552 Td[(in)-333(T)83(ab)1(le)]TJ -ET -1 0 0 1 214.6319 511.5253 cm +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-289(as:)-423(a)-290(ran)1(k)-290(one)-290(or)-289(t)28(w)27(o)-289(arra)27(y)-289(con)28(taining)-290(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-28(e)-290(sp)-28(eci\014ed)]TJ 0 -11.955 Td [(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -214.6319 -511.5253 cm -BT -/F8 9.9626 Tf 214.6319 511.5253 Td[(12)]TJ -ET -1 0 0 1 224.5946 511.5253 cm + [-333(12)]TJ 0 g 0 G -1 0 0 1 -224.5946 -511.5253 cm -BT -/F8 9.9626 Tf 224.5946 511.5253 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.9626 Tf 62.0175 0 Td[(x)]TJ/F8 9.9626 Tf 9.0148 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.9626 Tf 91.7118 0 Td[(y)]TJ/F8 9.9626 Tf 5.2419 0 Td[(.)]TJ -ET -1 0 0 1 145.7235 491.9321 cm + [(.)-445(The)-333(rank)-333(of)]TJ/F11 9.9626 Tf 111.001 0 Td [(x)]TJ/F8 9.9626 Tf 9.014 0 Td [(m)28(ust)-334(b)-27(e)-334(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 91.712 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -491.9321 cm -BT -/F29 9.9626 Tf 150.7049 491.9321 Td[(b)-32(eta)]TJ -ET -1 0 0 1 172.664 491.9321 cm +/F27 9.9626 Tf -241.876 -19.593 Td [(b)-32(eta)]TJ 0 g 0 G -1 0 0 1 -172.664 -491.9321 cm -BT -/F8 9.9626 Tf 177.6454 491.9321 Td[(th)1(e)-334(s)-1(calar)]TJ/F11 9.9626 Tf 45.4684 0 Td[(\014)]TJ/F8 9.9626 Tf 6.1609 0 Td[(.)]TJ -53.6632 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(global)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(n)28(um)28(b)-28(er)-333(of)-333(the)-333(data)-333(t)28(yp)-27(e)-334(in)1(dicate)-1(d)-332(in)-333(T)83(abl)1(e)]TJ -ET -1 0 0 1 433.8934 444.1114 cm +/F8 9.9626 Tf 26.941 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.468 0 Td [(\014)]TJ/F8 9.9626 Tf 6.161 0 Td [(.)]TJ -53.663 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)28(yp)-28(e)-334(ind)1(ic)-1(ated)-333(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -433.8934 -444.1114 cm -BT -/F8 9.9626 Tf 433.8934 444.1114 Td[(12)]TJ -ET -1 0 0 1 443.8561 444.1114 cm + [-333(12)]TJ 0 g 0 G -1 0 0 1 -443.8561 -444.1114 cm -BT -/F8 9.9626 Tf 443.8561 444.1114 Td[(.)]TJ -ET -1 0 0 1 145.7235 424.5182 cm + [(.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -424.5182 cm -BT -/F29 9.9626 Tf 150.7049 424.5182 Td[(y)]TJ -ET -1 0 0 1 156.7516 424.5182 cm +/F27 9.9626 Tf -24.907 -19.593 Td [(y)]TJ 0 g 0 G -1 0 0 1 -156.7516 -424.5182 cm -BT -/F8 9.9626 Tf 161.7329 424.5182 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 176.1177 0 Td[(y)]TJ/F8 9.9626 Tf 5.242 0 Td[(.)]TJ -167.4811 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(inout)]TJ/F8 9.9626 Tf 26.0964 0 Td[(.)]TJ -59.582 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-289(as:)-423(a)-289(ran)1(k)-290(on)1(e)-290(or)-290(t)28(w)28(o)-290(arr)1(a)28(y)-290(con)28(tain)1(ing)-289(n)28(um)28(b)-27(e)-1(rs)-290(of)-289(t)28(yp)-27(e)-290(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)]TJ 0 -11.9551 Td[(in)-333(T)83(ab)1(le)]TJ -ET -1 0 0 1 214.6319 364.7424 cm +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-289(as:)-423(a)-290(ran)1(k)-290(one)-290(or)-289(t)28(w)27(o)-289(arra)27(y)-289(con)28(taining)-290(n)28(um)28(b)-28(ers)-290(of)-289(t)28(yp)-28(e)-290(sp)-28(eci\014ed)]TJ 0 -11.955 Td [(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -214.6319 -364.7424 cm -BT -/F8 9.9626 Tf 214.6319 364.7424 Td[(12)]TJ -ET -1 0 0 1 224.5946 364.7424 cm + [-333(12)]TJ 0 g 0 G -1 0 0 1 -224.5946 -364.7424 cm -BT -/F8 9.9626 Tf 224.5946 364.7424 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.9626 Tf 62.0175 0 Td[(y)]TJ/F8 9.9626 Tf 8.5628 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.9626 Tf 91.7118 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -ET -1 0 0 1 145.7235 345.1492 cm + [(.)-445(The)-333(rank)-333(of)]TJ/F11 9.9626 Tf 111.001 0 Td [(y)]TJ/F8 9.9626 Tf 8.562 0 Td [(m)28(ust)-334(b)-27(e)-334(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 91.712 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -345.1492 cm -BT -/F29 9.9626 Tf 150.7049 345.1492 Td[(desc)]TJ +/F27 9.9626 Tf -241.876 -19.593 Td [(desc)]TJ ET -1 0 0 1 172.6195 345.1492 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 121.81 325.755 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -172.6195 -345.1492 cm BT -/F29 9.9626 Tf 176.0566 345.1492 Td[(a)]TJ -ET -1 0 0 1 181.6259 345.1492 cm +/F27 9.9626 Tf 125.247 325.556 Td [(a)]TJ 0 g 0 G -1 0 0 1 -181.6259 -345.1492 cm -BT -/F8 9.9626 Tf 186.6072 345.1492 Td[(con)28(tain)1(s)-334(data)-333(structu)1(re)-1(s)-333(for)-333(com)-1(m)28(un)1(ic)-1(ati)1(ons.)]TJ -10.9957 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3786 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ -ET -1 0 0 1 346.5264 297.3285 cm +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -346.5264 -297.3285 cm -BT -/F32 9.9626 Tf 346.5264 297.3285 Td[(psb)]TJ +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET -1 0 0 1 362.8451 297.3285 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 312.036 277.935 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -362.8451 -297.3285 cm BT -/F32 9.9626 Tf 365.9833 297.3285 Td[(desc)]TJ +/F30 9.9626 Tf 315.174 277.735 Td [(desc)]TJ ET -1 0 0 1 387.5322 297.3285 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 336.723 277.935 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -387.5322 -297.3285 cm BT -/F32 9.9626 Tf 390.6705 297.3285 Td[(type)]TJ -ET -1 0 0 1 411.5918 297.3285 cm +/F30 9.9626 Tf 339.861 277.735 Td [(type)]TJ 0 g 0 G -1 0 0 1 -411.5918 -297.3285 cm -BT -/F8 9.9626 Tf 411.5918 297.3285 Td[(.)]TJ -ET -1 0 0 1 145.7235 277.7353 cm +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -277.7353 cm -BT -/F29 9.9626 Tf 150.7049 277.7353 Td[(trans)]TJ -ET -1 0 0 1 176.3322 277.7353 cm +/F27 9.9626 Tf -260.887 -19.593 Td [(trans)]TJ 0 g 0 G -1 0 0 1 -176.3322 -277.7353 cm -BT -/F8 9.9626 Tf 181.3135 277.7353 Td[(sp)-28(ec)-1(i)1(fy)-333(with)]TJ/F19 9.9626 Tf 55.6802 0 Td[(unitd)]TJ/F8 9.9626 Tf 25.7256 0 Td[(th)1(e)-334(op)-28(erati)1(on)-333(to)-333(p)-28(erf)1(orm)-1(.)]TJ -ET -1 0 0 1 170.6302 258.1421 cm -0 g 0 G -1 0 0 1 -170.6302 -258.1421 cm -BT -/F29 9.9626 Tf 175.6115 258.1421 Td[(trans)-383(=)-383(')-1(N')]TJ -ET -1 0 0 1 233.1191 258.1421 cm +/F8 9.9626 Tf 30.609 0 Td [(sp)-28(ecify)-333(with)]TJ/F17 9.9626 Tf 55.68 0 Td [(unitd)]TJ/F8 9.9626 Tf 25.726 0 Td [(the)-333(op)-28(eration)-333(to)-334(p)-27(erform.)]TJ 0 g 0 G -1 0 0 1 -233.1191 -258.1421 cm -BT -/F8 9.9626 Tf 238.1004 258.1421 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(with)-333(n)1(o)-334(t)1(ransp)-27(os)-1(ed)-333(m)-1(at)1(rix)]TJ -ET -1 0 0 1 170.6302 242.534 cm +/F27 9.9626 Tf -87.108 -19.593 Td [(trans)-383(=)-384('N')]TJ 0 g 0 G -1 0 0 1 -170.6302 -242.534 cm -BT -/F29 9.9626 Tf 175.6115 242.534 Td[(trans)-383(=)-383(')-1(T')]TJ -ET -1 0 0 1 232.1229 242.534 cm +/F8 9.9626 Tf 62.489 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(no)-333(transp)-28(osed)-333(matrix)]TJ 0 g 0 G -1 0 0 1 -232.1229 -242.534 cm -BT -/F8 9.9626 Tf 237.1042 242.534 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(with)-333(t)1(ransp)-28(osed)-333(m)-1(atr)1(ix.)]TJ -ET -1 0 0 1 170.6302 226.9259 cm +/F27 9.9626 Tf -62.489 -15.608 Td [(trans)-383(=)-384('T')]TJ 0 g 0 G -1 0 0 1 -170.6302 -226.9259 cm -BT -/F29 9.9626 Tf 175.6115 226.9259 Td[(trans)-383(=)-383(')-1(C)1(')]TJ -ET -1 0 0 1 232.4273 226.9259 cm +/F8 9.9626 Tf 61.493 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(transp)-28(osed)-333(matrix.)]TJ 0 g 0 G -1 0 0 1 -232.4273 -226.9259 cm -BT -/F8 9.9626 Tf 237.4086 226.9259 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(with)-333(conj)1(ugate)-333(transp)-27(os)-1(ed)-333(matrix.)]TJ -61.7971 -19.5932 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3786 0 Td[(global)]TJ/F8 9.9626 Tf -32.3786 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6112 0 Td[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf -29.6112 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9551 Td[(Defau)1(lt:)]TJ/F11 9.9626 Tf 39.4356 0 Td[(tr)-28(ans)]TJ/F8 9.9626 Tf 27.0524 0 Td[(=)]TJ/F11 9.9626 Tf 10.5161 0 Td[(N)]TJ/F8 9.9626 Tf -77.0041 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(c)27(har)1(ac)-1(ter)-333(v)56(ariab)1(le)-1(.)]TJ -ET -1 0 0 1 145.7235 139.9188 cm +/F27 9.9626 Tf -61.493 -15.608 Td [(trans)-383(=)-384('C')]TJ 0 g 0 G -1 0 0 1 -145.7235 -139.9188 cm -BT -/F29 9.9626 Tf 150.7049 139.9188 Td[(unitd)]TJ -ET -1 0 0 1 177.4378 139.9188 cm +/F8 9.9626 Tf 61.797 0 Td 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Td[(th)1(e)-334(c)-1(omm)27(u)1(ni)1(c)-1(ation)-332(des)-1(crip)1(tor.)]TJ -10.9957 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ -ET -1 0 0 1 346.5264 391.1857 cm +/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td 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Td [(the)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(additional)-333(la)28(y)27(ers)-333(desired.)]TJ 10.378 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)]TJ/F11 9.9626 Tf 130.428 0 Td [(nl)]TJ/F14 9.9626 Tf 11.916 0 Td [(\025)]TJ/F8 9.9626 Tf 10.516 0 Td [(0.)]TJ 0 g 0 G -1 0 0 1 -145.7235 -302.7669 cm -BT -/F29 9.9626 Tf 150.7049 302.7669 Td[(ext)32(yp)-32(e)]TJ -ET -1 0 0 1 184.1211 302.7669 cm +/F27 9.9626 Tf -177.767 -20.299 Td [(ext)32(yp)-32(e)]TJ 0 g 0 G -1 0 0 1 -184.1211 -302.7669 cm -BT -/F8 9.9626 Tf 189.1024 302.7669 Td[(th)1(e)-334(kin)1(d)-333(of)-333(e)-1(stension)-333(requ)1(ired.)]TJ -13.4909 -11.9551 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0 g 0 G -1 0 0 1 -94.9141 -540.8585 cm -BT -/F29 9.9626 Tf 99.8954 540.8585 Td[(nz)]TJ -ET -1 0 0 1 111.3524 540.8585 cm + 0 -19.054 Td [(nz)]TJ 0 g 0 G -1 0 0 1 -111.3524 -540.8585 cm -BT -/F8 9.9626 Tf 116.3337 540.8585 Td[(th)1(e)-334(n)28(um)28(b)-27(e)-1(r)-333(of)-333(elem)-1(en)28(ts)-334(to)-333(b)-27(e)-334(in)1(s)-1(erted.)]TJ 8.4683 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(in)28(t)1(e)-1(ger)-333(s)-1(calar.)]TJ -ET -1 0 0 1 94.9141 473.0935 cm +/F8 9.9626 Tf 16.438 0 Td [(the)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(elemen)28(ts)-334(to)-333(b)-28(e)-333(inserted.)]TJ 8.468 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(sc)-1(alar)1(.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -473.0935 cm -BT -/F29 9.9626 Tf 99.8954 473.0935 Td[(ia)]TJ -ET -1 0 0 1 108.6472 473.0935 cm +/F27 9.9626 Tf -24.906 -19.054 Td [(ia)]TJ 0 g 0 G -1 0 0 1 -108.6472 -473.0935 cm -BT -/F8 9.9626 Tf 113.6285 473.0935 Td[(th)1(e)-334(ro)28(w)-334(i)1(ndi)1(c)-1(es)-334(of)-333(th)1(e)-334(e)-1(l)1(e)-1(me)-1(n)29(ts)-334(to)-333(b)-28(e)-333(inse)-1(r)1(te)-1(d)1(.)]TJ 11.1735 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(in)28(t)1(e)-1(ger)-333(arra)28(y)-333(of)-333(siz)-1(e)]TJ/F11 9.9626 Tf 160.9799 0 Td[(nz)]TJ/F8 9.9626 Tf 11.0512 0 Td[(.)]TJ -ET -1 0 0 1 94.9141 405.3285 cm +/F8 9.9626 Tf 13.733 0 Td [(the)-333(ro)27(w)-333(indices)-333(of)-334(th)1(e)-334(elemen)28(ts)-334(to)-333(b)-28(e)-333(inserted.)]TJ 11.173 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)-333(of)-333(size)]TJ/F11 9.9626 Tf 160.98 0 Td [(nz)]TJ/F8 9.9626 Tf 11.052 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -405.3285 cm -BT -/F29 9.9626 Tf 99.8954 405.3285 Td[(ja)]TJ -ET -1 0 0 1 108.9655 405.3285 cm +/F27 9.9626 Tf -196.938 -19.054 Td [(ja)]TJ 0 g 0 G -1 0 0 1 -108.9655 -405.3285 cm -BT -/F8 9.9626 Tf 113.9468 405.3285 Td[(th)1(e)-334(c)-1(ol)1(umn)-333(ind)1(ice)-1(s)-334(of)-332(the)-334(elem)-1(en)28(ts)-334(to)-333(b)-27(e)-334(in)1(s)-1(erted.)]TJ 10.8552 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(in)28(t)1(e)-1(ger)-333(arra)28(y)-333(of)-333(siz)-1(e)]TJ/F11 9.9626 Tf 160.9799 0 Td[(nz)]TJ/F8 9.9626 Tf 11.0512 0 Td[(.)]TJ -ET -1 0 0 1 94.9141 337.5635 cm +/F8 9.9626 Tf 14.051 0 Td [(the)-333(column)-334(indices)-333(of)-333(the)-334(elemen)28(ts)-333(to)-334(b)-27(e)-334(inserted.)]TJ 10.855 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)-333(of)-333(size)]TJ/F11 9.9626 Tf 160.98 0 Td [(nz)]TJ/F8 9.9626 Tf 11.051 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -337.5635 cm -BT -/F29 9.9626 Tf 99.8954 337.5635 Td[(v)64(al)]TJ -ET -1 0 0 1 114.0575 337.5635 cm +/F27 9.9626 Tf -196.937 -19.054 Td [(v)64(al)]TJ 0 g 0 G -1 0 0 1 -114.0575 -337.5635 cm -BT -/F8 9.9626 Tf 119.0388 337.5635 Td[(th)1(e)-334(e)-1(l)1(e)-1(me)-1(n)29(ts)-334(to)-333(b)-28(e)-333(inse)-1(r)1(te)-1(d)1(.)]TJ 5.7632 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.0731 0 Td[(.)]TJ -51.0239 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf 41.8983 0 Td[(.)]TJ -67.0817 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(an)-333(arr)1(a)27(y)-333(of)-333(size)]TJ/F11 9.9626 Tf 128.0201 0 Td[(nz)]TJ/F8 9.9626 Tf 11.0512 0 Td[(.)]TJ -ET -1 0 0 1 94.9141 269.7985 cm +/F8 9.9626 Tf 19.143 0 Td [(the)-333(elemen)27(ts)-333(to)-333(b)-28(e)-333(inse)-1(r)1(te)-1(d)1(.)]TJ 5.763 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-375(as:)-528(an)-375(arra)28(y)-375(of)-375(size)]TJ/F11 9.9626 Tf 130.933 0 Td [(nz)]TJ/F8 9.9626 Tf 11.051 0 Td [(.)-570(Must)-375(b)-28(e)-375(of)-375(the)-375(same)-375(t)28(yp)-28(e)-375(and)-375(kind)-375(of)]TJ -141.984 -11.955 Td [(the)]TJ/F30 9.9626 Tf 17.158 0 Td [(aspk)]TJ/F8 9.9626 Tf 24.242 0 Td [(comp)-28(onen)28(t)-333(of)-334(the)-333(sparse)-333(matrix)]TJ/F11 9.9626 Tf 141.858 0 Td [(a)]TJ/F8 9.9626 Tf 5.266 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -269.7985 cm -BT -/F29 9.9626 Tf 99.8954 269.7985 Td[(desc)]TJ +/F27 9.9626 Tf -213.43 -19.054 Td [(desc)]TJ ET -1 0 0 1 121.81 269.7985 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.4371 0.1992 l -S +1 0 0 1 172.619 266.915 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -1 0 0 1 -121.81 -269.7985 cm BT -/F29 9.9626 Tf 125.2471 269.7985 Td[(a)]TJ -ET -1 0 0 1 130.8165 269.7985 cm +/F27 9.9626 Tf 176.057 266.716 Td [(a)]TJ 0 g 0 G -1 0 0 1 -130.8165 -269.7985 cm -BT -/F8 9.9626 Tf 135.7978 269.7985 Td[(The)-334(comm)27(u)1(nication)-333(d)1(e)-1(sc)-1(r)1(iptor)1(.)]TJ -10.9958 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf 23.073 0 Td[(.)]TJ -55.4517 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf 41.8982 0 Td[(.)]TJ -71.5095 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(inout)]TJ/F8 9.9626 Tf 26.0964 0 Td[(.)]TJ -59.582 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(v)55(ar)1(iabl)1(e)-334(of)-333(t)28(yp)-27(e)]TJ -ET -1 0 0 1 262.1484 221.9779 cm +/F8 9.9626 Tf 10.55 0 Td [(The)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.51 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)56(ariable)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -1 0 0 1 -262.1484 -221.9779 cm -BT -/F32 9.9626 Tf 262.1484 221.9779 Td[(psb)]TJ +/F30 9.9626 Tf 137.347 0 Td [(psb)]TJ ET -1 0 0 1 278.467 221.9779 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 329.276 219.095 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -278.467 -221.9779 cm BT -/F32 9.9626 Tf 281.6052 221.9779 Td[(desc)]TJ +/F30 9.9626 Tf 332.415 218.895 Td [(desc)]TJ ET -1 0 0 1 303.1542 221.9779 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.1382 0.1992 l -S +1 0 0 1 353.964 219.095 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -1 0 0 1 -303.1542 -221.9779 cm BT -/F32 9.9626 Tf 306.2924 221.9779 Td[(type)]TJ -ET -1 0 0 1 327.2138 221.9779 cm +/F30 9.9626 Tf 357.102 218.895 Td [(type)]TJ 0 g 0 G -1 0 0 1 -327.2138 -221.9779 cm -BT -/F8 9.9626 Tf 327.2138 221.9779 Td[(.)]TJ -ET -1 0 0 1 94.9141 188.0906 cm +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -188.0906 cm -BT -/F29 9.9626 Tf 99.8954 188.0906 Td[(On)-383(R)-1(etur)1(n)]TJ -ET -1 0 0 1 154.4337 188.0906 cm +/F27 9.9626 Tf -227.318 -31.695 Td [(On)-383(Return)]TJ 0 g 0 G -1 0 0 1 -59.5196 -19.9443 cm 0 g 0 G -1 0 0 1 -94.9141 -168.1463 cm -BT -/F29 9.9626 Tf 99.8954 168.1463 Td[(a)]TJ -ET -1 0 0 1 105.4648 168.1463 cm + 0 -19.054 Td [(a)]TJ 0 g 0 G -1 0 0 1 -105.4648 -168.1463 cm -BT -/F8 9.9626 Tf 110.4461 168.1463 Td[(th)1(e)-334(m)-1(at)1(rix)-333(in)28(t)1(o)-334(whi)1(c)27(h)-333(ele)-1(men)28(ts)-334(will)-333(b)-27(e)-334(in)1(s)-1(erted.)]TJ 14.356 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 27.9508 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -27.9508 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 25.1834 0 Td[(required)]TJ/F8 9.9626 Tf -25.1834 -11.9552 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(inout)]TJ/F8 9.9626 Tf 26.0964 0 Td[(.)]TJ 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9.9626 Tf 4.982 0 Td [(A)]TJ/F14 9.9626 Tf 7.472 0 Td [(kk)]TJ/F11 9.9626 Tf 9.962 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(k)]TJ/F8 9.9626 Tf 7.195 0 Td [(+)]TJ/F14 9.9626 Tf 9.963 0 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(b)]TJ/F14 9.9626 Tf 4.276 0 Td [(k)]TJ/F8 9.9626 Tf 4.981 0 Td [(\051)]TJ/F11 9.9626 Tf 7.837 6.834 Td [(<)-278(eps)]TJ/F8 9.9626 Tf -211.034 -24.499 Td [(or)-333(the)-334(2-norm)-333(residual)-333(reduction)]TJ/F11 9.9626 Tf 133.771 -22.467 Td [(er)-28(r)]TJ/F8 9.9626 Tf 16.949 0 Td [(=)]TJ/F14 9.9626 Tf 12.179 6.739 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.316 1.494 Td [(k)]TJ ET -1 0 0 1 262.3274 549.814 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -18.7077 0.1992 l -S +1 0 0 1 313.137 550.013 cm +[]0 d 0 J 0.398 w 0 0 m 18.708 0 l S Q -1 0 0 1 -262.3274 -549.814 cm BT -/F14 9.9626 Tf 262.3274 540.6887 Td[(k)]TJ/F11 9.9626 Tf 4.9813 0 Td[(b)]TJ/F14 9.9626 Tf 4.2756 0 Td[(k)]TJ/F7 6.9738 Tf 4.9814 -1.4944 Td[(2)]TJ/F11 9.9626 Tf 8.4322 8.3283 Td[(<)-278(e)1(ps)]TJ/F8 9.9626 Tf -185.1025 -25.0525 Td[(acc)-1(ord)1(in)1(g)-413(to)-412(th)1(e)-413(v)56(alue)-412(pass)-1(ed)-412(thr)1(ough)-412(th)1(e)-413(istop)-412(argu)1(m)-1(en)28(t)-412(\050se)-1(e)-412(late)-1(r)1(\051.)-681(In)-412(the)]TJ 0 -11.9552 Td[(ab)-27(o)27(v)28(e)-320(f)1(orm)27(u)1(lae,)]TJ/F11 9.9626 Tf 71.7384 0 Td[(x)]TJ/F10 6.9738 Tf 5.6939 -1.4944 Td[(i)]TJ/F8 9.9626 Tf 6.5034 1.4944 Td[(is)-320(the)-320(ten)28(tativ)28(e)-320(solut)1(ion)-320(an)1(d)]TJ/F11 9.9626 Tf 125.3559 0 Td[(r)]TJ/F10 6.9738 Tf 4.4947 -1.4944 Td[(i)]TJ/F8 9.9626 Tf 6.0842 1.4944 Td[(=)]TJ/F11 9.9626 Tf 10.5161 0 Td[(b)]TJ/F14 9.9626 Tf 6.2208 0 Td[(\000)]TJ/F11 9.9626 Tf 9.6939 0 Td[(Ax)]TJ/F10 6.9738 Tf 13.1659 -1.4944 Td[(i)]TJ/F8 9.9626 Tf 6.5034 1.4944 Td[(th)1(e)-321(corresp)-28(on)1(din)1(g)]TJ -265.9706 -11.9552 Td[(res)-1(i)1(du)1(al)-334(at)-333(th)1(e)]TJ/F11 9.9626 Tf 66.5007 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(-th)-333(iteration)1(.)]TJ/F18 14.3462 Tf -69.933 -32.4803 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 0 -21.8209 Td[(call)-333(psb)]TJ +/F14 9.9626 Tf 313.137 540.689 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(b)]TJ/F14 9.9626 Tf 4.276 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.495 Td [(2)]TJ/F11 9.9626 Tf 8.432 8.329 Td [(<)-278(eps)]TJ/F8 9.9626 Tf -185.102 -25.053 Td [(according)-412(to)-413(the)-412(v)56(alue)-413(passed)-412(through)-412(the)-412(istop)-413(argumen)28(t)-412(\050see)-413(later\051.)-681(In)-412(the)]TJ 0 -11.955 Td [(ab)-28(o)28(v)28(e)-320(form)28(ulae,)]TJ/F11 9.9626 Tf 71.738 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F8 9.9626 Tf 6.504 1.494 Td [(is)-320(the)-320(ten)28(tativ)28(e)-320(solution)-320(and)]TJ/F11 9.9626 Tf 125.355 0 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.494 Td [(i)]TJ/F8 9.9626 Tf 6.084 1.494 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(b)]TJ/F14 9.9626 Tf 6.221 0 Td [(\000)]TJ/F11 9.9626 Tf 9.694 0 Td [(Ax)]TJ/F10 6.9738 Tf 13.166 -1.494 Td [(i)]TJ/F8 9.9626 Tf 6.503 1.494 Td [(the)-320(corresp)-28(onding)]TJ -265.97 -11.955 Td [(residual)-333(at)-334(the)]TJ/F11 9.9626 Tf 66.501 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(-th)-333(iteration.)]TJ/F16 14.3462 Tf -69.933 -32.481 Td [(Syn)31(tax)]TJ/F8 9.9626 Tf 0 -21.82 Td [(call)-333(psb)]TJ ET -1 0 0 1 133.7573 444.2585 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S +1 0 0 1 184.567 444.458 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -1 0 0 1 -133.7573 -444.2585 cm BT -/F8 9.9626 Tf 136.7462 444.2585 Td[(kr)1(ylo)28(v)]TJ 27.7842 -11.9552 Td[(\050)]TJ/F19 9.9626 Tf 3.8744 0 Td[(metho)51(d,a,pr)52(e)51(c,b,x)1(,eps,desc)]TJ +/F8 9.9626 Tf 187.556 444.258 Td [(krylo)28(v)]TJ 4.87 -11.955 Td [(\050)]TJ/F17 9.9626 Tf 3.874 0 Td [(metho)51(d,a,pr)51(e)51(c,b,x,eps,)1(desc)]TJ ET -1 0 0 1 281.9692 432.3033 cm q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.0552 0.1992 l -S +1 0 0 1 309.865 432.503 cm +[]0 d 0 J 0.398 w 0 0 m 3.055 0 l S Q -1 0 0 1 -281.9692 -432.3033 cm BT -/F19 9.9626 Tf 285.0244 432.3033 Td[(a,i)1(n)-1(f)1(o,itmax,)1(iter,er)1(r,i)1(t)-1(r)52(ac)51(e,i)1(rst,is)1(t)-1(op)]TJ/F8 9.9626 Tf 154.7077 0 Td[(\051)]TJ -ET -1 0 0 1 94.9141 408.393 cm +/F17 9.9626 Tf 312.92 432.303 Td [(a,info,itmax,iter,err,itr)52(ac)51(e,irst,istop,c)51(ond)]TJ/F8 9.9626 Tf 177.622 0 Td [(\051)]TJ 0 g 0 G -1 0 0 1 -94.9141 -408.393 cm -BT -/F29 9.9626 Tf 99.8954 408.393 Td[(T)32(yp)-32(e:)]TJ -ET -1 0 0 1 128.7108 408.393 cm +/F27 9.9626 Tf -339.837 -23.91 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -1 0 0 1 -128.7108 -408.393 cm -BT -/F8 9.9626 Tf 133.6921 408.393 Td[(Sy)1(nc)27(h)1(ron)1(ous.)]TJ -ET -1 0 0 1 94.9141 389.5489 cm +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -389.5489 cm -BT -/F29 9.9626 Tf 99.8954 389.5489 Td[(On)-383(En)32(tr)1(y)]TJ -ET -1 0 0 1 147.4806 389.5489 cm +/F27 9.9626 Tf -33.797 -18.844 Td [(On)-383(En)32(try)]TJ 0 g 0 G -1 0 0 1 -52.5665 -18.8441 cm 0 g 0 G -1 0 0 1 -94.9141 -370.7048 cm -BT -/F29 9.9626 Tf 99.8954 370.7048 Td[(met)-1(ho)-31(d)]TJ -ET -1 0 0 1 137.9262 370.7048 cm + 0 -18.844 Td [(metho)-32(d)]TJ 0 g 0 G -1 0 0 1 -137.9262 -370.7048 cm -BT -/F8 9.9626 Tf 142.9075 370.7048 Td[(a)-235(s)-1(t)1(rin)1(g)-236(th)1(at)-235(de\014n)1(e)-1(s)-235(the)-235(iterativ)28(e)-235(m)-1(etho)-27(d)-235(to)-235(b)-27(e)-236(use)-1(d)1(.)-412(S)1(up)1(p)-28(or)1(te)-1(d)-234(v)55(al)1(ues)]TJ -18.1055 -11.9552 Td[(are:)]TJ -ET -1 0 0 1 119.8207 339.9055 cm +/F8 9.9626 Tf 43.012 0 Td [(a)-235(string)-235(that)-235(de\014nes)-235(the)-236(iterativ)28(e)-235(metho)-28(d)-235(to)-235(b)-28(e)-235(used.)-412(Supp)-27(orted)-235(v)55(alues)]TJ -18.105 -11.955 Td [(are:)]TJ 0 g 0 G -1 0 0 1 -119.8207 -339.9055 cm -BT -/F29 9.9626 Tf 124.802 339.9055 Td[(CG)]TJ -ET -1 0 0 1 142.0843 339.9055 cm +/F27 9.9626 Tf 0 -18.844 Td [(CG:)]TJ 0 g 0 G -1 0 0 1 -142.0843 -339.9055 cm -BT -/F8 9.9626 Tf 147.0657 339.9055 Td[(:)-444(the)-333(C)-1(on)1(ju)1(gate)-334(Gr)1(adien)28(t)-333(m)-1(eth)1(o)-28(d;)]TJ -ET -1 0 0 1 119.8207 325.0465 cm +/F8 9.9626 Tf 25.446 0 Td [(the)-333(Conjugate)-334(Gradien)28(t)-333(metho)-28(d;)]TJ 0 g 0 G -1 0 0 1 -119.8207 -325.0465 cm -BT -/F29 9.9626 Tf 124.802 325.0465 Td[(CGS)]TJ -ET -1 0 0 1 148.4493 325.0465 cm +/F27 9.9626 Tf -25.446 -14.859 Td [(CGS:)]TJ 0 g 0 G -1 0 0 1 -148.4493 -325.0465 cm -BT -/F8 9.9626 Tf 153.4306 325.0465 Td[(:th)1(e)-334(Conj)1(ugate)-334(G)1(radi)1(e)-1(n)28(t)-333(S)1(tabil)1(iz)-1(ed)-333(me)-1(th)1(o)-28(d)1(;)]TJ -ET -1 0 0 1 119.8207 310.1874 cm +/F8 9.9626 Tf 31.811 0 Td [(the)-333(Conjugate)-334(Gradien)28(t)-333(Stabilized)-333(metho)-28(d;)]TJ 0 g 0 G -1 0 0 1 -119.8207 -310.1874 cm -BT -/F29 9.9626 Tf 124.802 310.1874 Td[(BICG)]TJ -ET -1 0 0 1 154.5791 310.1874 cm +/F27 9.9626 Tf -31.811 -14.86 Td [(BICG:)]TJ 0 g 0 G -1 0 0 1 -154.5791 -310.1874 cm -BT -/F8 9.9626 Tf 159.5604 310.1874 Td[(:)-444(the)-333(B)-1(i-Conj)1(ugate)-333(Grad)1(ie)-1(n)29(t)-334(metho)-28(d)1(;)]TJ -ET -1 0 0 1 119.8207 295.3284 cm +/F8 9.9626 Tf 37.94 0 Td [(the)-333(Bi-Conjugate)-334(Gradien)28(t)-333(metho)-28(d;)]TJ 0 g 0 G -1 0 0 1 -119.8207 -295.3284 cm -BT -/F29 9.9626 Tf 124.802 295.3284 Td[(BICGST)96(AB)]TJ -ET -1 0 0 1 184.7712 295.3284 cm +/F27 9.9626 Tf -37.94 -14.859 Td [(BICGST)96(AB:)]TJ 0 g 0 G -1 0 0 1 -184.7712 -295.3284 cm -BT -/F8 9.9626 Tf 189.7526 295.3284 Td[(:)-444(the)-333(B)-1(i-Conj)1(ugate)-333(Grad)1(ie)-1(n)29(t)-334(S)1(tabi)1(lize)-1(d)-333(me)-1(t)1(ho)-28(d)1(;)]TJ -ET -1 0 0 1 119.8207 280.4694 cm +/F8 9.9626 Tf 68.133 0 Td [(the)-333(Bi-Conjugate)-334(Gradien)28(t)-333(Stabilized)-333(metho)-28(d;)]TJ 0 g 0 G -1 0 0 1 -119.8207 -280.4694 cm -BT -/F29 9.9626 Tf 124.802 280.4694 Td[(BICGST)96(ABL)]TJ -ET -1 0 0 1 191.662 280.4694 cm +/F27 9.9626 Tf -68.133 -14.859 Td [(BICGST)96(ABL:)]TJ 0 g 0 G -1 0 0 1 -191.662 -280.4694 cm -BT -/F8 9.9626 Tf 196.6434 280.4694 Td[(:)-389(th)1(e)-223(Bi-Conju)1(gate)-223(G)1(radi)1(e)-1(n)28(t)-222(S)1(tabil)1(iz)-1(ed)-222(me)-1(t)1(ho)-28(d)-222(with)-221(res)-1(tar)1(t-)]TJ -49.9236 -11.9552 Td[(in)1(g;)]TJ -ET -1 0 0 1 119.8207 253.6552 cm +/F8 9.9626 Tf 75.023 0 Td [(the)-222(Bi-Conjugate)-222(G)-1(r)1(adien)27(t)-222(Stabilized)-222(metho)-28(d)-222(with)-222(restart-)]TJ -53.106 -11.955 Td [(ing;)]TJ 0 g 0 G -1 0 0 1 -119.8207 -253.6552 cm -BT -/F29 9.9626 Tf 124.802 253.6552 Td[(R)31(GM)1(R)-1(E)1(S)]TJ -ET -1 0 0 1 175.4452 253.6552 cm +/F27 9.9626 Tf -21.917 -14.859 Td [(R)32(GMRES:)]TJ 0 g 0 G -1 0 0 1 -175.4452 -253.6552 cm -BT -/F8 9.9626 Tf 180.4265 253.6552 Td[(:)-444(the)-333(Ge)-1(n)1(e)-1(r)1(alize)-1(d)-333(M)1(ini)1(m)-1(al)-333(Res)-1(id)1(ual)-333(me)-1(th)1(o)-28(d)-333(with)-333(r)1(e)-1(starti)1(ng.)]TJ -ET -1 0 0 1 94.9141 234.8111 cm +/F8 9.9626 Tf 58.807 0 Td [(the)-333(Generalized)-334(Minimal)-333(Residual)-333(metho)-28(d)-333(with)-334(restarting.)]TJ 0 g 0 G -1 0 0 1 -94.9141 -234.8111 cm -BT -/F29 9.9626 Tf 99.8954 234.8111 Td[(a)]TJ -ET -1 0 0 1 105.4647 234.8111 cm +/F27 9.9626 Tf -83.714 -18.844 Td [(a)]TJ 0 g 0 G -1 0 0 1 -105.4647 -234.8111 cm -BT -/F8 9.9626 Tf 110.4461 234.8111 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(glob)1(al)-333(s)-1(p)1(arse)-334(m)-1(at)1(rix)]TJ/F11 9.9626 Tf 178.9681 0 Td[(A)]TJ/F8 9.9626 Tf 7.472 0 Td[(.)]TJ -172.0842 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(lo)-32(ca)-1(l)]TJ/F8 9.9626 Tf -32.3787 -11.9552 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf -29.6113 -11.9551 Td[(In)28(ten)28(t:)]TJ/F29 9.9626 Tf 33.4856 0 Td[(in)]TJ/F8 9.9626 Tf 9.5475 0 Td[(.)]TJ -43.0331 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(dat)1(a)-334(of)-333(t)28(yp)-27(e)]TJ -ET -1 0 0 1 295.717 186.9904 cm +/F8 9.9626 Tf 10.551 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(sparse)-333(matrix)]TJ/F11 9.9626 Tf 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694 /CapHeight 683 /Descent -194 -/FontName /VLRIEC+CMSY10 -/ItalicAngle -14.035 -/StemV 85 +/ItalicAngle 0 +/StemV 69 /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 632 0 R ->> endobj -1614 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 -1613 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] +/CharSet (/A/B/C/D/E/F/G/H/I/J/K/L/M/N/O/P/R/S/T/U/V/W/a/ampersand/b/bracketleft/bracketright/c/colon/comma/d/e/eight/endash/equal/f/ff/ffi/fi/five/fl/four/g/h/hyphen/i/j/k/l/m/n/nine/o/one/p/parenleft/parenright/period/plus/q/quotedblleft/quotedblright/quoteright/r/s/semicolon/seven/six/slash/t/three/two/u/v/w/x/y/z/zero) +/FontFile 1604 0 R >> endobj -629 0 obj << -/Length1 907 -/Length2 3553 -/Length3 532 -/Length 4992 +1606 0 obj << +/Length1 769 +/Length2 1408 +/Length3 0 +/Length 2177 >> stream -%!PS-AdobeFont-1.1: CMMI7 1.100 -%%CreationDate: 1996 Jul 23 07:53:53 +%!PS-AdobeFont-1.1: CMR6 1.0 +%%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.100) readonly def +/version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI7) readonly def +/FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def -/ItalicAngle -14.04 def +/ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /AKHTUB+CMMI7 def +/FontName /YPSQTS+CMR6 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 +dup 49 /one put +dup 51 /three put +dup 50 /two put readonly def -/FontBBox{0 -250 1171 750}readonly def +/FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ 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+/FontFile 1606 0 R >> endobj -1616 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 -1615 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 -626 0 obj << +1608 0 obj << /Length1 787 /Length2 1497 -/Length3 532 -/Length 2816 +/Length3 0 +/Length 2284 >> stream %!PS-AdobeFont-1.1: CMR7 1.0 @@ -34806,16 +19891,16 @@ stream /ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /RPAEZT+CMR7 def +/FontName /EWABFK+CMR7 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 58 /colon put dup 49 /one put -dup 50 /two put dup 51 /three put -dup 58 /colon put +dup 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end @@ -34827,624 +19912,408 @@ _2 àR • ‚k ½v`5ŽÑeMþT­$lÞ…üÓÀ¿zp¹H{R~¨#À 9ÛaýfA±@üí…€ØgAÒIKN|¡ñ Ë°¥2¾œ«ëp£è!/xé<˜³w®(€þ9ºâ”Q…}³IdÚ&¬¤Í#Î(JÎ7Ø•qÿËgÞzãy·K2ì¬ÅóÞfΞè éo'e¿ì³VÞTüÜW»œ¨‘ów Á½V8Ì8΄QÔvƒˆÌJîÐ5mz}ç6Íï,š'U®®°¡‚†yÍež ½çXÁ@gÚÕÿÇÌô4qGagkôìKÝ“=-ïžB¡{­EŒ -¡b›x}‰èË÷…¹Òºz’™­ºs7'þõ¸­)Æãõ8-X“ûTåG`û‡9?óPíe•úã“:– “^­‘3¶›‚~§ÍhécîxbkÜå1!o^ëå™KÙWk«ìi7ݱ‚=3OÿÕá£ßø äô¼|ó0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -0000000000000000000000000000000000000000000000000000000000000000 -cleartomark +¡b›x}‰èË÷…¹Òºz’™­ºs7'þõ¸­)Æãõ8-X“ûTåG`û‡9?óPíe•úã“:– “^­‘3¶›‚~§ÍhécîxbkÜå1!o^ëå™KÙWk«ìi7ݱ‚=3OÿÕá£ßø äô¼|ó endstream endobj -627 0 obj << -/Type /Font -/Subtype /Type1 -/Encoding 1617 0 R -/FirstChar 49 -/LastChar 58 -/Widths 1618 0 R -/BaseFont /RPAEZT+CMR7 -/FontDescriptor 625 0 R ->> endobj -625 0 obj << +1609 0 obj << +/Type /FontDescriptor +/FontName /EWABFK+CMR7 +/Flags 4 +/FontBBox [-27 -250 1122 750] /Ascent 694 /CapHeight 683 /Descent -194 -/FontName /RPAEZT+CMR7 /ItalicAngle 0 /StemV 79 /XHeight 431 -/FontBBox [-27 -250 1122 750] -/Flags 4 -/CharSet (/one/two/three/colon) -/FontFile 626 0 R +/CharSet (/colon/one/three/two) +/FontFile 1608 0 R >> endobj -1618 0 obj -[569 569 569 0 0 0 0 0 0 323 ] -endobj -1617 0 obj << -/Type /Encoding -/Differences [ 0 /.notdef 49/one/two/three 52/.notdef 58/colon 59/.notdef] ->> endobj -621 0 obj << -/Length1 1775 -/Length2 11063 -/Length3 532 -/Length 13370 +1610 0 obj << +/Length1 1462 +/Length2 8120 +/Length3 0 +/Length 9582 >> stream -%!PS-AdobeFont-1.1: CMTT10 1.00B -%%CreationDate: 1992 Apr 26 10:42:42 +%!PS-AdobeFont-1.1: CMR8 1.0 +%%CreationDate: 1991 Aug 20 16:39:40 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.00B) readonly def +/version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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All Rights Reserved) readonly def -/FullName (CMTI12) readonly def +/FullName (CMTT10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def -/ItalicAngle -14.04 def -/isFixedPitch false def +/ItalicAngle 0 def +/isFixedPitch true def end readonly def -/FontName /UCFMZL+CMTI12 def +/FontName /XUVRTY+CMTT10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def @@ -35803,160 +20579,165 @@ end readonly def 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 66 /B put +dup 67 /C put +dup 68 /D put +dup 69 /E put +dup 70 /F put +dup 73 /I put +dup 75 /K put dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put dup 80 /P put +dup 82 /R put dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 87 /W put +dup 89 /Y put dup 97 /a put +dup 126 /asciitilde put +dup 42 /asterisk put dup 98 /b put +dup 92 /backslash put dup 99 /c put +dup 58 /colon put +dup 44 /comma put dup 100 /d put dup 101 /e put +dup 61 /equal put dup 102 /f put +dup 53 /five put +dup 52 /four put dup 103 /g put dup 104 /h put +dup 45 /hyphen put dup 105 /i put +dup 106 /j put +dup 107 /k put dup 108 /l put +dup 109 /m put dup 110 /n put +dup 57 /nine put dup 111 /o put +dup 49 /one put dup 112 /p put +dup 40 /parenleft put +dup 41 /parenright put +dup 46 /period put +dup 43 /plus put +dup 113 /q put dup 114 /r put dup 115 /s put +dup 54 /six put +dup 47 /slash put dup 116 /t put +dup 51 /three put +dup 50 /two put dup 117 /u put +dup 95 /underscore put +dup 118 /v put +dup 119 /w put +dup 120 /x put dup 121 /y put +dup 122 /z put +dup 48 /zero put readonly def -/FontBBox{-36 -251 1103 750}readonly def +/FontBBox{-4 -235 731 800}readonly def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸMÖ¨ð[G¯•ï(©ÅaÛܘÄ|õRPóÛ忲è>f·ù}Ý|àî·Zx½’'¿5+jÛŠÅz3þÔïp…±â¹3Þ`/÷gìÕtJã8¯) &÷Óh¬o%̸‚Û{sCVa’½h~I"Y‚‚0'Ó¶g; ·§æ€¦‚¹€#Óœ®¥Õ¸g ¦lŠ ÛÈ;–¨O6¬jy·g½Ìà -H@nÎ… -l‰²þÜ2qÂŽwÞ—Me]õÿ}Aíþq}’Šˆ_o¦ÏäÒÀ€Ž“yà–íÑ£ºg€+JIua; 5m˺ÔڳŞp¤pXõ!cÑsäÑø|:Jç#¢<ýy†üO½9“Géõ”cTàØ`üDjÿ DõÚ'Ìw|–­³ˆÑè5ÝËá#ûQvy¹·ïin QQ âdpAÀO¨ZH󬧨>5Õº )j¼YNÊ,²~’þÙ[Y\!å¿ §$ÔaË7{Þ_¹Œ-l ÉŒ@ƒéec!¿ÄEÍoÌ-ïâ}ÖúгR#±§ÖwŸ9Ç“O,;rЮmŽ;Ôxx]®§JøÇTƒ·eS戜-‡Œ:Õ?æ,åö0nÄÁŨ[úx÷ûÍ“pˆƒ*[Øoç—,œ„5v5h«fO[Æ! 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