diff --git a/docs/pdf/Makefile b/docs/pdf/Makefile index f7c4f182..e9da3a0d 100644 --- a/docs/pdf/Makefile +++ b/docs/pdf/Makefile @@ -85,7 +85,7 @@ TOPFILE = userguide.tex SECFILE = title.tex intro.tex commrout.tex datastruct.tex psbrout.tex toolsrout.tex\ - methods.tex precs.tex penv.tex error.tex + methods.tex precs.tex penv.tex error.tex util.tex FIGDIR = figures XPDFFLAGS = diff --git a/docs/pdf/commrout.tex b/docs/pdf/commrout.tex index 1587251f..53d4135b 100644 --- a/docs/pdf/commrout.tex +++ b/docs/pdf/commrout.tex @@ -33,8 +33,8 @@ Long Precision Complex & psb\_halo \\ \caption{Data types\label{tab:f90halo}} \end{table} -\syntax{CALL psb\_halo}{x, desc\_a, info} -\syntax*{CALL psb\_halo}{x, desc\_a, info, alpha, work} +\syntax{call psb\_halo}{x, desc\_a, info} +\syntax*{call psb\_halo}{x, desc\_a, info, alpha, work} \begin{description} \item[\bf On Entry] @@ -104,8 +104,8 @@ Long Precision Complex & psb\_ovrl \\ \caption{Data types\label{tab:f90ovrl}} \end{table} -\syntax{CALL psb\_ovrl}{x, desc\_a, info} -\syntax*{CALL psb\_ovrl}{x, desc\_a, info, update=update\_type, work=work} +\syntax{call psb\_ovrl}{x, desc\_a, info} +\syntax*{call psb\_ovrl}{x, desc\_a, info, update=update\_type, work=work} \begin{description} \item[\bf On Entry] @@ -142,10 +142,10 @@ Type: {\bf required} \\ Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90ovrl}. -\item[info] the local portion of result submatrix $y$.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} @@ -225,7 +225,7 @@ Specified as: a structured data of type \descdata. the processes will have a copy of the global vector.\\ Scope: {\bf global} \\ Type: {\bf optional}\\ -Specified as: an integer variable $0\le ix\le np$. +Specified as: an integer variable $-1\le ix\le np-1$, default $-1$. \item[iglobx] Row index to define a submatrix in glob\_x into which gather the local pieces.\\ Scope: {\bf global} \\ @@ -255,10 +255,10 @@ Specified as: an integer variable. Scope: {\bf global} \\ Type: {\bf required}\\ Specified as: a rank one or two array. -\item[info] the local portion of result submatrix $y$.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -314,7 +314,7 @@ Specified as: a structured data of type \descdata. the processes have a copy of the global vector.\\ Scope: {\bf global} \\ Type: {\bf optional}\\ -Specified as: an integer variable $0\le ix\le np$. +Specified as: an integer variable $-1\le ix\le np-1$, default $-1$. \item[iglobx] Row index to define a submatrix in glob\_x that has to be scattered into local pieces.\\ Scope: {\bf global} \\ @@ -346,10 +346,10 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a rank one or two array containing numbers of the type indicated in Table~\ref{tab:scatter}. -\item[info] the local portion of result submatrix $y$.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} %%% Local Variables: diff --git a/docs/pdf/datastruct.tex b/docs/pdf/datastruct.tex index c6a1464d..0d38078a 100644 --- a/docs/pdf/datastruct.tex +++ b/docs/pdf/datastruct.tex @@ -25,29 +25,31 @@ exchanged among processes. It is not necessary for the user to know the internal structure of \verb|psb_desc_type|, it is set in a transparent mode by the tools -routines of Sec.~\ref{sec:toolsrout} while creating a new sparse -matrix, and its fields may be accessed if necessary via appropriate -routines; nevertheless we include its description for the curious +routines of Sec.~\ref{sec:toolsrout}, and its fields may be accessed +if necessary via the routines of sec.~\ref{sec:dataquery}; +nevertheless we include a description for the curious reader: \begin{description} \item[{\bf matrix\_data}] includes general information about matrix and -process grid. More precisely: -\begin{description} -\item[matrix\_data[psb\_dec\_type\_\hbox{]}] Identifies the decomposition type -(global); the actual values are internally defined, so they should -never be accessed directly. -\item[matrix\_data[psb\_ctxt\_\hbox{]}] Communication context - associated with the processes comprised in the virtual parallel - machine (global). -\item[matrix\_data[psb\_m\_\hbox{]}] Total number of equations (global). -\item[matrix\_data[psb\_n\_\hbox{]}] Total number of variables (global). -\item[matrix\_data[psb\_n\_row\_\hbox{]}] Number of grid variables owned by the -current process (local); equivalent to the number of local rows in the -sparse coefficient matrix. -\item[matrix\_data[psb\_n\_col\_\hbox{]}] Total number of grid variables read by the -current process (local); equivalent to the number of local columns in -the sparse coefficient matrix. They include the halo. -\end{description} +process grid, such as the communication context, the size of the +global matrix, the size of the portion of matrix stored on the current +process, and so on. %% More precisely: +%% \begin{description} +%% \item[matrix\_data[psb\_dec\_type\_\hbox{]}] Identifies the decomposition type +%% (global); the actual values are internally defined, so they should +%% never be accessed directly. +%% \item[matrix\_data[psb\_ctxt\_\hbox{]}] Communication context +%% associated with the processes comprised in the virtual parallel +%% machine (global). +%% \item[matrix\_data[psb\_m\_\hbox{]}] Total number of equations (global). +%% \item[matrix\_data[psb\_n\_\hbox{]}] Total number of variables (global). +%% \item[matrix\_data[psb\_n\_row\_\hbox{]}] Number of grid variables owned by the +%% current process (local); equivalent to the number of local rows in the +%% sparse coefficient matrix. +%% \item[matrix\_data[psb\_n\_col\_\hbox{]}] Total number of grid variables read by the +%% current process (local); equivalent to the number of local columns in +%% the sparse coefficient matrix. They include the halo. +%% \end{description} Specified as: an allocatable integer array of dimension \verb|psb_mdata_size_|. \item[{\bf halo\_index}] A list of the halo and boundary elements for the current process to be exchanged with other processes; for each @@ -86,10 +88,9 @@ Specified as: an allocatable integer array of rank one. \item[{\bf loc\_to\_glob}] each element $i$ of this array contains global identifier of the local variable $i$.\\ Specified as: an allocatable integer array of rank one. -\item[{\bf glob\_to\_loc}] if global variable $i$ is read by current -process then element $i$ contains local index correpondent to global variable $i$; -else element $i$ contains -1 (NULL) value.\\ -Specified as: an allocatabled integer array of rank one. +\item[{\bf glob\_to\_loc, glb\_lc, hashv}] Contain a mapping from + global to local indices. The mapping may be stored in two different + ways depending on the size of the index space. \end{description} The Fortran95 definition for \verb|psb_desc_type| structures is as follows: @@ -101,6 +102,7 @@ type psb_desc_type integer, allocatable :: matrix_data(:), halo_index(:) integer, allocatable :: overlap_elem(:), overlap_index(:) integer, allocatable :: loc_to_glob(:), glob_to_loc(:) + integer, allocatable :: hashv(:), glb_lc(:,:) end type psb_desc_type \end{verbatim} \end{minipage} @@ -133,18 +135,18 @@ state, which can take the following values: \item[psb\_avg\_] Average overlapped elements %% \item[psb\_square\_root\_] Update with the square root of the average %% of overlapped elements; -\item[psb\_dec\_type\_] Entry holding decomposition type (in \verb|desc_a%matrix_data|) -\item[psb\_m\_] Entry holding total number of rows -\item[psb\_n\_] Entry holding total number of columns -\item[ psb\_n\_row\_] Entry holding the number of rows stored in the - current process -\item[psb\_n\_col\_] Entry holding the number of columns stored in the - current process -\item[psb\_ctxt\_] Entry holding a copy of the BLACS communication context -\item[psb\_desc\_asb\_] State of the descriptor: assembled, - i.e. suitable for computational tasks. -\item[psb\_desc\_bld\_] State of the descriptor: build, must be - assembled before computational use. +%% \item[psb\_dec\_type\_] Entry holding decomposition type (in \verb|desc_a%matrix_data|) +%% \item[psb\_m\_] Entry holding total number of rows +%% \item[psb\_n\_] Entry holding total number of columns +%% \item[ psb\_n\_row\_] Entry holding the number of rows stored in the +%% current process +%% \item[psb\_n\_col\_] Entry holding the number of columns stored in the +%% current process +%% \item[psb\_ctxt\_] Entry holding a copy of the BLACS communication context +%% \item[psb\_desc\_asb\_] State of the descriptor: assembled, +%% i.e. suitable for computational tasks. +%% \item[psb\_desc\_bld\_] State of the descriptor: build, must be +%% assembled before computational use. \end{description} @@ -274,14 +276,9 @@ values: \subsection{Preconditioner data structure} \label{sec:prec} -Our library offers support for many different types of -preconditioning schemes. Besides the simple well known preconditioners -like Diagonal Scaling or Block Jacobi with either incomplete -factorization ILU(0) or complete LU factorization. We also provide an -experimental package of complex -preconditioning methods like the Additive Schwarz and Multilevel -Additive Schwarz; these last preconditioners will be described in a -separate document. +Our base library offers support for simple well known preconditioners +like Diagonal Scaling or Block Jacobi with incomplete +factorization ILU(0). A preconditioner is held in the \hypertarget{precdata}{{\tt psb\_prec\_type}} data structure which depends on the @@ -310,23 +307,13 @@ to be interpreted. \begin{minipage}[tl]{0.9\textwidth} \begin{verbatim} - type psb_dbaseprc_type - + type psb_dprec_type type(psb_dspmat_type), allocatable :: av(:) real(kind(1.d0)), allocatable :: d(:) - type(psb_desc_type) :: desc_data , desc_ac + type(psb_desc_type) :: desc_data integer, allocatable :: iprcparm(:) real(kind(1.d0)), allocatable :: dprcparm(:) integer, allocatable :: perm(:), invperm(:) - integer, allocatable :: mlia(:), nlaggr(:) - type(psb_dspmat_type), pointer :: base_a => null() ! - type(psb_desc_type), pointer :: base_desc => null() ! - real(kind(1.d0)), allocatable :: dorig(:) - - end type psb_dbaseprc_type - - type psb_dprec_type - type(psb_dbaseprc_type), allocatable :: baseprecv(:) integer :: prec, base_prec end type psb_dprec_type @@ -339,25 +326,168 @@ to be interpreted. \end{center} \caption{\label{fig:prectype}The PSBLAS defined data type that contains a preconditioner.} \end{figure} -\subsubsection{Named Constants} -\label{sec:prec_constants} + +%% \subsection{Named Constants} +%% \label{sec:prec_constants} +%% \begin{description} +%% \item[f\_ilu\_n\_] Incomplete LU factorization with $n$ levels of +%% fill-in; currently only $n=0$ is implemented; +%% \item[f\_slu\_] Sparse factorization using SuperLU; +%% \item[f\_umf\_] Sparse factorization using UMFPACK; +%% \item[add\_ml\_prec\_] Additive multilevel correction; +%% \item[mult\_ml\_prec\_] Multiplicative multilevel correction; +%% \item[pre\_smooth\_] Pre-smoothing in applying multiplicative +%% multilevel corrections; +%% \item[post\_smooth\_] Post-smoothing in applying multiplicative +%% multilevel corrections; +%% \item[smooth\_both\_] Two-sided (i.e. symmetric) smoothing in applying multiplicative +%% multilevel corrections; +%% \item[mat\_distr\_] Coarse matrix distributed among processes +%% \item[mat\_repl\_] Coarse matrix replicated among processes +%% \end{description} + + +\subsection{Data structure query routines} +\label{sec:dataquery} +\subsubroutine{psb\_cd\_get\_local\_rows}{Get number of local rows} + +\syntax{nr = psb\_cd\_get\_local\_rows}{desc} + +\begin{description} +\item[\bf On Entry] +\item[desc] the communication descriptor.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: a structured data of type \descdata. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[Function value] The number of local rows, i.e. the number of + rows owned by the current process; as explained in~\ref{sec:intro}, + it is equal to $|{\cal I}_i| + |{\cal B}_i|$. The returned value is + specific to the calling process. +\end{description} + + +\subsubroutine{psb\_cd\_get\_local\_cols}{Get number of local cols} + +\syntax{nc = psb\_cd\_get\_local\_cols}{desc} + +\begin{description} +\item[\bf On Entry] +\item[desc] the communication descriptor.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: a structured data of type \descdata. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[Function value] The number of local cols, i.e. the number of + indices used by the current process, including both local and halo + indices; as explained in~\ref{sec:intro}, + it is equal to $|{\cal I}_i| + |{\cal B}_i| +|{\cal H}_i|$. The + returned value is specific to the calling process. +\end{description} + + +\subsubroutine{psb\_cd\_get\_global\_rows}{Get number of global rows} + +\syntax{nr = psb\_cd\_get\_global\_rows}{desc} + +\begin{description} +\item[\bf On Entry] +\item[desc] the communication descriptor.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: a structured data of type \descdata. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[Function value] The number of global rows in the mesh +\end{description} + + +\subsubroutine{psb\_cd\_get\_contex}{Get communication context} +\syntax{ictxt = psb\_cd\_get\_context}{desc} + +\begin{description} +\item[\bf On Entry] +\item[desc] the communication descriptor.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: a structured data of type \descdata. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[Function value] The communication context. +\end{description} + + + +\subsubroutine{psb\_sp\_get\_nrows}{Get number of rows in a sparse matrix} + +\syntax{nr = psb\_sp\_get\_nrows}{a} + +\begin{description} +\item[\bf On Entry] +\item[a] the sparse matrix\\ +Scope:{\bf local}\\ +Type:{\bf required}\\ +Specified as: a structured data of type \spdata. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[Function value] The number of rows of sparse matrix \verb|a|. +\end{description} + + +\subsubroutine{psb\_sp\_get\_ncols}{Get number of columns in a sparse matrix} + +\syntax{nr = psb\_sp\_get\_ncols}{a} + +\begin{description} +\item[\bf On Entry] +\item[a] the sparse matrix\\ +Scope:{\bf local}\\ +Type:{\bf required}\\ +Specified as: a structured data of type \spdata. +\end{description} + +\begin{description} +\item[\bf On Return] +\item[Function value] The number of columns of sparse matrix \verb|a|. +\end{description} + + +\subsubroutine{psb\_sp\_get\_nnzeros}{Get number of nonzero elements in a sparse matrix} + +\syntax{nr = psb\_sp\_get\_nnzeros}{a} + \begin{description} -\item[f\_ilu\_n\_] Incomplete LU factorization with $n$ levels of - fill-in; currently only $n=0$ is implemented; -\item[f\_slu\_] Sparse factorization using SuperLU; -\item[f\_umf\_] Sparse factorization using UMFPACK; -\item[add\_ml\_prec\_] Additive multilevel correction; -\item[mult\_ml\_prec\_] Multiplicative multilevel correction; -\item[pre\_smooth\_] Pre-smoothing in applying multiplicative - multilevel corrections; -\item[post\_smooth\_] Post-smoothing in applying multiplicative - multilevel corrections; -\item[smooth\_both\_] Two-sided (i.e. symmetric) smoothing in applying multiplicative - multilevel corrections; -\item[mat\_distr\_] Coarse matrix distributed among processes -\item[mat\_repl\_] Coarse matrix replicated among processes +\item[\bf On Entry] +\item[a] the sparse matrix\\ +Scope:{\bf local}\\ +Type:{\bf required}\\ +Specified as: a structured data of type \spdata. \end{description} +\begin{description} +\item[\bf On Return] +\item[Function value] The number of nonzero elements stored in sparse matrix \verb|a|. +\end{description} + +\subsubsection*{Notes} +\begin{enumerate} +\item The function value is specific to the storage format of matrix + \verb|a|; some storage formats employ padding, thus the returned + value for the same matrix may be different for different storage choices. +\end{enumerate} + %%% Local Variables: %%% mode: latex diff --git a/docs/pdf/methods.tex b/docs/pdf/methods.tex index dfbc2d84..1280eb96 100644 --- a/docs/pdf/methods.tex +++ b/docs/pdf/methods.tex @@ -13,8 +13,9 @@ methods. \subroutine{psb\_krylov \label{krylov}}{Krylov Methods Driver Routine} This subroutine is a driver that provides a general interface for all -the Krylov-Subspace family methods implemented in PSBLAS-2.0. The -stopping criterion is the normwise backward error, in the infinity +the Krylov-Subspace family methods implemented in PSBLAS-2.0. + +The stopping criterion is the normwise backward error, in the infinity norm, i.e. the iteration is stopped when \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] or @@ -84,487 +85,487 @@ Specified as: a rank one array. Scope: {\bf global} \\ Type: {\bf optional}\\ Returned as: an integer variable. -\item[err] The error estimate on exit.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: a real number. -\item[info] An error code.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\end{description} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% CG -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subroutine{psb\_cg \label{cg}}{CG Iterative Method} - -This subroutine implements the CG method with restarting. The -stopping criterion is the normwise backward error, in the infinity -norm, i.e. the iteration is stopped when -\[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] -or -\[ \frac{\|r_i\|}{\|b\|_2} < eps \] -according to the value passed through the istop argument (see later). - - -\syntax{call psb\_cg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} - -\begin{description} -\item[\bf On Entry] -\item[a] the local portion of global sparse matrix -$A$. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \spdata. -\item[prec] The data structure containing the preconditioner.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \precdata. -\item[b] The RHS vector. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[x] The initial guess. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[eps] The stopping tolerance. \\ -Scope: {\bf global} \\ -Type: {\bf required}\\ -Specified as: a real number. -\item[desc\_a] contains data structures for communications.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \descdata. -\item[itmax] The maximum number of iterations to perform.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: $itmax = 1000$.\\ -Specified as: an integer variable $itmax \ge 1$. -\item[itrace] If $>0$ print out an informational message about - convergence every $itrace$ iterations.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[istop] An integer specifying the stopping criterion.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ - -\item[\bf On Return] -\item[x] The computed solution. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[iter] The number of iterations performed.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\item[err] The error estimate on exit.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: a real number. -\item[info] An error code.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\end{description} -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% CGS -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subroutine{psb\_cgs \label{cgs}}{CGS Iterative Method} - -This subroutine implements the CGS method with restarting. The -stopping criterion is the normwise backward error, in the infinity -norm, i.e. the iteration is stopped when -\[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] -or -\[ \frac{\|r_i\|}{\|b\|_2} < eps \] -according to the value passed through the istop argument (see later). - - -\syntax{call psb\_cgs}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} - -\begin{description} -\item[\bf On Entry] -\item[a] the local portion of global sparse matrix -$A$. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \spdata. -\item[prec] The data structure containing the preconditioner.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \precdata. -\item[b] The RHS vector. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[x] The initial guess. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[eps] The stopping tolerance. \\ -Scope: {\bf global} \\ -Type: {\bf required}\\ -Specified as: a real number. -\item[desc\_a] contains data structures for communications.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \descdata. -\item[itmax] The maximum number of iterations to perform.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: $itmax = 1000$.\\ -Specified as: an integer variable $itmax \ge 1$. -\item[itrace] If $>0$ print out an informational message about - convergence every $itrace$ iterations.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[istop] An integer specifying the stopping criterion.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ - -\item[\bf On Return] -\item[x] The computed solution. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[iter] The number of iterations performed.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\item[err] The error estimate on exit.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: a real number. -\item[info] An error code.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\end{description} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% BiCG -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subroutine{psb\_bicg \label{bicg}}{BiCG Iterative Method} - -This subroutine implements the BiCG method with restarting. The -stopping criterion is the normwise backward error, in the infinity -norm, i.e. the iteration is stopped when -\[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] -or -\[ \frac{\|r_i\|}{\|b\|_2} < eps \] -according to the value passed through the istop argument (see later). - - -\syntax{call psb\_bicg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} - -\begin{description} -\item[\bf On Entry] -\item[a] the local portion of global sparse matrix -$A$. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \spdata. -\item[prec] The data structure containing the preconditioner.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \precdata. -\item[b] The RHS vector. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[x] The initial guess. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[eps] The stopping tolerance. \\ -Scope: {\bf global} \\ -Type: {\bf required}\\ -Specified as: a real number. -\item[desc\_a] contains data structures for communications.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \descdata. -\item[itmax] The maximum number of iterations to perform.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: $itmax = 1000$.\\ -Specified as: an integer variable $itmax \ge 1$. -\item[itrace] If $>0$ print out an informational message about - convergence every $itrace$ iterations.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[istop] An integer specifying the stopping criterion.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ - -\item[\bf On Return] -\item[x] The computed solution. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[iter] The number of iterations performed.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\item[err] The error estimate on exit.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: a real number. -\item[info] An error code.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\end{description} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% BiCGSTAB -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subroutine{psb\_bicgstab \label{bicgstab}}{BiCGSTAB Iterative Method} - -This subroutine implements the BiCGSTAB method with restarting. The -stopping criterion is the normwise backward error, in the infinity -norm, i.e. the iteration is stopped when -\[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] -or -\[ \frac{\|r_i\|}{\|b\|_2} < eps \] -according to the value passed through the istop argument (see later). - - -\syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} - -\begin{description} -\item[\bf On Entry] -\item[a] the local portion of global sparse matrix -$A$. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \spdata. -\item[prec] The data structure containing the preconditioner.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \precdata. -\item[b] The RHS vector. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[x] The initial guess. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[eps] The stopping tolerance. \\ -Scope: {\bf global} \\ -Type: {\bf required}\\ -Specified as: a real number. -\item[desc\_a] contains data structures for communications.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \descdata. -\item[itmax] The maximum number of iterations to perform.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: $itmax = 1000$.\\ -Specified as: an integer variable $itmax \ge 1$. -\item[itrace] If $>0$ print out an informational message about - convergence every $itrace$ iterations.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[istop] An integer specifying the stopping criterion.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ - -\item[\bf On Return] -\item[x] The computed solution. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[iter] The number of iterations performed.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\item[err] The error estimate on exit.\\ +\item[err] The convergence estimate on exit.\\ Scope: {\bf global} \\ Type: {\bf optional}\\ Returned as: a real number. -\item[info] An error code.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\end{description} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% BiCGSTAB(L) -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subroutine{psb\_bicgstabl \label{bicgstabl}}{BiCGSTAB-$l$ Iterative Method} - -This subroutine implements the BiCGSTAB-$l$ method with restarting. The -stopping criterion is the normwise backward error, in the infinity -norm, i.e. the iteration is stopped when -\[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] -or -\[ \frac{\|r_i\|}{\|b\|_2} < eps \] -according to the value passed through the istop argument (see later). - - -\syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} - -\begin{description} -\item[\bf On Entry] -\item[a] the local portion of global sparse matrix -$A$. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \spdata. -\item[prec] The data structure containing the preconditioner.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \precdata. -\item[b] The RHS vector. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[x] The initial guess. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[eps] The stopping tolerance. \\ -Scope: {\bf global} \\ -Type: {\bf required}\\ -Specified as: a real number. -\item[desc\_a] contains data structures for communications.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \descdata. -\item[itmax] The maximum number of iterations to perform.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: $itmax = 1000$.\\ -Specified as: an integer variable $itmax \ge 1$. -\item[itrace] If $>0$ print out an informational message about - convergence every $itrace$ iterations.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[irst] An integer specifying the restarting iteration.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[istop] An integer specifying the stopping criterion.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ - -\item[\bf On Return] -\item[x] The computed solution. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[iter] The number of iterations performed.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\item[err] The error estimate on exit.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: a real number. -\item[info] An error code.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -% -% GMRES -% -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subroutine{psb\_gmres \label{gmres}}{GMRES Iterative Method} - -This subroutine implements the GMRES method with restarting. The -stopping criterion is the normwise backward error, in the infinity -norm, i.e. the iteration is stopped when -\[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] -or -\[ \frac{\|r_i\|}{\|b\|_2} < eps \] -according to the value passed through the istop argument (see later). - - -\syntax{call psb\_gmres}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} - -\begin{description} -\item[\bf On Entry] -\item[a] the local portion of global sparse matrix -$A$. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \spdata. -\item[prec] The data structure containing the preconditioner.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \precdata. -\item[b] The RHS vector. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[x] The initial guess. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[eps] The stopping tolerance. \\ -Scope: {\bf global} \\ -Type: {\bf required}\\ -Specified as: a real number. -\item[desc\_a] contains data structures for communications.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a structured data of type \descdata. -\item[itmax] The maximum number of iterations to perform.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: $itmax = 1000$.\\ -Specified as: an integer variable $itmax \ge 1$. -\item[itrace] If $>0$ print out an informational message about - convergence every $itrace$ iterations.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[irst] An integer specifying the restart iteration.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -\item[istop] An integer specifying the stopping criterion.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ - -\item[\bf On Return] -\item[x] The computed solution. \\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one array. -\item[iter] The number of iterations performed.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\item[err] The error estimate on exit.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: a real number. -\item[info] An error code.\\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Returned as: an integer variable. -\end{description} +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % CG +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% \subroutine{psb\_cg \label{cg}}{CG Iterative Method} + +%% This subroutine implements the CG method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_cg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % CGS +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +%% \subroutine{psb\_cgs \label{cgs}}{CGS Iterative Method} + +%% This subroutine implements the CGS method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_cgs}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % BiCG +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_bicg \label{bicg}}{BiCG Iterative Method} + +%% This subroutine implements the BiCG method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_bicg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % BiCGSTAB +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_bicgstab \label{bicgstab}}{BiCGSTAB Iterative Method} + +%% This subroutine implements the BiCGSTAB method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % BiCGSTAB(L) +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_bicgstabl \label{bicgstabl}}{BiCGSTAB-$l$ Iterative Method} + +%% This subroutine implements the BiCGSTAB-$l$ method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_bicgstab}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[irst] An integer specifying the restarting iteration.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} + + +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% % +%% % GMRES +%% % +%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%% \subroutine{psb\_gmres \label{gmres}}{GMRES Iterative Method} + +%% This subroutine implements the GMRES method with restarting. The +%% stopping criterion is the normwise backward error, in the infinity +%% norm, i.e. the iteration is stopped when +%% \[ \frac{\|r\|}{(\|A\|\|x\|+\|b\|)} < eps \] +%% or +%% \[ \frac{\|r_i\|}{\|b\|_2} < eps \] +%% according to the value passed through the istop argument (see later). + + +%% \syntax{call psb\_gmres}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,irst,istop} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the local portion of global sparse matrix +%% $A$. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[prec] The data structure containing the preconditioner.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \precdata. +%% \item[b] The RHS vector. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[x] The initial guess. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[eps] The stopping tolerance. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf required}\\ +%% Specified as: a real number. +%% \item[desc\_a] contains data structures for communications.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a structured data of type \descdata. +%% \item[itmax] The maximum number of iterations to perform.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: $itmax = 1000$.\\ +%% Specified as: an integer variable $itmax \ge 1$. +%% \item[itrace] If $>0$ print out an informational message about +%% convergence every $itrace$ iterations.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[irst] An integer specifying the restart iteration.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% \item[istop] An integer specifying the stopping criterion.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ + +%% \item[\bf On Return] +%% \item[x] The computed solution. \\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a rank one array. +%% \item[iter] The number of iterations performed.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: an integer variable. +%% \item[err] The error estimate on exit.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Returned as: a real number. +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required} \\ +%% An integer value; 0 means no error has been detected. +%% \end{description} diff --git a/docs/pdf/precs.tex b/docs/pdf/precs.tex index c98fc06e..af4bcbcb 100644 --- a/docs/pdf/precs.tex +++ b/docs/pdf/precs.tex @@ -53,7 +53,7 @@ Scope: {\bf global} \\ Type: {\bf required}\\ Error code: if no error, 0 is returned. \end{description} -\section*{Usage Notes} +\subsection*{Usage Notes} %% The PSBLAS 2.0 contains a number of preconditioners, ranging from a %% simple diagonal scaling to 2-level domain decomposition. These %% preconditioners may use the SuperLU or the UMFPACK software, if @@ -169,10 +169,10 @@ Specified as: a character. Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a precondtioner data structure \precdata\\ -\item[info] the return error code.\\ -Scope: {\bf global} \\ -Type: {\bf required}\\ -Specified as: an integer, upon successful completion $info=0$ \\ +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -212,10 +212,10 @@ Specified as: a double precision array. Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a double precision array. -\item[info] the return error code.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer, upon successful completion $info=0$ .\\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} diff --git a/docs/pdf/psbrout.tex b/docs/pdf/psbrout.tex index 03e6f4ca..d2ecaac7 100644 --- a/docs/pdf/psbrout.tex +++ b/docs/pdf/psbrout.tex @@ -88,10 +88,10 @@ Scope: {\bf local} \\ Type: {\bf required} \\ Specified as: a rank one or two array containing numbers of the type indicated in Table~\ref{tab:f90axpby}. -\item[info] the local portion of result submatrix $y$.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} @@ -172,10 +172,10 @@ Specified as: a structured data of type \descdata. \item[Function value] is the dot product of subvectors $x$ and $y$.\\ Scope: {\bf global} \\ Specified as: a number of the data type indicated in Table~\ref{tab:f90dot}. -\item[info] the local portion of result submatrix $y$.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % @@ -183,7 +183,7 @@ An integer value that contains an error code. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subroutine{psb\_gedot}{Generalized Dot Product} +\subroutine{psb\_gedots}{Generalized Dot Product} This subroutine computes a series of dot products among the columns of two dense matrices $x$ and $y$: @@ -193,15 +193,15 @@ usual convention applies, i.e. the conjugate transpose of $x$ is used. If $x$ and $y$ are of rank one, then $res$ is a scalar, else it is a rank one array. -\syntax{psb\_gedot}{res, x, y, desc\_a, info} +\syntax{call psb\_gedots}{res, x, y, desc\_a, info} \begin{table}[h] \begin{center} \begin{tabular}{ll} \hline $res$, $x$, $y$ & {\bf Subroutine}\\ \hline -Long Precision Real & psb\_gedot \\ -Long Precision Complex & psb\_gedot \\ +Long Precision Real & psb\_gedots \\ +Long Precision Complex & psb\_gedots \\ \hline \end{tabular} \end{center} @@ -233,10 +233,10 @@ Specified as: a structured data of type \descdata. Scope: {\bf global} \\ Specified as: a number or a rank-one array of the data type indicated in Table~\ref{tab:f90dot}. -\item[info] +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -304,10 +304,10 @@ Specified as: a structured data of type \descdata. \item[Function value] is the infinity norm of subvector $x$.\\ Scope: {\bf global} \\ Specified as: a long precision real number. -\item[info] -Scope: {\bf global} \\ +\item[info] Error code.\\ +Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % @@ -315,21 +315,21 @@ An integer value that contains an error code. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\subroutine{psb\_geamax}{Generalized Infinity Norm} +\subroutine{psb\_geamaxs}{Generalized Infinity Norm} This subroutine computes a series of infinity norms on the columns of a dense matrix $x$: \[ res(i) \leftarrow \max_k |x(k,i)| \] -\syntax{psb\_geamax}{res, x, desc\_a, info} +\syntax{call psb\_geamaxs}{res, x, desc\_a, info} \begin{table}[h] \begin{center} \begin{tabular}{lll} \hline $res$& $x$& {\bf Subroutine}\\ \hline -Long Precision Real &Long Precision Real & psb\_geamax\\ -Long Precision Real &Long Precision Complex & psb\_geamax\\ +Long Precision Real &Long Precision Real & psb\_geamaxs\\ +Long Precision Real &Long Precision Complex & psb\_geamaxs\\ \hline \end{tabular} \end{center} @@ -353,10 +353,10 @@ Specified as: a structured data of type \descdata. \item[res] is the infinity norm of the columns of $x$.\\ Scope: {\bf global} \\ Specified as: a number or a rank-one array of long precision real numbers. -\item[info] +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -372,7 +372,7 @@ This function computes the 1-norm of a vector $x$.\\ If $x$ is a double precision real vector computes 1-norm as: \[ asum \leftarrow \|x_i\|\] -else if $x$ ic double precision complex vector then computes 1-norm as: +else if $x$ is double precision complex vector then computes 1-norm as: \[ asum \leftarrow \|re(x)\|_1 + \|im(x)\|_1\] @@ -412,10 +412,66 @@ Specified as: a structured data of type \descdata. \item[Function value] is the 1-norm of vector $x$.\\ Scope: {\bf global} \\ Specified as: a long precision real number. -\item[info] +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. +\end{description} + + +\subroutine{psb\_geasums}{Generalized 1-Norm of Vector} + +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: +\[ res(i) \leftarrow \|x_i\|\] +else if $x$ is double precision complex vector then computes 1-norm as: +\[ res(i) \leftarrow \|re(x)\|_1 + \|im(x)\|_1\] + + +\syntax{call psb\_geasums}{res, x, desc\_a, info} + +\begin{table}[h] +\begin{center} +\begin{tabular}{lll} +\hline +$res$ & $x$ & {\bf Subroutine}\\ +\hline +Long Precision Real&Long Precision Real & psb\_geasums \\ +Long Precision Real&Long Precision Complex & psb\_geasums \\ +\hline +\end{tabular} +\end{center} +\caption{Data types\label{tab:f90asums}} +\end{table} + +\begin{description} +\item[\bf On Entry] +\item[x] the local portion of global dense matrix +$x$. %% This function computes the location of the first element of +%% local subarray used, based on the field $matrix\_data$ of $desc\_a$ . +\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +Specified as: a rank one or two array +containing numbers of type specified in +Table~\ref{tab:f90asums}. +\item[desc\_a] contains data structures for communications.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a structured data of type \descdata. + +\item[\bf On Return] +\item[res] contains the 1-norm of (the columns of) $x$.\\ +Scope: {\bf global} \\ +Specified as: a long precision real number. +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} @@ -482,12 +538,72 @@ Specified as: a structured data of type \descdata. Scope: {\bf global} \\ Type: {\bf required} \\ Specified as: a long precision real number. -\item[info] +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} + + +\subroutine{psb\_genrm2s}{Generalized 1-Norm of Vector} + +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: +\[ res(i) \leftarrow \sqrt{x^T x}\] + +else if $x$ is double precision complex vector then computes 1-norm as: +\[ res(i) \leftarrow \sqrt{x^H x}\] + + +\syntax{call psb\_genrm2s}{res, x, desc\_a, info} + +\begin{table}[h] +\begin{center} +\begin{tabular}{lll} +\hline +$res$ & $x$ & {\bf Subroutine}\\ +\hline +Long Precision Real&Long Precision Real & psb\_genrm2s \\ +Long Precision Real&Long Precision Complex & psb\_genrm2s \\ +\hline +\end{tabular} +\end{center} +\caption{Data types\label{tab:f90nrm2s}} +\end{table} + +\begin{description} +\item[\bf On Entry] +\item[x] the local portion of global dense matrix +$x$. %% This function computes the location of the first element of +%% local subarray used, based on the field $matrix\_data$ of $desc\_a$ . +\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +Specified as: a rank one or two array +containing numbers of type specified in +Table~\ref{tab:f90nrm2s}. +\item[desc\_a] contains data structures for communications.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a structured data of type \descdata. + +\item[\bf On Return] +\item[res] contains the 1-norm of (the columns of) $x$.\\ +Scope: {\bf global} \\ +Specified as: a long precision real number. +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. +\end{description} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % INFINITY-NORM OF A MATRIX @@ -536,10 +652,10 @@ Specified as: a structured data of type \descdata. \item[Function value] is the infinity-norm of sparse submatrix $A$.\\ Scope: {\bf global} \\ Specified as: a long precision real number. -\item[info] +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} @@ -589,8 +705,8 @@ Long Precision Complex & psb\_spmm \\ \caption{Data types\label{tab:f90spmm}} \end{table} -\syntax{CALL psb\_spmm}{alpha, a, x, beta, y, desc\_a, info} -\syntax*{CALL psb\_spmm}{alpha, a, x, beta, y,desc\_a, info, +\syntax{call psb\_spmm}{alpha, a, x, beta, y, desc\_a, info} +\syntax*{call psb\_spmm}{alpha, a, x, beta, y,desc\_a, info, trans, work} \begin{description} @@ -674,10 +790,10 @@ Type: {\bf required} \\ Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90spmm}. -\item[info] +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -713,8 +829,8 @@ where: \item[$P_r, P_c$] are the permutation matrices. \end{description} -\syntax{CALL psb\_spsm}{alpha, t, x, beta, y, desc\_a, info} -\syntax*{CALL psb\_spsm}{alpha, t, x, beta, y, desc\_a, info, +\syntax{call psb\_spsm}{alpha, t, x, beta, y, desc\_a, info} +\syntax*{call psb\_spsm}{alpha, t, x, beta, y, desc\_a, info, trans, unit, choice, diag, work} \begin{table}[h] @@ -826,10 +942,10 @@ Type: {\bf required} \\ Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90spsm}. -\item[info] +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -An integer value that contains an error code. +An integer value; 0 means no error has been detected. \end{description} diff --git a/docs/pdf/toolsrout.tex b/docs/pdf/toolsrout.tex index fe752853..e0617d16 100644 --- a/docs/pdf/toolsrout.tex +++ b/docs/pdf/toolsrout.tex @@ -53,10 +53,10 @@ Specified as: an integer array. Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: a structured data of type \descdata. -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable.\\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} @@ -124,10 +124,10 @@ Specified as: an integer array of length $nz$. Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: a structured data of type \descdata. -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} \begin{enumerate} @@ -154,10 +154,10 @@ Specified as: a structured data of type \descdata. \begin{description} \item[\bf On Return] -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. %\item[arg] \end{description} \section*{Notes} @@ -190,10 +190,10 @@ Specified as: a structured data of type \descdata. Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: a structured data of type \descdata. -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable.\\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -214,10 +214,10 @@ Specified as: a structured data of type \descdata. \begin{description} \item[\bf On Return] -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -309,10 +309,10 @@ Specified as: an integer value. Scope:{\bf local}\\ Type:{\bf required}\\ Specified as: a structured data of type \spdata. -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} \begin{enumerate} @@ -378,7 +378,8 @@ Type: {\bf required}.\\ Specified as: a variable of type \descdata.\\ \item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} @@ -388,7 +389,7 @@ Type: {\bf required}\\ \item On entry to this routine the sparse matrix may be in either the build or update state. \item If the descriptor is in the build state, then the sparse matrix - ought also be in the build state; the action of the routine is to + must also be in the build state; the action of the routine is to (implicitly) call \verb|psb_cdins| to add entries to the sparsity pattern; \item If the descriptor is in the assembled state, then any entries in @@ -432,10 +433,10 @@ Specified as: integer, possible values: \verb|psb_dupl_ovwrt_|, Scope:{\bf local}\\ Type:{\bf required}\\ Specified as: a structured data of type \spdata. -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} @@ -510,10 +511,10 @@ Specified as: a structured data of type \descdata. \begin{description} \item[\bf On Return] -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -544,10 +545,10 @@ Default: true. \begin{description} \item[\bf On Return] -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} \begin{enumerate} @@ -631,10 +632,10 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a rank one or two array with the ALLOCATABLE attribute, of type real, complex or integer.\\ -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -680,10 +681,10 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a rank one or two array with the ALLOCATABLE attribute, of type real, complex or integer.\\ -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} @@ -718,8 +719,8 @@ Specified as: a rank one or two array with the ALLOCATABLE attribute, of type real, complex or integer.\\ \item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} % %% psb_free %% @@ -747,8 +748,8 @@ Specified as: a variable of type \descdata.\\ \item[\bf On Return] \item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -783,8 +784,8 @@ Specified as: a variable of type \descdata.\\ \item[\bf On Return] \item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -832,10 +833,10 @@ Specified as: a rank one integer array. Scope: {\bf global} \\ Type: {\bf optional}\\ Specified as: a rank one integer array. -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} @@ -884,41 +885,10 @@ Specified as: a rank one integer array. Scope: {\bf global} \\ Type: {\bf optional}\\ Specified as: a rank one integer array. -\item[info] Error code. -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. -\end{description} - - -\subroutine{psb\_geall}{Allocates a dense matrix} - -\syntax{call psb\_geall}{x, desc\_a, info, n} - -\begin{description} -\item[\bf On Entry] -\item[desc\_a] The communication descriptor.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a variable of type \descdata.\\ -\item[n] The number of columns of the dense matrix to be allocated.\\ -Scope: {\bf local} \\ -Type: {\bf optional}\\ -Specified as: Integer scalar, default $1$. It is ignored if $x$ is a -rank-1 array. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[x] The dense matrix to be allocated.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a rank one or two array with the ALLOCATABLE -attribute, of type real, complex or integer.\\ -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} @@ -945,17 +915,17 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a rank one array with the ALLOCATABLE attribute, of type integer.\\ -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} \begin{enumerate} \item If there are no boundary elements (i.e., if the local part of the connectivity graph is self-contained) the output vector is set - to \verb|NULL()| + to the ``not allocated'' state. \item Otherwise the size of \verb|bndel| will be exactly equal to the number of boundary elements. \end{enumerate} @@ -980,159 +950,21 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a rank one array with the ALLOCATABLE attribute, of type integer.\\ -\item[info] Error code. +\item[info] Error code.\\ Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. +Type: {\bf required} \\ +An integer value; 0 means no error has been detected. \end{description} \section*{Notes} \begin{enumerate} \item If there are no overlap elements the output vector is set - to \verb|NULL()| + to the ``not allocated'' state. \item Otherwise the size of \verb|ovrel| will be exactly equal to the number of overlap elements. \end{enumerate} -\subroutine{psb\_cd\_get\_local\_rows}{Get number of local rows} - -\syntax{nr = psb\_cd\_get\_local\_rows}{desc} - -\begin{description} -\item[\bf On Entry] -\item[desc] the communication descriptor.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[Function value] The number of local rows, i.e. the number of - rows owned by the current process; as explained in~\ref{sec:intro}, - it is equal to $|{\cal I}_i| + |{\cal B}_i|$. The returned value is - specific to the calling process. -\end{description} - - -\subroutine{psb\_cd\_get\_local\_cols}{Get number of local cols} - -\syntax{nc = psb\_cd\_get\_local\_cols}{desc} - -\begin{description} -\item[\bf On Entry] -\item[desc] the communication descriptor.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[Function value] The number of local cols, i.e. the number of - indices used by the current process, including both local and halo - indices; as explained in~\ref{sec:intro}, - it is equal to $|{\cal I}_i| + |{\cal B}_i| +|{\cal H}_i|$. The - returned value is specific to the calling process. -\end{description} - - -\subroutine{psb\_cd\_get\_global\_rows}{Get number of global rows} - -\syntax{nr = psb\_cd\_get\_global\_rows}{desc} - -\begin{description} -\item[\bf On Entry] -\item[desc] the communication descriptor.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[Function value] The number of global rows in the mesh -\end{description} - - -\subroutine{psb\_cd\_get\_contex}{Get communication context} -\syntax{ictxt = psb\_cd\_get\_context}{desc} - -\begin{description} -\item[\bf On Entry] -\item[desc] the communication descriptor.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[Function value] The communication context. -\end{description} - - - -\subroutine{psb\_sp\_get\_nrows}{Get number of rows in a sparse matrix} - -\syntax{nr = psb\_sp\_get\_nrows}{a} - -\begin{description} -\item[\bf On Entry] -\item[a] the sparse matrix\\ -Scope:{\bf local}\\ -Type:{\bf required}\\ -Specified as: a structured data of type \spdata. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[Function value] The number of rows of sparse matrix \verb|a|. -\end{description} - - -\subroutine{psb\_sp\_get\_ncols}{Get number of columns in a sparse matrix} - -\syntax{nr = psb\_sp\_get\_ncols}{a} - -\begin{description} -\item[\bf On Entry] -\item[a] the sparse matrix\\ -Scope:{\bf local}\\ -Type:{\bf required}\\ -Specified as: a structured data of type \spdata. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[Function value] The number of columns of sparse matrix \verb|a|. -\end{description} - - -\subroutine{psb\_sp\_get\_nnzeros}{Get number of nonzero elements in a sparse matrix} - -\syntax{nr = psb\_sp\_get\_nnzeros}{a} - -\begin{description} -\item[\bf On Entry] -\item[a] the sparse matrix\\ -Scope:{\bf local}\\ -Type:{\bf required}\\ -Specified as: a structured data of type \spdata. -\end{description} - -\begin{description} -\item[\bf On Return] -\item[Function value] The number of nonzero elements stored in sparse matrix \verb|a|. -\end{description} - -\section*{Notes} -\begin{enumerate} -\item The function value is specific to the storage format of matrix - \verb|a|; some storage formats employ padding, thus the returned - value for the same matrix may be different for different storage choices. -\end{enumerate} %%% Local Variables: diff --git a/docs/pdf/userguide.tex b/docs/pdf/userguide.tex index 74d32f8a..7e59e671 100644 --- a/docs/pdf/userguide.tex +++ b/docs/pdf/userguide.tex @@ -41,6 +41,11 @@ \section*{\flushleft #1---#2 \endflushleft}% \addcontentsline{toc}{subsection}{#1}% \markright{#1}}% +\newcommand{\subsubroutine}[2]{% +\stepcounter{subroutine}% + \subsection*{\flushleft #1---#2 \endflushleft}% + \addcontentsline{toc}{subsubsection}{#1}% + \markright{#1}}% \newcommand{\examplename}{Example} \newcommand{\syntaxname}{Syntax} \makeatletter diff --git a/docs/userguide.pdf b/docs/userguide.pdf index a389889e..615cce00 100644 --- a/docs/userguide.pdf +++ b/docs/userguide.pdf @@ -78,483 +78,459 @@ endobj (3.3 Preconditioner data structure) endobj 57 0 obj -<< /S /GoTo /D (subsubsection.3.3.1) >> +<< /S /GoTo /D (subsection.3.4) >> endobj 60 0 obj -(3.3.1 Named Constants) +(3.4 Data structure query routines) endobj 61 0 obj -<< /S /GoTo /D (section.4) >> +<< /S /GoTo /D (section*.2) >> endobj 64 0 obj -(4 Computational routines) +(psb\137cd\137get\137local\137rows) endobj 65 0 obj -<< /S /GoTo /D (section*.2) >> +<< /S /GoTo /D (section*.4) >> endobj 68 0 obj -(psb\137geaxpby) +(psb\137cd\137get\137local\137cols) endobj 69 0 obj -<< /S /GoTo /D (section*.4) >> +<< /S /GoTo /D (section*.6) >> endobj 72 0 obj -(psb\137gedot) 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0.1992 l +S +Q +1 0 0 1 -153.3506 -443.7511 cm +BT +/F8 9.9626 Tf 156.3394 443.7511 Td[(sp)]TJ +ET +1 0 0 1 166.4017 443.7511 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S +Q +1 0 0 1 -166.4017 -443.7511 cm +BT +/F8 9.9626 Tf 169.3905 443.7511 Td[(get)]TJ +ET +1 0 0 1 183.2718 443.7511 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S +Q +1 0 0 1 -183.2718 -443.7511 cm +BT +/F8 9.9626 Tf 186.2606 443.7511 Td[(ncols)]TJ +ET +1 0 0 1 207.9017 443.7511 cm +0 g 0 G +1 0 0 1 -207.9017 -443.7511 cm +BT +/F8 9.9626 Tf 210.8665 443.7511 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 443.7511 cm +0 g 0 G +1 0 0 1 -433.6438 -443.7511 cm +BT +/F8 9.9626 Tf 433.6438 443.7511 Td[(15)]TJ +ET +1 0 0 1 443.6065 443.7511 cm +0 g 0 G +1 0 0 1 -305.853 -12.2096 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -409.1998 cm +1 0 0 1 -137.7535 -431.5415 cm +BT +/F8 9.9626 Tf 137.7535 431.5415 Td[(psb)]TJ +ET +1 0 0 1 153.3506 431.5415 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S +Q +1 0 0 1 -153.3506 -431.5415 cm BT -/F8 9.9626 Tf 114.8394 409.1998 Td[(psb)]TJ +/F8 9.9626 Tf 156.3394 431.5415 Td[(sp)]TJ ET -1 0 0 1 130.4364 409.1998 cm +1 0 0 1 166.4017 431.5415 cm q []0 d 0 J @@ -1101,25 +1273,50 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -409.1998 cm +1 0 0 1 -166.4017 -431.5415 cm BT -/F8 9.9626 Tf 133.4253 409.1998 Td[(genrm2)]TJ +/F8 9.9626 Tf 169.3905 431.5415 Td[(get)]TJ ET -1 0 0 1 165.5549 409.1998 cm +1 0 0 1 183.2718 431.5415 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S +Q +1 0 0 1 -183.2718 -431.5415 cm +BT +/F8 9.9626 Tf 186.2606 431.5415 Td[(nn)1(z)-1(eros)]TJ +ET +1 0 0 1 218.999 431.5415 cm 0 g 0 G -1 0 0 1 -165.5549 -409.1998 cm +1 0 0 1 -218.999 -431.5415 cm BT -/F8 9.9626 Tf 172.1235 409.1998 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 +/F8 9.9626 Tf 226.3637 431.5415 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 409.1998 cm +1 0 0 1 433.6438 431.5415 cm 0 g 0 G -1 0 0 1 -433.6438 -409.1998 cm +1 0 0 1 -433.6438 -431.5415 cm BT -/F8 9.9626 Tf 433.6438 409.1998 Td[(25)]TJ +/F8 9.9626 Tf 433.6438 431.5415 Td[(16)]TJ ET -1 0 0 1 443.6065 409.1998 cm +1 0 0 1 443.6065 431.5415 cm 0 g 0 G -1 0 0 1 -328.7671 -12.2096 cm +1 0 0 1 -343.7111 -22.3417 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.8954 -409.1998 cm +BT +/F29 9.9626 Tf 99.8954 409.1998 Td[(4)-925(Computati)-1(on)1(al)-384(routines)]TJ +ET +1 0 0 1 234.032 409.1998 cm +0 g 0 G +1 0 0 1 -234.032 -409.1998 cm +BT +/F29 9.9626 Tf 432.1495 409.1998 Td[(17)]TJ +ET +1 0 0 1 114.8394 396.9902 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -114.8394 -396.9902 cm BT @@ -1136,11 +1333,11 @@ S Q 1 0 0 1 -130.4364 -396.9902 cm BT -/F8 9.9626 Tf 133.4253 396.9902 Td[(spnr)1(m)-1(i)]TJ +/F8 9.9626 Tf 133.4253 396.9902 Td[(geaxpb)28(y)]TJ ET -1 0 0 1 163.3963 396.9902 cm +1 0 0 1 169.1248 396.9902 cm 0 g 0 G -1 0 0 1 -163.3963 -396.9902 cm +1 0 0 1 -169.1248 -396.9902 cm BT /F8 9.9626 Tf 172.1235 396.9902 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 @@ -1148,7 +1345,7 @@ ET 0 g 0 G 1 0 0 1 -433.6438 -396.9902 cm BT -/F8 9.9626 Tf 433.6438 396.9902 Td[(26)]TJ +/F8 9.9626 Tf 433.6438 396.9902 Td[(18)]TJ ET 1 0 0 1 443.6065 396.9902 cm 0 g 0 G @@ -1169,11 +1366,11 @@ S Q 1 0 0 1 -130.4364 -384.7807 cm BT -/F8 9.9626 Tf 133.4253 384.7807 Td[(spmm)]TJ +/F8 9.9626 Tf 133.4253 384.7807 Td[(gedot)]TJ ET -1 0 0 1 159.4942 384.7807 cm +1 0 0 1 157.225 384.7807 cm 0 g 0 G -1 0 0 1 -159.4942 -384.7807 cm +1 0 0 1 -157.225 -384.7807 cm BT /F8 9.9626 Tf 164.3749 384.7807 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 @@ -1181,7 +1378,7 @@ ET 0 g 0 G 1 0 0 1 -433.6438 -384.7807 cm BT -/F8 9.9626 Tf 433.6438 384.7807 Td[(27)]TJ +/F8 9.9626 Tf 433.6438 384.7807 Td[(20)]TJ ET 1 0 0 1 443.6065 384.7807 cm 0 g 0 G @@ -1202,11 +1399,11 @@ S Q 1 0 0 1 -130.4364 -372.5712 cm BT -/F8 9.9626 Tf 133.4253 372.5712 Td[(spsm)]TJ +/F8 9.9626 Tf 133.4253 372.5712 Td[(gedots)]TJ ET -1 0 0 1 155.1217 372.5712 cm +1 0 0 1 161.1547 372.5712 cm 0 g 0 G -1 0 0 1 -155.1217 -372.5712 cm +1 0 0 1 -161.1547 -372.5712 cm BT /F8 9.9626 Tf 164.3749 372.5712 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 @@ -1214,29 +1411,17 @@ ET 0 g 0 G 1 0 0 1 -433.6438 -372.5712 cm BT -/F8 9.9626 Tf 433.6438 372.5712 Td[(29)]TJ +/F8 9.9626 Tf 433.6438 372.5712 Td[(22)]TJ ET 1 0 0 1 443.6065 372.5712 cm 0 g 0 G -1 0 0 1 -343.7111 -22.3418 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -99.8954 -350.2294 cm -BT -/F29 9.9626 Tf 99.8954 350.2294 Td[(5)-925(Comm)32(unic)-1(ation)-384(r)1(outi)-1(nes)]TJ -ET -1 0 0 1 238.3284 350.2294 cm -0 g 0 G -1 0 0 1 -238.3284 -350.2294 cm -BT -/F29 9.9626 Tf 432.1495 350.2294 Td[(32)]TJ -ET -1 0 0 1 114.8394 338.0199 cm +1 0 0 1 -328.7671 -12.2096 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -338.0199 cm +1 0 0 1 -114.8394 -360.3616 cm BT -/F8 9.9626 Tf 114.8394 338.0199 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 360.3616 Td[(psb)]TJ ET -1 0 0 1 130.4364 338.0199 cm +1 0 0 1 130.4364 360.3616 cm q []0 d 0 J @@ -1245,31 +1430,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -338.0199 cm +1 0 0 1 -130.4364 -360.3616 cm BT -/F8 9.9626 Tf 133.4253 338.0199 Td[(hal)1(o)]TJ +/F8 9.9626 Tf 133.4253 360.3616 Td[(geam)-1(ax)]TJ ET -1 0 0 1 151.6902 338.0199 cm +1 0 0 1 166.3574 360.3616 cm 0 g 0 G -1 0 0 1 -151.6902 -338.0199 cm +1 0 0 1 -166.3574 -360.3616 cm BT -/F8 9.9626 Tf 156.6262 338.0199 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 +/F8 9.9626 Tf 172.1235 360.3616 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 338.0199 cm +1 0 0 1 433.6438 360.3616 cm 0 g 0 G -1 0 0 1 -433.6438 -338.0199 cm +1 0 0 1 -433.6438 -360.3616 cm BT -/F8 9.9626 Tf 433.6438 338.0199 Td[(33)]TJ +/F8 9.9626 Tf 433.6438 360.3616 Td[(24)]TJ ET -1 0 0 1 443.6065 338.0199 cm +1 0 0 1 443.6065 360.3616 cm 0 g 0 G 1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -325.8104 cm +1 0 0 1 -114.8394 -348.1521 cm BT -/F8 9.9626 Tf 114.8394 325.8104 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 348.1521 Td[(psb)]TJ ET -1 0 0 1 130.4364 325.8104 cm +1 0 0 1 130.4364 348.1521 cm q []0 d 0 J @@ -1278,31 +1463,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -325.8104 cm +1 0 0 1 -130.4364 -348.1521 cm BT -/F8 9.9626 Tf 133.4253 325.8104 Td[(o)28(vrl)]TJ +/F8 9.9626 Tf 133.4253 348.1521 Td[(geam)-1(axs)]TJ ET -1 0 0 1 150.0574 325.8104 cm +1 0 0 1 170.2871 348.1521 cm 0 g 0 G -1 0 0 1 -150.0574 -325.8104 cm +1 0 0 1 -170.2871 -348.1521 cm BT -/F8 9.9626 Tf 156.6262 325.8104 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 +/F8 9.9626 Tf 179.8721 348.1521 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 325.8104 cm +1 0 0 1 433.6438 348.1521 cm 0 g 0 G -1 0 0 1 -433.6438 -325.8104 cm +1 0 0 1 -433.6438 -348.1521 cm BT -/F8 9.9626 Tf 433.6438 325.8104 Td[(35)]TJ +/F8 9.9626 Tf 433.6438 348.1521 Td[(25)]TJ ET -1 0 0 1 443.6065 325.8104 cm +1 0 0 1 443.6065 348.1521 cm 0 g 0 G -1 0 0 1 -328.7671 -12.2096 cm +1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -313.6008 cm +1 0 0 1 -114.8394 -335.9426 cm BT -/F8 9.9626 Tf 114.8394 313.6008 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 335.9426 Td[(psb)]TJ ET -1 0 0 1 130.4364 313.6008 cm +1 0 0 1 130.4364 335.9426 cm q []0 d 0 J @@ -1311,31 +1496,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -313.6008 cm +1 0 0 1 -130.4364 -335.9426 cm BT -/F8 9.9626 Tf 133.4253 313.6008 Td[(gath)1(e)-1(r)]TJ +/F8 9.9626 Tf 133.4253 335.9426 Td[(geas)-1(u)1(m)]TJ ET -1 0 0 1 161.127 313.6008 cm +1 0 0 1 165.5825 335.9426 cm 0 g 0 G -1 0 0 1 -161.127 -313.6008 cm +1 0 0 1 -165.5825 -335.9426 cm BT -/F8 9.9626 Tf 164.3749 313.6008 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 +/F8 9.9626 Tf 172.1235 335.9426 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 313.6008 cm +1 0 0 1 433.6438 335.9426 cm 0 g 0 G -1 0 0 1 -433.6438 -313.6008 cm +1 0 0 1 -433.6438 -335.9426 cm BT -/F8 9.9626 Tf 433.6438 313.6008 Td[(37)]TJ +/F8 9.9626 Tf 433.6438 335.9426 Td[(26)]TJ ET -1 0 0 1 443.6065 313.6008 cm +1 0 0 1 443.6065 335.9426 cm 0 g 0 G 1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -301.3913 cm +1 0 0 1 -114.8394 -323.7331 cm BT -/F8 9.9626 Tf 114.8394 301.3913 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 323.7331 Td[(psb)]TJ ET -1 0 0 1 130.4364 301.3913 cm +1 0 0 1 130.4364 323.7331 cm q []0 d 0 J @@ -1344,43 +1529,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -301.3913 cm -BT -/F8 9.9626 Tf 133.4253 301.3913 Td[(sc)-1(atter)]TJ -ET -1 0 0 1 162.8428 301.3913 cm -0 g 0 G -1 0 0 1 -162.8428 -301.3913 cm +1 0 0 1 -130.4364 -323.7331 cm BT -/F8 9.9626 Tf 172.1235 301.3913 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 +/F8 9.9626 Tf 133.4253 323.7331 Td[(geas)-1(u)1(m)-1(s)]TJ ET -1 0 0 1 433.6438 301.3913 cm +1 0 0 1 169.5122 323.7331 cm 0 g 0 G -1 0 0 1 -433.6438 -301.3913 cm +1 0 0 1 -169.5122 -323.7331 cm BT -/F8 9.9626 Tf 433.6438 301.3913 Td[(39)]TJ +/F8 9.9626 Tf 172.1235 323.7331 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 1 443.6065 301.3913 cm +1 0 0 1 433.6438 323.7331 cm 0 g 0 G -1 0 0 1 -343.7111 -22.3418 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -99.8954 -279.0495 cm +1 0 0 1 -433.6438 -323.7331 cm BT -/F29 9.9626 Tf 99.8954 279.0495 Td[(6)-925(Data)-384(managemen)32(t)-384(r)1(out)-1(ines)]TJ +/F8 9.9626 Tf 433.6438 323.7331 Td[(27)]TJ ET -1 0 0 1 250.7747 279.0495 cm +1 0 0 1 443.6065 323.7331 cm 0 g 0 G -1 0 0 1 -250.7747 -279.0495 cm -BT -/F29 9.9626 Tf 432.1495 279.0495 Td[(41)]TJ -ET -1 0 0 1 114.8394 266.84 cm +1 0 0 1 -328.7671 -12.2096 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -266.84 cm +1 0 0 1 -114.8394 -311.5235 cm BT -/F8 9.9626 Tf 114.8394 266.84 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 311.5235 Td[(psb)]TJ ET -1 0 0 1 130.4364 266.84 cm +1 0 0 1 130.4364 311.5235 cm q []0 d 0 J @@ -1389,31 +1562,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -266.84 cm +1 0 0 1 -130.4364 -311.5235 cm BT -/F8 9.9626 Tf 133.4253 266.84 Td[(cdall)]TJ +/F8 9.9626 Tf 133.4253 311.5235 Td[(genrm2)]TJ ET -1 0 0 1 153.9041 266.84 cm +1 0 0 1 165.5549 311.5235 cm 0 g 0 G -1 0 0 1 -153.9041 -266.84 cm +1 0 0 1 -165.5549 -311.5235 cm BT -/F8 9.9626 Tf 156.6262 266.84 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 +/F8 9.9626 Tf 172.1235 311.5235 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 266.84 cm +1 0 0 1 433.6438 311.5235 cm 0 g 0 G -1 0 0 1 -433.6438 -266.84 cm +1 0 0 1 -433.6438 -311.5235 cm BT -/F8 9.9626 Tf 433.6438 266.84 Td[(42)]TJ +/F8 9.9626 Tf 433.6438 311.5235 Td[(28)]TJ ET -1 0 0 1 443.6065 266.84 cm +1 0 0 1 443.6065 311.5235 cm 0 g 0 G 1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -254.6305 cm +1 0 0 1 -114.8394 -299.314 cm BT -/F8 9.9626 Tf 114.8394 254.6305 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 299.314 Td[(psb)]TJ ET -1 0 0 1 130.4364 254.6305 cm +1 0 0 1 130.4364 299.314 cm q []0 d 0 J @@ -1422,31 +1595,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -254.6305 cm +1 0 0 1 -130.4364 -299.314 cm BT -/F8 9.9626 Tf 133.4253 254.6305 Td[(cdin)1(s)]TJ +/F8 9.9626 Tf 133.4253 299.314 Td[(genrm2s)]TJ ET -1 0 0 1 155.6199 254.6305 cm +1 0 0 1 169.4846 299.314 cm 0 g 0 G -1 0 0 1 -155.6199 -254.6305 cm +1 0 0 1 -169.4846 -299.314 cm BT -/F8 9.9626 Tf 164.3749 254.6305 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 +/F8 9.9626 Tf 172.1235 299.314 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 254.6305 cm +1 0 0 1 433.6438 299.314 cm 0 g 0 G -1 0 0 1 -433.6438 -254.6305 cm +1 0 0 1 -433.6438 -299.314 cm BT -/F8 9.9626 Tf 433.6438 254.6305 Td[(44)]TJ +/F8 9.9626 Tf 433.6438 299.314 Td[(29)]TJ ET -1 0 0 1 443.6065 254.6305 cm +1 0 0 1 443.6065 299.314 cm 0 g 0 G -1 0 0 1 -328.7671 -12.2096 cm +1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -242.4209 cm +1 0 0 1 -114.8394 -287.1045 cm BT -/F8 9.9626 Tf 114.8394 242.4209 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 287.1045 Td[(psb)]TJ ET -1 0 0 1 130.4364 242.4209 cm +1 0 0 1 130.4364 287.1045 cm q []0 d 0 J @@ -1455,31 +1628,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -242.4209 cm +1 0 0 1 -130.4364 -287.1045 cm BT -/F8 9.9626 Tf 133.4253 242.4209 Td[(cdasb)]TJ +/F8 9.9626 Tf 133.4253 287.1045 Td[(spnr)1(m)-1(i)]TJ ET -1 0 0 1 157.8338 242.4209 cm +1 0 0 1 163.3963 287.1045 cm 0 g 0 G -1 0 0 1 -157.8338 -242.4209 cm +1 0 0 1 -163.3963 -287.1045 cm BT -/F8 9.9626 Tf 164.3749 242.4209 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 +/F8 9.9626 Tf 172.1235 287.1045 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 242.4209 cm +1 0 0 1 433.6438 287.1045 cm 0 g 0 G -1 0 0 1 -433.6438 -242.4209 cm +1 0 0 1 -433.6438 -287.1045 cm BT -/F8 9.9626 Tf 433.6438 242.4209 Td[(45)]TJ +/F8 9.9626 Tf 433.6438 287.1045 Td[(30)]TJ ET -1 0 0 1 443.6065 242.4209 cm +1 0 0 1 443.6065 287.1045 cm 0 g 0 G -1 0 0 1 -328.7671 -12.2095 cm +1 0 0 1 -328.7671 -12.2096 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -230.2114 cm +1 0 0 1 -114.8394 -274.8949 cm BT -/F8 9.9626 Tf 114.8394 230.2114 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 274.8949 Td[(psb)]TJ ET -1 0 0 1 130.4364 230.2114 cm +1 0 0 1 130.4364 274.8949 cm q []0 d 0 J @@ -1488,31 +1661,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -230.2114 cm +1 0 0 1 -130.4364 -274.8949 cm BT -/F8 9.9626 Tf 133.4253 230.2114 Td[(cdcp)28(y)]TJ +/F8 9.9626 Tf 133.4253 274.8949 Td[(spmm)]TJ ET -1 0 0 1 158.3319 230.2114 cm +1 0 0 1 159.4942 274.8949 cm 0 g 0 G -1 0 0 1 -158.3319 -230.2114 cm +1 0 0 1 -159.4942 -274.8949 cm BT -/F8 9.9626 Tf 164.3749 230.2114 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 +/F8 9.9626 Tf 164.3749 274.8949 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 230.2114 cm +1 0 0 1 433.6438 274.8949 cm 0 g 0 G -1 0 0 1 -433.6438 -230.2114 cm +1 0 0 1 -433.6438 -274.8949 cm BT -/F8 9.9626 Tf 433.6438 230.2114 Td[(46)]TJ +/F8 9.9626 Tf 433.6438 274.8949 Td[(31)]TJ ET -1 0 0 1 443.6065 230.2114 cm +1 0 0 1 443.6065 274.8949 cm 0 g 0 G 1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -218.0019 cm +1 0 0 1 -114.8394 -262.6854 cm BT -/F8 9.9626 Tf 114.8394 218.0019 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 262.6854 Td[(psb)]TJ ET -1 0 0 1 130.4364 218.0019 cm +1 0 0 1 130.4364 262.6854 cm q []0 d 0 J @@ -1521,31 +1694,43 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -218.0019 cm +1 0 0 1 -130.4364 -262.6854 cm BT -/F8 9.9626 Tf 133.4253 218.0019 Td[(cdfr)1(e)-1(e)]TJ +/F8 9.9626 Tf 133.4253 262.6854 Td[(spsm)]TJ ET -1 0 0 1 159.1898 218.0019 cm +1 0 0 1 155.1217 262.6854 cm 0 g 0 G -1 0 0 1 -159.1898 -218.0019 cm +1 0 0 1 -155.1217 -262.6854 cm BT -/F8 9.9626 Tf 164.3749 218.0019 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 +/F8 9.9626 Tf 164.3749 262.6854 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 218.0019 cm +1 0 0 1 433.6438 262.6854 cm 0 g 0 G -1 0 0 1 -433.6438 -218.0019 cm +1 0 0 1 -433.6438 -262.6854 cm BT -/F8 9.9626 Tf 433.6438 218.0019 Td[(47)]TJ +/F8 9.9626 Tf 433.6438 262.6854 Td[(33)]TJ ET -1 0 0 1 443.6065 218.0019 cm +1 0 0 1 443.6065 262.6854 cm 0 g 0 G -1 0 0 1 -328.7671 -12.2096 cm +1 0 0 1 -343.7111 -22.3418 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.8954 -240.3436 cm +BT +/F29 9.9626 Tf 99.8954 240.3436 Td[(5)-925(Comm)32(unic)-1(ation)-384(r)1(outi)-1(nes)]TJ +ET +1 0 0 1 238.3284 240.3436 cm +0 g 0 G +1 0 0 1 -238.3284 -240.3436 cm +BT +/F29 9.9626 Tf 432.1495 240.3436 Td[(36)]TJ +ET +1 0 0 1 114.8394 228.1341 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -205.7923 cm +1 0 0 1 -114.8394 -228.1341 cm BT -/F8 9.9626 Tf 114.8394 205.7923 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 228.1341 Td[(psb)]TJ ET -1 0 0 1 130.4364 205.7923 cm +1 0 0 1 130.4364 228.1341 cm q []0 d 0 J @@ -1554,31 +1739,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -205.7923 cm +1 0 0 1 -130.4364 -228.1341 cm BT -/F8 9.9626 Tf 133.4253 205.7923 Td[(spall)]TJ +/F8 9.9626 Tf 133.4253 228.1341 Td[(hal)1(o)]TJ ET -1 0 0 1 153.4059 205.7923 cm +1 0 0 1 151.6902 228.1341 cm 0 g 0 G -1 0 0 1 -153.4059 -205.7923 cm +1 0 0 1 -151.6902 -228.1341 cm BT -/F8 9.9626 Tf 156.6262 205.7923 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 +/F8 9.9626 Tf 156.6262 228.1341 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 1 433.6438 205.7923 cm +1 0 0 1 433.6438 228.1341 cm 0 g 0 G -1 0 0 1 -433.6438 -205.7923 cm +1 0 0 1 -433.6438 -228.1341 cm BT -/F8 9.9626 Tf 433.6438 205.7923 Td[(48)]TJ +/F8 9.9626 Tf 433.6438 228.1341 Td[(37)]TJ ET -1 0 0 1 443.6065 205.7923 cm +1 0 0 1 443.6065 228.1341 cm 0 g 0 G 1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -193.5828 cm +1 0 0 1 -114.8394 -215.9246 cm BT -/F8 9.9626 Tf 114.8394 193.5828 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 215.9246 Td[(psb)]TJ ET -1 0 0 1 130.4364 193.5828 cm +1 0 0 1 130.4364 215.9246 cm q []0 d 0 J @@ -1587,31 +1772,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -193.5828 cm +1 0 0 1 -130.4364 -215.9246 cm BT -/F8 9.9626 Tf 133.4253 193.5828 Td[(spin)1(s)]TJ +/F8 9.9626 Tf 133.4253 215.9246 Td[(o)28(vrl)]TJ ET -1 0 0 1 155.1217 193.5828 cm +1 0 0 1 150.0574 215.9246 cm 0 g 0 G -1 0 0 1 -155.1217 -193.5828 cm +1 0 0 1 -150.0574 -215.9246 cm BT -/F8 9.9626 Tf 164.3749 193.5828 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 +/F8 9.9626 Tf 156.6262 215.9246 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 1 433.6438 193.5828 cm +1 0 0 1 433.6438 215.9246 cm 0 g 0 G -1 0 0 1 -433.6438 -193.5828 cm +1 0 0 1 -433.6438 -215.9246 cm BT -/F8 9.9626 Tf 433.6438 193.5828 Td[(49)]TJ +/F8 9.9626 Tf 433.6438 215.9246 Td[(39)]TJ ET -1 0 0 1 443.6065 193.5828 cm +1 0 0 1 443.6065 215.9246 cm 0 g 0 G -1 0 0 1 -328.7671 -12.2095 cm +1 0 0 1 -328.7671 -12.2096 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -181.3733 cm +1 0 0 1 -114.8394 -203.715 cm BT -/F8 9.9626 Tf 114.8394 181.3733 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 203.715 Td[(psb)]TJ ET -1 0 0 1 130.4364 181.3733 cm +1 0 0 1 130.4364 203.715 cm q []0 d 0 J @@ -1620,31 +1805,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -181.3733 cm +1 0 0 1 -130.4364 -203.715 cm BT -/F8 9.9626 Tf 133.4253 181.3733 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181.3733 cm +1 0 0 1 443.6065 203.715 cm 0 g 0 G 1 0 0 1 -328.7671 -12.2095 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.8394 -169.1638 cm +1 0 0 1 -114.8394 -191.5055 cm BT -/F8 9.9626 Tf 114.8394 169.1638 Td[(psb)]TJ +/F8 9.9626 Tf 114.8394 191.5055 Td[(psb)]TJ ET -1 0 0 1 130.4364 169.1638 cm +1 0 0 1 130.4364 191.5055 cm q []0 d 0 J @@ -1653,25 +1838,37 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -130.4364 -169.1638 cm +1 0 0 1 -130.4364 -191.5055 cm BT -/F8 9.9626 Tf 133.4253 169.1638 Td[(spfr)1(e)-1(e)]TJ +/F8 9.9626 Tf 133.4253 191.5055 Td[(sc)-1(atter)]TJ ET -1 0 0 1 158.6917 169.1638 cm +1 0 0 1 162.8428 191.5055 cm 0 g 0 G -1 0 0 1 -158.6917 -169.1638 cm +1 0 0 1 -162.8428 -191.5055 cm BT -/F8 9.9626 Tf 164.3749 169.1638 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 +/F8 9.9626 Tf 172.1235 191.5055 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1 -484.4533 -633.3946 cm +1 0 0 1 -484.4533 -598.5323 cm BT -/F8 9.9626 Tf 484.4533 633.3946 Td[(66)]TJ +/F8 9.9626 Tf 484.4533 598.5323 Td[(63)]TJ ET -1 0 0 1 494.4159 633.3946 cm +1 0 0 1 494.4159 598.5323 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9551 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -621.2722 cm +1 0 0 1 -165.6488 -586.5772 cm BT -/F8 9.9626 Tf 165.6488 621.2722 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 586.5772 Td[(psb)]TJ ET -1 0 0 1 181.2459 621.2722 cm +1 0 0 1 181.2459 586.5772 cm q []0 d 0 J @@ -2464,11 +2682,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -621.2722 cm +1 0 0 1 -181.2459 -586.5772 cm +BT +/F8 9.9626 Tf 184.2347 586.5772 Td[(gelp)]TJ +ET +1 0 0 1 201.9461 586.5772 cm +0 g 0 G +1 0 0 1 -201.9461 -586.5772 cm +BT +/F8 9.9626 Tf 207.4357 586.5772 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 586.5772 cm +0 g 0 G +1 0 0 1 -484.4533 -586.5772 cm +BT +/F8 9.9626 Tf 484.4533 586.5772 Td[(64)]TJ +ET +1 0 0 1 494.4159 586.5772 cm +0 g 0 G +1 0 0 1 -328.7671 -11.9552 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -165.6488 -574.622 cm BT -/F8 9.9626 Tf 184.2347 621.2722 Td[(cd)]TJ +/F8 9.9626 Tf 165.6488 574.622 Td[(psb)]TJ ET -1 0 0 1 194.7951 621.2722 cm +1 0 0 1 181.2459 574.622 cm q []0 d 0 J @@ -2477,11 +2715,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -194.7951 -621.2722 cm +1 0 0 1 -181.2459 -574.622 cm BT -/F8 9.9626 Tf 197.7839 621.2722 Td[(get)]TJ +/F8 9.9626 Tf 184.2347 574.622 Td[(glob)]TJ ET -1 0 0 1 211.6652 621.2722 cm +1 0 0 1 203.0974 574.622 cm q []0 d 0 J @@ -2490,11 +2728,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -211.6652 -621.2722 cm +1 0 0 1 -203.0974 -574.622 cm BT -/F8 9.9626 Tf 214.654 621.2722 Td[(lo)-28(cal)]TJ +/F8 9.9626 Tf 206.0862 574.622 Td[(to)]TJ ET -1 0 0 1 235.4539 621.2722 cm +1 0 0 1 215.5396 574.622 cm q []0 d 0 J @@ -2503,44 +2741,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -235.4539 -621.2722 cm +1 0 0 1 -215.5396 -574.622 cm BT -/F8 9.9626 Tf 238.4427 621.2722 Td[(ro)28(ws)]TJ +/F8 9.9626 Tf 218.5284 574.622 Td[(lo)-28(c)]TJ ET -1 0 0 1 258.1743 621.2722 cm +1 0 0 1 230.9818 574.622 cm 0 g 0 G -1 0 0 1 -258.1743 -621.2722 cm +1 0 0 1 -230.9818 -574.622 cm BT -/F8 9.9626 Tf 261.676 621.2722 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 +/F8 9.9626 Tf 238.4301 574.622 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 621.2722 cm +1 0 0 1 484.4533 574.622 cm 0 g 0 G -1 0 0 1 -484.4533 -621.2722 cm +1 0 0 1 -484.4533 -574.622 cm BT -/F8 9.9626 Tf 484.4533 621.2722 Td[(67)]TJ +/F8 9.9626 Tf 484.4533 574.622 Td[(65)]TJ ET -1 0 0 1 494.4159 621.2722 cm +1 0 0 1 494.4159 574.622 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1223 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -609.1499 cm -BT -/F8 9.9626 Tf 165.6488 609.1499 Td[(psb)]TJ -ET -1 0 0 1 181.2459 609.1499 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -609.1499 cm +1 0 0 1 -165.6488 -562.6668 cm BT -/F8 9.9626 Tf 184.2347 609.1499 Td[(cd)]TJ +/F8 9.9626 Tf 165.6488 562.6668 Td[(psb)]TJ ET -1 0 0 1 194.7951 609.1499 cm +1 0 0 1 181.2459 562.6668 cm q []0 d 0 J @@ -2549,11 +2774,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -194.7951 -609.1499 cm +1 0 0 1 -181.2459 -562.6668 cm BT -/F8 9.9626 Tf 197.7839 609.1499 Td[(get)]TJ +/F8 9.9626 Tf 184.2347 562.6668 Td[(lo)-28(c)]TJ ET -1 0 0 1 211.6652 609.1499 cm +1 0 0 1 197.2858 562.6668 cm q []0 d 0 J @@ -2562,11 +2787,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -211.6652 -609.1499 cm +1 0 0 1 -197.2858 -562.6668 cm BT -/F8 9.9626 Tf 214.654 609.1499 Td[(lo)-28(cal)]TJ +/F8 9.9626 Tf 200.2746 562.6668 Td[(to)]TJ ET -1 0 0 1 235.4539 609.1499 cm +1 0 0 1 209.7281 562.6668 cm q []0 d 0 J @@ -2575,31 +2800,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -235.4539 -609.1499 cm +1 0 0 1 -209.7281 -562.6668 cm BT -/F8 9.9626 Tf 238.4427 609.1499 Td[(cols)]TJ +/F8 9.9626 Tf 212.7169 562.6668 Td[(glob)]TJ ET -1 0 0 1 254.549 609.1499 cm +1 0 0 1 230.9818 562.6668 cm 0 g 0 G -1 0 0 1 -254.549 -609.1499 cm +1 0 0 1 -230.9818 -562.6668 cm BT -/F8 9.9626 Tf 261.676 609.1499 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 +/F8 9.9626 Tf 238.4301 562.6668 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 609.1499 cm +1 0 0 1 484.4533 562.6668 cm 0 g 0 G -1 0 0 1 -484.4533 -609.1499 cm +1 0 0 1 -484.4533 -562.6668 cm BT -/F8 9.9626 Tf 484.4533 609.1499 Td[(68)]TJ +/F8 9.9626 Tf 484.4533 562.6668 Td[(67)]TJ ET -1 0 0 1 494.4159 609.1499 cm +1 0 0 1 494.4159 562.6668 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9551 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -597.0275 cm +1 0 0 1 -165.6488 -550.7117 cm BT -/F8 9.9626 Tf 165.6488 597.0275 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 550.7117 Td[(psb)]TJ ET -1 0 0 1 181.2459 597.0275 cm +1 0 0 1 181.2459 550.7117 cm q []0 d 0 J @@ -2608,11 +2833,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -597.0275 cm +1 0 0 1 -181.2459 -550.7117 cm BT -/F8 9.9626 Tf 184.2347 597.0275 Td[(cd)]TJ +/F8 9.9626 Tf 184.2347 550.7117 Td[(get)]TJ ET -1 0 0 1 194.7951 597.0275 cm +1 0 0 1 198.116 550.7117 cm q []0 d 0 J @@ -2621,11 +2846,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -194.7951 -597.0275 cm +1 0 0 1 -198.116 -550.7117 cm +BT +/F8 9.9626 Tf 201.1048 550.7117 Td[(b)-27(oun)1(dary)]TJ +ET +1 0 0 1 242.6436 550.7117 cm +0 g 0 G +1 0 0 1 -242.6436 -550.7117 cm +BT +/F8 9.9626 Tf 246.1787 550.7117 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 550.7117 cm +0 g 0 G +1 0 0 1 -484.4533 -550.7117 cm +BT +/F8 9.9626 Tf 484.4533 550.7117 Td[(68)]TJ +ET +1 0 0 1 494.4159 550.7117 cm +0 g 0 G +1 0 0 1 -328.7671 -11.9552 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -165.6488 -538.7565 cm BT -/F8 9.9626 Tf 197.7839 597.0275 Td[(get)]TJ +/F8 9.9626 Tf 165.6488 538.7565 Td[(psb)]TJ ET -1 0 0 1 211.6652 597.0275 cm +1 0 0 1 181.2459 538.7565 cm q []0 d 0 J @@ -2634,11 +2879,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -211.6652 -597.0275 cm +1 0 0 1 -181.2459 -538.7565 cm BT -/F8 9.9626 Tf 214.654 597.0275 Td[(glob)1(al)]TJ +/F8 9.9626 Tf 184.2347 538.7565 Td[(get)]TJ ET -1 0 0 1 241.2654 597.0275 cm +1 0 0 1 198.116 538.7565 cm q []0 d 0 J @@ -2647,57 +2892,43 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -241.2654 -597.0275 cm +1 0 0 1 -198.116 -538.7565 cm BT -/F8 9.9626 Tf 244.2542 597.0275 Td[(ro)28(ws)]TJ +/F8 9.9626 Tf 201.1048 538.7565 Td[(o)28(v)28(e)-1(r)1(lap)]TJ ET -1 0 0 1 263.9858 597.0275 cm +1 0 0 1 232.4042 538.7565 cm 0 g 0 G -1 0 0 1 -263.9858 -597.0275 cm +1 0 0 1 -232.4042 -538.7565 cm BT -/F8 9.9626 Tf 269.4246 597.0275 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 +/F8 9.9626 Tf 238.4301 538.7565 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 597.0275 cm +1 0 0 1 484.4533 538.7565 cm 0 g 0 G -1 0 0 1 -484.4533 -597.0275 cm +1 0 0 1 -484.4533 -538.7565 cm BT -/F8 9.9626 Tf 484.4533 597.0275 Td[(69)]TJ +/F8 9.9626 Tf 484.4533 538.7565 Td[(69)]TJ ET -1 0 0 1 494.4159 597.0275 cm +1 0 0 1 494.4159 538.7565 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -343.7111 -21.9178 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -584.9051 cm +1 0 0 1 -150.7048 -516.8387 cm BT -/F8 9.9626 Tf 165.6488 584.9051 Td[(psb)]TJ +/F29 9.9626 Tf 150.7048 516.8387 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 1 181.2459 584.9051 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -584.9051 cm +1 0 0 1 314.6808 516.8387 cm +0 g 0 G +1 0 0 1 -314.6808 -516.8387 cm BT -/F8 9.9626 Tf 184.2347 584.9051 Td[(cd)]TJ +/F29 9.9626 Tf 482.959 516.8387 Td[(70)]TJ ET -1 0 0 1 194.7951 584.9051 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -194.7951 -584.9051 cm +1 0 0 1 165.6488 504.8835 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -165.6488 -504.8835 cm BT -/F8 9.9626 Tf 197.7839 584.9051 Td[(get)]TJ +/F8 9.9626 Tf 165.6488 504.8835 Td[(psb)]TJ ET -1 0 0 1 211.6652 584.9051 cm +1 0 0 1 181.2459 504.8835 cm q []0 d 0 J @@ -2706,31 +2937,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -211.6652 -584.9051 cm +1 0 0 1 -181.2459 -504.8835 cm BT -/F8 9.9626 Tf 214.654 584.9051 Td[(con)28(te)-1(x)]TJ +/F8 9.9626 Tf 184.2347 504.8835 Td[(in)1(it)]TJ ET -1 0 0 1 242.8816 584.9051 cm +1 0 0 1 199.1787 504.8835 cm 0 g 0 G -1 0 0 1 -242.8816 -584.9051 cm +1 0 0 1 -199.1787 -504.8835 cm BT -/F8 9.9626 Tf 246.1787 584.9051 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 +/F8 9.9626 Tf 207.4357 504.8835 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 584.9051 cm +1 0 0 1 484.4533 504.8835 cm 0 g 0 G -1 0 0 1 -484.4533 -584.9051 cm +1 0 0 1 -484.4533 -504.8835 cm BT -/F8 9.9626 Tf 484.4533 584.9051 Td[(70)]TJ +/F8 9.9626 Tf 484.4533 504.8835 Td[(71)]TJ ET -1 0 0 1 494.4159 584.9051 cm +1 0 0 1 494.4159 504.8835 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -572.7827 cm +1 0 0 1 -165.6488 -492.9283 cm BT -/F8 9.9626 Tf 165.6488 572.7827 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 492.9283 Td[(psb)]TJ ET -1 0 0 1 181.2459 572.7827 cm +1 0 0 1 181.2459 492.9283 cm q []0 d 0 J @@ -2739,24 +2970,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -572.7827 cm +1 0 0 1 -181.2459 -492.9283 cm BT -/F8 9.9626 Tf 184.2347 572.7827 Td[(sp)]TJ +/F8 9.9626 Tf 184.2347 492.9283 Td[(in)1(fo)]TJ ET -1 0 0 1 194.297 572.7827 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -194.297 -572.7827 cm +1 0 0 1 200.5625 492.9283 cm +0 g 0 G +1 0 0 1 -200.5625 -492.9283 cm +BT +/F8 9.9626 Tf 207.4357 492.9283 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 492.9283 cm +0 g 0 G +1 0 0 1 -484.4533 -492.9283 cm +BT +/F8 9.9626 Tf 484.4533 492.9283 Td[(72)]TJ +ET +1 0 0 1 494.4159 492.9283 cm +0 g 0 G +1 0 0 1 -328.7671 -11.9551 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -165.6488 -480.9732 cm BT -/F8 9.9626 Tf 197.2858 572.7827 Td[(get)]TJ +/F8 9.9626 Tf 165.6488 480.9732 Td[(psb)]TJ ET -1 0 0 1 211.1671 572.7827 cm +1 0 0 1 181.2459 480.9732 cm q []0 d 0 J @@ -2765,44 +3003,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -211.1671 -572.7827 cm +1 0 0 1 -181.2459 -480.9732 cm BT -/F8 9.9626 Tf 214.1559 572.7827 Td[(nr)1(o)28(w)-1(s)]TJ +/F8 9.9626 Tf 184.2347 480.9732 Td[(exit)]TJ ET -1 0 0 1 239.4223 572.7827 cm +1 0 0 1 200.5624 480.9732 cm 0 g 0 G -1 0 0 1 -239.4223 -572.7827 cm +1 0 0 1 -200.5624 -480.9732 cm BT -/F8 9.9626 Tf 246.1787 572.7827 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 +/F8 9.9626 Tf 207.4357 480.9732 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 572.7827 cm +1 0 0 1 484.4533 480.9732 cm 0 g 0 G -1 0 0 1 -484.4533 -572.7827 cm +1 0 0 1 -484.4533 -480.9732 cm BT -/F8 9.9626 Tf 484.4533 572.7827 Td[(71)]TJ +/F8 9.9626 Tf 484.4533 480.9732 Td[(73)]TJ ET -1 0 0 1 494.4159 572.7827 cm +1 0 0 1 494.4159 480.9732 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1223 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -560.6604 cm -BT -/F8 9.9626 Tf 165.6488 560.6604 Td[(psb)]TJ -ET -1 0 0 1 181.2459 560.6604 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -560.6604 cm +1 0 0 1 -165.6488 -469.018 cm BT -/F8 9.9626 Tf 184.2347 560.6604 Td[(sp)]TJ +/F8 9.9626 Tf 165.6488 469.018 Td[(psb)]TJ ET -1 0 0 1 194.297 560.6604 cm +1 0 0 1 181.2459 469.018 cm q []0 d 0 J @@ -2811,11 +3036,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -194.297 -560.6604 cm +1 0 0 1 -181.2459 -469.018 cm BT -/F8 9.9626 Tf 197.2858 560.6604 Td[(get)]TJ +/F8 9.9626 Tf 184.2347 469.018 Td[(get)]TJ ET -1 0 0 1 211.1671 560.6604 cm +1 0 0 1 198.116 469.018 cm q []0 d 0 J @@ -2824,31 +3049,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -211.1671 -560.6604 cm +1 0 0 1 -198.116 -469.018 cm BT -/F8 9.9626 Tf 214.1559 560.6604 Td[(ncols)]TJ +/F8 9.9626 Tf 201.1048 469.018 Td[(mpicomm)]TJ ET -1 0 0 1 235.797 560.6604 cm +1 0 0 1 243.7229 469.018 cm 0 g 0 G -1 0 0 1 -235.797 -560.6604 cm +1 0 0 1 -243.7229 -469.018 cm BT -/F8 9.9626 Tf 238.4301 560.6604 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 +/F8 9.9626 Tf 253.9274 469.018 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 560.6604 cm +1 0 0 1 484.4533 469.018 cm 0 g 0 G -1 0 0 1 -484.4533 -560.6604 cm +1 0 0 1 -484.4533 -469.018 cm BT -/F8 9.9626 Tf 484.4533 560.6604 Td[(72)]TJ +/F8 9.9626 Tf 484.4533 469.018 Td[(74)]TJ ET -1 0 0 1 494.4159 560.6604 cm +1 0 0 1 494.4159 469.018 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -548.538 cm +1 0 0 1 -165.6488 -457.0628 cm BT -/F8 9.9626 Tf 165.6488 548.538 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 457.0628 Td[(psb)]TJ ET -1 0 0 1 181.2459 548.538 cm +1 0 0 1 181.2459 457.0628 cm q []0 d 0 J @@ -2857,11 +3082,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -548.538 cm +1 0 0 1 -181.2459 -457.0628 cm BT -/F8 9.9626 Tf 184.2347 548.538 Td[(sp)]TJ +/F8 9.9626 Tf 184.2347 457.0628 Td[(get)]TJ ET -1 0 0 1 194.297 548.538 cm +1 0 0 1 198.116 457.0628 cm q []0 d 0 J @@ -2870,11 +3095,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -194.297 -548.538 cm +1 0 0 1 -198.116 -457.0628 cm +BT +/F8 9.9626 Tf 201.1048 457.0628 Td[(ran)1(k)]TJ +ET +1 0 0 1 220.7811 457.0628 cm +0 g 0 G +1 0 0 1 -220.7811 -457.0628 cm +BT +/F8 9.9626 Tf 230.6815 457.0628 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 457.0628 cm +0 g 0 G +1 0 0 1 -484.4533 -457.0628 cm +BT +/F8 9.9626 Tf 484.4533 457.0628 Td[(75)]TJ +ET +1 0 0 1 494.4159 457.0628 cm +0 g 0 G +1 0 0 1 -328.7671 -11.9551 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -165.6488 -445.1077 cm BT -/F8 9.9626 Tf 197.2858 548.538 Td[(get)]TJ +/F8 9.9626 Tf 165.6488 445.1077 Td[(psb)]TJ ET -1 0 0 1 211.1671 548.538 cm +1 0 0 1 181.2459 445.1077 cm q []0 d 0 J @@ -2883,43 +3128,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -211.1671 -548.538 cm +1 0 0 1 -181.2459 -445.1077 cm BT -/F8 9.9626 Tf 214.1559 548.538 Td[(nn)1(z)-1(eros)]TJ +/F8 9.9626 Tf 184.2347 445.1077 Td[(wtime)]TJ ET -1 0 0 1 246.8943 548.538 cm +1 0 0 1 210.8018 445.1077 cm 0 g 0 G -1 0 0 1 -246.8943 -548.538 cm +1 0 0 1 -210.8018 -445.1077 cm BT -/F8 9.9626 Tf 253.9274 548.538 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 +/F8 9.9626 Tf 215.1843 445.1077 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 548.538 cm +1 0 0 1 484.4533 445.1077 cm 0 g 0 G -1 0 0 1 -484.4533 -548.538 cm +1 0 0 1 -484.4533 -445.1077 cm BT -/F8 9.9626 Tf 484.4533 548.538 Td[(73)]TJ +/F8 9.9626 Tf 484.4533 445.1077 Td[(76)]TJ ET -1 0 0 1 494.4159 548.538 cm +1 0 0 1 494.4159 445.1077 cm 0 g 0 G -1 0 0 1 -343.7111 -22.1965 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -150.7048 -526.3415 cm -BT -/F29 9.9626 Tf 150.7048 526.3415 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 526.3415 cm -0 g 0 G -1 0 0 1 -314.6808 -526.3415 cm -BT -/F29 9.9626 Tf 482.959 526.3415 Td[(74)]TJ -ET -1 0 0 1 165.6488 514.2191 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -514.2191 cm +1 0 0 1 -165.6488 -433.1525 cm BT -/F8 9.9626 Tf 165.6488 514.2191 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 433.1525 Td[(psb)]TJ ET -1 0 0 1 181.2459 514.2191 cm +1 0 0 1 181.2459 433.1525 cm q []0 d 0 J @@ -2928,31 +3161,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -514.2191 cm +1 0 0 1 -181.2459 -433.1525 cm BT -/F8 9.9626 Tf 184.2347 514.2191 Td[(in)1(it)]TJ +/F8 9.9626 Tf 184.2347 433.1525 Td[(bar)1(rier)]TJ ET -1 0 0 1 199.1787 514.2191 cm +1 0 0 1 213.6522 433.1525 cm 0 g 0 G -1 0 0 1 -199.1787 -514.2191 cm +1 0 0 1 -213.6522 -433.1525 cm BT -/F8 9.9626 Tf 207.4357 514.2191 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 +/F8 9.9626 Tf 222.9329 433.1525 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 514.2191 cm +1 0 0 1 484.4533 433.1525 cm 0 g 0 G -1 0 0 1 -484.4533 -514.2191 cm +1 0 0 1 -484.4533 -433.1525 cm BT -/F8 9.9626 Tf 484.4533 514.2191 Td[(75)]TJ +/F8 9.9626 Tf 484.4533 433.1525 Td[(77)]TJ ET -1 0 0 1 494.4159 514.2191 cm +1 0 0 1 494.4159 433.1525 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1223 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -502.0968 cm +1 0 0 1 -165.6488 -421.1973 cm BT -/F8 9.9626 Tf 165.6488 502.0968 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 421.1973 Td[(psb)]TJ ET -1 0 0 1 181.2459 502.0968 cm +1 0 0 1 181.2459 421.1973 cm q []0 d 0 J @@ -2961,31 +3194,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -502.0968 cm +1 0 0 1 -181.2459 -421.1973 cm BT -/F8 9.9626 Tf 184.2347 502.0968 Td[(in)1(fo)]TJ +/F8 9.9626 Tf 184.2347 421.1973 Td[(ab)-27(ort)]TJ ET -1 0 0 1 200.5625 502.0968 cm +1 0 0 1 207.7854 421.1973 cm 0 g 0 G -1 0 0 1 -200.5625 -502.0968 cm +1 0 0 1 -207.7854 -421.1973 cm BT -/F8 9.9626 Tf 207.4357 502.0968 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 +/F8 9.9626 Tf 215.1843 421.1973 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 502.0968 cm +1 0 0 1 484.4533 421.1973 cm 0 g 0 G -1 0 0 1 -484.4533 -502.0968 cm +1 0 0 1 -484.4533 -421.1973 cm BT -/F8 9.9626 Tf 484.4533 502.0968 Td[(76)]TJ +/F8 9.9626 Tf 484.4533 421.1973 Td[(78)]TJ ET -1 0 0 1 494.4159 502.0968 cm +1 0 0 1 494.4159 421.1973 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9551 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -489.9744 cm +1 0 0 1 -165.6488 -409.2422 cm BT -/F8 9.9626 Tf 165.6488 489.9744 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 409.2422 Td[(psb)]TJ ET -1 0 0 1 181.2459 489.9744 cm +1 0 0 1 181.2459 409.2422 cm q []0 d 0 J @@ -2994,31 +3227,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -489.9744 cm +1 0 0 1 -181.2459 -409.2422 cm BT -/F8 9.9626 Tf 184.2347 489.9744 Td[(exit)]TJ +/F8 9.9626 Tf 184.2347 409.2422 Td[(b)-27(c)-1(ast)]TJ ET -1 0 0 1 200.5624 489.9744 cm +1 0 0 1 207.2596 409.2422 cm 0 g 0 G -1 0 0 1 -200.5624 -489.9744 cm +1 0 0 1 -207.2596 -409.2422 cm BT -/F8 9.9626 Tf 207.4357 489.9744 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 +/F8 9.9626 Tf 215.1843 409.2422 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 489.9744 cm +1 0 0 1 484.4533 409.2422 cm 0 g 0 G -1 0 0 1 -484.4533 -489.9744 cm +1 0 0 1 -484.4533 -409.2422 cm BT -/F8 9.9626 Tf 484.4533 489.9744 Td[(77)]TJ +/F8 9.9626 Tf 484.4533 409.2422 Td[(79)]TJ ET -1 0 0 1 494.4159 489.9744 cm +1 0 0 1 494.4159 409.2422 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -477.852 cm +1 0 0 1 -165.6488 -397.287 cm BT -/F8 9.9626 Tf 165.6488 477.852 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 397.287 Td[(psb)]TJ ET -1 0 0 1 181.2459 477.852 cm +1 0 0 1 181.2459 397.287 cm q []0 d 0 J @@ -3027,11 +3260,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -477.852 cm +1 0 0 1 -181.2459 -397.287 cm +BT +/F8 9.9626 Tf 184.2347 397.287 Td[(sum)]TJ +ET +1 0 0 1 202.0015 397.287 cm +0 g 0 G +1 0 0 1 -202.0015 -397.287 cm +BT +/F8 9.9626 Tf 207.4357 397.287 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 397.287 cm +0 g 0 G +1 0 0 1 -484.4533 -397.287 cm +BT +/F8 9.9626 Tf 484.4533 397.287 Td[(80)]TJ +ET +1 0 0 1 494.4159 397.287 cm +0 g 0 G +1 0 0 1 -328.7671 -11.9552 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -165.6488 -385.3318 cm BT -/F8 9.9626 Tf 184.2347 477.852 Td[(get)]TJ +/F8 9.9626 Tf 165.6488 385.3318 Td[(psb)]TJ ET -1 0 0 1 198.116 477.852 cm +1 0 0 1 181.2459 385.3318 cm q []0 d 0 J @@ -3040,31 +3293,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -198.116 -477.852 cm +1 0 0 1 -181.2459 -385.3318 cm BT -/F8 9.9626 Tf 201.1048 477.852 Td[(mpicomm)]TJ +/F8 9.9626 Tf 184.2347 385.3318 Td[(amx)]TJ ET -1 0 0 1 243.7229 477.852 cm +1 0 0 1 202.7764 385.3318 cm 0 g 0 G -1 0 0 1 -243.7229 -477.852 cm +1 0 0 1 -202.7764 -385.3318 cm BT -/F8 9.9626 Tf 253.9274 477.852 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 +/F8 9.9626 Tf 207.4357 385.3318 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 477.852 cm +1 0 0 1 484.4533 385.3318 cm 0 g 0 G -1 0 0 1 -484.4533 -477.852 cm +1 0 0 1 -484.4533 -385.3318 cm BT -/F8 9.9626 Tf 484.4533 477.852 Td[(78)]TJ +/F8 9.9626 Tf 484.4533 385.3318 Td[(81)]TJ ET -1 0 0 1 494.4159 477.852 cm +1 0 0 1 494.4159 385.3318 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9551 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -465.7296 cm +1 0 0 1 -165.6488 -373.3767 cm BT -/F8 9.9626 Tf 165.6488 465.7296 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 373.3767 Td[(psb)]TJ ET -1 0 0 1 181.2459 465.7296 cm +1 0 0 1 181.2459 373.3767 cm q []0 d 0 J @@ -3073,275 +3326,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -465.7296 cm +1 0 0 1 -181.2459 -373.3767 cm BT -/F8 9.9626 Tf 184.2347 465.7296 Td[(get)]TJ +/F8 9.9626 Tf 184.2347 373.3767 Td[(amn)]TJ ET -1 0 0 1 198.116 465.7296 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -198.116 -465.7296 cm -BT -/F8 9.9626 Tf 201.1048 465.7296 Td[(ran)1(k)]TJ -ET -1 0 0 1 220.7811 465.7296 cm -0 g 0 G -1 0 0 1 -220.7811 -465.7296 cm -BT -/F8 9.9626 Tf 230.6815 465.7296 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 465.7296 cm -0 g 0 G -1 0 0 1 -484.4533 -465.7296 cm -BT -/F8 9.9626 Tf 484.4533 465.7296 Td[(79)]TJ -ET -1 0 0 1 494.4159 465.7296 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1223 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -453.6073 cm -BT -/F8 9.9626 Tf 165.6488 453.6073 Td[(psb)]TJ -ET -1 0 0 1 181.2459 453.6073 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -453.6073 cm -BT -/F8 9.9626 Tf 184.2347 453.6073 Td[(wtime)]TJ -ET -1 0 0 1 210.8018 453.6073 cm -0 g 0 G -1 0 0 1 -210.8018 -453.6073 cm -BT -/F8 9.9626 Tf 215.1843 453.6073 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 453.6073 cm -0 g 0 G -1 0 0 1 -484.4533 -453.6073 cm -BT -/F8 9.9626 Tf 484.4533 453.6073 Td[(80)]TJ -ET -1 0 0 1 494.4159 453.6073 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -441.4849 cm -BT -/F8 9.9626 Tf 165.6488 441.4849 Td[(psb)]TJ -ET -1 0 0 1 181.2459 441.4849 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -441.4849 cm -BT -/F8 9.9626 Tf 184.2347 441.4849 Td[(bar)1(rier)]TJ -ET -1 0 0 1 213.6522 441.4849 cm -0 g 0 G -1 0 0 1 -213.6522 -441.4849 cm -BT -/F8 9.9626 Tf 222.9329 441.4849 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 441.4849 cm -0 g 0 G -1 0 0 1 -484.4533 -441.4849 cm -BT -/F8 9.9626 Tf 484.4533 441.4849 Td[(81)]TJ -ET -1 0 0 1 494.4159 441.4849 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -429.3625 cm -BT -/F8 9.9626 Tf 165.6488 429.3625 Td[(psb)]TJ -ET -1 0 0 1 181.2459 429.3625 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -429.3625 cm -BT -/F8 9.9626 Tf 184.2347 429.3625 Td[(ab)-27(ort)]TJ -ET -1 0 0 1 207.7854 429.3625 cm -0 g 0 G -1 0 0 1 -207.7854 -429.3625 cm -BT -/F8 9.9626 Tf 215.1843 429.3625 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 429.3625 cm -0 g 0 G -1 0 0 1 -484.4533 -429.3625 cm -BT -/F8 9.9626 Tf 484.4533 429.3625 Td[(82)]TJ -ET -1 0 0 1 494.4159 429.3625 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1223 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -417.2402 cm -BT -/F8 9.9626 Tf 165.6488 417.2402 Td[(psb)]TJ -ET -1 0 0 1 181.2459 417.2402 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -417.2402 cm -BT -/F8 9.9626 Tf 184.2347 417.2402 Td[(b)-27(c)-1(ast)]TJ -ET -1 0 0 1 207.2596 417.2402 cm -0 g 0 G -1 0 0 1 -207.2596 -417.2402 cm -BT -/F8 9.9626 Tf 215.1843 417.2402 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 417.2402 cm -0 g 0 G -1 0 0 1 -484.4533 -417.2402 cm -BT -/F8 9.9626 Tf 484.4533 417.2402 Td[(83)]TJ -ET -1 0 0 1 494.4159 417.2402 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -405.1178 cm -BT -/F8 9.9626 Tf 165.6488 405.1178 Td[(psb)]TJ -ET -1 0 0 1 181.2459 405.1178 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -405.1178 cm -BT -/F8 9.9626 Tf 184.2347 405.1178 Td[(sum)]TJ -ET -1 0 0 1 202.0015 405.1178 cm -0 g 0 G -1 0 0 1 -202.0015 -405.1178 cm -BT -/F8 9.9626 Tf 207.4357 405.1178 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 405.1178 cm -0 g 0 G -1 0 0 1 -484.4533 -405.1178 cm -BT -/F8 9.9626 Tf 484.4533 405.1178 Td[(84)]TJ -ET -1 0 0 1 494.4159 405.1178 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -392.9954 cm -BT -/F8 9.9626 Tf 165.6488 392.9954 Td[(psb)]TJ -ET -1 0 0 1 181.2459 392.9954 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -392.9954 cm -BT -/F8 9.9626 Tf 184.2347 392.9954 Td[(amx)]TJ -ET -1 0 0 1 202.7764 392.9954 cm -0 g 0 G -1 0 0 1 -202.7764 -392.9954 cm -BT -/F8 9.9626 Tf 207.4357 392.9954 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 392.9954 cm -0 g 0 G -1 0 0 1 -484.4533 -392.9954 cm -BT -/F8 9.9626 Tf 484.4533 392.9954 Td[(85)]TJ -ET -1 0 0 1 494.4159 392.9954 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -380.873 cm -BT -/F8 9.9626 Tf 165.6488 380.873 Td[(psb)]TJ -ET -1 0 0 1 181.2459 380.873 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -380.873 cm -BT -/F8 9.9626 Tf 184.2347 380.873 Td[(amn)]TJ -ET -1 0 0 1 203.0531 380.873 cm +1 0 0 1 203.0531 373.3767 cm 0 g 0 G -1 0 0 1 -203.0531 -380.873 cm +1 0 0 1 -203.0531 -373.3767 cm BT -/F8 9.9626 Tf 207.4357 380.873 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 +/F8 9.9626 Tf 207.4357 373.3767 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 380.873 cm +1 0 0 1 484.4533 373.3767 cm 0 g 0 G -1 0 0 1 -484.4533 -380.873 cm +1 0 0 1 -484.4533 -373.3767 cm BT -/F8 9.9626 Tf 484.4533 380.873 Td[(86)]TJ +/F8 9.9626 Tf 484.4533 373.3767 Td[(82)]TJ ET -1 0 0 1 494.4159 380.873 cm +1 0 0 1 494.4159 373.3767 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1223 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -368.7507 cm +1 0 0 1 -165.6488 -361.4215 cm BT -/F8 9.9626 Tf 165.6488 368.7507 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 361.4215 Td[(psb)]TJ ET -1 0 0 1 181.2459 368.7507 cm +1 0 0 1 181.2459 361.4215 cm q []0 d 0 J @@ -3350,31 +3359,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -368.7507 cm +1 0 0 1 -181.2459 -361.4215 cm BT -/F8 9.9626 Tf 184.2347 368.7507 Td[(snd)]TJ +/F8 9.9626 Tf 184.2347 361.4215 Td[(snd)]TJ ET -1 0 0 1 199.2341 368.7507 cm +1 0 0 1 199.2341 361.4215 cm 0 g 0 G -1 0 0 1 -199.2341 -368.7507 cm +1 0 0 1 -199.2341 -361.4215 cm BT -/F8 9.9626 Tf 207.4357 368.7507 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 +/F8 9.9626 Tf 207.4357 361.4215 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 368.7507 cm +1 0 0 1 484.4533 361.4215 cm 0 g 0 G -1 0 0 1 -484.4533 -368.7507 cm +1 0 0 1 -484.4533 -361.4215 cm BT -/F8 9.9626 Tf 484.4533 368.7507 Td[(87)]TJ +/F8 9.9626 Tf 484.4533 361.4215 Td[(83)]TJ ET -1 0 0 1 494.4159 368.7507 cm +1 0 0 1 494.4159 361.4215 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -356.6283 cm +1 0 0 1 -165.6488 -349.4663 cm BT -/F8 9.9626 Tf 165.6488 356.6283 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 349.4663 Td[(psb)]TJ ET -1 0 0 1 181.2459 356.6283 cm +1 0 0 1 181.2459 349.4663 cm q []0 d 0 J @@ -3383,43 +3392,43 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -356.6283 cm +1 0 0 1 -181.2459 -349.4663 cm BT -/F8 9.9626 Tf 184.2347 356.6283 Td[(rcv)]TJ +/F8 9.9626 Tf 184.2347 349.4663 Td[(rcv)]TJ ET -1 0 0 1 197.8227 356.6283 cm +1 0 0 1 197.8227 349.4663 cm 0 g 0 G -1 0 0 1 -197.8227 -356.6283 cm +1 0 0 1 -197.8227 -349.4663 cm BT -/F8 9.9626 Tf 207.4357 356.6283 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 +/F8 9.9626 Tf 207.4357 349.4663 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 356.6283 cm +1 0 0 1 484.4533 349.4663 cm 0 g 0 G -1 0 0 1 -484.4533 -356.6283 cm +1 0 0 1 -484.4533 -349.4663 cm BT -/F8 9.9626 Tf 484.4533 356.6283 Td[(88)]TJ +/F8 9.9626 Tf 484.4533 349.4663 Td[(84)]TJ ET -1 0 0 1 494.4159 356.6283 cm +1 0 0 1 494.4159 349.4663 cm 0 g 0 G -1 0 0 1 -343.7111 -22.1965 cm +1 0 0 1 -343.7111 -21.9178 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -150.7048 -334.4318 cm +1 0 0 1 -150.7048 -327.5485 cm BT -/F29 9.9626 Tf 150.7048 334.4318 Td[(8)-925(Er)1(ror)-383(hand)1(l)-1(ing)]TJ +/F29 9.9626 Tf 150.7048 327.5485 Td[(8)-925(Er)1(ror)-383(hand)1(l)-1(ing)]TJ ET -1 0 0 1 240.0016 334.4318 cm +1 0 0 1 240.0016 327.5485 cm 0 g 0 G -1 0 0 1 -240.0016 -334.4318 cm +1 0 0 1 -240.0016 -327.5485 cm BT -/F29 9.9626 Tf 482.959 334.4318 Td[(89)]TJ +/F29 9.9626 Tf 482.959 327.5485 Td[(85)]TJ ET -1 0 0 1 165.6488 322.3094 cm +1 0 0 1 165.6488 315.5933 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -322.3094 cm +1 0 0 1 -165.6488 -315.5933 cm BT -/F8 9.9626 Tf 165.6488 322.3094 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 315.5933 Td[(psb)]TJ ET -1 0 0 1 181.2459 322.3094 cm +1 0 0 1 181.2459 315.5933 cm q []0 d 0 J @@ -3428,31 +3437,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -322.3094 cm +1 0 0 1 -181.2459 -315.5933 cm BT -/F8 9.9626 Tf 184.2347 322.3094 Td[(errp)1(ush)]TJ +/F8 9.9626 Tf 184.2347 315.5933 Td[(errp)1(ush)]TJ ET -1 0 0 1 217.0008 322.3094 cm +1 0 0 1 217.0008 315.5933 cm 0 g 0 G -1 0 0 1 -217.0008 -322.3094 cm +1 0 0 1 -217.0008 -315.5933 cm BT -/F8 9.9626 Tf 222.9329 322.3094 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 +/F8 9.9626 Tf 222.9329 315.5933 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 322.3094 cm +1 0 0 1 484.4533 315.5933 cm 0 g 0 G -1 0 0 1 -484.4533 -322.3094 cm +1 0 0 1 -484.4533 -315.5933 cm BT -/F8 9.9626 Tf 484.4533 322.3094 Td[(91)]TJ +/F8 9.9626 Tf 484.4533 315.5933 Td[(87)]TJ ET -1 0 0 1 494.4159 322.3094 cm +1 0 0 1 494.4159 315.5933 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1223 cm +1 0 0 1 -328.7671 -11.9551 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -310.1871 cm +1 0 0 1 -165.6488 -303.6382 cm BT -/F8 9.9626 Tf 165.6488 310.1871 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 303.6382 Td[(psb)]TJ ET -1 0 0 1 181.2459 310.1871 cm +1 0 0 1 181.2459 303.6382 cm q []0 d 0 J @@ -3461,31 +3470,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -310.1871 cm +1 0 0 1 -181.2459 -303.6382 cm BT -/F8 9.9626 Tf 184.2347 310.1871 Td[(error)]TJ +/F8 9.9626 Tf 184.2347 303.6382 Td[(error)]TJ ET -1 0 0 1 205.35 310.1871 cm +1 0 0 1 205.35 303.6382 cm 0 g 0 G -1 0 0 1 -205.35 -310.1871 cm +1 0 0 1 -205.35 -303.6382 cm BT -/F8 9.9626 Tf 215.1843 310.1871 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 +/F8 9.9626 Tf 215.1843 303.6382 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 310.1871 cm +1 0 0 1 484.4533 303.6382 cm 0 g 0 G -1 0 0 1 -484.4533 -310.1871 cm +1 0 0 1 -484.4533 -303.6382 cm BT -/F8 9.9626 Tf 484.4533 310.1871 Td[(92)]TJ +/F8 9.9626 Tf 484.4533 303.6382 Td[(88)]TJ ET -1 0 0 1 494.4159 310.1871 cm +1 0 0 1 494.4159 303.6382 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -298.0647 cm +1 0 0 1 -165.6488 -291.683 cm BT -/F8 9.9626 Tf 165.6488 298.0647 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 291.683 Td[(psb)]TJ ET -1 0 0 1 181.2459 298.0647 cm +1 0 0 1 181.2459 291.683 cm q []0 d 0 J @@ -3494,11 +3503,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -298.0647 cm +1 0 0 1 -181.2459 -291.683 cm BT -/F8 9.9626 Tf 184.2347 298.0647 Td[(se)-1(t)]TJ +/F8 9.9626 Tf 184.2347 291.683 Td[(se)-1(t)]TJ ET -1 0 0 1 197.0644 298.0647 cm +1 0 0 1 197.0644 291.683 cm q []0 d 0 J @@ -3507,31 +3516,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -197.0644 -298.0647 cm +1 0 0 1 -197.0644 -291.683 cm BT -/F8 9.9626 Tf 200.0532 298.0647 Td[(errv)28(erb)-27(os)-1(i)1(t)27(y)]TJ +/F8 9.9626 Tf 200.0532 291.683 Td[(errv)28(erb)-27(os)-1(i)1(t)27(y)]TJ ET -1 0 0 1 251.9421 298.0647 cm +1 0 0 1 251.9421 291.683 cm 0 g 0 G -1 0 0 1 -251.9421 -298.0647 cm +1 0 0 1 -251.9421 -291.683 cm BT -/F8 9.9626 Tf 261.676 298.0647 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 +/F8 9.9626 Tf 261.676 291.683 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 1 484.4533 298.0647 cm +1 0 0 1 484.4533 291.683 cm 0 g 0 G -1 0 0 1 -484.4533 -298.0647 cm +1 0 0 1 -484.4533 -291.683 cm BT -/F8 9.9626 Tf 484.4533 298.0647 Td[(93)]TJ +/F8 9.9626 Tf 484.4533 291.683 Td[(89)]TJ ET -1 0 0 1 494.4159 298.0647 cm +1 0 0 1 494.4159 291.683 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -285.9423 cm +1 0 0 1 -165.6488 -279.7278 cm BT -/F8 9.9626 Tf 165.6488 285.9423 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 279.7278 Td[(psb)]TJ ET -1 0 0 1 181.2459 285.9423 cm +1 0 0 1 181.2459 279.7278 cm q []0 d 0 J @@ -3540,11 +3549,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -285.9423 cm +1 0 0 1 -181.2459 -279.7278 cm BT -/F8 9.9626 Tf 184.2347 285.9423 Td[(se)-1(t)]TJ +/F8 9.9626 Tf 184.2347 279.7278 Td[(se)-1(t)]TJ ET -1 0 0 1 197.0644 285.9423 cm +1 0 0 1 197.0644 279.7278 cm q []0 d 0 J @@ -3553,31 +3562,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -197.0644 -285.9423 cm +1 0 0 1 -197.0644 -279.7278 cm BT -/F8 9.9626 Tf 200.0532 285.9423 Td[(erraction)]TJ +/F8 9.9626 Tf 200.0532 279.7278 Td[(erraction)]TJ ET -1 0 0 1 238.8522 285.9423 cm +1 0 0 1 238.8522 279.7278 cm 0 g 0 G -1 0 0 1 -238.8522 -285.9423 cm +1 0 0 1 -238.8522 -279.7278 cm BT -/F8 9.9626 Tf 246.1787 285.9423 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 +/F8 9.9626 Tf 246.1787 279.7278 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 285.9423 cm +1 0 0 1 484.4533 279.7278 cm 0 g 0 G -1 0 0 1 -484.4533 -285.9423 cm +1 0 0 1 -484.4533 -279.7278 cm BT -/F8 9.9626 Tf 484.4533 285.9423 Td[(94)]TJ +/F8 9.9626 Tf 484.4533 279.7278 Td[(90)]TJ ET -1 0 0 1 494.4159 285.9423 cm +1 0 0 1 494.4159 279.7278 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9552 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -273.8199 cm +1 0 0 1 -165.6488 -267.7726 cm BT -/F8 9.9626 Tf 165.6488 273.8199 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 267.7726 Td[(psb)]TJ ET -1 0 0 1 181.2459 273.8199 cm +1 0 0 1 181.2459 267.7726 cm q []0 d 0 J @@ -3586,109 +3595,55 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -273.8199 cm -BT -/F8 9.9626 Tf 184.2347 273.8199 Td[(errcom)-1(m)]TJ -ET -1 0 0 1 222.4803 273.8199 cm -0 g 0 G -1 0 0 1 -222.4803 -273.8199 cm +1 0 0 1 -181.2459 -267.7726 cm BT -/F8 9.9626 Tf 230.6815 273.8199 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 +/F8 9.9626 Tf 184.2347 267.7726 Td[(errcom)-1(m)]TJ ET -1 0 0 1 484.4533 273.8199 cm +1 0 0 1 222.4803 267.7726 cm 0 g 0 G -1 0 0 1 -484.4533 -273.8199 cm +1 0 0 1 -222.4803 -267.7726 cm BT -/F8 9.9626 Tf 484.4533 273.8199 Td[(95)]TJ +/F8 9.9626 Tf 230.6815 267.7726 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 1 494.4159 273.8199 cm +1 0 0 1 484.4533 267.7726 cm 0 g 0 G -1 0 0 1 -343.7111 -22.1965 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -150.7048 -251.6234 cm +1 0 0 1 -484.4533 -267.7726 cm BT -/F29 9.9626 Tf 150.7048 251.6234 Td[(9)-925(Preconditi)-1(oner)-383(r)1(outi)-1(nes)]TJ +/F8 9.9626 Tf 484.4533 267.7726 Td[(91)]TJ ET -1 0 0 1 284.2881 251.6234 cm +1 0 0 1 494.4159 267.7726 cm 0 g 0 G -1 0 0 1 -284.2881 -251.6234 cm -BT -/F29 9.9626 Tf 482.959 251.6234 Td[(96)]TJ -ET -1 0 0 1 165.6488 239.5011 cm +1 0 0 1 -343.7111 -21.9178 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -239.5011 cm -BT -/F8 9.9626 Tf 165.6488 239.5011 Td[(psb)]TJ -ET -1 0 0 1 181.2459 239.5011 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -239.5011 cm -BT -/F8 9.9626 Tf 184.2347 239.5011 Td[(pr)1(e)-1(cs)-1(et)]TJ -ET -1 0 0 1 214.7592 239.5011 cm -0 g 0 G -1 0 0 1 -214.7592 -239.5011 cm +1 0 0 1 -150.7048 -245.8548 cm BT -/F8 9.9626 Tf 222.9329 239.5011 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 +/F29 9.9626 Tf 150.7048 245.8548 Td[(9)-925(Util)-1(iti)-1(es)]TJ ET -1 0 0 1 484.4533 239.5011 cm +1 0 0 1 205.8741 245.8548 cm 0 g 0 G -1 0 0 1 -484.4533 -239.5011 cm +1 0 0 1 -205.8741 -245.8548 cm BT -/F8 9.9626 Tf 484.4533 239.5011 Td[(97)]TJ +/F29 9.9626 Tf 482.959 245.8548 Td[(92)]TJ ET -1 0 0 1 494.4159 239.5011 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 150.7048 223.937 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -227.3787 cm -BT -/F8 9.9626 Tf 165.6488 227.3787 Td[(psb)]TJ -ET -1 0 0 1 181.2459 227.3787 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -227.3787 cm -BT -/F8 9.9626 Tf 184.2347 227.3787 Td[(pr)1(e)-1(cbl)1(d)]TJ -ET -1 0 0 1 216.3643 227.3787 cm -0 g 0 G -1 0 0 1 -216.3643 -227.3787 cm +1 0 0 1 -150.7048 -223.937 cm BT -/F8 9.9626 Tf 222.9329 227.3787 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 +/F29 9.9626 Tf 150.7048 223.937 Td[(10)-350(Preconditi)-1(oner)-383(r)1(outi)-1(nes)]TJ ET -1 0 0 1 484.4533 227.3787 cm +1 0 0 1 284.2881 223.937 cm 0 g 0 G -1 0 0 1 -484.4533 -227.3787 cm +1 0 0 1 -284.2881 -223.937 cm BT -/F8 9.9626 Tf 484.4533 227.3787 Td[(98)]TJ +/F29 9.9626 Tf 482.959 223.937 Td[(93)]TJ ET -1 0 0 1 494.4159 227.3787 cm -0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 165.6488 211.9818 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -215.2563 cm +1 0 0 1 -165.6488 -211.9818 cm BT -/F8 9.9626 Tf 165.6488 215.2563 Td[(psb)]TJ +/F8 9.9626 Tf 165.6488 211.9818 Td[(psb)]TJ ET -1 0 0 1 181.2459 215.2563 cm +1 0 0 1 181.2459 211.9818 cm q []0 d 0 J @@ -3697,44 +3652,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -181.2459 -215.2563 cm +1 0 0 1 -181.2459 -211.9818 cm BT -/F8 9.9626 Tf 184.2347 215.2563 Td[(pr)1(e)-1(capl)1(y)]TJ +/F8 9.9626 Tf 184.2347 211.9818 Td[(pr)1(e)-1(cs)-1(et)]TJ ET -1 0 0 1 221.0689 215.2563 cm +1 0 0 1 214.7592 211.9818 cm 0 g 0 G -1 0 0 1 -221.0689 -215.2563 cm +1 0 0 1 -214.7592 -211.9818 cm BT -/F8 9.9626 Tf 230.6815 215.2563 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 +/F8 9.9626 Tf 222.9329 211.9818 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 215.2563 cm +1 0 0 1 484.4533 211.9818 cm 0 g 0 G -1 0 0 1 -484.4533 -215.2563 cm +1 0 0 1 -484.4533 -211.9818 cm BT -/F8 9.9626 Tf 484.4533 215.2563 Td[(99)]TJ +/F8 9.9626 Tf 484.4533 211.9818 Td[(94)]TJ ET -1 0 0 1 494.4159 215.2563 cm +1 0 0 1 494.4159 211.9818 cm 0 g 0 G -1 0 0 1 -328.7671 -12.1224 cm +1 0 0 1 -328.7671 -11.9551 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -165.6488 -203.1339 cm -BT -/F8 9.9626 Tf 165.6488 203.1339 Td[(psb)]TJ -ET -1 0 0 1 181.2459 203.1339 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -181.2459 -203.1339 cm +1 0 0 1 -165.6488 -200.0267 cm BT -/F8 9.9626 Tf 184.2347 203.1339 Td[(pr)1(e)-1(c)]TJ +/F8 9.9626 Tf 165.6488 200.0267 Td[(psb)]TJ ET -1 0 0 1 203.125 203.1339 cm +1 0 0 1 181.2459 200.0267 cm q []0 d 0 J @@ -3743,43 +3685,31 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -203.125 -203.1339 cm -BT -/F8 9.9626 Tf 206.1138 203.1339 Td[(desc)-1(r)]TJ -ET -1 0 0 1 228.3361 203.1339 cm -0 g 0 G -1 0 0 1 -228.3361 -203.1339 cm +1 0 0 1 -181.2459 -200.0267 cm BT -/F8 9.9626 Tf 238.4301 203.1339 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 +/F8 9.9626 Tf 184.2347 200.0267 Td[(pr)1(e)-1(cbl)1(d)]TJ ET -1 0 0 1 479.4719 203.1339 cm +1 0 0 1 216.3643 200.0267 cm 0 g 0 G -1 0 0 1 -479.4719 -203.1339 cm +1 0 0 1 -216.3643 -200.0267 cm BT -/F8 9.9626 Tf 479.4719 203.1339 Td[(100)]TJ +/F8 9.9626 Tf 222.9329 200.0267 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 1 494.4159 203.1339 cm +1 0 0 1 484.4533 200.0267 cm 0 g 0 G -1 0 0 1 -343.7111 -22.1965 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -150.7048 -180.9375 cm +1 0 0 1 -484.4533 -200.0267 cm BT -/F29 9.9626 Tf 150.7048 180.9375 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Td[(exc)27(h)1(anges)-370(ar)1(e)-370(i)1(m)-1(p)1(lem)-1(en)28(ted)-369(th)1(rou)1(gh)-369(t)1(he)-369(B)-1(asic)-369(Lin)1(e)-1(ar)-368(Algebra)-368(C)-1(omm)27(u)1(ni)1(c)-1(ation)]TJ 0 -11.9551 Td[(Su)1(br)1(outin)1(e)-1(s)-303(\050BLA)27(CS)1(\051)-303(lib)1(rary)-303([)]TJ ET -1 0 0 1 284.1571 515.7174 cm +1 0 0 1 284.1571 515.3444 cm 0 1 0 rg 0 1 0 RG -1 0 0 1 -284.1571 -515.7174 cm +1 0 0 1 -284.1571 -515.3444 cm BT -/F8 9.9626 Tf 284.1571 515.7174 Td[(14)]TJ +/F8 9.9626 Tf 284.1571 515.3444 Td[(14)]TJ ET -1 0 0 1 294.1197 515.7174 cm +1 0 0 1 294.1197 515.3444 cm 0 g 0 G -1 0 0 1 -294.1197 -515.7174 cm +1 0 0 1 -294.1197 -515.3444 cm BT -/F8 9.9626 Tf 294.1197 515.7174 Td[(])-303(th)1(at)-303(guar)1(an)28(te)-1(es)-304(a)-303(p)-27(ort)1(able)-303(and)-303(e\016c)-1(ien)28(t)-303(com-)]TJ -143.4148 -11.9552 Td[(m)27(u)1(ni)1(c)-1(ation)-398(la)28(y)28(e)-1(r)1(.)-642(T)-1(h)1(e)-400(Mess)-1(age)-400(P)29(as)-1(sing)-399(In)28(terf)1(ac)-1(e)-399(c)-1(o)-28(d)1(e)-400(is)-399(e)-1(n)1(c)-1(ap)1(s)-1(u)1(late)-1(d)-398(w)-1(i)1(thin)]TJ 0 -11.9551 Td[(th)1(e)-386(BLA)27(CS)-384(la)28(y)28(e)-1(r)1(.)-600(Ho)28(w)27(ev)28(er,)-398(in)-384(s)-1(ome)-386(case)-1(s,)-398(MP)1(I)-385(routi)1(nes)-386(are)-385(di)1(re)-1(ctly)-384(use)-1(d)-385(ei-)]TJ 0 -11.9552 Td[(th)1(e)-1(r)-403(to)-404(i)1(m)-1(p)1(ro)28(v)28(e)-404(e)-1(\016c)-1(i)1(e)-1(n)1(c)-1(y)-403(or)-403(to)-404(impl)1(e)-1(me)-1(n)29(t)-404(com)-1(m)28(un)1(ic)-1(at)1(ion)-403(pattern)1(s)-404(for)-403(w)-1(h)1(ic)27(h)]TJ 0 -11.9552 Td[(th)1(e)-334(B)-1(LA)28(CS)-333(p)1(ac)27(k)56(age)-334(do)-27(e)-1(sn't)-333(pr)1(o)28(vide)-333(an)28(y)-333(m)-1(eth)1(o)-28(d.)]TJ 14.9439 -12.6097 Td[(In)-416(an)29(y)-416(c)-1(ase)-417(w)28(e)-416(pro)28(vi)1(de)-416(w)-1(r)1(app)-27(e)-1(r)1(s)-417(ar)1(oun)1(d)-416(th)1(e)-417(BLA)28(C)-1(S)-415(rou)1(tines)-416(s)-1(o)-416(th)1(at)-416(the)]TJ -14.944 -11.9551 Td[(user)-333(do)-28(es)-334(not)-333(n)1(e)-1(ed)-333(to)-333(delv)28(e)-334(in)28(t)1(o)-334(th)1(e)-1(i)1(r)-333(details)-334(\050see)-334(Sec)-1(.)]TJ +/F8 9.9626 Tf 294.1197 515.3444 Td[(])-303(th)1(at)-303(guar)1(an)28(te)-1(es)-304(a)-303(p)-27(ort)1(able)-303(and)-303(e\016c)-1(ien)28(t)-303(com-)]TJ -143.4148 -11.9552 Td[(m)27(u)1(ni)1(c)-1(ation)-398(la)28(y)28(e)-1(r)1(.)-642(T)-1(h)1(e)-400(Mess)-1(age)-400(P)29(as)-1(sing)-399(In)28(terf)1(ac)-1(e)-399(c)-1(o)-28(d)1(e)-400(is)-399(e)-1(n)1(c)-1(ap)1(s)-1(u)1(late)-1(d)-398(w)-1(i)1(thin)]TJ 0 -11.9552 Td[(th)1(e)-386(BLA)27(CS)-384(la)28(y)28(e)-1(r)1(.)-600(Ho)28(w)27(ev)28(er,)-398(in)-384(s)-1(ome)-386(case)-1(s,)-398(MP)1(I)-385(routi)1(nes)-386(are)-385(di)1(re)-1(ctly)-384(use)-1(d)-385(ei-)]TJ 0 -11.9551 Td[(th)1(e)-1(r)-403(to)-404(i)1(m)-1(p)1(ro)28(v)28(e)-404(e)-1(\016c)-1(i)1(e)-1(n)1(c)-1(y)-403(or)-403(to)-404(impl)1(e)-1(me)-1(n)29(t)-404(com)-1(m)28(un)1(ic)-1(at)1(ion)-403(pattern)1(s)-404(for)-403(w)-1(h)1(ic)27(h)]TJ 0 -11.9552 Td[(th)1(e)-334(B)-1(LA)28(CS)-333(p)1(ac)27(k)56(age)-334(do)-27(e)-1(sn't)-333(pr)1(o)28(vide)-333(an)28(y)-333(m)-1(eth)1(o)-28(d.)]TJ 14.9439 -12.8102 Td[(In)-416(an)29(y)-416(c)-1(ase)-417(w)28(e)-416(pro)28(vi)1(de)-416(w)-1(r)1(app)-27(e)-1(r)1(s)-417(ar)1(oun)1(d)-416(th)1(e)-417(BLA)28(C)-1(S)-415(rou)1(tines)-416(s)-1(o)-416(th)1(at)-416(the)]TJ -14.944 -11.9552 Td[(user)-333(do)-28(es)-334(not)-333(n)1(e)-1(ed)-333(to)-333(delv)28(e)-334(in)28(t)1(o)-334(th)1(e)-1(i)1(r)-333(details)-334(\050see)-334(Sec)-1(.)]TJ ET -1 0 0 1 388.9783 443.3319 cm +1 0 0 1 388.9783 442.7583 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -388.9783 -443.3319 cm +1 0 0 1 -388.9783 -442.7583 cm BT -/F8 9.9626 Tf 388.9783 443.3319 Td[(7)]TJ +/F8 9.9626 Tf 388.9783 442.7583 Td[(7)]TJ ET -1 0 0 1 393.9596 443.3319 cm +1 0 0 1 393.9596 442.7583 cm 0 g 0 G -1 0 0 1 -393.9596 -443.3319 cm +1 0 0 1 -393.9596 -442.7583 cm +BT +/F8 9.9626 Tf 393.9596 442.7583 Td[(\051.)]TJ -228.3108 -12.8101 Td[(The)-439(t)28(yp)-27(e)-439(of)-438(li)1(near)-438(s)-1(ystem)-439(m)-1(at)1(rice)-1(s)-439(t)1(hat)-438(w)27(e)-439(ad)1(dr)1(e)-1(ss)-439(t)28(ypi)1(c)-1(all)1(y)-439(ar)1(is)-1(e)-438(in)-438(the)]TJ -14.9439 -11.9552 Td[(n)28(u)1(m)-1(erical)-428(soluti)1(on)-428(of)-428(P)1(DEs;)-475(in)-428(suc)28(h)-428(a)-428(c)-1(on)29(te)-1(x)1(t,)-452(it)-428(i)1(s)-429(n)1(e)-1(ce)-1(ss)-1(ar)1(y)-428(to)-428(pa)28(y)-428(sp)-28(ec)-1(i)1(al)]TJ 0 -11.9552 Td[(atten)28(tion)-295(to)-296(t)1(he)-296(s)-1(t)1(ructur)1(e)-296(of)-296(th)1(e)-296(prob)1(lem)-296(from)-296(wh)1(ic)27(h)-295(the)-296(ap)1(pli)1(c)-1(ati)1(on)-296(or)1(iginat)1(e)-1(s.)]TJ 0 -11.9551 Td[(The)-322(non)1(z)-1(ero)-322(pat)1(te)-1(r)1(n)-322(of)-322(a)-322(matr)1(ix)-322(arisin)1(g)-322(from)-322(th)1(e)-323(d)1(is)-1(cretization)-322(of)-321(a)-322(PDE)-321(is)-322(in-)]TJ 0 -11.9552 Td[(\015u)1(e)-1(n)1(c)-1(ed)-332(b)29(y)-332(v)55(ar)1(ious)-332(factors,)-332(s)-1(u)1(c)27(h)-332(as)-332(the)-332(s)-1(h)1(ap)-28(e)-332(of)-332(th)1(e)-333(domain)1(,)-332(the)-332(disc)-1(r)1(e)-1(ti)1(z)-1(ation)]TJ 0 -11.9552 Td[(strategy)83(,)-396(an)1(d)-383(the)-383(e)-1(qu)1(ation)1(/unk)1(no)28(wn)-383(orderi)1(ng.)-595(Th)1(e)-384(m)-1(atr)1(ix)-383(itse)-1(lf)-383(can)-383(b)-27(e)-384(in)28(ter-)]TJ 0 -11.9551 Td[(pr)1(e)-1(ted)-358(as)-358(the)-358(adj)1(ac)-1(ency)-358(matrix)-358(of)-357(the)-358(grap)1(h)-358(ass)-1(o)-28(ciated)-358(with)-357(the)-358(disc)-1(r)1(e)-1(ti)1(z)-1(ation)]TJ 0 -11.9552 Td[(me)-1(sh.)]TJ 14.9439 -12.8102 Td[(The)-241(d)1(is)-1(t)1(ribu)1(tion)-240(of)-240(the)-241(co)-28(e\016)-1(cien)28(t)-240(m)-1(atr)1(ix)-241(f)1(or)-240(the)-241(li)1(near)-241(syste)-1(m)-241(i)1(s)-241(base)-1(d)-240(on)-240(the)]TJ -14.9439 -11.9551 Td[(\134o)28(wner)-247(c)-1(ompu)1(tes)-1(")-247(ru)1(le:)-402(t)1(he)-248(v)56(ar)1(iable)-247(as)-1(so)-28(ciated)-247(to)-247(eac)27(h)-247(me)-1(sh)-247(p)-27(oin)28(t)-247(i)1(s)-248(ass)-1(ign)1(e)-1(d)-246(to)]TJ 0 -11.9552 Td[(a)-307(pro)-27(c)-1(es)-1(s)-308(th)1(at)-308(wil)1(l)-308(o)28(wn)-307(the)-307(c)-1(orr)1(e)-1(sp)-27(ondi)1(ng)-307(ro)28(w)-308(in)-307(th)1(e)-308(c)-1(o)-27(e)-1(\016c)-1(i)1(e)-1(n)28(t)-307(matrix)-307(and)-307(wil)1(l)]TJ 0 -11.9552 Td[(carry)-377(out)-378(al)1(l)-378(related)-377(c)-1(ompu)1(tations.)-577(T)-1(h)1(is)-378(allo)-28(cation)-377(s)-1(t)1(rategy)-378(is)-378(equiv)56(alen)28(t)-377(to)-378(a)]TJ 0 -11.9551 Td[(par)1(tition)-292(of)-293(th)1(e)-294(d)1(is)-1(cretization)-293(mes)-1(h)-293(i)1(n)28(to)]TJ/F19 9.9626 Tf 174.8745 0 Td[(sub-)1(do)-1(m)1(ains)]TJ/F8 9.9626 Tf 53.7205 0 Td[(.)-431(Ou)1(r)-293(li)1(brar)1(y)-293(s)-1(u)1(pp)-27(orts)-293(an)28(y)]TJ -228.595 -11.9552 Td[(di)1(s)-1(tr)1(ibu)1(tion)-278(t)1(hat)-278(k)28(ee)-1(p)1(s)-279(together)-278(th)1(e)-279(co)-28(e)-1(\016cie)-1(n)29(ts)-279(of)-278(eac)27(h)-277(m)-1(atr)1(ix)-278(ro)28(w;)-296(there)-278(are)-279(n)1(o)]TJ 0 -11.9552 Td[(oth)1(e)-1(r)-261(constrai)1(n)28(ts)-262(on)-260(the)-261(v)56(ariab)1(le)-261(as)-1(signmen)28(t.)-420(T)-1(h)1(is)-261(c)27(hoi)1(c)-1(e)-261(is)-261(c)-1(on)1(s)-1(isten)28(t)-261(with)-261(d)1(ata)]TJ 0 -11.9551 Td[(di)1(s)-1(tr)1(ibu)1(tion)1(s)-310(comm)-1(on)1(ly)-308(use)-1(d)-308(in)-308(ScaLAP)84(A)28(C)-1(K)-308(suc)27(h)-308(as)]TJ/F32 9.9626 Tf 233.5332 0 Td[(CYCLIC\050N\051)]TJ/F8 9.9626 Tf 50.1475 0 Td[(and)]TJ/F32 9.9626 Tf 19.1256 0 Td[(BLOCK)]TJ/F8 9.9626 Tf 26.1517 0 Td[(,)-308(as)]TJ -328.958 -11.9552 Td[(w)28(e)-1(ll)-421(as)-421(c)-1(ompletely)-421(arb)1(itrar)1(y)-422(assignme)-1(n)29(ts)-422(of)-421(equati)1(on)-421(in)1(dice)-1(s)-421(to)-422(p)1(ro)-28(ce)-1(sse)-1(s.)-708(I)-1(n)]TJ 0 -11.9552 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 -11.9551 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 1 329.7366 213.9002 cm +0 1 0 rg 0 1 0 RG +1 0 0 1 -329.7366 -213.9002 cm BT -/F8 9.9626 Tf 393.9596 443.3319 Td[(\051.)]TJ +/F8 9.9626 Tf 329.7366 213.9002 Td[(19)]TJ ET -1 0 0 1 150.7049 427.577 cm +1 0 0 1 339.6993 213.9002 cm 0 g 0 G -1 0 0 1 105.6748 -130.4988 cm +1 0 0 1 -339.6993 -213.9002 cm +BT +/F8 9.9626 Tf 339.6993 213.9002 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 -11.9552 Td[(matrix)-333(r)1(o)27(ws.)]TJ 14.9439 -12.8101 Td[(W)84(e)-414(ass)-1(u)1(m)-1(e)-413(th)1(at)-413(the)-413(s)-1(p)1(arse)-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 -14.9439 -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 -11.9552 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 -11.9551 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 1 266.4315 141.3142 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -266.4315 -141.3142 cm +BT +/F7 6.9738 Tf 266.4315 144.9295 Td[(1)]TJ +ET +1 0 0 1 270.9009 141.3142 cm 0 g 0 G +1 0 0 1 -270.9009 -141.3142 cm +BT +/F8 9.9626 Tf 270.9009 141.3142 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 +ET +1 0 0 1 150.7049 126.9906 cm 0 g 0 G -1 0 0 1 4.9813 0 cm - q 0.45 0 0 0.45 0 0 cm +1 0 0 1 0 2.5903 cm q -1 0 0 1 0 0 cm -/Im1 Do +[]0 d +0 J +0.3985 w +0 0.1992 m +137.4823 0.1992 l +S Q - Q -1 0 0 1 -46.2728 -31.8804 cm -0 g 0 G -1 0 0 1 -215.0882 -265.1978 cm +1 0 0 1 -150.7049 -129.5809 cm BT -/F8 9.9626 Tf 215.0882 265.1978 Td[(Figu)1(re)-334(1:)-444(P)1(SBLAS)-333(lib)1(rary)-333(com)-1(p)-27(on)1(e)-1(n)28(ts)-333(hierar)1(c)27(h)28(y)84(.)]TJ +/F34 5.9776 Tf 161.7969 123.1384 Td[(1)]TJ/F33 7.9701 Tf 4.151 -2.8128 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-1.4944 Td[(i)]TJ/F14 9.9626 Tf 3.3169 1.4944 Td[(j)]TJ/F8 9.9626 Tf 2.7674 0 Td[(,)-304(an)1(d)-296(the)-297(n)29(um)28(b)-28(er)-296(of)-296(lo)-28(cal)-297(colu)1(m)-1(n)1(s)]TJ -196.5949 -11.9552 Td[(\050i.)1(e)-1(.)-514(those)-358(f)1(or)-357(wh)1(ic)27(h)-356(there)-357(exists)-357(at)-357(leas)-1(t)-356(one)-357(non)1(-)-1(ze)-1(r)1(o)-357(en)28(try)-356(in)-356(the)-357(lo)-28(cal)-357(r)1(o)27(ws\051)]TJ 0 -11.9552 Td[(is)]TJ/F14 9.9626 Tf 10.018 0 Td[(jI)]TJ/F10 6.9738 Tf 8.1922 -1.4943 Td[(i)]TJ/F14 9.9626 Tf 3.3169 1.4944 Td[(j)]TJ/F8 9.9626 Tf 4.9812 0 Td[(+)]TJ/F14 9.9626 Tf 9.9626 0 Td[(jB)]TJ/F10 6.9738 Tf 9.311 -1.4944 Td[(i)]TJ/F14 9.9626 Tf 3.3168 1.4944 Td[(j)]TJ/F8 9.9626 Tf 4.9813 0 Td[(+)]TJ/F14 9.9626 Tf 9.9626 0 Td[(jH)]TJ/F10 6.9738 Tf 11.181 -1.4944 Td[(i)]TJ/F14 9.9626 Tf 3.3169 1.4944 Td[(j)]TJ/F8 9.9626 Tf 2.7674 0 Td[(.)]TJ -ET -1 0 0 1 150.7049 584.5777 cm -0 g 0 G -1 0 0 1 97.5748 0 cm -0 g 0 G -0 g 0 G -1 0 0 1 4.9814 0 cm - q 0 -1 1 0 0 0 cm - q 0.45 0 0 0.45 0 0 cm -q -1 0 0 1 0 0 cm -/Im2 Do -Q - Q - Q -1 0 0 1 6.6868 -151.1389 cm -0 g 0 G -1 0 0 1 -259.9479 -433.4388 cm -BT -/F8 9.9626 Tf 259.9479 433.4388 Td[(Figu)1(re)-334(2:)-444(P)28(oi)1(n)28(t)-333(c)-1(lass\014cation.)]TJ -ET -1 0 0 1 385.173 433.4388 cm -0 g 0 G -1 0 0 1 -234.4681 -1.9371 cm -0 g 0 G -1 0 0 1 -150.7049 -431.5017 cm -BT -/F8 9.9626 Tf 165.6488 410.5732 Td[(This)-267(class)-1(i\014)1(c)-1(at)1(ion)-266(of)-267(mes)-1(h)-266(p)-27(oin)28(ts)-267(gui)1(des)-267(the)-267(namin)1(g)-267(sc)27(heme)-268(t)1(hat)-267(w)28(e)-267(adop)1(te)-1(d)]TJ -14.9439 -11.9552 Td[(in)-473(the)-474(lib)1(rary)-473(in)28(ternal)1(s)-475(an)1(d)-474(in)-473(the)-474(data)-474(stru)1(c)-1(tu)1(res)-1(.)-866(W)84(e)-475(expl)1(ic)-1(i)1(tly)-474(n)1(ote)-475(th)1(at)]TJ 0 -11.9551 Td[(\134Halo")-333(p)-27(oin)28(ts)-334(ar)1(e)-334(also)-334(of)1(te)-1(n)-333(called)-333(\134gh)1(os)-1(t")-333(p)-27(oin)28(ts)-334(i)1(n)-333(the)-334(l)1(iteratur)1(e)-1(.)]TJ/F18 11.9552 Tf 0 -27.677 Td[(2.)-1(2)-1125(Li)-1(brar)-1(y)-375(con)31(te)-1(n)32(t)-1(s)]TJ/F8 9.9626 Tf 0 -18.3893 Td[(The)-334(P)1(SBLAS)-333(li)1(brar)1(y)-333(c)-1(on)1(s)-1(ists)-334(of)-333(v)56(ari)1(ous)-334(class)-1(es)-334(of)-333(subr)1(outi)1(nes)-1(:)]TJ -ET -1 0 0 1 145.7236 321.6538 cm -0 g 0 G -1 0 0 1 -145.7236 -321.6538 cm -BT -/F29 9.9626 Tf 150.7049 321.6538 Td[(Computati)-1(on)1(al)-384(routines)]TJ -ET -1 0 0 1 269.8975 321.6538 cm -0 g 0 G -1 0 0 1 -269.8975 -321.6538 cm -BT -/F8 9.9626 Tf 274.8788 321.6538 Td[(com)-1(p)1(rising:)]TJ -ET -1 0 0 1 175.6115 302.2197 cm -0 g 0 G -1 0 0 1 -175.6115 -302.2197 cm -BT -/F14 9.9626 Tf 187.5666 302.2197 Td[(\017)]TJ -ET -1 0 0 1 192.548 302.2197 cm -0 g 0 G -1 0 0 1 -192.548 -302.2197 cm -BT -/F8 9.9626 Tf 197.5293 302.2197 Td[(Sp)1(arse)-334(matrix)-333(b)28(y)-333(d)1(e)-1(n)1(s)-1(e)-333(m)-1(atr)1(ix)-333(pro)-27(du)1(c)-1(t;)]TJ -ET -1 0 0 1 175.6115 286.7707 cm -0 g 0 G -1 0 0 1 -175.6115 -286.7707 cm -BT -/F14 9.9626 Tf 187.5666 286.7707 Td[(\017)]TJ -ET -1 0 0 1 192.548 286.7707 cm -0 g 0 G -1 0 0 1 -192.548 -286.7707 cm -BT -/F8 9.9626 Tf 197.5293 286.7707 Td[(Sp)1(arse)-334(tri)1(angu)1(lar)-333(s)-1(y)1(s)-1(tem)-1(s)-333(s)-1(olu)1(tion)-333(f)1(or)-333(blo)-27(c)27(k)-333(diagon)1(al)-333(m)-1(at)1(rice)-1(s;)]TJ -ET -1 0 0 1 175.6115 271.3217 cm -0 g 0 G -1 0 0 1 -175.6115 -271.3217 cm -BT -/F14 9.9626 Tf 187.5666 271.3217 Td[(\017)]TJ -ET -1 0 0 1 192.548 271.3217 cm -0 g 0 G -1 0 0 1 -192.548 -271.3217 cm -BT -/F8 9.9626 Tf 197.5293 271.3217 Td[(V)83(ec)-1(t)1(or)-333(and)-333(matrix)-333(n)1(orms)-1(;)]TJ -ET -1 0 0 1 175.6115 255.8727 cm -0 g 0 G -1 0 0 1 -175.6115 -255.8727 cm -BT -/F14 9.9626 Tf 187.5666 255.8727 Td[(\017)]TJ +/F8 9.9626 Tf 175.6115 706.1289 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 -11.9552 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 1 192.548 255.8727 cm +1 0 0 1 145.7235 661.1346 cm 0 g 0 G -1 0 0 1 -192.548 -255.8727 cm +1 0 0 1 -145.7235 -661.1346 cm BT -/F8 9.9626 Tf 197.5293 255.8727 Td[(Dense)-334(matrix)-333(sums)-1(;)]TJ +/F29 9.9626 Tf 150.7049 661.1346 Td[(Boundar)1(y)96(.)]TJ ET -1 0 0 1 175.6115 240.4237 cm +1 0 0 1 202.2405 661.1346 cm 0 g 0 G -1 0 0 1 -175.6115 -240.4237 cm +1 0 0 1 -202.2405 -661.1346 cm BT -/F14 9.9626 Tf 187.5666 240.4237 Td[(\017)]TJ +/F8 9.9626 Tf 207.2218 661.1346 Td[(A)-438(p)-27(oin)28(t)-438(of)-438(a)-438(giv)28(en)-438(d)1(om)-1(ai)1(n)-438(is)-438(a)-438(b)-28(ou)1(nd)1(ary)-438(p)-27(oin)28(t)-438(if)-437(it)]TJ/F19 9.9626 Tf 238.7061 0 Td[(dep)51(ends)]TJ/F8 9.9626 Tf 37.9719 0 Td[(on)]TJ -308.2883 -11.9552 Td[(p)-27(oin)28(ts)-334(b)-27(elongi)1(ng)-333(to)-334(ot)1(he)-1(r)-333(d)1(omains.)]TJ ET -1 0 0 1 192.548 240.4237 cm +1 0 0 1 145.7235 628.0955 cm 0 g 0 G -1 0 0 1 -192.548 -240.4237 cm +1 0 0 1 -145.7235 -628.0955 cm BT -/F8 9.9626 Tf 197.5293 240.4237 Td[(Dot)-333(pr)1(o)-28(du)1(c)-1(ts.)]TJ +/F29 9.9626 Tf 150.7049 628.0955 Td[(Halo.)]TJ ET -1 0 0 1 145.7235 220.9897 cm +1 0 0 1 177.334 628.0955 cm 0 g 0 G -1 0 0 1 -145.7235 -220.9897 cm +1 0 0 1 -177.334 -628.0955 cm BT -/F29 9.9626 Tf 150.7049 220.9897 Td[(Comm)32(unic)-1(ation)-384(r)1(outi)-1(nes)]TJ +/F8 9.9626 Tf 182.3153 628.0955 Td[(A)-321(halo)-321(p)-27(oin)28(t)-321(for)-321(a)-321(giv)28(en)-321(domain)-321(i)1(s)-322(a)-321(p)-28(oin)29(t)-322(b)-27(elongi)1(ng)-321(to)-322(an)1(other)-321(domain)]TJ -6.7038 -11.9552 Td[(suc)27(h)-346(that)-346(there)-347(is)-347(a)-347(b)-27(oun)1(dary)-346(p)-28(oi)1(n)28(t)-347(whi)1(c)27(h)]TJ/F19 9.9626 Tf 188.3186 0 Td[(dep)51(ends)]TJ/F8 9.9626 Tf 37.8802 0 Td[(on)-346(it.)-485(Wh)1(e)-1(n)1(e)-1(v)28(er)-347(p)-27(er-)]TJ -226.1988 -11.9551 Td[(for)1(m)-1(i)1(ng)-281(a)-280(c)-1(ompu)1(tation)1(al)-281(ste)-1(p)1(,)-291(suc)27(h)-280(as)-281(a)-281(matri)1(x-)-1(v)28(ector)-281(p)1(ro)-28(d)1(uct,)-291(the)-281(v)56(alu)1(e)-1(s)]TJ 0 -11.9552 Td[(ass)-1(o)-28(ciated)-346(with)-346(h)1(alo)-346(p)-28(oin)29(ts)-347(are)-346(re)-1(q)1(ues)-1(ted)-346(fr)1(om)-347(oth)1(e)-1(r)-346(d)1(om)-1(ai)1(ns.)-483(A)-347(b)-27(oun)1(d-)]TJ 0 -11.9552 Td[(ary)-321(p)-28(oin)29(t)-322(of)-322(a)-322(giv)28(en)-322(d)1(om)-1(ai)1(n)-322(is)-322(a)-322(halo)-322(p)-27(oin)29(t)-322(for)-322(\050at)-321(le)-1(ast\051)-322(an)1(other)-322(domain)1(;)]TJ 0 -11.9551 Td[(th)1(e)-1(refor)1(e)-384(th)1(e)-384(c)-1(ar)1(din)1(alit)28(y)-383(of)-383(th)1(e)-384(b)-27(ound)1(ary)-383(p)-27(oin)28(ts)-384(set)-384(d)1(e)-1(n)1(ote)-1(s)-383(the)-384(amou)1(n)28(t)]TJ 0 -11.9552 Td[(of)-333(d)1(ata)-334(se)-1(n)29(t)-334(t)1(o)-334(oth)1(e)-1(r)-333(d)1(om)-1(ai)1(ns.)]TJ ET -1 0 0 1 274.1939 220.9897 cm +1 0 0 1 145.7235 535.2806 cm 0 g 0 G -1 0 0 1 -274.1939 -220.9897 cm +1 0 0 1 -145.7235 -535.2806 cm BT -/F8 9.9626 Tf 279.1752 220.9897 Td[(han)1(dl)1(ing)-333(hal)1(o)-334(an)1(d)-333(o)28(v)28(e)-1(rl)1(ap)-333(c)-1(omm)27(u)1(nication)1(s)-1(;)]TJ +/F29 9.9626 Tf 150.7049 535.2806 Td[(Ov)32(erlap.)]TJ ET -1 0 0 1 145.7235 201.5556 cm +1 0 0 1 193.3088 535.2806 cm 0 g 0 G -1 0 0 1 -145.7235 -201.5556 cm +1 0 0 1 -193.3088 -535.2806 cm BT -/F29 9.9626 Tf 150.7049 201.5556 Td[(Data)-384(managemen)32(t)-384(and)-383(auxil)-1(iary)-383(routines)]TJ +/F8 9.9626 Tf 198.2901 535.2806 Td[(An)-339(o)28(v)28(erlap)-338(p)-28(oi)1(n)28(t)-339(is)-339(a)-339(b)-28(ou)1(nd)1(ary)-339(p)-27(oin)28(t)-339(ass)-1(i)1(gned)-339(to)-339(m)28(ulti)1(ple)-339(domains.)]TJ -22.6786 -11.9552 Td[(An)28(y)-296(op)-28(erati)1(on)-297(th)1(at)-297(in)29(v)28(olv)28(e)-1(s)-297(an)-296(o)28(v)28(e)-1(rl)1(ap)-297(p)-27(oin)28(t)-296(has)-297(to)-297(b)-27(e)-297(repli)1(c)-1(ated)-296(for)-296(e)-1(ac)27(h)]TJ 0 -11.9551 Td[(ass)-1(ign)1(m)-1(en)28(t.)]TJ -24.9066 -20.7943 Td[(Ov)28(erlap)-328(p)-27(oin)29(ts)-329(do)-328(not)-328(u)1(s)-1(u)1(ally)-328(e)-1(x)1(is)-1(t)-328(in)-327(the)-329(b)1(as)-1(i)1(c)-329(data)-328(di)1(s)-1(tr)1(ibu)1(tion,)-329(b)1(ut)-328(th)1(e)-1(y)-328(are)]TJ 0 -11.9552 Td[(a)-422(fea)-1(t)1(ure)-423(of)-422(Domain)-422(Decom)-1(p)-27(os)-1(i)1(tion)-422(Sc)28(h)28(w)27(ar)1(z)-423(pr)1(e)-1(cond)1(ition)1(e)-1(rs)-422(w)-1(h)1(ic)27(h)-422(w)28(e)-423(are)-423(in)]TJ 0 -11.9551 Td[(th)1(e)-334(pr)1(o)-28(c)-1(es)-1(s)-333(of)-333(inclu)1(din)1(g)-334(i)1(n)-333(our)-333(d)1(is)-1(tr)1(ibu)1(tion)-333([)]TJ ET -1 0 0 1 356.4405 201.5556 cm -0 g 0 G -1 0 0 1 -356.4405 -201.5556 cm -BT -/F8 9.9626 Tf 361.4218 201.5556 Td[(in)1(c)-1(lu)1(di)1(ng:)]TJ -ET -1 0 0 1 175.6115 182.1216 cm -0 g 0 G -1 0 0 1 -175.6115 -182.1216 cm +1 0 0 1 343.5653 466.6657 cm +0 1 0 rg 0 1 0 RG +1 0 0 1 -343.5653 -466.6657 cm BT -/F14 9.9626 Tf 187.5666 182.1216 Td[(\017)]TJ +/F8 9.9626 Tf 343.5653 466.6657 Td[(6)]TJ ET -1 0 0 1 192.548 182.1216 cm +1 0 0 1 348.5467 466.6657 cm 0 g 0 G -1 0 0 1 -192.548 -182.1216 cm +1 0 0 1 -348.5467 -466.6657 cm BT -/F8 9.9626 Tf 197.5293 182.1216 Td[(P)28(ar)1(allel)-334(en)28(vi)1(ronmen)28(t)-333(m)-1(an)1(age)-1(me)-1(n)29(t)]TJ +/F8 9.9626 Tf 348.5467 466.6657 Td[(,)]TJ ET -1 0 0 1 175.6115 166.6726 cm -0 g 0 G -1 0 0 1 -175.6115 -166.6726 cm +1 0 0 1 354.635 466.6657 cm +0 1 0 rg 0 1 0 RG +1 0 0 1 -354.635 -466.6657 cm BT -/F14 9.9626 Tf 187.5666 166.6726 Td[(\017)]TJ +/F8 9.9626 Tf 354.635 466.6657 Td[(11)]TJ ET -1 0 0 1 192.548 166.6726 cm +1 0 0 1 364.5976 466.6657 cm 0 g 0 G -1 0 0 1 -192.548 -166.6726 cm +1 0 0 1 -364.5976 -466.6657 cm BT -/F8 9.9626 Tf 197.5293 166.6726 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Td[(in)-370(whic)28(h)-371(w)28(e)-372(sp)-28(ecify)-371(t)1(he)-371(s)-1(ize)-371(of)-371(th)1(e)-372(i)1(ndex)-371(space)]TJ/F11 9.9626 Tf -137.8771 -11.9552 Td[(n)]TJ/F8 9.9626 Tf 9.1424 0 Td[(and)-317(t)1(he)-318(all)1(o)-28(c)-1(ati)1(on)-317(of)-317(the)-318(elem)-1(en)28(ts)-318(of)-317(th)1(e)-318(in)1(dex)-318(space)-318(to)-317(the)-318(v)56(ari)1(ous)-318(p)1(ro)-28(ce)-1(ss)-1(es)]TJ -9.1424 -11.9551 Td[(makin)1(g)-334(u)1(p)-333(the)-333(MPI)-333(\050vir)1(tual\051)-333(p)1(arallel)-333(mac)27(hi)1(ne.)]TJ 14.9439 -12.1687 Td[(The)-309(i)1(ndex)-308(s)-1(p)1(ac)-1(e)-308(is)-309(par)1(tition)1(e)-1(d)-308(amon)1(g)-309(p)1(ro)-28(ce)-1(ss)-1(es,)-314(an)1(d)-308(thi)1(s)-309(c)-1(r)1(e)-1(ates)-309(a)-308(m)-1(ap)1(pin)1(g)]TJ -14.9439 -11.9552 Td[(fr)1(om)-250(t)1(he)-250(\134gl)1(obal")-249(n)29(um)27(b)-27(erin)1(g)-249(1)]TJ/F11 9.9626 Tf 132.8519 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 21.7442 0 Td[(to)-249(a)-249(n)28(u)1(m)27(b)-27(e)-1(r)1(ing)-249(\134l)1(o)-28(c)-1(al)1(")-249(to)-249(e)-1(ac)27(h)-248(pr)1(o)-28(c)-1(ess)-1(;)-277(eac)27(h)]TJ -154.5961 -11.9551 Td[(pr)1(o)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 33.7713 0 Td[(i)]TJ/F8 9.9626 Tf 5.7936 0 Td[(will)-237(o)28(wn)-237(a)-237(ce)-1(r)1(tain)-236(s)-1(u)1(bse)-1(t)-237(1)]TJ/F11 9.9626 Tf 113.5085 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 -1.4944 Td[(ro)28(w)]TJ/F9 4.9813 Tf 15.8019 -0.9963 Td[(i)]TJ/F8 9.9626 Tf 3.6541 2.4907 Td[(,)-256(e)-1(ac)28(h)-237(elem)-1(en)28(t)-237(of)-236(w)-1(h)1(ic)27(h)-236(c)-1(or)1(re)-1(sp)-27(ond)1(s)]TJ -191.7927 -11.9552 Td[(to)-390(a)-389(c)-1(ertai)1(n)-390(elem)-1(en)28(t)-389(of)-389(1)]TJ/F11 9.9626 Tf 111.3133 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 0 Td[(.)-613(The)-390(u)1(s)-1(er)-390(d)1(o)-28(es)-390(not)-390(set)-390(expli)1(c)-1(it)1(ly)-390(t)1(his)-390(mapp)1(ing;)]TJ -130.5766 -11.9552 Td[(when)-392(the)-392(app)1(lication)-392(needs)-393(to)-392(in)1(dicate)-393(to)-392(whi)1(c)27(h)-392(ele)-1(men)28(t)-392(of)-392(the)-392(ind)1(e)-1(x)-392(space)-393(a)]TJ 0 -11.9551 Td[(ce)-1(rt)1(ain)-273(it)1(e)-1(m)-273(is)-273(relate)-1(d)1(,)-285(suc)27(h)-272(as)-273(the)-273(ro)28(w)-273(and)-272(c)-1(olu)1(m)-1(n)-272(in)1(dex)-273(of)-273(a)-273(matr)1(ix)-273(co)-28(e)-1(\016cie)-1(n)29(t,)]TJ 0 -11.9552 Td[(it)-448(do)-28(es)-449(s)-1(o)-448(in)-448(the)-449(\134glob)1(al")-449(n)29(um)28(b)-28(erin)1(g,)-477(and)-448(the)-449(li)1(brar)1(y)-449(wil)1(l)-449(tr)1(anslate)-449(in)28(to)-448(the)]TJ 0 -11.9552 Td[(app)1(rop)1(riate)-333(\134lo)-28(cal")-334(n)29(um)27(b)-27(erin)1(g.)]TJ 14.944 -12.1686 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 -11.9552 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 -11.9551 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 -11.9552 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 -11.9551 Td[(n)]TJ/F8 9.9626 Tf 5.9799 -1.4944 Td[(ro)28(w)]TJ/F9 4.9813 Tf 15.8019 -0.9963 Td[(i)]TJ/F8 9.9626 Tf 5.9852 2.4907 Td[(+)-234(1)]TJ/F11 9.9626 Tf 16.7216 0 Td[(:)-166(:)-167(:)-166(n)]TJ/F8 9.9626 Tf 19.2633 -3.487 Td[(col)]TJ/F9 4.9813 Tf 12.1766 -0.9962 Td[(i)]TJ/F8 9.9626 Tf 3.6541 4.4832 Td[(,)-355(denoti)1(ng)-351(ele)-1(men)28(ts)-352(of)-350(the)-351(in)1(dex)-351(space)-352(th)1(at)-351(are)]TJ/F19 9.9626 Tf 209.5968 0 Td[(not)]TJ/F8 9.9626 Tf 18.4447 0 Td[(ass)-1(ign)1(e)-1(d)]TJ -307.6241 -11.9552 Td[(to)-284(p)1(ro)-28(ce)-1(ss)]TJ/F11 9.9626 Tf 45.9205 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(;)-300(ho)28(w)28(e)-1(v)28(er)-284(th)1(e)-284(v)55(ar)1(iabl)1(e)-1(s)-284(as)-1(so)-28(ciated)-284(with)-283(th)1(e)-1(m)-284(are)-284(n)1(e)-1(eded)-284(to)-283(c)-1(omplete)]TJ -49.3528 -11.9552 Td[(com)-1(p)1(utati)1(ons)-410(ass)-1(o)-28(ciated)-409(w)-1(i)1(th)-409(the)-410(spar)1(s)-1(e)-410(matri)1(x)]TJ/F11 9.9626 Tf 216.3159 0 Td[(A)]TJ/F8 9.9626 Tf 7.472 0 Td[(,)-428(and)-409(th)28(u)1(s)-410(they)-409(ha)28(v)28(e)-410(to)-410(b)-27(e)]TJ -223.7879 -11.9551 Td[(fetc)27(h)1(e)-1(d)-463(f)1(rom)-464(\050n)1(e)-1(igh)29(b)-28(ou)1(rin)1(g\051)-464(p)1(ro)-28(ce)-1(ss)-1(es)-1(.)-835(The)-464(d)1(e)-1(sc)-1(r)1(ipt)1(or)-464(of)-463(th)1(e)-465(i)1(nd)1(e)-1(x)-463(s)-1(p)1(ac)-1(e)-464(is)]TJ 0 -11.9552 Td[(bu)1(ilt)-393(e)-1(xactly)-393(for)-394(t)1(he)-394(pu)1(rp)-27(os)-1(e)-394(of)-394(p)1(rop)-27(e)-1(r)1(ly)-394(se)-1(q)1(ue)-1(n)1(c)-1(i)1(ng)-394(th)1(e)-395(comm)27(u)1(nication)-393(s)-1(teps)]TJ 0 -11.9552 Td[(requ)1(ired)-333(to)-333(ac)27(hi)1(e)-1(v)28(e)-334(th)1(is)-334(ob)-55(j)1(e)-1(ctiv)28(e.)]TJ 14.944 -12.1686 Td[(A)-306(simple)-306(app)1(lication)-305(s)-1(tr)1(uctur)1(e)-307(wil)1(l)-306(w)28(alk)-306(th)1(rou)1(gh)-306(th)1(e)-307(i)1(ndex)-306(space)-306(allo)-28(cation)1(,)]TJ -14.944 -11.9552 Td[(matrix)1(/v)28(e)-1(ctor)-333(c)-1(r)1(e)-1(ati)1(on)-333(and)-333(li)1(near)-333(s)-1(ystem)-334(s)-1(ol)1(ution)-332(as)-334(foll)1(o)27(ws:)]TJ ET -1 0 0 1 170.6302 297.3493 cm +1 0 0 1 150.7049 271.402 cm 0 g 0 G -1 0 0 1 -170.6302 -297.3493 cm +1 0 0 1 -150.7049 -271.402 cm BT -/F8 9.9626 Tf 175.6115 297.3493 Td[(Call)-333(the)-333(iterativ)28(e)-334(metho)-28(d)-333(of)-332(c)27(hoi)1(c)-1(e,)-333(e)-1(.g.)]TJ/F32 9.9626 Tf 176.8648 0 Td[(psb_bicgstab)]TJ/F8 9.9626 Tf -201.7714 -20.1121 Td[(This)-333(is)-334(th)1(e)-334(s)-1(t)1(ructur)1(e)-334(of)-333(th)1(e)-334(s)-1(ampl)1(e)-334(pr)1(ogram)]TJ/F32 9.9626 Tf 194.3271 0 Td[(test/pargen/ppde90.f90)]TJ/F8 9.9626 Tf 115.0675 0 Td[(.)]TJ -294.4507 -12.0174 Td[(F)84(or)-292(a)-291(s)-1(im)28(ulat)1(ion)-291(in)-291(w)-1(h)1(ic)27(h)-291(th)1(e)-292(s)-1(ame)-292(disc)-1(r)1(e)-1(ti)1(z)-1(ation)-291(me)-1(sh)-291(is)-292(use)-1(d)-291(o)28(v)28(er)-292(m)28(ulti)1(ple)]TJ -14.9439 -11.9552 Td[(time)-334(ste)-1(p)1(s)-1(,)-333(th)1(e)-334(f)1(ollo)28(wing)-333(s)-1(t)1(ructur)1(e)-334(ma)27(y)-333(b)-27(e)-334(more)-334(ap)1(pr)1(opri)1(ate)-1(:)]TJ +/F8 9.9626 Tf 162.8814 271.402 Td[(1.)]TJ ET -1 0 0 1 150.7049 233.1525 cm +1 0 0 1 170.6302 271.402 cm 0 g 0 G -1 0 0 1 -150.7049 -233.1525 cm +1 0 0 1 -170.6302 -271.402 cm BT -/F8 9.9626 Tf 162.8814 233.1525 Td[(1.)]TJ +/F8 9.9626 Tf 175.6115 271.402 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 1 170.6302 233.1525 cm +1 0 0 1 150.7049 250.6227 cm 0 g 0 G -1 0 0 1 -170.6302 -233.1525 cm +1 0 0 1 -150.7049 -250.6227 cm BT -/F8 9.9626 Tf 175.6115 233.1525 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 +/F8 9.9626 Tf 162.8814 250.6227 Td[(2.)]TJ ET -1 0 0 1 150.7049 212.9782 cm +1 0 0 1 170.6302 250.6227 cm 0 g 0 G -1 0 0 1 -150.7049 -212.9782 cm +1 0 0 1 -170.6302 -250.6227 cm BT -/F8 9.9626 Tf 162.8814 212.9782 Td[(2.)]TJ +/F8 9.9626 Tf 175.6115 250.6227 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 1 170.6302 212.9782 cm +1 0 0 1 150.7049 229.8435 cm 0 g 0 G -1 0 0 1 -170.6302 -212.9782 cm +1 0 0 1 -150.7049 -229.8435 cm BT -/F8 9.9626 Tf 175.6115 212.9782 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 +/F8 9.9626 Tf 162.8814 229.8435 Td[(3.)]TJ ET -1 0 0 1 150.7049 192.8038 cm +1 0 0 1 170.6302 229.8435 cm 0 g 0 G -1 0 0 1 -150.7049 -192.8038 cm +1 0 0 1 -170.6302 -229.8435 cm BT -/F8 9.9626 Tf 162.8814 192.8038 Td[(3.)]TJ +/F8 9.9626 Tf 175.6115 229.8435 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 1 170.6302 192.8038 cm +1 0 0 1 150.7049 209.0643 cm 0 g 0 G -1 0 0 1 -170.6302 -192.8038 cm +1 0 0 1 -150.7049 -209.0643 cm BT -/F8 9.9626 Tf 175.6115 192.8038 Td[(Lo)-28(op)-271(o)28(v)28(er)-272(t)1(he)-272(top)-27(ology)-271(of)-271(the)-272(d)1(isc)-1(r)1(e)-1(tization)-271(me)-1(sh)-271(and)-271(b)1(ui)1(ld)-271(the)-272(d)1(e)-1(sc)-1(r)1(ipt)1(or)]TJ 0 -11.9552 Td[(with)]TJ/F32 9.9626 Tf 22.6927 0 Td[(psb_cdins)]TJ +/F8 9.9626 Tf 162.8814 209.0643 Td[(4.)]TJ ET -1 0 0 1 150.7049 160.6743 cm +1 0 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562.481 cm q []0 d 0 J @@ -6111,11 +6098,11 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -209.8188 -353.2717 cm +1 0 0 1 -172.3967 -562.481 cm BT -/F29 9.9626 Tf 213.2559 353.2717 Td[(data[)-1(p)1(sb)]TJ +/F29 9.9626 Tf 175.8338 562.481 Td[(to)]TJ ET -1 0 0 1 256.3341 353.2717 cm +1 0 0 1 186.7052 562.481 cm q []0 d 0 J @@ -6124,11 +6111,11 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -256.3341 -353.2717 cm +1 0 0 1 -186.7052 -562.481 cm BT -/F29 9.9626 Tf 259.7712 353.2717 Td[(n)]TJ +/F29 9.9626 Tf 190.1423 562.481 Td[(lo)-32(c,)-384(gl)-1(b)]TJ ET -1 0 0 1 266.8236 353.2717 cm +1 0 0 1 227.4283 562.481 cm q []0 d 0 J @@ -6137,87 +6124,105 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -266.8236 -353.2717 cm +1 0 0 1 -227.4283 -562.481 cm BT -/F29 9.9626 Tf 270.2607 353.2717 Td[(])]TJ +/F29 9.9626 Tf 230.8655 562.481 Td[(lc)-1(,)-383(hash)32(v)]TJ ET -1 0 0 1 273.4432 353.2717 cm +1 0 0 1 274.6884 562.481 cm 0 g 0 G -1 0 0 1 -273.4432 -353.2717 cm +1 0 0 1 -274.6884 -562.481 cm BT -/F8 9.9626 Tf 278.4245 353.2717 Td[(T)83(otal)-333(n)28(u)1(m)27(b)-27(e)-1(r)-333(of)-332(v)55(ar)1(iables)-334(\050gl)1(obal\051.)]TJ +/F8 9.9626 Tf 279.6697 562.481 Td[(Con)28(tain)-431(a)-431(mapp)1(ing)-431(f)1(rom)-432(glob)1(al)-431(to)-431(lo)-28(cal)-431(ind)1(ic)-1(es.)]TJ -104.0582 -11.9552 Td[(The)-366(m)-1(ap)1(pin)1(g)-366(m)-1(a)28(y)-366(b)-27(e)-367(stored)-366(in)-366(t)28(w)28(o)-366(di\013e)-1(r)1(e)-1(n)29(t)-367(w)28(a)28(ys)-367(d)1(e)-1(p)-27(endi)1(ng)-366(on)-366(th)1(e)-367(siz)-1(e)]TJ 0 -11.9551 Td[(of)-333(th)1(e)-334(in)1(dex)-334(space.)]TJ -24.9066 -19.9563 Td[(The)-334(F)84(ortr)1(an95)-333(de\014n)1(ition)-333(f)1(or)]TJ/F32 9.9626 Tf 126.1383 0 Td[(psb_desc_type)]TJ/F8 9.9626 Tf 71.3153 0 Td[(structu)1(re)-1(s)-333(is)-334(as)-334(f)1(ollo)28(ws)-1(:)]TJ ET -1 0 0 1 170.6302 336.8483 cm +1 0 0 1 150.7049 504.4247 cm 0 g 0 G -1 0 0 1 -170.6302 -336.8483 cm -BT -/F29 9.9626 Tf 175.6115 336.8483 Td[(mat)-1(r)1(i)-1(x)]TJ -ET -1 0 0 1 209.8188 336.8483 cm +1 0 0 1 2.1762 -54.8609 cm +0 g 0 G +0 g 0 G +1 0 0 1 4.9813 44.4998 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.4371 0.1992 l +329.396 0.1992 l S Q -1 0 0 1 -209.8188 -336.8483 cm -BT -/F29 9.9626 Tf 213.2559 336.8483 Td[(data[)-1(p)1(sb)]TJ -ET -1 0 0 1 256.3341 336.8483 cm +1 0 0 1 0 -84.0183 cm q []0 d 0 J 0.3985 w -0 0.1992 m -3.4371 0.1992 l +0.1992 0 m +0.1992 84.0183 l S Q -1 0 0 1 -256.3341 -336.8483 cm +1 0 0 1 3.3873 69.9599 cm +0 g 0 G +0 g 0 G +1 0 0 1 -161.2497 -480.0052 cm BT -/F29 9.9626 Tf 259.7712 336.8483 Td[(n)]TJ +/F32 9.9626 Tf 166.231 480.0052 Td[(type)-525(psb_desc_type)]TJ 15.6911 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(matrix_data\050:\051,)-525(halo_index\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(overlap_elem\050:\051,)-525(overlap_index\050:\051)]TJ 0 -11.9551 Td[(integer,)-525(allocatable)-525(::)-525(loc_to_glob\050:\051,)-525(glob_to_loc\050:\051)]TJ 0 -11.9552 Td[(integer,)-525(allocatable)-525(::)-525(hashv\050:\051,)-525(glb_lc\050:,:\051)]TJ -15.6911 -11.9552 Td[(end)-525(type)-525(psb_desc_type)]TJ ET -1 0 0 1 266.8236 336.8483 cm +1 0 0 1 486.8599 410.0453 cm q []0 d 0 J 0.3985 w -0 0.1992 m -3.4371 0.1992 l +0.1992 0 m +0.1992 84.0183 l S Q -1 0 0 1 -266.8236 -336.8483 cm -BT -/F29 9.9626 Tf 270.2607 336.8483 Td[(ro)32(w)]TJ -ET -1 0 0 1 289.3512 336.8483 cm +1 0 0 1 -328.9975 -0.3985 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.4371 0.1992 l +329.396 0.1992 l S Q -1 0 0 1 -289.3512 -336.8483 cm +1 0 0 1 -157.8624 -409.6468 cm +BT +/F8 9.9626 Tf 150.7049 381.8068 Td[(Figu)1(re)-464(3:)-705(T)-1(h)1(e)-465(P)1(SBLAS)-463(de\014ned)-463(data)-464(t)28(yp)-27(e)-464(that)-464(con)28(tai)1(ns)-464(the)-464(c)-1(omm)27(u)1(ni)1(c)-1(ation)]TJ 0 -11.9552 Td[(desc)-1(ri)1(ptor)1(.)]TJ +ET +1 0 0 1 150.7049 367.9144 cm +0 g 0 G +1 0 0 1 -150.7049 -367.9144 cm +BT +/F8 9.9626 Tf 165.6488 346.187 Td[(A)-445(com)-1(m)28(un)1(ic)-1(at)1(ion)-445(d)1(e)-1(sc)-1(r)1(iptor)-444(as)-1(so)-28(ciate)-1(d)-444(with)-445(a)-445(spar)1(s)-1(e)-445(matrix)-445(h)1(as)-446(a)-445(state,)]TJ -14.9439 -11.9552 Td[(whic)28(h)-333(c)-1(an)-332(tak)28(e)-334(the)-333(foll)1(o)27(win)1(g)-334(v)56(alu)1(e)-1(s:)]TJ +ET +1 0 0 1 145.7235 314.2756 cm +0 g 0 G +1 0 0 1 -145.7235 -314.2756 cm +BT +/F29 9.9626 Tf 150.7049 314.2756 Td[(Buil)-1(d:)]TJ +ET +1 0 0 1 181.1323 314.2756 cm +0 g 0 G +1 0 0 1 -181.1323 -314.2756 cm +BT +/F8 9.9626 Tf 186.1136 314.2756 Td[(St)1(ate)-307(en)28(tere)-1(d)-305(after)-306(th)1(e)-307(\014r)1(s)-1(t)-306(al)1(lo)-28(cation,)-311(and)-305(b)-28(efor)1(e)-307(th)1(e)-307(\014)1(rs)-1(t)-306(ass)-1(em)27(b)1(ly;)-315(i)1(n)]TJ -10.5021 -11.9552 Td[(th)1(is)-224(s)-1(tate)-224(i)1(t)-224(is)-224(p)-27(oss)-1(ib)1(le)-224(to)-224(ad)1(d)-223(c)-1(omm)27(u)1(nication)-223(r)1(e)-1(qu)1(irem)-1(en)28(ts)-224(among)-223(di\013eren)28(t)]TJ 0 -11.9552 Td[(pr)1(o)-28(ce)-1(ss)-1(es)-1(.)]TJ +ET +1 0 0 1 145.7235 270.3987 cm +0 g 0 G +1 0 0 1 -145.7235 -270.3987 cm BT -/F29 9.9626 Tf 292.7883 336.8483 Td[(])]TJ +/F29 9.9626 Tf 150.7049 270.3987 Td[(Assem)32(ble)-1(d)1(:)]TJ ET -1 0 0 1 295.9708 336.8483 cm +1 0 0 1 207.2315 270.3987 cm 0 g 0 G -1 0 0 1 -295.9708 -336.8483 cm +1 0 0 1 -207.2315 -270.3987 cm BT -/F8 9.9626 Tf 300.9521 336.8483 Td[(Num)28(b)-27(e)-1(r)-374(o)-1(f)-374(gri)1(d)-375(v)56(ariab)1(les)-376(o)28(wned)-375(b)29(y)-375(the)-375(cur-)]TJ -103.4228 -11.9552 Td[(ren)28(t)-429(pr)1(o)-28(c)-1(es)-1(s)-430(\050)1(lo)-28(cal\051;)-477(e)-1(qu)1(iv)56(alen)28(t)-430(t)1(o)-430(th)1(e)-430(n)28(um)28(b)-28(er)-429(of)-429(lo)-28(cal)-429(ro)28(ws)-430(in)-429(the)]TJ 0 -11.9551 Td[(sparse)-334(co)-28(e)-1(\016cie)-1(n)29(t)-334(matr)1(ix.)]TJ +/F8 9.9626 Tf 212.2128 270.3987 Td[(St)1(ate)-352(en)28(tered)-351(af)1(ter)-351(th)1(e)-352(ass)-1(em)27(b)1(ly;)-359(com)-1(p)1(utati)1(ons)-351(using)-350(the)-351(ass)-1(o)-28(ci-)]TJ -36.6013 -11.9552 Td[(ated)-391(s)-1(p)1(ars)-1(e)-392(matr)1(ix,)-406(suc)27(h)-391(as)-392(matr)1(ix-v)28(e)-1(ctor)-391(pro)-27(du)1(c)-1(ts,)-406(are)-392(on)1(ly)-391(p)-28(oss)-1(i)1(ble)-392(in)]TJ 0 -11.9552 Td[(th)1(is)-334(state)-1(.)]TJ/F29 9.9626 Tf -24.9066 -25.9506 Td[(3.1.)-1(1)-1150(Named)-384(C)1(onstan)32(ts)]TJ ET -1 0 0 1 170.6302 296.5146 cm +1 0 0 1 145.7235 202.1291 cm 0 g 0 G -1 0 0 1 -170.6302 -296.5146 cm +1 0 0 1 -145.7235 -202.1291 cm BT -/F29 9.9626 Tf 175.6115 296.5146 Td[(mat)-1(r)1(i)-1(x)]TJ +/F29 9.9626 Tf 150.7049 202.1291 Td[(ps)1(b)]TJ ET -1 0 0 1 209.8188 296.5146 cm +1 0 0 1 168.6413 202.1291 cm q []0 d 0 J @@ -6226,11 +6231,11 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -209.8188 -296.5146 cm +1 0 0 1 -168.6413 -202.1291 cm BT -/F29 9.9626 Tf 213.2559 296.5146 Td[(data[)-1(p)1(sb)]TJ +/F29 9.9626 Tf 172.0785 202.1291 Td[(none)]TJ ET -1 0 0 1 256.3341 296.5146 cm +1 0 0 1 196.4754 202.1291 cm q []0 d 0 J @@ -6239,11 +6244,19 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -256.3341 -296.5146 cm +1 0 0 1 3.4371 0 cm +0 g 0 G +1 0 0 1 -199.9125 -202.1291 cm +BT +/F8 9.9626 Tf 204.8939 202.1291 Td[(Generic)-333(no-op;)]TJ +ET +1 0 0 1 145.7235 182.1625 cm +0 g 0 G +1 0 0 1 -145.7235 -182.1625 cm BT -/F29 9.9626 Tf 259.7712 296.5146 Td[(n)]TJ +/F29 9.9626 Tf 150.7049 182.1625 Td[(ps)1(b)]TJ ET -1 0 0 1 266.8236 296.5146 cm +1 0 0 1 168.6413 182.1625 cm q []0 d 0 J @@ -6252,11 +6265,11 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -266.8236 -296.5146 cm +1 0 0 1 -168.6413 -182.1625 cm BT -/F29 9.9626 Tf 270.2607 296.5146 Td[(col)]TJ +/F29 9.9626 Tf 172.0785 182.1625 Td[(nohalo)]TJ ET -1 0 0 1 284.951 296.5146 cm +1 0 0 1 205.7046 182.1625 cm q []0 d 0 J @@ -6265,23 +6278,19 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -284.951 -296.5146 cm -BT -/F29 9.9626 Tf 288.3881 296.5146 Td[(])]TJ -ET -1 0 0 1 291.5706 296.5146 cm +1 0 0 1 3.4371 0 cm 0 g 0 G -1 0 0 1 -291.5706 -296.5146 cm +1 0 0 1 -209.1417 -182.1625 cm BT -/F8 9.9626 Tf 296.552 296.5146 Td[(T)83(otal)-230(n)29(um)27(b)-27(er)-230(of)-230(gri)1(d)-230(v)56(ariab)1(le)-1(s)-230(read)-230(b)28(y)-230(th)1(e)-231(cur)1(-)]TJ -99.0227 -11.9552 Td[(ren)28(t)-289(p)1(ro)-28(ces)-1(s)-289(\050lo)-28(cal\051;)-303(e)-1(q)1(uiv)56(alen)28(t)-289(to)-288(the)-289(n)28(u)1(m)27(b)-27(e)-1(r)-288(of)-289(l)1(o)-28(c)-1(al)-288(c)-1(ol)1(umns)-289(in)-288(the)]TJ 0 -11.9552 Td[(sparse)-334(co)-28(e)-1(\016cie)-1(n)29(t)-334(matr)1(ix.)-444(The)-1(y)-333(i)1(nclud)1(e)-334(the)-333(halo.)]TJ -21.9178 -20.8916 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-310(as:)-433(an)-310(al)1(lo)-28(catable)-310(in)28(tege)-1(r)-310(arr)1(a)28(y)-311(of)-310(d)1(ime)-1(n)1(s)-1(i)1(on)]TJ/F32 9.9626 Tf 237.5819 0 Td[(psb_mdata_size_)]TJ/F8 9.9626 Tf 78.4551 0 Td[(.)]TJ +/F8 9.9626 Tf 214.1231 182.1625 Td[(Do)-333(not)-333(fetc)27(h)-332(halo)-333(e)-1(l)1(e)-1(me)-1(n)29(ts)-1(;)]TJ ET -1 0 0 1 145.7235 230.8211 cm +1 0 0 1 145.7235 162.1959 cm 0 g 0 G -1 0 0 1 -145.7235 -230.8211 cm +1 0 0 1 -145.7235 -162.1959 cm BT -/F29 9.9626 Tf 150.7049 230.8211 Td[(halo)]TJ +/F29 9.9626 Tf 150.7049 162.1959 Td[(ps)1(b)]TJ ET -1 0 0 1 172.2375 230.8211 cm +1 0 0 1 168.6413 162.1959 cm q []0 d 0 J @@ -6290,134 +6299,131 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -172.2375 -230.8211 cm -BT -/F29 9.9626 Tf 175.6747 230.8211 Td[(index)]TJ -ET -1 0 0 1 202.885 230.8211 cm -0 g 0 G -1 0 0 1 -202.885 -230.8211 cm -BT -/F8 9.9626 Tf 207.8663 230.8211 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)-384(for)-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(ea)-1(c)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 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Td[(The)-460(n)28(um)28(b)-28(er)-460(of)-460(lo)-27(c)-1(al)-460(r)1(o)27(ws,)-492(i.e.)-825(th)1(e)-461(n)28(u)1(m)27(b)-27(e)-1(r)-460(of)-459(ro)28(ws)-461(o)28(w)-1(n)1(e)-1(d)]TJ -53.4796 -11.9551 Td[(b)28(y)-401(th)1(e)-402(cur)1(ren)28(t)-401(pr)1(o)-28(c)-1(es)-1(s;)-435(as)-401(e)-1(xp)1(lain)1(e)-1(d)-400(in)]TJ +ET +1 0 0 1 352.2268 617.2246 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -352.2268 -617.2246 cm BT -/F8 9.9626 Tf 136.3917 581.6032 Td[(Des)-1(crib)-27(e)-334(th)1(e)-334(c)27(h)1(aracte)-1(r)1(is)-1(t)1(ic)-334(of)-333(th)1(e)-334(distri)1(bu)1(te)-1(d)-333(spar)1(s)-1(e)-334(matr)1(ix.)]TJ -11.5897 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(arr)1(a)27(y)-333(of)-333(c)28(haracter)-333(of)-333(le)-1(n)1(gth)-333(9.)]TJ +/F8 9.9626 Tf 352.2268 617.2246 Td[(1)]TJ ET -1 0 0 1 94.9141 548.0648 cm +1 0 0 1 357.2082 617.2246 cm 0 g 0 G -1 0 0 1 -94.9141 -548.0648 cm +1 0 0 1 -357.2082 -617.2246 cm BT -/F29 9.9626 Tf 99.8954 548.0648 Td[(pl)]TJ +/F8 9.9626 Tf 357.2082 617.2246 Td[(,)-418(it)-401(i)1(s)-402(equal)-401(to)]TJ/F14 9.9626 Tf 68.0806 0 Td[(jI)]TJ/F10 6.9738 Tf 8.1922 -1.4944 Td[(i)]TJ/F14 9.9626 Tf 3.3169 1.4944 Td[(j)]TJ/F8 9.9626 Tf 5.4314 0 Td[(+)]TJ/F14 9.9626 Tf 10.4127 0 Td[(jB)]TJ/F10 6.9738 Tf 9.311 -1.4944 Td[(i)]TJ/F14 9.9626 Tf 3.3168 1.4944 Td[(j)]TJ/F8 9.9626 Tf 2.7674 0 Td[(.)-648(Th)1(e)]TJ -292.4257 -11.9552 Td[(retur)1(ned)-333(v)56(alue)-333(is)-334(sp)-28(ec)-1(i)1(\014c)-334(to)-333(the)-333(c)-1(all)1(ing)-333(pr)1(o)-28(ce)-1(ss)-1(.)]TJ ET -1 0 0 1 109.4429 548.0648 cm +1 0 0 1 145.7235 555.9906 cm +0 g 0 G 0 g 0 G -1 0 0 1 -109.4429 -548.0648 cm +1 0 0 1 -145.7235 -555.9906 cm BT -/F8 9.9626 Tf 114.4242 548.0648 Td[(Sp)-27(ec)-1(i\014)1(e)-1(s)-353(t)1(he)-353(lo)-28(cal)-352(ro)28(w)-353(p)-27(e)-1(rm)28(utat)1(ion)-352(of)-352(distrib)1(uted)-352(s)-1(p)1(arse)-353(m)-1(at)1(rix.)-502(If)-352(p)1(l\0501\051)-353(i)1(s)]TJ 10.3778 -11.9552 Td[(equal)-333(to)-333(0,)-333(then)-333(th)1(e)-1(re)-333(is)-1(n)1('t)-333(ro)28(w)-334(p)-27(erm)27(u)1(tation)1(.)]TJ 0 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-301(as)-1(:)-428(an)-302(allo)-27(c)-1(atab)1(le)-303(i)1(n)28(tege)-1(r)-302(ar)1(ra)28(y)-302(of)-302(d)1(ime)-1(nsion)-301(e)-1(qu)1(al)-302(to)-302(n)28(u)1(m)27(b)-27(e)-1(r)-302(of)]TJ 0 -11.9552 Td[(lo)-28(cal)-333(ro)28(w)-334(\050)1(m)-1(atr)1(ix)]TJ +/F18 11.9552 Tf 150.7049 555.9906 Td[(psb)]TJ ET -1 0 0 1 201.0053 512.1993 cm +1 0 0 1 171.7609 555.9906 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +4.0349 0.1992 l S Q -1 0 0 1 -201.0053 -512.1993 cm +1 0 0 1 -171.7609 -555.9906 cm BT -/F8 9.9626 Tf 203.9941 512.1993 Td[(dat)1(a[psb)]TJ +/F18 11.9552 Tf 175.7958 555.9906 Td[(cd)]TJ ET -1 0 0 1 241.7305 512.1993 cm +1 0 0 1 190.0523 555.9906 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +4.0349 0.1992 l S Q -1 0 0 1 -241.7305 -512.1993 cm +1 0 0 1 -190.0523 -555.9906 cm BT -/F8 9.9626 Tf 244.7193 512.1993 Td[(n)]TJ +/F18 11.9552 Tf 194.0872 555.9906 Td[(ge)-1(t)]TJ ET -1 0 0 1 250.8518 512.1993 cm +1 0 0 1 212.986 555.9906 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +4.0349 0.1992 l S Q -1 0 0 1 -250.8518 -512.1993 cm +1 0 0 1 -212.986 -555.9906 cm BT -/F8 9.9626 Tf 253.8407 512.1993 Td[(ro)28(w)]TJ +/F18 11.9552 Tf 217.0209 555.9906 Td[(lo)-32(cal)]TJ ET -1 0 0 1 270.2403 512.1993 cm +1 0 0 1 244.9138 555.9906 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +4.0349 0.1992 l S Q -1 0 0 1 -270.2403 -512.1993 cm +1 0 0 1 -244.9138 -555.9906 cm BT -/F8 9.9626 Tf 273.2291 512.1993 Td[(]\051)]TJ +/F18 11.9552 Tf 248.9487 555.9906 Td[(col)-1(s|Get)-376(n)31(um)31(b)-31(er)-376(of)-375(l)-1(o)-31(cal)-376(col)-1(s)]TJ/F18 14.3462 Tf -98.2438 -31.9031 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 100.5285 -21.8209 Td[(nc)-333(=)-333(psb)]TJ ET -1 0 0 1 94.9141 490.616 cm -0 g 0 G -1 0 0 1 -94.9141 -490.616 cm +1 0 0 1 291.1836 502.2666 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S +Q +1 0 0 1 -291.1836 -502.2666 cm BT -/F29 9.9626 Tf 99.8954 490.616 Td[(pr)]TJ +/F8 9.9626 Tf 294.1724 502.2666 Td[(cd)]TJ ET -1 0 0 1 110.9788 490.616 cm -0 g 0 G -1 0 0 1 -110.9788 -490.616 cm +1 0 0 1 304.7328 502.2666 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S +Q +1 0 0 1 -304.7328 -502.2666 cm BT -/F8 9.9626 Tf 115.9601 490.616 Td[(Sp)-27(ec)-1(i\014)1(e)-1(s)-512(th)1(e)-513(lo)-27(c)-1(al)-512(colu)1(m)-1(n)-511(p)-28(erm)28(utati)1(on)-512(of)-512(d)1(istrib)1(uted)-512(spar)1(s)-1(e)-512(m)-1(atr)1(ix.)-980(If)]TJ 8.8419 -11.9551 Td[(PR\0501\051)-333(is)-333(e)-1(qu)1(al)-333(to)-333(0,)-334(t)1(hen)-333(there)-334(isn')1(t)-334(colu)1(m)-1(n)1(m)-334(p)-27(e)-1(r)1(m)27(u)1(tation.)]TJ 0 -11.9552 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-301(as)-1(:)-428(an)-302(allo)-27(c)-1(atab)1(le)-303(i)1(n)28(tege)-1(r)-302(ar)1(ra)28(y)-302(of)-302(d)1(ime)-1(n)1(s)-1(ion)-301(e)-1(qu)1(al)-302(to)-302(n)28(u)1(m)27(b)-27(e)-1(r)-302(of)]TJ 0 -11.9552 Td[(lo)-28(cal)-333(ro)28(w)-334(\050)1(m)-1(atr)1(ix)]TJ +/F8 9.9626 Tf 307.7217 502.2666 Td[(get)]TJ ET -1 0 0 1 201.0053 454.7505 cm +1 0 0 1 321.6029 502.2666 cm q []0 d 0 J @@ -7507,11 +7693,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -201.0053 -454.7505 cm +1 0 0 1 -321.6029 -502.2666 cm BT -/F8 9.9626 Tf 203.9941 454.7505 Td[(dat)1(a[psb)]TJ +/F8 9.9626 Tf 324.5918 502.2666 Td[(lo)-28(cal)]TJ ET -1 0 0 1 241.7305 454.7505 cm +1 0 0 1 345.3916 502.2666 cm q []0 d 0 J @@ -7520,622 +7706,872 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -241.7305 -454.7505 cm +1 0 0 1 -345.3916 -502.2666 cm +BT +/F8 9.9626 Tf 348.3804 502.2666 Td[(cols)-334(\050)]TJ/F19 9.9626 Tf 23.3015 0 Td[(desc)]TJ/F8 9.9626 Tf 18.3312 0 Td[(\051)]TJ +ET +1 0 0 1 145.7235 478.3562 cm +0 g 0 G +1 0 0 1 -145.7235 -478.3562 cm +BT +/F29 9.9626 Tf 150.7049 478.3562 Td[(On)-383(En)32(tr)1(y)]TJ +ET +1 0 0 1 198.2901 478.3562 cm +0 g 0 G +1 0 0 1 -52.5665 -19.7082 cm +0 g 0 G +1 0 0 1 -145.7236 -458.648 cm +BT +/F29 9.9626 Tf 150.7049 458.648 Td[(desc)]TJ +ET +1 0 0 1 171.9321 458.648 cm +0 g 0 G +1 0 0 1 -171.9321 -458.648 cm +BT +/F8 9.9626 Tf 176.9134 458.648 Td[(th)1(e)-334(c)-1(omm)27(u)1(ni)1(c)-1(ation)-332(des)-1(crip)1(tor.)]TJ -1.3019 -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[(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 422.7825 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -346.5264 -422.7825 cm BT -/F8 9.9626 Tf 244.7193 454.7505 Td[(n)]TJ +/F32 9.9626 Tf 346.5264 422.7825 Td[(psb)]TJ ET -1 0 0 1 250.8518 454.7505 cm +1 0 0 1 362.8451 422.7825 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.1382 0.1992 l S Q -1 0 0 1 -250.8518 -454.7505 cm +1 0 0 1 -362.8451 -422.7825 cm BT -/F8 9.9626 Tf 253.8407 454.7505 Td[(col)]TJ +/F32 9.9626 Tf 365.9833 422.7825 Td[(desc)]TJ ET -1 0 0 1 266.615 454.7505 cm +1 0 0 1 387.5322 422.7825 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.1382 0.1992 l S Q -1 0 0 1 -266.615 -454.7505 cm +1 0 0 1 -387.5322 -422.7825 cm BT -/F8 9.9626 Tf 269.6038 454.7505 Td[(]\051)]TJ +/F32 9.9626 Tf 390.6705 422.7825 Td[(type)]TJ ET -1 0 0 1 94.9141 433.1673 cm +1 0 0 1 411.5918 422.7825 cm 0 g 0 G -1 0 0 1 -94.9141 -433.1673 cm +1 0 0 1 -411.5918 -422.7825 cm BT -/F29 9.9626 Tf 99.8954 433.1673 Td[(m)]TJ +/F8 9.9626 Tf 411.5918 422.7825 Td[(.)]TJ ET -1 0 0 1 109.4429 433.1673 cm +1 0 0 1 145.7235 401.4071 cm 0 g 0 G -1 0 0 1 -109.4429 -433.1673 cm +1 0 0 1 -145.7235 -401.4071 cm BT -/F8 9.9626 Tf 114.4242 433.1673 Td[(Num)28(b)-27(e)-1(r)-243(of)-244(r)1(o)28(w)-1(s;)-273(if)-243(ro)28(w)-244(ind)1(ice)-1(s)-244(are)-244(stored)-244(exp)1(licitly)84(,)-262(as)-244(in)-243(Co)-28(or)1(din)1(ate)-244(Storage,)]TJ 10.3778 -11.9552 Td[(shoul)1(d)-225(b)-27(e)-225(greate)-1(r)-224(than)-224(or)-224(e)-1(qu)1(al)-225(to)-224(the)-225(maxim)28(um)-225(ro)28(w)-225(in)1(dex)-225(actuall)1(y)-225(p)1(re)-1(sen)28(t)]TJ 0 -11.9552 Td[(in)-333(th)1(e)-334(sparse)-334(matri)1(x.)-444(Sp)-27(e)-1(ci\014ed)-333(as:)-445(i)1(n)28(te)-1(ger)-333(v)56(ariab)1(le.)]TJ +/F29 9.9626 Tf 150.7049 401.4071 Td[(On)-383(R)-1(etur)1(n)]TJ ET -1 0 0 1 94.9141 387.6737 cm +1 0 0 1 205.2431 401.4071 cm +0 g 0 G +1 0 0 1 -59.5196 -19.7083 cm 0 g 0 G -1 0 0 1 -94.9141 -387.6737 cm +1 0 0 1 -145.7235 -381.6988 cm BT -/F29 9.9626 Tf 99.8954 387.6737 Td[(k)]TJ +/F29 9.9626 Tf 150.7049 381.6988 Td[(F)96(unction)-384(v)64(alue)]TJ ET -1 0 0 1 105.9421 387.6737 cm +1 0 0 1 224.1097 381.6988 cm 0 g 0 G -1 0 0 1 -105.9421 -387.6737 cm +1 0 0 1 -224.1097 -381.6988 cm BT -/F8 9.9626 Tf 110.9235 387.6737 Td[(Num)28(b)-27(e)-1(r)-338(of)-337(columns;)-340(if)-337(c)-1(olu)1(m)-1(n)-337(in)1(dice)-1(s)-338(are)-338(s)-1(t)1(ore)-1(d)-337(expli)1(c)-1(it)1(ly)83(,)-339(as)-338(in)-337(Co)-28(ord)1(inate)]TJ 13.8785 -11.9552 Td[(St)1(orage)-228(or)-226(Com)-1(p)1(res)-1(se)-1(d)-226(Sp)1(arse)-228(Ro)28(ws)-1(,)-248(shou)1(ld)-227(b)-27(e)-227(greate)-1(r)-226(than)-226(or)-227(equal)-226(to)-227(the)]TJ 0 -11.9552 Td[(maxim)28(um)-374(c)-1(olu)1(mn)-374(in)1(dex)-374(ac)-1(t)1(ually)-373(prese)-1(n)28(t)-374(i)1(n)-374(th)1(e)-375(spar)1(s)-1(e)-374(m)-1(atr)1(ix.)-566(Sp)-27(ec)-1(i\014)1(e)-1(d)]TJ 0 -11.9551 Td[(as:)-445(i)1(n)28(te)-1(ger)-333(v)56(ariab)1(le.)]TJ -24.9066 -21.1688 Td[(F)28(OR)83(TRAN95)-320(i)1(n)28(te)-1(r)1(face)-321(f)1(or)-320(d)1(istrib)1(uted)-319(s)-1(p)1(ars)-1(e)-320(matri)1(c)-1(es)-321(con)28(tain)1(in)1(g)-320(dou)1(ble)-320(p)1(re)-1(ci-)]TJ 0 -11.9552 Td[(sion)-333(real)-333(e)-1(n)28(t)1(ries)-334(is)-334(d)1(e)-1(\014)1(ned)-333(as)-334(in)-333(\014)1(gur)1(e)]TJ +/F8 9.9626 Tf 229.0911 381.6988 Td[(The)-361(n)29(um)27(b)-27(er)-361(of)-360(l)1(o)-28(c)-1(al)-360(cols)-1(,)-367(i)1(.e)-1(.)-525(the)-361(n)29(um)27(b)-27(er)-360(of)-361(i)1(nd)1(ic)-1(es)-361(used)-361(b)29(y)]TJ -53.4796 -11.9551 Td[(th)1(e)-422(cur)1(re)-1(n)29(t)-421(pr)1(o)-28(c)-1(es)-1(s,)-443(i)1(nclud)1(ing)-421(b)-27(oth)-420(lo)-28(cal)-421(and)-420(hal)1(o)-421(ind)1(ice)-1(s;)-465(as)-421(e)-1(x)1(plain)1(e)-1(d)]TJ 0 -11.9552 Td[(in)]TJ ET -1 0 0 1 267.6277 318.6842 cm +1 0 0 1 187.3364 357.7885 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -267.6277 -318.6842 cm +1 0 0 1 -187.3364 -357.7885 cm BT -/F8 9.9626 Tf 267.6277 318.6842 Td[(4)]TJ +/F8 9.9626 Tf 187.3364 357.7885 Td[(1)]TJ ET -1 0 0 1 272.6091 318.6842 cm +1 0 0 1 192.3177 357.7885 cm 0 g 0 G -1 0 0 1 -272.6091 -318.6842 cm +1 0 0 1 -192.3177 -357.7885 cm BT -/F8 9.9626 Tf 272.6091 318.6842 Td[(.)]TJ +/F8 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Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(\051)]TJ/F14 9.9626 Tf 3.8744 0 Td[(k)]TJ/F7 6.9738 Tf 4.9813 -1.4944 Td[(1)]TJ/F8 9.9626 Tf 6.6833 1.4944 Td[(+)]TJ/F14 9.9626 Tf 9.9626 0 Td[(k)]TJ/F11 9.9626 Tf 4.9813 0 Td[(im)]TJ/F8 9.9626 Tf 12.1796 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8744 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(\051)]TJ/F14 9.9626 Tf 3.8744 0 Td[(k)]TJ/F7 6.9738 Tf 4.9813 -1.4944 Td[(1)]TJ/F18 14.3462 Tf -232.5234 -30.9896 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 89.4913 -21.8209 Td[(call)-333(psb)]TJ ET -1 0 0 1 287.0588 624.7867 cm +1 0 0 1 223.2486 487.0636 cm q []0 d 0 J 0.3985 w 0 0.1992 m -17.664 0.1992 l +2.9888 0.1992 l S Q -1 0 0 1 -287.0588 -624.7867 cm +1 0 0 1 -223.2486 -487.0636 cm BT -/F11 9.9626 Tf 287.0588 615.4475 Td[(x)]TJ/F10 6.9738 Tf 5.6939 2.8781 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -2.8781 Td[(x)]TJ/F8 9.9626 Tf -199.1334 -21.9178 Td[(els)-1(e)-333(if)]TJ/F11 9.9626 Tf 28.0061 0 Td[(x)]TJ/F8 9.9626 Tf 9.0148 0 Td[(is)-334(d)1(oub)1(le)-334(p)1(rec)-1(ision)-333(com)-1(p)1(lex)-334(v)28(ector)-333(then)-333(c)-1(omp)1(utes)-334(2-norm)-333(as)-1(:)]TJ/F11 9.9626 Tf 101.2227 -23.0323 Td[(nr)-28(m)]TJ/F8 9.9626 Tf 19.4987 0 Td[(2)]TJ/F14 9.9626 Tf 7.7487 0 Td[(\040)]TJ 12.73 9.3392 Td[(p)]TJ +/F8 9.9626 Tf 226.2374 487.0636 Td[(geas)-1(u)1(m)-1(s)-334(\050)]TJ/F19 9.9626 Tf 43.2822 0 Td[(r)51(es)1(,)-358(x,)-357(desc)]TJ ET -1 0 0 1 286.4186 579.8366 cm +1 0 0 1 318.6705 487.0636 cm q []0 d 0 J 0.3985 w 0 0.1992 m -18.9442 0.1992 l +3.0552 0.1992 l S Q -1 0 0 1 -286.4186 -579.8366 cm +1 0 0 1 -318.6705 -487.0636 cm BT -/F11 9.9626 Tf 286.4186 570.4973 Td[(x)]TJ/F10 6.9738 Tf 5.6939 2.8781 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -2.8781 Td[(x)]TJ +/F19 9.9626 Tf 321.7257 487.0636 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ ET -1 0 0 1 99.8954 548.3547 cm +1 0 0 1 99.8954 461.7352 cm 0 g 0 G -1 0 0 1 26.7107 -21.0212 cm +1 0 0 1 24.488 -21.0211 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.9813 20.6227 cm +1 0 0 1 4.9813 20.6226 cm q []0 d 0 J 0.3985 w 0 0.1992 m -280.3271 0.1992 l +284.7725 0.1992 l S Q -1 0 0 1 -131.5874 -547.9562 cm +1 0 0 1 -129.3647 -461.3367 cm BT -/F11 9.9626 Tf 137.565 539.5876 Td[(nr)-28(m)]TJ/F8 9.9626 Tf 19.4987 0 Td[(2)]TJ/F11 9.9626 Tf 79.8511 0 Td[(x)]TJ/F29 9.9626 Tf 118.3066 0 Td[(F)96(unction)]TJ +/F11 9.9626 Tf 135.3423 452.9681 Td[(r)-28(es)-8558(x)]TJ/F29 9.9626 Tf 217.6564 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 131.5874 535.6025 cm +1 0 0 1 129.3647 448.9831 cm q []0 d 0 J 0.3985 w 0 0.1992 m -280.3271 0.1992 l +284.7725 0.1992 l S Q -1 0 0 1 -131.5874 -535.6025 cm +1 0 0 1 -129.3647 -448.9831 cm BT -/F8 9.9626 Tf 137.565 527.2339 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-1200(Long)-333(Pr)1(e)-1(cis)-1(i)1(on)-333(Re)-1(al)-3102(psb)]TJ +/F8 9.9626 Tf 135.3423 440.6145 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-1200(Long)-333(Pr)1(e)-1(cis)-1(i)1(on)-333(Re)-1(al)-3102(psb)]TJ ET -1 0 0 1 370.8185 527.2339 cm +1 0 0 1 368.5958 440.6145 cm q []0 d 0 J @@ -10959,11 +11121,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -370.8185 -527.2339 cm +1 0 0 1 -368.5958 -440.6145 cm BT -/F8 9.9626 Tf 373.8073 527.2339 Td[(genrm2)]TJ -236.2423 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-1200(Long)-333(Pr)1(e)-1(cis)-1(i)1(on)-333(Com)-1(p)1(le)-1(x)-1199(psb)]TJ +/F8 9.9626 Tf 371.5846 440.6145 Td[(geas)-1(u)1(m)-1(s)]TJ -236.2423 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-1200(Long)-333(Pr)1(e)-1(cis)-1(i)1(on)-333(Com)-1(p)1(le)-1(x)-1199(psb)]TJ ET -1 0 0 1 370.8185 515.2787 cm +1 0 0 1 368.5958 428.6593 cm q []0 d 0 J @@ -10972,98 +11134,68 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -370.8185 -515.2787 cm +1 0 0 1 -368.5958 -428.6593 cm BT -/F8 9.9626 Tf 373.8073 515.2787 Td[(genrm2)]TJ +/F8 9.9626 Tf 371.5846 428.6593 Td[(geas)-1(u)1(m)-1(s)]TJ ET -1 0 0 1 131.5874 511.2936 cm +1 0 0 1 129.3647 424.6742 cm q []0 d 0 J 0.3985 w 0 0.1992 m -280.3271 0.1992 l +284.7725 0.1992 l S Q -1 0 0 1 96.4801 -27.84 cm +1 0 0 1 98.7028 -27.84 cm 0 g 0 G -1 0 0 1 -228.0675 -483.4536 cm +1 0 0 1 -228.0675 -396.8342 cm BT -/F8 9.9626 Tf 228.0675 483.4536 Td[(T)83(ab)1(le)-334(7:)-444(Data)-333(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 228.0675 396.8342 Td[(T)83(ab)1(le)-334(7:)-444(Data)-333(t)28(yp)-28(es)]TJ ET -1 0 0 1 315.4344 483.4536 cm +1 0 0 1 315.4344 396.8342 cm 0 g 0 G 1 0 0 1 -215.539 -1.9372 cm 0 g 0 G -1 0 0 1 -99.8954 -481.5164 cm -BT -/F18 14.3462 Tf 99.8954 436.8403 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 110.0862 -21.8209 Td[(psb)]TJ -ET -1 0 0 1 225.5787 415.0193 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -225.5787 -415.0193 cm -BT -/F8 9.9626 Tf 228.5675 415.0193 Td[(genrm2)-333(\050)]TJ/F19 9.9626 Tf 39.3248 0 Td[(x,)-357(desc)]TJ -ET -1 0 0 1 298.0756 415.0193 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -3.0552 0.1992 l -S -Q -1 0 0 1 -298.0756 -415.0193 cm -BT -/F19 9.9626 Tf 301.1308 415.0193 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ -ET -1 0 0 1 94.9141 391.109 cm +1 0 0 1 -4.9813 -27.628 cm 0 g 0 G -1 0 0 1 -94.9141 -391.109 cm +1 0 0 1 -94.9141 -367.269 cm BT -/F29 9.9626 Tf 99.8954 391.109 Td[(On)-383(En)32(tr)1(y)]TJ +/F29 9.9626 Tf 99.8954 367.269 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 147.4806 391.109 cm +1 0 0 1 147.4806 367.269 cm 0 g 0 G -1 0 0 1 -52.5665 -19.9253 cm +1 0 0 1 -52.5665 -18.8527 cm 0 g 0 G -1 0 0 1 -94.9141 -371.1837 cm +1 0 0 1 -94.9141 -348.4163 cm BT -/F29 9.9626 Tf 99.8954 371.1837 Td[(x)]TJ +/F29 9.9626 Tf 99.8954 348.4163 Td[(x)]TJ ET -1 0 0 1 105.9421 371.1837 cm +1 0 0 1 105.9421 348.4163 cm 0 g 0 G -1 0 0 1 -105.9421 -371.1837 cm +1 0 0 1 -105.9421 -348.4163 cm BT -/F8 9.9626 Tf 110.9235 371.1837 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 -167.9331 -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 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf -29.6113 -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 -11.9552 Td[(in)-333(T)83(ab)1(le)]TJ +/F8 9.9626 Tf 110.9235 348.4163 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 -167.9331 -11.9551 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 -11.9552 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 1 163.8224 323.3631 cm +1 0 0 1 163.8224 300.5957 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -163.8224 -323.3631 cm +1 0 0 1 -163.8224 -300.5957 cm BT -/F8 9.9626 Tf 163.8224 323.3631 Td[(7)]TJ +/F8 9.9626 Tf 163.8224 300.5957 Td[(7)]TJ ET -1 0 0 1 168.8038 323.3631 cm +1 0 0 1 168.8038 300.5957 cm 0 g 0 G -1 0 0 1 -168.8038 -323.3631 cm +1 0 0 1 -168.8038 -300.5957 cm BT -/F8 9.9626 Tf 168.8038 323.3631 Td[(.)]TJ +/F8 9.9626 Tf 168.8038 300.5957 Td[(.)]TJ ET -1 0 0 1 94.9141 303.4378 cm +1 0 0 1 94.9141 281.743 cm 0 g 0 G -1 0 0 1 -94.9141 -303.4378 cm +1 0 0 1 -94.9141 -281.743 cm BT -/F29 9.9626 Tf 99.8954 303.4378 Td[(desc)]TJ +/F29 9.9626 Tf 99.8954 281.743 Td[(desc)]TJ ET -1 0 0 1 121.81 303.4378 cm +1 0 0 1 121.81 281.743 cm q []0 d 0 J @@ -11072,23 +11204,23 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -121.81 -303.4378 cm +1 0 0 1 -121.81 -281.743 cm BT -/F29 9.9626 Tf 125.2471 303.4378 Td[(a)]TJ +/F29 9.9626 Tf 125.2471 281.743 Td[(a)]TJ ET -1 0 0 1 130.8165 303.4378 cm +1 0 0 1 130.8165 281.743 cm 0 g 0 G -1 0 0 1 -130.8165 -303.4378 cm +1 0 0 1 -130.8165 -281.743 cm BT -/F8 9.9626 Tf 135.7978 303.4378 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 -10.9958 -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 -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[(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 +/F8 9.9626 Tf 135.7978 281.743 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 -10.9958 -11.9551 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 -11.9552 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 1 295.717 267.5723 cm +1 0 0 1 295.717 245.8775 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -267.5723 cm +1 0 0 1 -295.717 -245.8775 cm BT -/F32 9.9626 Tf 295.717 267.5723 Td[(psb)]TJ +/F32 9.9626 Tf 295.717 245.8775 Td[(psb)]TJ ET -1 0 0 1 312.0356 267.5723 cm +1 0 0 1 312.0356 245.8775 cm q []0 d 0 J @@ -11097,11 +11229,11 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -312.0356 -267.5723 cm +1 0 0 1 -312.0356 -245.8775 cm BT -/F32 9.9626 Tf 315.1738 267.5723 Td[(desc)]TJ +/F32 9.9626 Tf 315.1738 245.8775 Td[(desc)]TJ ET -1 0 0 1 336.7228 267.5723 cm +1 0 0 1 336.7228 245.8775 cm q []0 d 0 J @@ -11110,98 +11242,98 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -336.7228 -267.5723 cm +1 0 0 1 -336.7228 -245.8775 cm BT -/F32 9.9626 Tf 339.861 267.5723 Td[(type)]TJ +/F32 9.9626 Tf 339.861 245.8775 Td[(type)]TJ ET -1 0 0 1 360.7824 267.5723 cm +1 0 0 1 360.7824 245.8775 cm 0 g 0 G -1 0 0 1 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[]0 d 0 J 0.3985 w 0 0.1992 m -185.4227 0.1992 l +17.664 0.1992 l S Q -1 0 0 1 -179.0396 -473.2229 cm +1 0 0 1 -287.4494 -588.7669 cm BT -/F11 9.9626 Tf 185.0172 464.8543 Td[(A)]TJ/F8 9.9626 Tf 7.472 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/F8 9.9626 Tf 5.2419 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(\013)]TJ/F8 9.9626 Tf 6.41 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(\014)]TJ/F29 9.9626 Tf 69.1356 0 Td[(Subr)1(outi)-1(ne)]TJ +/F11 9.9626 Tf 287.4494 579.4276 Td[(x)]TJ/F10 6.9738 Tf 5.6939 2.8781 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -2.8781 Td[(x)]TJ/F8 9.9626 Tf -184.5801 -19.017 Td[(els)-1(e)-333(if)]TJ/F11 9.9626 Tf 28.0061 0 Td[(x)]TJ/F8 9.9626 Tf 9.0148 0 Td[(is)-334(d)1(oub)1(le)-334(p)1(rec)-1(ision)-333(com)-1(p)1(lex)-334(v)28(ector)-333(then)-333(c)-1(omp)1(utes)-334(1-norm)-333(as)-1(:)]TJ/F11 9.9626 Tf 85.8881 -20.1316 Td[(r)-28(es)]TJ/F8 9.9626 Tf 14.0804 0 Td[(\050)]TJ/F11 9.9626 Tf 3.8743 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(\051)]TJ/F14 9.9626 Tf 6.6417 0 Td[(\040)]TJ 12.73 9.3393 Td[(p)]TJ ET -1 0 0 1 179.0396 460.8692 cm +1 0 0 1 286.8093 549.6182 cm q []0 d 0 J 0.3985 w 0 0.1992 m -185.4227 0.1992 l +18.9442 0.1992 l S Q -1 0 0 1 -179.0396 -460.8692 cm +1 0 0 1 -286.8093 -549.6182 cm BT -/F8 9.9626 Tf 185.0172 452.5006 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-3103(psb)]TJ +/F11 9.9626 Tf 286.8093 540.279 Td[(x)]TJ/F10 6.9738 Tf 5.6939 2.8781 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -2.8781 Td[(x)]TJ/F18 14.3462 Tf -200.1642 -32.4463 Td[(Syn)31(tax)]TJ/F8 9.9626 Tf 89.5051 -21.8209 Td[(call)-333(psb)]TJ ET -1 0 0 1 318.9209 452.5006 cm +1 0 0 1 223.2625 486.0117 cm q []0 d 0 J @@ -11699,73 +11730,68 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -318.9209 -452.5006 cm +1 0 0 1 -223.2625 -486.0117 cm BT -/F8 9.9626 Tf 321.9097 452.5006 Td[(spmm)]TJ -136.8925 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 226.2513 486.0117 Td[(genrm2s)-334(\050)]TJ/F19 9.9626 Tf 43.2545 0 Td[(r)51(es)1(,)-358(x,)-357(desc)]TJ ET -1 0 0 1 318.9209 440.5454 cm +1 0 0 1 318.6567 486.0117 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.0552 0.1992 l S Q -1 0 0 1 -318.9209 -440.5454 cm +1 0 0 1 -318.6567 -486.0117 cm BT -/F8 9.9626 Tf 321.9097 440.5454 Td[(spmm)]TJ +/F19 9.9626 Tf 321.7119 486.0117 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ ET -1 0 0 1 179.0396 436.5604 cm +1 0 0 1 99.8954 460.7711 cm +0 g 0 G +1 0 0 1 24.488 -21.0212 cm +0 g 0 G +0 g 0 G +1 0 0 1 4.9813 20.6227 cm q []0 d 0 J 0.3985 w 0 0.1992 m -185.4227 0.1992 l +284.7725 0.1992 l S Q -1 0 0 1 49.0279 -27.8401 cm -0 g 0 G -1 0 0 1 -228.0675 -408.7203 cm -BT -/F8 9.9626 Tf 228.0675 408.7203 Td[(T)83(ab)1(le)-334(9:)-444(Data)-333(t)28(yp)-28(es)]TJ -ET -1 0 0 1 315.4344 408.7203 cm -0 g 0 G -1 0 0 1 -215.539 -1.9372 cm -0 g 0 G -1 0 0 1 -99.8954 -406.7831 cm +1 0 0 1 -129.3647 -460.3726 cm BT -/F18 14.3462 Tf 99.8954 365.5872 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 59.7059 -21.8209 Td[(CALL)-334(p)1(s)-1(b)]TJ +/F11 9.9626 Tf 135.3423 452.004 Td[(r)-28(es)-8558(x)]TJ/F29 9.9626 Tf 217.6564 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 205.6398 343.7663 cm +1 0 0 1 129.3647 448.0189 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +284.7725 0.1992 l S Q -1 0 0 1 -205.6398 -343.7663 cm +1 0 0 1 -129.3647 -448.0189 cm BT -/F8 9.9626 Tf 208.6287 343.7663 Td[(spmm)-334(\050)]TJ/F19 9.9626 Tf 33.2642 0 Td[(alpha,)-357(a)-1(,)-357(x,)-357(b)51(eta)-1(,)-357(y,)-357(desc)]TJ +/F8 9.9626 Tf 135.3423 439.6503 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-1200(Long)-333(Pr)1(e)-1(cis)-1(i)1(on)-333(Re)-1(al)-3102(psb)]TJ ET -1 0 0 1 348.4558 343.7663 cm +1 0 0 1 368.5958 439.6503 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +2.9888 0.1992 l S Q -1 0 0 1 -348.4558 -343.7663 cm +1 0 0 1 -368.5958 -439.6503 cm BT -/F19 9.9626 Tf 351.5111 343.7663 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ -246.394 -23.9103 Td[(CALL)-334(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 371.5846 439.6503 Td[(genrm2s)]TJ -236.2423 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-1200(Long)-333(Pr)1(e)-1(cis)-1(i)1(on)-333(Com)-1(p)1(le)-1(x)-1199(psb)]TJ ET -1 0 0 1 179.6707 319.856 cm +1 0 0 1 368.5958 427.6951 cm q []0 d 0 J @@ -11774,74 +11800,93 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -179.6707 -319.856 cm +1 0 0 1 -368.5958 -427.6951 cm BT -/F8 9.9626 Tf 182.6596 319.856 Td[(spmm)-334(\050)]TJ/F19 9.9626 Tf 33.2642 0 Td[(alpha,)-357(a)-1(,)-357(x,)-357(b)51(eta)-1(,)-357(y,)1(desc)]TJ +/F8 9.9626 Tf 371.5846 427.6951 Td[(genrm2s)]TJ ET -1 0 0 1 318.9224 319.856 cm +1 0 0 1 129.3647 423.7101 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +284.7725 0.1992 l S Q -1 0 0 1 -318.9224 -319.856 cm +1 0 0 1 98.7028 -27.8401 cm +0 g 0 G +1 0 0 1 -228.0675 -395.87 cm BT -/F19 9.9626 Tf 321.9776 319.856 Td[(a,)-358(i)1(nfo,)-358(tr)52(a)-1(ns,)-357(w)-1(or)1(k)]TJ/F8 9.9626 Tf 84.0177 0 Td[(\051)]TJ +/F8 9.9626 Tf 228.0675 395.87 Td[(T)83(ab)1(le)-334(9:)-444(Data)-333(t)28(yp)-28(es)]TJ ET -1 0 0 1 94.9141 295.9456 cm +1 0 0 1 315.4344 395.87 cm 0 g 0 G -1 0 0 1 -94.9141 -295.9456 cm +1 0 0 1 -215.539 -1.9372 cm +0 g 0 G +1 0 0 1 -4.9813 -27.3212 cm +0 g 0 G +1 0 0 1 -94.9141 -366.6116 cm BT -/F29 9.9626 Tf 99.8954 295.9456 Td[(On)-383(En)32(tr)1(y)]TJ +/F29 9.9626 Tf 99.8954 366.6116 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 147.4806 295.9456 cm +1 0 0 1 147.4806 366.6116 cm 0 g 0 G -1 0 0 1 -52.5665 -18.6894 cm +1 0 0 1 -52.5665 -18.765 cm 0 g 0 G -1 0 0 1 -94.9141 -277.2562 cm +1 0 0 1 -94.9141 -347.8466 cm BT -/F29 9.9626 Tf 99.8954 277.2562 Td[(alpha)]TJ +/F29 9.9626 Tf 99.8954 347.8466 Td[(x)]TJ ET -1 0 0 1 126.9465 277.2562 cm +1 0 0 1 105.9421 347.8466 cm 0 g 0 G -1 0 0 1 -126.9465 -277.2562 cm +1 0 0 1 -105.9421 -347.8466 cm BT -/F8 9.9626 Tf 131.9279 277.2562 Td[(th)1(e)-334(s)-1(calar)]TJ/F11 9.9626 Tf 45.4684 0 Td[(\013)]TJ/F8 9.9626 Tf 6.41 0 Td[(.)]TJ -59.0043 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(global)]TJ/F8 9.9626 Tf -32.3787 -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[(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 +/F8 9.9626 Tf 110.9235 347.8466 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 -167.9331 -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 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf -29.6113 -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 -11.9552 Td[(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 383.0839 241.3907 cm +1 0 0 1 163.8224 300.0259 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -383.0839 -241.3907 cm +1 0 0 1 -163.8224 -300.0259 cm BT -/F8 9.9626 Tf 383.0839 241.3907 Td[(9)]TJ +/F8 9.9626 Tf 163.8224 300.0259 Td[(9)]TJ ET -1 0 0 1 388.0653 241.3907 cm +1 0 0 1 168.8038 300.0259 cm 0 g 0 G -1 0 0 1 -388.0653 -241.3907 cm +1 0 0 1 -168.8038 -300.0259 cm BT -/F8 9.9626 Tf 388.0653 241.3907 Td[(.)]TJ +/F8 9.9626 Tf 168.8038 300.0259 Td[(.)]TJ ET -1 0 0 1 94.9141 222.7012 cm +1 0 0 1 94.9141 281.2609 cm 0 g 0 G -1 0 0 1 -94.9141 -222.7012 cm +1 0 0 1 -94.9141 -281.2609 cm BT -/F29 9.9626 Tf 99.8954 222.7012 Td[(a)]TJ +/F29 9.9626 Tf 99.8954 281.2609 Td[(desc)]TJ ET -1 0 0 1 105.4647 222.7012 cm +1 0 0 1 121.81 281.2609 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +3.4371 0.1992 l +S +Q +1 0 0 1 -121.81 -281.2609 cm +BT +/F29 9.9626 Tf 125.2471 281.2609 Td[(a)]TJ +ET +1 0 0 1 130.8165 281.2609 cm 0 g 0 G -1 0 0 1 -105.4647 -222.7012 cm +1 0 0 1 -130.8165 -281.2609 cm BT -/F8 9.9626 Tf 110.4461 222.7012 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(th)1(e)-334(sparse)-334(matrix)]TJ/F11 9.9626 Tf 166.7915 0 Td[(A)]TJ/F8 9.9626 Tf 7.472 0 Td[(.)]TJ -159.9075 -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[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(s)-1(tr)1(uctured)-333(d)1(a)-1(t)1(a)-334(of)-333(t)28(yp)-27(e)]TJ +/F8 9.9626 Tf 135.7978 281.2609 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 -10.9958 -11.9551 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 -11.9552 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 1 295.717 186.8357 cm +1 0 0 1 295.717 245.3954 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -186.8357 cm +1 0 0 1 -295.717 -245.3954 cm BT -/F32 9.9626 Tf 295.717 186.8357 Td[(psb)]TJ +/F32 9.9626 Tf 295.717 245.3954 Td[(psb)]TJ ET -1 0 0 1 312.0356 186.8357 cm +1 0 0 1 312.0356 245.3954 cm q []0 d 0 J @@ -11850,11 +11895,11 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -312.0356 -186.8357 cm +1 0 0 1 -312.0356 -245.3954 cm BT -/F32 9.9626 Tf 315.1738 186.8357 Td[(spmat)]TJ +/F32 9.9626 Tf 315.1738 245.3954 Td[(desc)]TJ ET -1 0 0 1 341.9531 186.8357 cm +1 0 0 1 336.7228 245.3954 cm q []0 d 0 J @@ -11863,45 +11908,53 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -341.9531 -186.8357 cm +1 0 0 1 -336.7228 -245.3954 cm BT -/F32 9.9626 Tf 345.0913 186.8357 Td[(type)]TJ +/F32 9.9626 Tf 339.861 245.3954 Td[(type)]TJ ET -1 0 0 1 366.0127 186.8357 cm +1 0 0 1 360.7824 245.3954 cm 0 g 0 G -1 0 0 1 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Td[(\014)-52(y)]TJ -107.0994 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2045 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8062 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2267 0 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0586 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -100.3812 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(D)-28(P)]TJ/F10 6.9738 Tf 21.3311 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2267 0 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0586 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -108.9062 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2057 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2266 0 Td[(T)]TJ/F11 9.9626 Tf 6.2761 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(D)-28(x)]TJ/F8 9.9626 Tf 16.4328 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -108.9062 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2057 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2266 0 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -101.6615 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(D)-28(P)]TJ/F10 6.9738 Tf 21.3311 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2056 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2267 0 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0586 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ -110.1865 -14.944 Td[(y)]TJ/F14 9.9626 Tf 15.2046 0 Td[(\040)]TJ/F11 9.9626 Tf 19.9253 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4117 1.4944 Td[(T)]TJ/F13 6.9738 Tf 7.2057 4.1135 Td[(\000)]TJ/F10 6.9738 Tf 6.2266 0 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3962 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(D)-28(x)]TJ/F8 9.9626 Tf 16.4328 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ/F8 9.9626 Tf -206.3034 -38.4875 Td[(where:)]TJ +/F11 9.9626 Tf 225.3942 581.3772 Td[(y)]TJ/F14 9.9626 Tf 8.0093 0 Td[(\040)]TJ/F11 9.9626 Tf 12.73 0 Td[(\013)-3(P)]TJ/F10 6.9738 Tf 12.8061 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4118 1.4944 Td[(A)]TJ/F10 6.9738 Tf 7.472 4.1135 Td[(H)]TJ/F11 9.9626 Tf 7.5564 -4.1135 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(c)]TJ/F11 9.9626 Tf 4.0585 1.4944 Td[(x)]TJ/F8 9.9626 Tf 7.9078 0 Td[(+)]TJ/F11 9.9626 Tf 9.9626 0 Td[(\014)-52(y)]TJ ET -1 0 0 1 94.9141 431.0861 cm +1 0 0 1 430.8764 581.3772 cm 0 g 0 G -1 0 0 1 -94.9141 -431.0861 cm +1 0 0 1 -430.8764 -581.3772 cm BT -/F11 9.9626 Tf 99.8954 431.0861 Td[(x)]TJ +/F8 9.9626 Tf 430.8764 581.3772 Td[(\0503\051)]TJ ET -1 0 0 1 105.5893 431.0861 cm +1 0 0 1 443.6065 581.3772 cm 0 g 0 G -1 0 0 1 -105.5893 -431.0861 cm +1 0 0 1 -443.6065 -581.3772 cm BT -/F8 9.9626 Tf 110.5706 431.0861 Td[(is)-334(t)1(he)-334(glob)1(al)-333(dense)-334(submatri)1(x)]TJ/F11 9.9626 Tf 131.092 0 Td[(x)]TJ/F7 6.9738 Tf 5.6939 -1.4944 Td[(:)]TJ/F10 6.9738 Tf 2.2555 0 Td[(;)]TJ/F7 6.9738 Tf 2.3661 0 Td[(:)]TJ +/F8 9.9626 Tf 114.8394 565.2982 Td[(where:)]TJ ET -1 0 0 1 94.9141 408.9932 cm +1 0 0 1 94.9141 547.8446 cm 0 g 0 G -1 0 0 1 -94.9141 -408.9932 cm +1 0 0 1 -94.9141 -547.8446 cm BT -/F11 9.9626 Tf 99.8954 408.9932 Td[(y)]TJ +/F11 9.9626 Tf 99.8954 547.8446 Td[(x)]TJ ET -1 0 0 1 105.1373 408.9932 cm +1 0 0 1 105.5893 547.8446 cm 0 g 0 G -1 0 0 1 -105.1373 -408.9932 cm +1 0 0 1 -105.5893 -547.8446 cm BT -/F8 9.9626 Tf 110.1187 408.9932 Td[(is)-334(t)1(he)-334(glob)1(al)-333(dense)-334(submatr)1(ix)]TJ/F11 9.9626 Tf 131.0919 0 Td[(y)]TJ/F7 6.9738 Tf 4.8845 -1.4944 Td[(:)]TJ/F10 6.9738 Tf 2.2555 0 Td[(;)]TJ/F7 6.9738 Tf 2.3661 0 Td[(:)]TJ +/F8 9.9626 Tf 110.5706 547.8446 Td[(is)-334(t)1(he)-334(glob)1(al)-333(dense)-334(submatri)1(x)]TJ/F11 9.9626 Tf 131.092 0 Td[(x)]TJ/F7 6.9738 Tf 5.6939 -1.4944 Td[(:)]TJ/F10 6.9738 Tf 2.2555 0 Td[(;)]TJ/F7 6.9738 Tf 2.3661 0 Td[(:)]TJ ET -1 0 0 1 94.9141 386.9003 cm +1 0 0 1 94.9141 529.1552 cm 0 g 0 G -1 0 0 1 -94.9141 -386.9003 cm +1 0 0 1 -94.9141 -529.1552 cm BT -/F11 9.9626 Tf 99.8954 386.9003 Td[(T)]TJ +/F11 9.9626 Tf 99.8954 529.1552 Td[(y)]TJ ET -1 0 0 1 107.101 386.9003 cm +1 0 0 1 105.1373 529.1552 cm 0 g 0 G -1 0 0 1 -107.101 -386.9003 cm +1 0 0 1 -105.1373 -529.1552 cm BT -/F8 9.9626 Tf 112.0823 386.9003 Td[(is)-334(t)1(he)-334(glob)1(al)-333(s)-1(p)1(arse)-334(bl)1(o)-28(c)27(k)-333(tri)1(angul)1(ar)-333(s)-1(u)1(bmatrix)]TJ/F11 9.9626 Tf 206.7806 0 Td[(T)]TJ +/F8 9.9626 Tf 110.1187 529.1552 Td[(is)-334(t)1(he)-334(glob)1(al)-333(dense)-334(submatr)1(ix)]TJ/F11 9.9626 Tf 131.0919 0 Td[(y)]TJ/F7 6.9738 Tf 4.8845 -1.4944 Td[(:)]TJ/F10 6.9738 Tf 2.2555 0 Td[(;)]TJ/F7 6.9738 Tf 2.3661 0 Td[(:)]TJ ET -1 0 0 1 94.9141 364.8074 cm +1 0 0 1 94.9141 510.4658 cm 0 g 0 G -1 0 0 1 -94.9141 -364.8074 cm +1 0 0 1 -94.9141 -510.4658 cm BT -/F11 9.9626 Tf 99.8954 364.8074 Td[(D)]TJ +/F11 9.9626 Tf 99.8954 510.4658 Td[(A)]TJ ET -1 0 0 1 108.4204 364.8074 cm +1 0 0 1 107.3674 510.4658 cm 0 g 0 G -1 0 0 1 -108.4204 -364.8074 cm +1 0 0 1 -107.3674 -510.4658 cm BT -/F8 9.9626 Tf 113.4017 364.8074 Td[(is)-334(t)1(he)-334(sc)-1(al)1(ing)-333(di)1(agonal)-333(ma)-1(t)1(rix.)]TJ +/F8 9.9626 Tf 112.3487 510.4658 Td[(is)-334(t)1(he)-334(glob)1(al)-333(s)-1(p)1(arse)-334(s)-1(u)1(bmatri)1(x)]TJ/F11 9.9626 Tf 133.9424 0 Td[(A)]TJ ET -1 0 0 1 94.9141 342.7145 cm +1 0 0 1 94.9141 491.7763 cm 0 g 0 G -1 0 0 1 -94.9141 -342.7145 cm +1 0 0 1 -94.9141 -491.7763 cm BT -/F11 9.9626 Tf 99.8954 342.7145 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4118 1.4944 Td[(;)-166(P)]TJ/F10 6.9738 Tf 10.8239 -1.4944 Td[(c)]TJ +/F11 9.9626 Tf 99.8954 491.7763 Td[(P)]TJ/F10 6.9738 Tf 6.3961 -1.4944 Td[(r)]TJ/F11 9.9626 Tf 4.4118 1.4944 Td[(;)-166(P)]TJ/F10 6.9738 Tf 10.8239 -1.4944 Td[(c)]TJ ET -1 0 0 1 125.5857 342.7145 cm +1 0 0 1 125.5857 491.7763 cm 0 g 0 G -1 0 0 1 -125.5857 -342.7145 cm +1 0 0 1 -125.5857 -491.7763 cm BT -/F8 9.9626 Tf 130.5671 342.7145 Td[(are)-333(the)-334(p)-27(erm)27(u)1(tation)-333(matri)1(c)-1(es)-1(.)]TJ/F18 14.3462 Tf -30.6717 -35.8209 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 62.7833 -22.2876 Td[(CALL)-334(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 130.5671 491.7763 Td[(are)-333(the)-334(p)-27(erm)27(u)1(tation)-333(matri)1(c)-1(es)-1(.)]TJ ET -1 0 0 1 208.7172 284.606 cm +1 0 0 1 99.8954 473.6214 cm +0 g 0 G +1 0 0 1 74.1629 -21.0212 cm +0 g 0 G +0 g 0 G +1 0 0 1 4.9813 20.6227 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +185.4227 0.1992 l S Q -1 0 0 1 -208.7172 -284.606 cm +1 0 0 1 -179.0396 -473.2229 cm BT -/F8 9.9626 Tf 211.706 284.606 Td[(spsm)-334(\050)]TJ/F19 9.9626 Tf 28.8917 0 Td[(alpha,)-357(t)-1(,)-357(x,)-357(b)51(et)-1(a,)-357(y,)-357(desc)]TJ +/F11 9.9626 Tf 185.0172 464.8543 Td[(A)]TJ/F8 9.9626 Tf 7.472 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/F8 9.9626 Tf 5.2419 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(\013)]TJ/F8 9.9626 Tf 6.41 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(\014)]TJ/F29 9.9626 Tf 69.1356 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 345.3785 284.606 cm +1 0 0 1 179.0396 460.8692 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +185.4227 0.1992 l S Q -1 0 0 1 -345.3785 -284.606 cm +1 0 0 1 -179.0396 -460.8692 cm BT -/F19 9.9626 Tf 348.4337 284.606 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ -277.0534 -23.9103 Td[(CALL)-334(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 185.0172 452.5006 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-3103(psb)]TJ ET -1 0 0 1 145.9339 260.6957 cm +1 0 0 1 318.9209 452.5006 cm q []0 d 0 J @@ -12409,29 +12497,24 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -145.9339 -260.6957 cm +1 0 0 1 -318.9209 -452.5006 cm BT -/F8 9.9626 Tf 148.9227 260.6957 Td[(spsm)]TJ 13.6097 -11.9552 Td[(\050)]TJ/F19 9.9626 Tf 3.8744 0 Td[(alpha,)-357(t)-1(,)-357(x,)-357(b)51(et)-1(a,)-357(y,)-357(desc)]TJ +/F8 9.9626 Tf 321.9097 452.5006 Td[(spmm)]TJ -136.8925 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Complex)-1200(psb)]TJ ET -1 0 0 1 271.1875 248.7405 cm +1 0 0 1 318.9209 440.5454 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +2.9888 0.1992 l S Q -1 0 0 1 -271.1875 -248.7405 cm +1 0 0 1 -318.9209 -440.5454 cm BT -/F19 9.9626 Tf 274.2427 248.7405 Td[(a,)-358(i)1(nfo,)-358(tr)52(a)-1(ns,)-357(unit,)-357(cho)-1(i)1(c)51(e,)-358(di)1(ag,)-358(work)]TJ/F8 9.9626 Tf 165.4894 0 Td[(\051)]TJ +/F8 9.9626 Tf 321.9097 440.5454 Td[(spmm)]TJ ET -1 0 0 1 99.8954 221.2557 cm -0 g 0 G -1 0 0 1 74.1629 -21.0212 cm -0 g 0 G -0 g 0 G -1 0 0 1 4.9813 20.6227 cm +1 0 0 1 179.0396 436.5604 cm q []0 d 0 J @@ -12440,37 +12523,47 @@ q 185.4227 0.1992 l S Q -1 0 0 1 -179.0396 -220.8572 cm +1 0 0 1 46.5372 -27.8401 cm +0 g 0 G +1 0 0 1 -225.5768 -408.7203 cm +BT +/F8 9.9626 Tf 225.5768 408.7203 Td[(T)83(ab)1(le)-334(11:)-444(Data)-333(t)28(yp)-28(es)]TJ +ET +1 0 0 1 317.9251 408.7203 cm +0 g 0 G +1 0 0 1 -218.0297 -1.9372 cm +0 g 0 G +1 0 0 1 -99.8954 -406.7831 cm BT -/F11 9.9626 Tf 185.0172 212.4886 Td[(T)]TJ/F8 9.9626 Tf 7.2056 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/F8 9.9626 Tf 5.2419 0 Td[(,)]TJ/F11 9.9626 Tf 6.0883 0 Td[(D)]TJ/F8 9.9626 Tf 8.525 0 Td[(,)]TJ/F11 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-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[(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 425.3152 cm +1 0 0 1 214.6319 602.5174 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -214.6319 -425.3152 cm +1 0 0 1 -214.6319 -602.5174 cm BT -/F8 9.9626 Tf 214.6319 425.3152 Td[(10)]TJ +/F8 9.9626 Tf 214.6319 602.5174 Td[(11)]TJ ET -1 0 0 1 224.5946 425.3152 cm +1 0 0 1 224.5946 602.5174 cm 0 g 0 G -1 0 0 1 -224.5946 -425.3152 cm +1 0 0 1 -224.5946 -602.5174 cm BT -/F8 9.9626 Tf 224.5946 425.3152 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 +/F8 9.9626 Tf 224.5946 602.5174 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 405.9213 cm +1 0 0 1 145.7235 582.5921 cm 0 g 0 G -1 0 0 1 -145.7235 -405.9213 cm +1 0 0 1 -145.7235 -582.5921 cm BT -/F29 9.9626 Tf 150.7049 405.9213 Td[(desc)]TJ +/F29 9.9626 Tf 150.7049 582.5921 Td[(desc)]TJ ET -1 0 0 1 172.6195 405.9213 cm +1 0 0 1 172.6195 582.5921 cm q []0 d 0 J @@ -12686,23 +12830,23 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -172.6195 -405.9213 cm +1 0 0 1 -172.6195 -582.5921 cm BT -/F29 9.9626 Tf 176.0566 405.9213 Td[(a)]TJ +/F29 9.9626 Tf 176.0566 582.5921 Td[(a)]TJ ET -1 0 0 1 181.6259 405.9213 cm +1 0 0 1 181.6259 582.5921 cm 0 g 0 G -1 0 0 1 -181.6259 -405.9213 cm +1 0 0 1 -181.6259 -582.5921 cm BT -/F8 9.9626 Tf 186.6072 405.9213 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[(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 +/F8 9.9626 Tf 186.6072 582.5921 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[(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 370.0558 cm +1 0 0 1 346.5264 546.7266 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -346.5264 -370.0558 cm +1 0 0 1 -346.5264 -546.7266 cm BT -/F32 9.9626 Tf 346.5264 370.0558 Td[(psb)]TJ +/F32 9.9626 Tf 346.5264 546.7266 Td[(psb)]TJ ET -1 0 0 1 362.8451 370.0558 cm +1 0 0 1 362.8451 546.7266 cm q []0 d 0 J @@ -12711,11 +12855,11 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -362.8451 -370.0558 cm +1 0 0 1 -362.8451 -546.7266 cm BT -/F32 9.9626 Tf 365.9833 370.0558 Td[(desc)]TJ +/F32 9.9626 Tf 365.9833 546.7266 Td[(desc)]TJ ET -1 0 0 1 387.5322 370.0558 cm +1 0 0 1 387.5322 546.7266 cm q []0 d 0 J @@ -12724,507 +12868,381 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -387.5322 -370.0558 cm +1 0 0 1 -387.5322 -546.7266 cm BT -/F32 9.9626 Tf 390.6705 370.0558 Td[(type)]TJ +/F32 9.9626 Tf 390.6705 546.7266 Td[(type)]TJ ET -1 0 0 1 411.5918 370.0558 cm +1 0 0 1 411.5918 546.7266 cm 0 g 0 G -1 0 0 1 -411.5918 -370.0558 cm +1 0 0 1 -411.5918 -546.7266 cm BT -/F8 9.9626 Tf 411.5918 370.0558 Td[(.)]TJ +/F8 9.9626 Tf 411.5918 546.7266 Td[(.)]TJ ET -1 0 0 1 145.7235 350.6619 cm +1 0 0 1 145.7235 526.8013 cm 0 g 0 G -1 0 0 1 -145.7235 -350.6619 cm +1 0 0 1 -145.7235 -526.8013 cm BT -/F29 9.9626 Tf 150.7049 350.6619 Td[(trans)]TJ +/F29 9.9626 Tf 150.7049 526.8013 Td[(trans)]TJ ET -1 0 0 1 176.3322 350.6619 cm +1 0 0 1 176.3322 526.8013 cm 0 g 0 G -1 0 0 1 -176.3322 -350.6619 cm +1 0 0 1 -176.3322 -526.8013 cm BT -/F8 9.9626 Tf 181.3135 350.6619 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 +/F8 9.9626 Tf 181.3135 526.8013 Td[(in)1(dicate)-334(what)-333(ki)1(nd)-333(of)-333(op)-27(e)-1(r)1(ation)-333(to)-333(p)-27(e)-1(r)1(form.)]TJ ET -1 0 0 1 170.6302 331.2679 cm +1 0 0 1 170.6302 506.8761 cm 0 g 0 G -1 0 0 1 -170.6302 -331.2679 cm +1 0 0 1 -170.6302 -506.8761 cm BT -/F29 9.9626 Tf 175.6115 331.2679 Td[(trans)-383(=)-383(')-1(N')]TJ +/F29 9.9626 Tf 175.6115 506.8761 Td[(trans)-383(=)-383(N)]TJ ET -1 0 0 1 233.1191 331.2679 cm +1 0 0 1 226.7541 506.8761 cm 0 g 0 G -1 0 0 1 -233.1191 -331.2679 cm +1 0 0 1 -226.7541 -506.8761 cm BT -/F8 9.9626 Tf 238.1004 331.2679 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 +/F8 9.9626 Tf 231.7355 506.8761 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(equation)]TJ ET -1 0 0 1 170.6302 315.859 cm -0 g 0 G -1 0 0 1 -170.6302 -315.859 cm +1 0 0 1 398.1949 506.8761 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -398.1949 -506.8761 cm BT -/F29 9.9626 Tf 175.6115 315.859 Td[(trans)-383(=)-383(')-1(T')]TJ +/F8 9.9626 Tf 398.1949 506.8761 Td[(1)]TJ ET -1 0 0 1 232.1229 315.859 cm +1 0 0 1 403.1762 506.8761 cm +0 g 0 G +1 0 0 1 -232.546 -15.9403 cm 0 g 0 G -1 0 0 1 -232.1229 -315.859 cm +1 0 0 1 -170.6302 -490.9358 cm BT -/F8 9.9626 Tf 237.1042 315.859 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 +/F29 9.9626 Tf 175.6115 490.9358 Td[(trans)-383(=)-383(T)]TJ ET -1 0 0 1 170.6302 300.4502 cm +1 0 0 1 225.7579 490.9358 cm 0 g 0 G -1 0 0 1 -170.6302 -300.4502 cm +1 0 0 1 -225.7579 -490.9358 cm BT -/F29 9.9626 Tf 175.6115 300.4502 Td[(trans)-383(=)-383(')-1(C)1(')]TJ +/F8 9.9626 Tf 230.7392 490.9358 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(e)-1(q)1(uation)]TJ ET -1 0 0 1 232.4273 300.4502 cm -0 g 0 G -1 0 0 1 -232.4273 -300.4502 cm +1 0 0 1 397.1986 490.9358 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -397.1986 -490.9358 cm BT -/F8 9.9626 Tf 237.4086 300.4502 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 -19.394 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 -11.9551 Td[(Defau)1(lt:)]TJ/F11 9.9626 Tf 39.4355 0 Td[(tr)-28(ans)]TJ/F8 9.9626 Tf 27.0525 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 +/F8 9.9626 Tf 397.1986 490.9358 Td[(2)]TJ ET -1 0 0 1 145.7235 225.7968 cm +1 0 0 1 402.1799 490.9358 cm +0 g 0 G +1 0 0 1 -231.5497 -15.9402 cm 0 g 0 G -1 0 0 1 -145.7235 -225.7968 cm +1 0 0 1 -170.6302 -474.9956 cm BT -/F29 9.9626 Tf 150.7049 225.7968 Td[(unitd)]TJ +/F29 9.9626 Tf 175.6115 474.9956 Td[(trans)-383(=)-383(C)]TJ ET -1 0 0 1 177.4378 225.7968 cm +1 0 0 1 226.0623 474.9956 cm 0 g 0 G -1 0 0 1 -177.4378 -225.7968 cm +1 0 0 1 -226.0623 -474.9956 cm BT -/F8 9.9626 Tf 182.4191 225.7968 Td[(sp)-28(ec)-1(i)1(fy)-333(with)]TJ/F19 9.9626 Tf 55.6802 0 Td[(tr)51(ans)]TJ/F8 9.9626 Tf 25.0891 0 Td[(th)1(e)-334(op)-28(erati)1(on)-333(to)-333(p)-28(erf)1(orm.)]TJ +/F8 9.9626 Tf 231.0436 474.9956 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(e)-1(q)1(uation)]TJ ET -1 0 0 1 170.6302 206.4028 cm -0 g 0 G -1 0 0 1 -170.6302 -206.4028 cm +1 0 0 1 397.503 474.9956 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -397.503 -474.9956 cm BT -/F29 9.9626 Tf 175.6115 206.4028 Td[(unitd)-384(=)-383(')-1(U')]TJ +/F8 9.9626 Tf 397.503 474.9956 Td[(3)]TJ ET -1 0 0 1 234.0725 206.4028 cm +1 0 0 1 402.4844 474.9956 cm 0 g 0 G -1 0 0 1 -234.0725 -206.4028 cm +1 0 0 1 -402.4844 -474.9956 cm BT -/F8 9.9626 Tf 239.0538 206.4028 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(with)-333(n)1(o)-333(s)-1(caling)]TJ +/F8 9.9626 Tf 175.6115 455.0703 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 -11.9551 Td[(Defau)1(lt:)]TJ/F11 9.9626 Tf 39.4355 0 Td[(tr)-28(ans)]TJ/F8 9.9626 Tf 27.0525 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 1 170.6302 190.9939 cm +1 0 0 1 145.7235 399.2795 cm 0 g 0 G -1 0 0 1 -170.6302 -190.9939 cm +1 0 0 1 -145.7235 -399.2795 cm BT -/F29 9.9626 Tf 175.6115 190.9939 Td[(unitd)-384(=)-383(')-1(L')]TJ +/F29 9.9626 Tf 150.7049 399.2795 Td[(w)32(or)1(k)]TJ ET -1 0 0 1 232.1492 190.9939 cm +1 0 0 1 175.1547 399.2795 cm 0 g 0 G -1 0 0 1 -232.1492 -190.9939 cm +1 0 0 1 -175.1547 -399.2795 cm BT -/F8 9.9626 Tf 237.1305 190.9939 Td[(th)1(e)-334(op)-28(erati)1(on)-333(is)-334(with)-333(l)1(e)-1(f)1(t)-334(sc)-1(al)1(ing)]TJ +/F8 9.9626 Tf 180.136 399.2795 Td[(w)28(ork)-333(arra)28(y)84(.)]TJ -4.5245 -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[(opti)-1(on)1(al)]TJ/F8 9.9626 Tf -29.6112 -11.9552 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Td[(is)-334(t)1(he)-334(lo)-27(c)-1(al)-333(p)-27(ortion)-332(of)-333(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matri)1(x)-333(on)-333(pro)-27(c)-1(es)-1(s)]TJ/F11 9.9626 Tf 234.7036 0 Td[(i)]TJ/F8 9.9626 Tf 3.4323 0 Td[(.)]TJ +/F8 9.9626 Tf 225.5768 490.7455 Td[(T)83(ab)1(le)-334(14:)-444(Data)-333(t)28(yp)-28(es)]TJ ET -1 0 0 1 94.9141 537.8827 cm +1 0 0 1 317.9251 490.7455 cm 0 g 0 G -1 0 0 1 -94.9141 -537.8827 cm -BT -/F11 9.9626 Tf 99.8954 537.8827 Td[(co)1(l)-21(l)-20(e)1(ct)]TJ -ET -1 0 0 1 127.9212 537.8827 cm +1 0 0 1 -218.0297 -1.9372 cm 0 g 0 G -1 0 0 1 -127.9212 -537.8827 cm +1 0 0 1 -99.8954 -488.8083 cm BT -/F8 9.9626 Tf 132.9025 537.8827 Td[(is)-334(t)1(he)-334(collec)-1(t)-333(f)1(unction)1(.)]TJ +/F18 14.3462 Tf 99.8954 447.0554 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 108.7025 -21.8209 Td[(call)-333(psb)]TJ ET -1 0 0 1 99.8954 519.1001 cm -0 g 0 G -1 0 0 1 74.1629 -21.0212 cm -0 g 0 G -0 g 0 G -1 0 0 1 4.9813 20.6227 cm +1 0 0 1 242.4598 425.2345 cm q []0 d 0 J 0.3985 w 0 0.1992 m -185.4227 0.1992 l +2.9888 0.1992 l S Q -1 0 0 1 -179.0396 -518.7016 cm +1 0 0 1 -242.4598 -425.2345 cm BT -/F11 9.9626 Tf 185.0172 510.333 Td[(x)]TJ/F10 6.9738 Tf 5.6939 -1.4944 Td[(i)]TJ/F11 9.9626 Tf 3.3169 1.4944 Td[(;)-166(y)]TJ/F29 9.9626 Tf 109.2958 0 Td[(Subr)1(outi)-1(ne)]TJ +/F8 9.9626 Tf 245.4487 425.2345 Td[(o)28(vrl)-333(\050)]TJ/F19 9.9626 Tf 23.8273 0 Td[(x,)-357(desc)]TJ ET -1 0 0 1 179.0396 506.3479 cm +1 0 0 1 299.4593 425.2345 cm q []0 d 0 J 0.3985 w 0 0.1992 m -185.4227 0.1992 l +3.0552 0.1992 l S Q -1 0 0 1 -179.0396 -506.3479 cm +1 0 0 1 -299.4593 -425.2345 cm BT -/F8 9.9626 Tf 185.0172 497.9794 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-3103(psb)]TJ +/F19 9.9626 Tf 302.5145 425.2345 Td[(a,)-358(i)1(nfo)]TJ/F8 9.9626 Tf 28.5151 0 Td[(\051)]TJ -195.6799 -23.9103 Td[(call)-333(psb)]TJ ET -1 0 0 1 318.9209 497.9794 cm +1 0 0 1 169.2117 401.3242 cm q []0 d 0 J @@ -14375,165 +14535,218 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -318.9209 -497.9794 cm +1 0 0 1 -169.2117 -401.3242 cm BT -/F8 9.9626 Tf 321.9097 497.9794 Td[(gath)1(e)-1(r)]TJ -136.8925 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 172.2005 401.3242 Td[(o)28(vrl)-333(\050)]TJ/F19 9.9626 Tf 23.8274 0 Td[(x,)-357(desc)]TJ ET -1 0 0 1 318.9209 486.0242 cm +1 0 0 1 226.2111 401.3242 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.0552 0.1992 l S Q -1 0 0 1 -318.9209 -486.0242 cm +1 0 0 1 -226.2111 -401.3242 cm BT -/F8 9.9626 Tf 321.9097 486.0242 Td[(gath)1(e)-1(r)]TJ +/F19 9.9626 Tf 229.2663 401.3242 Td[(a,)-358(i)1(nfo,)-358(u)1(p)51(da)-1(te=)1(up)51(dat)-1(e)]TJ ET -1 0 0 1 179.0396 482.0391 cm +1 0 0 1 328.6618 401.3242 cm q []0 d 0 J 0.3985 w 0 0.1992 m -185.4227 0.1992 l +3.0552 0.1992 l S Q -1 0 0 1 46.5372 -27.84 cm +1 0 0 1 -328.6618 -401.3242 cm +BT +/F19 9.9626 Tf 331.717 401.3242 Td[(typ)51(e,)-357(w)-1(or)1(k=w)-1(or)1(k)]TJ/F8 9.9626 Tf 72.5607 0 Td[(\051)]TJ +ET +1 0 0 1 94.9141 377.4138 cm 0 g 0 G -1 0 0 1 -225.5768 -454.1991 cm +1 0 0 1 -94.9141 -377.4138 cm BT -/F8 9.9626 Tf 225.5768 454.1991 Td[(T)83(ab)1(le)-334(13:)-444(Data)-333(t)28(yp)-28(es)]TJ +/F29 9.9626 Tf 99.8954 377.4138 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 317.9251 454.1991 cm +1 0 0 1 147.4806 377.4138 cm 0 g 0 G -1 0 0 1 -218.0297 -1.9372 cm +1 0 0 1 -52.5665 -19.0788 cm 0 g 0 G -1 0 0 1 -99.8954 -452.2619 cm +1 0 0 1 -94.9141 -358.335 cm BT -/F18 14.3462 Tf 99.8954 407.9057 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 5.2666 -21.8209 Td[(call)-333(psb)]TJ +/F29 9.9626 Tf 99.8954 358.335 Td[(x)]TJ ET -1 0 0 1 139.024 386.0848 cm -q -[]0 d -0 J -0.3985 w -0 0.1992 m -2.9888 0.1992 l -S -Q -1 0 0 1 -139.024 -386.0848 cm +1 0 0 1 105.9421 358.335 cm +0 g 0 G +1 0 0 1 -105.9421 -358.335 cm BT -/F8 9.9626 Tf 142.0128 386.0848 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.9626 Tf 34.897 0 Td[(glob)]TJ +/F8 9.9626 Tf 110.9235 358.335 Td[(glob)1(al)-333(dense)-334(m)-1(at)1(rix)]TJ/F11 9.9626 Tf 88.9167 0 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -80.7321 -11.9551 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 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -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 1 194.3243 386.0848 cm +1 0 0 1 163.8224 310.5144 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -163.8224 -310.5144 cm +BT +/F8 9.9626 Tf 163.8224 310.5144 Td[(14)]TJ +ET +1 0 0 1 173.7851 310.5144 cm +0 g 0 G +1 0 0 1 -173.7851 -310.5144 cm +BT +/F8 9.9626 Tf 173.7851 310.5144 Td[(.)]TJ +ET +1 0 0 1 94.9141 291.4356 cm +0 g 0 G +1 0 0 1 -94.9141 -291.4356 cm +BT +/F29 9.9626 Tf 99.8954 291.4356 Td[(desc)]TJ +ET +1 0 0 1 121.81 291.4356 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -194.3243 -386.0848 cm +1 0 0 1 -121.81 -291.4356 cm BT -/F19 9.9626 Tf 197.3795 386.0848 Td[(x,)-357(lo)51(c)]TJ +/F29 9.9626 Tf 125.2471 291.4356 Td[(a)]TJ ET -1 0 0 1 220.9432 386.0848 cm +1 0 0 1 130.8165 291.4356 cm +0 g 0 G +1 0 0 1 -130.8165 -291.4356 cm +BT +/F8 9.9626 Tf 135.7978 291.4356 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 -10.9958 -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 -32.3787 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf -29.6113 -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 1 295.717 255.5701 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -295.717 -255.5701 cm +BT +/F32 9.9626 Tf 295.717 255.5701 Td[(psb)]TJ +ET +1 0 0 1 312.0356 255.5701 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +3.1382 0.1992 l S Q -1 0 0 1 -220.9432 -386.0848 cm +1 0 0 1 -312.0356 -255.5701 cm BT -/F19 9.9626 Tf 223.9984 386.0848 Td[(x,)-357(desc)]TJ +/F32 9.9626 Tf 315.1738 255.5701 Td[(desc)]TJ ET -1 0 0 1 254.1817 386.0848 cm +1 0 0 1 336.7228 255.5701 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +3.1382 0.1992 l S Q -1 0 0 1 -254.1817 -386.0848 cm +1 0 0 1 -336.7228 -255.5701 cm BT -/F19 9.9626 Tf 257.2369 386.0848 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot)-1(,)-357(igl)1(obx,)-358(j)1(globx,)-357(ilo)51(cx)1(,)-358(jl)1(o)51(cx,)-357(k)]TJ/F8 9.9626 Tf 177.2286 0 Td[(\051)]TJ/F18 14.3462 Tf -334.5701 -29.8879 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 39.4216 -21.8209 Td[(call)-333(psb)]TJ +/F32 9.9626 Tf 339.861 255.5701 Td[(type)]TJ ET -1 0 0 1 173.179 334.376 cm +1 0 0 1 360.7824 255.5701 cm +0 g 0 G +1 0 0 1 -360.7824 -255.5701 cm +BT +/F8 9.9626 Tf 360.7824 255.5701 Td[(.)]TJ +ET +1 0 0 1 94.9141 236.4913 cm +0 g 0 G +1 0 0 1 -94.9141 -236.4913 cm +BT +/F29 9.9626 Tf 99.8954 236.4913 Td[(up)-32(date)]TJ +ET +1 0 0 1 134.5846 236.4913 cm +0 g 0 G +1 0 0 1 -134.5846 -236.4913 cm +BT +/F8 9.9626 Tf 139.5659 236.4913 Td[(Up)-27(date)-334(op)-27(erator.)]TJ +ET +1 0 0 1 119.8207 205.4574 cm +0 g 0 G +1 0 0 1 -119.8207 -205.4574 cm +BT +/F29 9.9626 Tf 124.802 205.4574 Td[(up)-32(date)-383(=)-384(psb)]TJ +ET +1 0 0 1 193.9766 205.4574 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -173.179 -334.376 cm +1 0 0 1 -193.9766 -205.4574 cm BT -/F8 9.9626 Tf 176.1678 334.376 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.9626 Tf 34.897 0 Td[(glob)]TJ +/F29 9.9626 Tf 197.4138 205.4574 Td[(none)]TJ ET -1 0 0 1 228.4793 334.376 cm +1 0 0 1 221.8107 205.4574 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -228.4793 -334.376 cm +1 0 0 1 3.4371 0 cm +0 g 0 G +1 0 0 1 -225.2478 -205.4574 cm BT -/F19 9.9626 Tf 231.5345 334.376 Td[(x,)-357(lo)51(c)]TJ +/F8 9.9626 Tf 230.2291 205.4574 Td[(Do)-333(noth)1(ing;)]TJ ET -1 0 0 1 255.0982 334.376 cm +1 0 0 1 119.8207 190.3636 cm +0 g 0 G +1 0 0 1 -119.8207 -190.3636 cm +BT +/F29 9.9626 Tf 124.802 190.3636 Td[(up)-32(date)-383(=)-384(psb)]TJ +ET +1 0 0 1 193.9766 190.3636 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -255.0982 -334.376 cm +1 0 0 1 -193.9766 -190.3636 cm BT -/F19 9.9626 Tf 258.1534 334.376 Td[(x,)-357(desc)]TJ +/F29 9.9626 Tf 197.4138 190.3636 Td[(add)]TJ ET -1 0 0 1 288.3367 334.376 cm +1 0 0 1 216.4004 190.3636 cm q []0 d 0 J 0.3985 w 0 0.1992 m -3.0552 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -288.3367 -334.376 cm -BT -/F19 9.9626 Tf 291.3919 334.376 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot)-1(,)-357(igl)1(obx,)-358(i)1(lo)51(cx)]TJ/F8 9.9626 Tf 108.9186 0 Td[(\051)]TJ -ET -1 0 0 1 94.9141 310.4656 cm +1 0 0 1 3.4372 0 cm 0 g 0 G -1 0 0 1 -94.9141 -310.4656 cm +1 0 0 1 -219.8376 -190.3636 cm BT -/F29 9.9626 Tf 99.8954 310.4656 Td[(On)-383(En)32(tr)1(y)]TJ +/F8 9.9626 Tf 224.8189 190.3636 Td[(Su)1(m)-334(o)28(v)28(erlap)-333(en)28(tri)1(e)-1(s,)-333(i.e.)-445(ap)1(ply)]TJ/F11 9.9626 Tf 136.5438 0 Td[(P)]TJ/F10 6.9738 Tf 7.7798 3.6154 Td[(T)]TJ/F8 9.9626 Tf 6.2761 -3.6154 Td[(;)]TJ ET -1 0 0 1 147.4806 310.4656 cm -0 g 0 G -1 0 0 1 -52.5665 -19.5444 cm +1 0 0 1 119.8207 175.2699 cm 0 g 0 G -1 0 0 1 -94.9141 -290.9212 cm +1 0 0 1 -119.8207 -175.2699 cm BT -/F29 9.9626 Tf 99.8954 290.9213 Td[(lo)-32(c)]TJ +/F29 9.9626 Tf 124.802 175.2699 Td[(up)-32(date)-383(=)-384(psb)]TJ ET -1 0 0 1 114.904 290.9213 cm +1 0 0 1 193.9766 175.2699 cm q []0 d 0 J @@ -14542,169 +14755,114 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -114.904 -290.9213 cm -BT -/F29 9.9626 Tf 118.3411 290.9213 Td[(x)]TJ -ET -1 0 0 1 124.3879 290.9213 cm -0 g 0 G -1 0 0 1 -124.3879 -290.9213 cm +1 0 0 1 -193.9766 -175.2699 cm BT -/F8 9.9626 Tf 129.3692 290.9213 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[(g)-36(l)-20(ob)]TJ +/F29 9.9626 Tf 197.4138 175.2699 Td[(a)32(vg)]TJ ET -1 0 0 1 323.4674 290.9213 cm +1 0 0 1 215.1274 175.2699 cm q []0 d 0 J 0.3985 w 0 0.1992 m -2.9888 0.1992 l +3.4371 0.1992 l S Q -1 0 0 1 -323.4674 -290.9213 cm -BT -/F11 9.9626 Tf 326.4562 290.9213 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -207.3481 -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 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-472(as:)-722(a)-473(ran)1(k)-472(one)-473(or)-472(t)28(w)28(o)-473(arr)1(a)28(y)-473(con)28(tain)1(in)1(g)-473(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-473(of)-472(the)-472(t)27(y)1(p)-28(e)]TJ 0 -11.9552 Td[(in)1(dicated)-333(in)-333(T)83(ab)1(le)]TJ -ET -1 0 0 1 206.9939 243.1006 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -206.9939 -243.1006 cm -BT -/F8 9.9626 Tf 206.9939 243.1006 Td[(13)]TJ -ET -1 0 0 1 216.9566 243.1006 cm -0 g 0 G -1 0 0 1 -216.9566 -243.1006 cm -BT -/F8 9.9626 Tf 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Td[(is)-334(t)1(he)-334(sc)-1(att)1(e)-1(r)-333(f)1(unction)1(.)]TJ +/F8 9.9626 Tf 132.9025 537.8827 Td[(is)-334(t)1(he)-334(collec)-1(t)-333(f)1(unction)1(.)]TJ ET -1 0 0 1 99.8954 510.6752 cm +1 0 0 1 99.8954 519.1001 cm 0 g 0 G 1 0 0 1 74.1629 -21.0212 cm 0 g 0 G @@ -15100,11 +15148,11 @@ q 185.4227 0.1992 l S Q -1 0 0 1 -179.0396 -510.2767 cm +1 0 0 1 -179.0396 -518.7016 cm BT -/F11 9.9626 Tf 185.0172 501.9081 Td[(x)]TJ/F10 6.9738 Tf 5.6939 -1.4944 Td[(i)]TJ/F11 9.9626 Tf 3.3169 1.4944 Td[(;)-166(y)]TJ/F29 9.9626 Tf 109.2958 0 Td[(Subr)1(outi)-1(ne)]TJ +/F11 9.9626 Tf 185.0172 510.333 Td[(x)]TJ/F10 6.9738 Tf 5.6939 -1.4944 Td[(i)]TJ/F11 9.9626 Tf 3.3169 1.4944 Td[(;)-166(y)]TJ/F29 9.9626 Tf 109.2958 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 179.0396 497.923 cm +1 0 0 1 179.0396 506.3479 cm q []0 d 0 J @@ -15113,11 +15161,11 @@ q 185.4227 0.1992 l S Q -1 0 0 1 -179.0396 -497.923 cm +1 0 0 1 -179.0396 -506.3479 cm BT -/F8 9.9626 Tf 185.0172 489.5544 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-3103(psb)]TJ +/F8 9.9626 Tf 185.0172 497.9794 Td[(Long)-333(P)1(re)-1(cision)-333(Real)-3103(psb)]TJ ET -1 0 0 1 318.9209 489.5544 cm +1 0 0 1 318.9209 497.9794 cm q []0 d 0 J @@ -15126,11 +15174,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -318.9209 -489.5544 cm +1 0 0 1 -318.9209 -497.9794 cm BT -/F8 9.9626 Tf 321.9097 489.5544 Td[(sc)-1(atter)]TJ -136.8925 -11.9551 Td[(Long)-333(P)1(re)-1(cision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 321.9097 497.9794 Td[(gath)1(e)-1(r)]TJ -136.8925 -11.9552 Td[(Long)-333(P)1(re)-1(cision)-333(Complex)-1200(psb)]TJ ET -1 0 0 1 318.9209 477.5993 cm +1 0 0 1 318.9209 486.0242 cm q []0 d 0 J @@ -15139,11 +15187,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -318.9209 -477.5993 cm +1 0 0 1 -318.9209 -486.0242 cm BT -/F8 9.9626 Tf 321.9097 477.5993 Td[(sc)-1(atter)]TJ +/F8 9.9626 Tf 321.9097 486.0242 Td[(gath)1(e)-1(r)]TJ ET -1 0 0 1 179.0396 473.6142 cm +1 0 0 1 179.0396 482.0391 cm q []0 d 0 J @@ -15154,19 +15202,19 @@ S Q 1 0 0 1 46.5372 -27.84 cm 0 g 0 G -1 0 0 1 -225.5768 -445.7742 cm +1 0 0 1 -225.5768 -454.1991 cm BT -/F8 9.9626 Tf 225.5768 445.7742 Td[(T)83(ab)1(le)-334(14:)-444(Data)-333(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 225.5768 454.1991 Td[(T)83(ab)1(le)-334(15:)-444(Data)-333(t)28(yp)-28(es)]TJ ET -1 0 0 1 317.9251 445.7742 cm +1 0 0 1 317.9251 454.1991 cm 0 g 0 G 1 0 0 1 -218.0297 -1.9372 cm 0 g 0 G -1 0 0 1 -99.8954 -443.837 cm +1 0 0 1 -99.8954 -452.2619 cm BT -/F18 14.3462 Tf 99.8954 398.4085 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 4.4087 -21.893 Td[(call)-333(psb)]TJ +/F18 14.3462 Tf 99.8954 407.9057 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 5.2666 -21.8209 Td[(call)-333(psb)]TJ ET -1 0 0 1 138.1661 376.5155 cm +1 0 0 1 139.024 386.0848 cm q []0 d 0 J @@ -15175,11 +15223,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -138.1661 -376.5155 cm +1 0 0 1 -139.024 -386.0848 cm BT -/F8 9.9626 Tf 141.1549 376.5155 Td[(sc)-1(atter)-333(\050)]TJ/F19 9.9626 Tf 36.6127 0 Td[(glob)]TJ +/F8 9.9626 Tf 142.0128 386.0848 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.9626 Tf 34.897 0 Td[(glob)]TJ ET -1 0 0 1 195.1822 376.5155 cm +1 0 0 1 194.3243 386.0848 cm q []0 d 0 J @@ -15188,11 +15236,11 @@ q 3.0552 0.1992 l S Q -1 0 0 1 -195.1822 -376.5155 cm +1 0 0 1 -194.3243 -386.0848 cm BT -/F19 9.9626 Tf 198.2374 376.5155 Td[(x,)-357(lo)51(c)]TJ +/F19 9.9626 Tf 197.3795 386.0848 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 221.8011 376.5155 cm +1 0 0 1 220.9432 386.0848 cm q []0 d 0 J @@ -15201,11 +15249,11 @@ q 3.0552 0.1992 l S Q -1 0 0 1 -221.8011 -376.5155 cm +1 0 0 1 -220.9432 -386.0848 cm BT -/F19 9.9626 Tf 224.8563 376.5155 Td[(x,)-357(desc)]TJ +/F19 9.9626 Tf 223.9984 386.0848 Td[(x,)-357(desc)]TJ ET -1 0 0 1 255.0395 376.5155 cm +1 0 0 1 254.1817 386.0848 cm q []0 d 0 J @@ -15214,11 +15262,11 @@ q 3.0552 0.1992 l S Q -1 0 0 1 -255.0395 -376.5155 cm +1 0 0 1 -254.1817 -386.0848 cm BT -/F19 9.9626 Tf 258.0948 376.5155 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot)-1(,)-357(igl)1(obx,)-358(j)1(globx,)-357(ilo)51(cx)1(,)-358(jl)1(o)51(cx,)-357(k)]TJ/F8 9.9626 Tf 177.2286 0 Td[(\051)]TJ/F18 14.3462 Tf -335.428 -29.9716 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 38.5638 -21.893 Td[(call)-333(psb)]TJ +/F19 9.9626 Tf 257.2369 386.0848 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot)-1(,)-357(igl)1(obx,)-358(j)1(globx,)-357(ilo)51(cx)1(,)-358(jl)1(o)51(cx,)-357(k)]TJ/F8 9.9626 Tf 177.2286 0 Td[(\051)]TJ/F18 14.3462 Tf -334.5701 -29.8879 Td[(Syn)32(t)-1(ax)]TJ/F8 9.9626 Tf 39.4216 -21.8209 Td[(call)-333(psb)]TJ ET -1 0 0 1 172.3211 324.651 cm +1 0 0 1 173.179 334.376 cm q []0 d 0 J @@ -15227,11 +15275,11 @@ q 2.9888 0.1992 l S Q -1 0 0 1 -172.3211 -324.651 cm +1 0 0 1 -173.179 -334.376 cm BT -/F8 9.9626 Tf 175.3099 324.651 Td[(sc)-1(atter)-333(\050)]TJ/F19 9.9626 Tf 36.6128 0 Td[(glob)]TJ +/F8 9.9626 Tf 176.1678 334.376 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.9626 Tf 34.897 0 Td[(glob)]TJ ET -1 0 0 1 229.3372 324.651 cm +1 0 0 1 228.4793 334.376 cm q []0 d 0 J @@ -15240,11 +15288,11 @@ q 3.0552 0.1992 l S Q -1 0 0 1 -229.3372 -324.651 cm +1 0 0 1 -228.4793 -334.376 cm BT -/F19 9.9626 Tf 232.3924 324.651 Td[(x,)-357(lo)51(c)]TJ +/F19 9.9626 Tf 231.5345 334.376 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 255.9561 324.651 cm +1 0 0 1 255.0982 334.376 cm q []0 d 0 J @@ -15253,11 +15301,11 @@ q 3.0552 0.1992 l S Q -1 0 0 1 -255.9561 -324.651 cm +1 0 0 1 -255.0982 -334.376 cm BT -/F19 9.9626 Tf 259.0113 324.651 Td[(x,)-357(desc)]TJ +/F19 9.9626 Tf 258.1534 334.376 Td[(x,)-357(desc)]TJ ET -1 0 0 1 289.1946 324.651 cm +1 0 0 1 288.3367 334.376 cm q []0 d 0 J @@ -15266,25 +15314,25 @@ q 3.0552 0.1992 l S Q -1 0 0 1 -289.1946 -324.651 cm +1 0 0 1 -288.3367 -334.376 cm BT -/F19 9.9626 Tf 292.2498 324.651 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot)-1(,)-357(igl)1(obx,)-358(i)1(lo)51(cx)]TJ/F8 9.9626 Tf 108.9186 0 Td[(\051)]TJ +/F19 9.9626 Tf 291.3919 334.376 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot)-1(,)-357(igl)1(obx,)-358(i)1(lo)51(cx)]TJ/F8 9.9626 Tf 108.9186 0 Td[(\051)]TJ ET -1 0 0 1 94.9141 300.657 cm +1 0 0 1 94.9141 310.4656 cm 0 g 0 G -1 0 0 1 -94.9141 -300.657 cm +1 0 0 1 -94.9141 -310.4656 cm BT -/F29 9.9626 Tf 99.8954 300.657 Td[(On)-383(En)32(tr)1(y)]TJ +/F29 9.9626 Tf 99.8954 310.4656 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 147.4806 300.657 cm +1 0 0 1 147.4806 310.4656 cm 0 g 0 G -1 0 0 1 -52.5665 -20.2599 cm +1 0 0 1 -52.5665 -19.5444 cm 0 g 0 G -1 0 0 1 -94.9141 -280.3971 cm +1 0 0 1 -94.9141 -290.9212 cm BT -/F29 9.9626 Tf 99.8954 280.3971 Td[(glob)]TJ +/F29 9.9626 Tf 99.8954 290.9213 Td[(lo)-32(c)]TJ ET -1 0 0 1 121.5872 280.3971 cm +1 0 0 1 114.904 290.9213 cm q []0 d 0 J @@ -15293,23 +15341,48 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -121.5872 -280.3971 cm +1 0 0 1 -114.904 -290.9213 cm BT -/F29 9.9626 Tf 125.0244 280.3971 Td[(x)]TJ +/F29 9.9626 Tf 118.3411 290.9213 Td[(x)]TJ ET -1 0 0 1 131.0711 280.3971 cm +1 0 0 1 124.3879 290.9213 cm 0 g 0 G -1 0 0 1 -131.0711 -280.3971 cm +1 0 0 1 -124.3879 -290.9213 cm BT -/F8 9.9626 Tf 136.0524 280.3971 Td[(The)-334(ar)1(ra)28(y)-333(that)-333(m)28(ust)-334(b)-27(e)-334(sc)-1(attered)-333(in)28(t)1(o)-334(lo)-27(c)-1(al)-333(p)1(ie)-1(ce)-1(s.)]TJ -11.2504 -11.9552 Td[(Scop)-27(e)-1(:)]TJ/F29 9.9626 Tf 32.3787 0 Td[(global)]TJ/F8 9.9626 Tf -32.3787 -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[(Sp)-27(ec)-1(i\014)1(e)-1(d)-332(as)-1(:)-444(a)-333(rank)-333(on)1(e)-334(or)-333(t)28(w)27(o)-333(arr)1(a)27(y)84(.)]TJ +/F8 9.9626 Tf 129.3692 290.9213 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[(g)-36(l)-20(ob)]TJ ET -1 0 0 1 94.9141 224.2717 cm +1 0 0 1 323.4674 290.9213 cm +q +[]0 d +0 J +0.3985 w +0 0.1992 m +2.9888 0.1992 l +S +Q +1 0 0 1 -323.4674 -290.9213 cm +BT +/F11 9.9626 Tf 326.4562 290.9213 Td[(x)]TJ/F8 9.9626 Tf 5.6939 0 Td[(.)]TJ -207.3481 -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 29.6112 0 Td[(required)]TJ/F8 9.9626 Tf -29.6112 -11.9551 Td[(Sp)-27(ec)-1(i\014)1(e)-1(d)-472(as:)-722(a)-473(ran)1(k)-472(one)-473(or)-472(t)28(w)28(o)-473(arr)1(a)28(y)-473(con)28(tain)1(in)1(g)-473(n)28(u)1(m)27(b)-27(e)-1(r)1(s)-473(of)-472(the)-472(t)27(y)1(p)-28(e)]TJ 0 -11.9552 Td[(in)1(dicated)-333(in)-333(T)83(ab)1(le)]TJ +ET +1 0 0 1 206.9939 243.1006 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -206.9939 -243.1006 cm +BT +/F8 9.9626 Tf 206.9939 243.1006 Td[(15)]TJ +ET +1 0 0 1 216.9566 243.1006 cm 0 g 0 G -1 0 0 1 -94.9141 -224.2717 cm +1 0 0 1 -216.9566 -243.1006 cm BT -/F29 9.9626 Tf 99.8954 224.2717 Td[(desc)]TJ +/F8 9.9626 Tf 216.9566 243.1006 Td[(.)]TJ ET -1 0 0 1 121.81 224.2717 cm +1 0 0 1 94.9141 223.5562 cm +0 g 0 G +1 0 0 1 -94.9141 -223.5562 cm +BT +/F29 9.9626 Tf 99.8954 223.5562 Td[(desc)]TJ +ET +1 0 0 1 121.81 223.5562 cm q []0 d 0 J @@ -15318,23 +15391,23 @@ q 3.4371 0.1992 l S Q -1 0 0 1 -121.81 -224.2717 cm +1 0 0 1 -121.81 -223.5562 cm BT -/F29 9.9626 Tf 125.2471 224.2717 Td[(a)]TJ +/F29 9.9626 Tf 125.2471 223.5562 Td[(a)]TJ ET -1 0 0 1 130.8165 224.2717 cm +1 0 0 1 130.8165 223.5562 cm 0 g 0 G -1 0 0 1 -130.8165 -224.2717 cm +1 0 0 1 -130.8165 -223.5562 cm BT -/F8 9.9626 Tf 135.7978 224.2717 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 -10.9958 -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 -32.3787 -11.9551 Td[(T)28(yp)-28(e:)]TJ/F29 9.9626 Tf 29.6113 0 Td[(required)]TJ/F8 9.9626 Tf -29.6113 -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 +/F8 9.9626 Tf 135.7978 223.5562 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 -10.9958 -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 -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[(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 1 295.717 188.4062 cm +1 0 0 1 295.717 187.6907 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -188.4062 cm +1 0 0 1 -295.717 -187.6907 cm BT -/F32 9.9626 Tf 295.717 188.4062 Td[(psb)]TJ +/F32 9.9626 Tf 295.717 187.6907 Td[(psb)]TJ ET -1 0 0 1 312.0356 188.4062 cm +1 0 0 1 312.0356 187.6907 cm q []0 d 0 J @@ -15343,11 +15416,11 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -312.0356 -188.4062 cm +1 0 0 1 -312.0356 -187.6907 cm BT -/F32 9.9626 Tf 315.1738 188.4062 Td[(desc)]TJ +/F32 9.9626 Tf 315.1738 187.6907 Td[(desc)]TJ ET -1 0 0 1 336.7228 188.4062 cm +1 0 0 1 336.7228 187.6907 cm q []0 d 0 J @@ -15356,15 +15429,15 @@ q 3.1382 0.1992 l S Q -1 0 0 1 -336.7228 -188.4062 cm +1 0 0 1 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def -/FullName (CMMI5) readonly def +/FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def -/FontName /FNDCSR+CMMI5 def +/FontName /WUVZNP+CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for +dup 59 /comma put +dup 72 /H put +dup 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 121 /y put readonly def -/FontBBox{37 -250 1349 750}readonly def +/FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£ÐªÚ‡üqc¥¢§V¥˜ú°v3‰Þ‹²ÕÛF'HJ€¤1¶¯Û»ò=AWÔ¯á~k…=Ô%øLÕT«ˆ«~ïÞÛòÂÇ1½%V|S´tÌ÷9Š“9 ŠœKçYMyD+,ŠgD}äF˜2E×h›‘ï#^¨¶ªŽ#€dñT(@–ÄÂUNþ߯øÓÎ0à™“uÀþæù’Þ¥ü8—âÌ‹z#Žaä"Þ€ô8Ý™Ls'\Å"IÙöho‡ó”û{¶h‹! ìžFAZXɸ}}Ó5L*%* - 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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. 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