diff --git a/Changelog b/Changelog index 98a765f9..9c9dc163 100644 --- a/Changelog +++ b/Changelog @@ -1,7 +1,11 @@ Changelog. A lot less detailed than usual, at least for past history. -2006/04/21: A bunch of fixes related to various scratch spmat(s) initialization +2006/04/24: Rewritten documentation; minor changes to the interface of + dense tools routines, trying to achieve a uniform + look & feel. + +2006/04/21: A bunch of fixes related to various matrix initialization problems that were revealed while testing on SP5. 2006/04/18: Changed interface to spasb and csdp: better handling of diff --git a/Make.inc.gfortran b/Make.inc.gcc42 similarity index 85% rename from Make.inc.gfortran rename to Make.inc.gcc42 index 776fd399..12ecdc1b 100644 --- a/Make.inc.gfortran +++ b/Make.inc.gcc42 @@ -6,10 +6,10 @@ ####################### Section 1 ####################### # Define your compilers and compiler flags here # ########################################################## -F90=/usr/local/gfortran/bin/gfortran -FC=/usr/local/gfortran/bin/gfortran +F90=/usr/local/gcc42/bin/gfortran +FC=/usr/local/gcc42/bin/gfortran F77=$(FC) -CC=/usr/local/gfortran/bin/gcc +CC=/usr/local/gcc42/bin/gcc F90COPT= -O3 -ffast-math -march=pentium4 -msse2 -mfpmath=sse FCOPT=-O3 -ffast-math -march=pentium4 -msse2 -mfpmath=sse CCOPT=-O3 -ffast-math -march=pentium4 -msse2 -mfpmath=sse @@ -17,17 +17,17 @@ CCOPT=-O3 -ffast-math -march=pentium4 -msse2 -mfpmath=sse ####################### Section 2 ####################### # Define your linker and linker flags here # ########################################################## -F90LINK=/usr/local/mpich-gfortran/bin/mpif90 -FLINK=/usr/local/mpich-gfortran/bin/mpif77 -MPF90=/usr/local/mpich-gfortran/bin/mpif90 -MPF77=/usr/local/mpich-gfortran/bin/mpif77 -MPCC=/usr/local/mpich-gfortran/bin/mpicc +F90LINK=/usr/local/mpich-gcc42/bin/mpif90 +FLINK=/usr/local/mpich-gcc42/bin/mpif77 +MPF90=/usr/local/mpich-gcc42/bin/mpif90 +MPF77=/usr/local/mpich-gcc42/bin/mpif77 +MPCC=/usr/local/mpich-gcc42/bin/mpicc ####################### Section 3 ####################### # Specify paths to libraries # ########################################################## -BLAS=-lblas-gcc41 -L$(HOME)/LIB -BLACS=-lmpiblacs-gfortran -L$(HOME)/LIB +BLAS=-lblas-gcc42 -L$(HOME)/LIB +BLACS=-lmpiblacs-gcc42 -L$(HOME)/LIB EXTRA_BLACS_ENV_OBJS=extra_env.o @@ -35,7 +35,7 @@ EXTRA_BLACS_ENV_OBJS=extra_env.o # Other useful tools&defines # ########################################################## SLUDIR=/usr/local/SuperLU_3.0 -SLU=-lslu_lx_gfort -L$(SLUDIR) +SLU=-lslu_lx_gcc42 -L$(SLUDIR) SLUDEF=-DHave_SLU_ -I$(SLUDIR) UMFDIR=$(HOME)/LIB/Umfpack_gcc41 diff --git a/Makefile b/Makefile index e5f7ed84..7f35ee2f 100644 --- a/Makefile +++ b/Makefile @@ -1,6 +1,6 @@ include Make.inc -lib: +library: ( [ -d lib ] || mkdir lib) (cd src; make lib) @echo "=====================================" diff --git a/docs/pdf/commrout.tex b/docs/pdf/commrout.tex index 591f9fa4..ede035ad 100644 --- a/docs/pdf/commrout.tex +++ b/docs/pdf/commrout.tex @@ -39,7 +39,7 @@ Long Precision Complex & psb\_halo \\ \item[x] global dense matrix $x$.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array with the TARGET attribute containing numbers of type specified in Table~\ref{tab:f90halo}. \item[desc\_a] contains data structures for communications.\\ @@ -61,7 +61,7 @@ POINTER attribute. \item[x] global dense result matrix $x$.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Returned as: a rank one or two array with the POINTER attribute +Returned as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90halo}. \item[info] the local portion of result submatrix $y$.\\ @@ -104,37 +104,29 @@ Long Precision Complex & psb\_ovrl \\ \end{table} \syntax{CALL psb\_ovrl}{x, desc\_a, info} -\syntax*{CALL psb\_ovrl}{x, desc\_a, info, choice=choice, -update\_type=update\_type, work=work} +\syntax*{CALL psb\_ovrl}{x, desc\_a, info, update=update\_type, work=work} \begin{description} \item[\bf On Entry] \item[x] global dense matrix $x$.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90ovrl}. \item[desc\_a] contains data structures for communications.\\ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a structured data of type \descdata. -\item[choice] specify if exchange overlap elements. +\item[update] Update operator. \\ \begin{description} -\item[choice = .true.] exchange overlap elements, i.e. apply operator -$P^{T}$; -\item[choice = .false.] don't exchange overlap elements +\item[update = psb\_none\_] Do nothing; +\item[update = psb\_add\_] Sum overlap entries; +\item[update = psb\_avg\_] Average overlap entries; +%% \item[update = psb\_square\_root\_] square root update $\sqrt{P_a}$; \end{description} Scope: {\bf global} \\ -Type: {\bf optional} \\ -Default: $choice = .true. $\\ -Specified as: a logical variable. -\begin{description} -\item[update\_type = 1] normal update $P_a$; -\item[update\_type = 2] square root update $\sqrt{P_a}$; -\end{description} -Scope: {\bf global} \\ -Default: $update\_type = .true. $\\ +Default: $update\_type = psb\_avg\_ $\\ Scope: {\bf global} \\ Specified as: a integer variable. \item[work] the work array. \\ @@ -146,7 +138,7 @@ Specified as: a one dimensional array of the same type of $x$. \item[x] global dense result matrix $x$.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a pointer to array of rank one or two +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 $y$.\\ diff --git a/docs/pdf/datastruct.tex b/docs/pdf/datastruct.tex index 98d3d359..b5f138b4 100644 --- a/docs/pdf/datastruct.tex +++ b/docs/pdf/datastruct.tex @@ -21,7 +21,7 @@ Fields contained in Sparse matrix structures are: \item[{\bf aspk}] Contains values of the local distributed sparse matrix.\\ Specified as: a pointer to an array of rank one of type corresponding -to matrix entries type . +to matrix entries type. \item[{\bf ia1}] Holds integer information on distributed sparse matrix. Actual information will depend on data format used.\\ Specified as: a pointer to an integer array of rank one. @@ -30,7 +30,7 @@ matrix. Actual information will depend on data format used.\\ Specified as: a pointer to an integer array of rank one. \item[{\bf infoa}] On entry can hold auxiliary information on distributed sparse matrix. Actual information will depend on data format used.\\ -Specified as: integer array of length 10. +Specified as: integer array of length \verb|psb_ifasize_|. \item[{\bf fida}] Defines the format of the distributed sparse matrix.\\ Specified as: a string of length 5 \item[{\bf descra}] Describe the characteristic of the distributed sparse matrix.\\ @@ -61,7 +61,7 @@ type psb_dspmat_type integer :: m, k character :: fida(5) character :: descra(10) - integer :: infoa(10) + integer :: infoa(psb_ifa_size_) real(kind(1.d0)), pointer :: aspk(:) integer, pointer :: ia1(:), ia2(:), pr(:), pl(:) end type psb_dspmat_type @@ -72,7 +72,9 @@ end type psb_dspmat_type \begin{center} \fbox{\TheSbox} \end{center} - \caption{\label{fig:spmattype}The PSBLAS defined data type that contains a sparse matrix.} + \caption{\label{fig:spmattype} + The PSBLAS defined data type that + contains a sparse matrix.} \end{figure} The following two cases are among the most commonly used: @@ -98,6 +100,36 @@ column index are stored into \verb|apsk(j)|, \verb|ia1(j)| and \verb|ia2(j)| respectively. \end{enumerate} \end{description} +A sparse matrix has an associated state, which can take the following +values: +\begin{description} +\item[Build:] State entered after the first allocation, and before the + first assembly; in this state it is possible to add nonzero entries. +\item[Assembled:] State entered after the assembly; computations using + the sparse matrix, such as matrix-vector products, are only possible + in this state; +\item[Update:] State entered after a reinitalization; this is used to + handle applications in which the same sparsity pattern is used + multiple times with different coefficients. In this state it is only + possible to enter coefficients for already existing nonzero entries. +\end{description} +\subsubsection{Named Constants} +\label{sec:sp_constants} +\begin{description} +\item[psb\_nztotreq\_] Request to fetch the total number of nonzeroes + stored in a sparse matrix +\item[psb\_nzrowreq\_] Request to fetch the number of nonzeroes in a + given row in a sparse matrix +\item[psb\_dupl\_ovwrt\_] Duplicate coefficients should be overwritten + (i.e. ignore duplications) +\item[psb\_dupl\_add\_] Duplicate coefficients should be added; +\item[psb\_dupl\_err\_] Duplicate coefficients should trigger an error conditino +\item[psb\_upd\_dflt\_] Default update strategy for matrix coefficients; +\item[psb\_upd\_srch\_] Update strategy based on search into the data structure; +\item[psb\_upd\_perm\_] Update strategy based on additional + permutation data (see tools routine description). +\end{description} + \subsection{Descriptor data structure} @@ -196,6 +228,41 @@ end type psb_desc_type contains the communication descriptor.} \end{figure} +A communication descriptor associated with a sparse matrix has a +state, which can take the following values: +\begin{description} +\item[Build:] State entered after the first allocation, and before the + first assembly; in this state it is possible to add communication + requirements among different processes. +\item[Assembled:] State entered after the assembly; computations using + the associated sparse matrix, such as matrix-vector products, are + only possible in this state. +\end{description} +\subsubsection{Named Constants} +\label{sec:cd_constants} +\begin{description} +\item[psb\_none\_] Generic no-op; +\item[psb\_nohalo\_] Do not fetch halo elements; +\item[psb\_halo\_] Fetch halo elements from neighbouring processes; +\item[psb\_sum\_] Sum overlapped elements +\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. +\end{description} + + \subsection{Preconditioner data structure} \label{sec:prec} PSBLAS-2.0 offers the possibility to use many different types of @@ -203,8 +270,9 @@ preconditioning schemes. Besides the simple well known preconditioners like Diagonal Scaling or Block Jacobi (with ILU(0) incomplete factorization) also more complex preconditioning methods are implemented like the Additive Schwarz and Two-Level ones. A -preconditioner is held in the \hypertarget{precdata}{{\tt psb\_prec\_type}} data structure -which depends on the \verb|psb_base_prec| reported in +preconditioner is held in the \hypertarget{precdata}{{\tt + psb\_prec\_type}} data structure which depends on the +\verb|psb_base_prec| reported in figure~\ref{fig:prectype}. The \verb|psb_base_prec| data type may contain a simple preconditioning matrix with the associated communication descriptor which may be different than the @@ -216,7 +284,7 @@ The user can choose the type of preconditioner to be used by means of the \verb|psb_precset| subroutine; once the type of preconditioning method is specified, along with all the parameters that characterize it, the preconditioner data structure can be built using the -\verb|psb_precbuild| subroutine. +\verb|psb_precbld| subroutine. This data structure wants to be flexible enough to easily allow the implementation of new kind of preconditioners. The values contained in the \verb|iprcparm| and \verb|dprcparm| define tha type of @@ -257,8 +325,24 @@ 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} +\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} %%% Local Variables: diff --git a/docs/pdf/intro.tex b/docs/pdf/intro.tex index ff5c70fb..7b7b7c2a 100644 --- a/docs/pdf/intro.tex +++ b/docs/pdf/intro.tex @@ -124,6 +124,15 @@ internally defined in the PSBLAS software package: Interface overloading allows the usage of the same subroutine interfaces for both real and complex data. \end{itemize} +In the description of the subroutines, arguments or argument entries +are classified as: +\begin{description} +\item[global] For input arguments, the value must be the same on all processes + participating in the subroutine call; for output arguments the value + is guaranteed to be the same. +\item[local] Each process has its own value(s) independently. +\end{description} + %%% Local Variables: %%% mode: latex diff --git a/docs/pdf/methods.tex b/docs/pdf/methods.tex index e8c5b058..1b0f03e8 100644 --- a/docs/pdf/methods.tex +++ b/docs/pdf/methods.tex @@ -23,7 +23,7 @@ or 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} +\syntax{call psb\_cg}{a,prec,b,x,eps,desc\_a,info,itmax,iter,err,itrace,istop} \begin{description} \item[\bf On Entry] @@ -57,7 +57,7 @@ Scope: {\bf global} \\ Type: {\bf optional}\\ Default: $itmax = 1000$.\\ Specified as: an integer variable $itmax \ge 1$. -\item[itrace] A tracing parameter.\\ +\item[itrace] If $>0$ print out a convergence message every $itrace$ iterations.\\ Scope: {\bf global} \\ Type: {\bf optional}\\ \item[istop] An integer specifying the stopping criterion.\\ diff --git a/docs/pdf/psbrout.tex b/docs/pdf/psbrout.tex index 73d975a1..3f03d31b 100644 --- a/docs/pdf/psbrout.tex +++ b/docs/pdf/psbrout.tex @@ -10,14 +10,14 @@ This subroutine is an interface to the computational kernel for dense matrix sum: \[ y \leftarrow \alpha\> x+ \beta y \] -where: -\begin{description} -\item[$x$] represents the global dense submatrix $x_{:, jx:jx+n-1}$ -\item[$y$] represents the global dense submatrix $y_{:, jy:jy+n-1}$ -\end{description} +%% where: +%% \begin{description} +%% \item[$x$] represents the global dense submatrix $x_{:, :1}$ +%% \item[$y$] represents the global dense submatrix $y_{:, :}$ +%% \end{description} \syntax{call psb\_geaxpby}{alpha, x, beta, y, desc\_a, info} -\syntax*{call psb\_geaxpby}{alpha, x, beta, y, desc\_a, info, n, jx, jy} +%% \syntax*{call psb\_geaxpby}{alpha, x, beta, y, desc\_a, info, n, jx, jy} %( calculating y <- alpha*x+beta*y ) \begin{table}[h] @@ -44,7 +44,7 @@ Specified as: a number of the data type indicated in Table~\ref{tab:f90axpby}. $x$.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90axpby}. The rank of $x$ must be the same of $y$. \item[beta] the scalar $\beta$.\\ @@ -55,30 +55,29 @@ Specified as: a number of the data type indicated in Table~\ref{tab:f90axpby}. $y$. \\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER -attributecontaining numbers of the type +Specified as: a rank one or two array containing numbers of the type indicated in Table~\ref{tab:f90axpby}. The rank of $y$ must be the same of $x$. \item[desc\_a] contains data structures for communications.\\ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a structured data of type \descdata. -\item[n] number of columns in dense submatrices $x$ and $y$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ -Default: \verb|min(size(x,2),size(y,2))|.\\ -Specified as: an integer variable $n\ge 0$. -\item[jx] the column index of the global dense matrix $x$, -identifying the first column of the submatrix $x$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ -Default: $jx = 1$.\\ -Specified as: an integer variable $jx\ge 1$. -\item[jy] the column index of the global dense matrix $y$, -identifying the first column of the submatrix $y$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ -Default: $jy = 1$.\\ -Specified as: an integer variable $jy\ge 1$. +%% \item[n] number of columns in dense submatrices $x$ and $y$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ +%% Default: \verb|min(size(x,2),size(y,2))|.\\ +%% Specified as: an integer variable $n\ge 0$. +%% \item[jx] the column index of the global dense matrix $x$, +%% identifying the first column of the submatrix $x$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ +%% Default: $jx = 1$.\\ +%% Specified as: an integer variable $jx\ge 1$. +%% \item[jy] the column index of the global dense matrix $y$, +%% identifying the first column of the submatrix $y$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ +%% Default: $jy = 1$.\\ +%% Specified as: an integer variable $jy\ge 1$. \end{description} @@ -111,14 +110,14 @@ computes dot-product as: \[dot \leftarrow x^T y\] Else if $x$ and $y$ are double precision complex vectors then computes dot-product as: \[dot \leftarrow x^H y\] -where: -\begin{description} -\item[$x$] represents the global subvector $x_{:,jx}$ -\item[$y$] represents the global subvector $y_{:,jy}$ -\end{description} +%% where: +%% \begin{description} +%% \item[$x$] represents the global subvector $x_{:,jx}$ +%% \item[$y$] represents the global subvector $y_{:,jy}$ +%% \end{description} \syntax{psb\_gedot}{x, y, desc\_a, info} -\syntax*{psb\_gedot}{x, y, desc\_a, info, jx, jy} +%% \syntax*{psb\_gedot}{x, y, desc\_a, info, jx, jy} \begin{table}[h] \begin{center} \begin{tabular}{ll} @@ -136,37 +135,39 @@ Long Precision Complex & psb\_gedot \\ \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 $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ +$x$.\\ +%% This function computes the location of the first element of +%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a pointer to array of rank one or two +Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90dot}. The rank of $x$ must be the same of $y$. \item[y] the local portion of global dense matrix -$y$. This function computes the location of the first element of -local subarray used, based on $iy, jy$ and the field $matrix\_data$ of $desc\_a$ . \\ +$y$. \\ +%% This function computes the location of the first element of +%% local subarray used, based on $iy, jy$ and the field $matrix\_data$ of $desc\_a$ . \\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a pointer to array of rank one or two +Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90dot}. The rank of $y$ must be the same of $x$. \item[desc\_a] contains data structures for communications.\\ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a structured data of type \descdata. -\item[jx] the column index of global dense matrix $x$, -identifying the column of subvector $x$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ -Default: $jx = 1$.\\ - -\item[jy] the column index of global dense matrix $y$, -identifying the column of subvector $y$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ -Default: $jy = 1$.\\ -Specified as: an integer variable $jy\ge 1$. +%% \item[jx] the column index of global dense matrix $x$, +%% identifying the column of subvector $x$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ +%% Default: $jx = 1$.\\ + +%% \item[jy] the column index of global dense matrix $y$, +%% identifying the column of subvector $y$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\ +%% Default: $jy = 1$.\\ +%% Specified as: an integer variable $jy\ge 1$. \item[\bf On Return] \item[Function value] is the dot product of subvectors $x$ and $y$.\\ Scope: {\bf global} \\ @@ -213,14 +214,14 @@ Long Precision Complex & psb\_gedot \\ $x$. \\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a pointer to array of rank one or two +Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90mdot}. The rank of $x$ must be the same of $y$. \item[y] the local portion of global dense matrix $y$. \\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a pointer to array of rank one or two +Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90mdot}. The rank of $y$ must be the same of $x$. \item[desc\_a] contains data structures for communications.\\ @@ -232,7 +233,7 @@ 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] the local portion of result submatrix $y$.\\ +\item[info] Scope: {\bf local} \\ Type: {\bf required} \\ An integer value that contains an error code. @@ -254,13 +255,13 @@ computes infinity norm as: \[ amax \leftarrow \max_i |x_i|\] else if $x$ is a double precision complex vector then computes infinity-norm as: \[ amax \leftarrow \max_i {(|re(x_i)| + |im(x_i)|)}\] -where: -\begin{description} -\item[$x$] represents the global subvector $x_{:,jx}$ -\end{description} +%% where: +%% \begin{description} +%% \item[$x$] represents the global subvector $x_{:,jx}$ +%% \end{description} \syntax{psb\_geamax}{x, desc\_a, info} -\syntax*{psb\_geamax}{x, desc\_a, info, jx} +%% \syntax*{psb\_geamax}{x, desc\_a, info, jx} \begin{table}[h] \begin{center} @@ -280,30 +281,31 @@ Long Precision Real&Long Precision Complex & psb\_geamax \\ \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 $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ +$x$. %% This function computes the location of the first element of +%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . +\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90amax}. \item[desc\_a] contains data structures for communications.\\ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a structured data of type \descdata. -\item[jx] the column index of global dense matrix $x$, -identifying the column of subvector $x$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ -Default: $jx = 1$\\ -Specified as: an integer variable $jx\ge 1$. +%% \item[jx] the column index of global dense matrix $x$, +%% identifying the column of subvector $x$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ +%% Default: $jx = 1$\\ +%% Specified as: an integer variable $jx\ge 1$. \item[\bf On Return] \item[Function value] is the infinity norm of subvector $x$.\\ Scope: {\bf global} \\ -Specified as: a number of the data type indicated in Table~\ref{tab:f90amax}. -\item[info] the local portion of result submatrix $y$.\\ -Scope: {\bf local} \\ +Specified as: a long precision real number. +\item[info] +Scope: {\bf global} \\ Type: {\bf required} \\ An integer value that contains an error code. \end{description} @@ -340,7 +342,7 @@ Long Precision Real &Long Precision Complex & psb\_geamax\\ $x$. \\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90mamax}. \item[desc\_a] contains data structures for communications.\\ @@ -350,9 +352,8 @@ Specified as: a structured data of type \descdata. \item[\bf On Return] \item[res] is the infinity norm of the columns of $x$.\\ Scope: {\bf global} \\ -Specified as: a number or a rank-one array of the data type indicated -in Table~\ref{tab:f90amax}. -\item[info] the local portion of result submatrix $y$.\\ +Specified as: a number or a rank-one array of long precision real numbers. +\item[info] Scope: {\bf local} \\ Type: {\bf required} \\ An integer value that contains an error code. @@ -373,22 +374,18 @@ computes 1-norm as: \[ asum \leftarrow \|x_i\|\] else if $x$ ic double precision complex vector then computes 1-norm as: \[ asum \leftarrow \|re(x)\|_1 + \|im(x)\|_1\] -where: -\begin{description} -\item[$x$] represents the global subvector $x_{:,jx}$ -\end{description} + \syntax{psb\_geasum}{x, desc\_a, info} -\syntax*{psb\_geasum}{x, desc\_a, info, jx} \begin{table}[h] \begin{center} -\begin{tabular}{ll} +\begin{tabular}{lll} \hline -$dot$, $x$, $y$ & {\bf Function}\\ +$asum$ & $x$ & {\bf Function}\\ \hline -Long Precision Real & psb\_geasum \\ -Long Precision Complex & psb\_geasum \\ +Long Precision Real&Long Precision Real & psb\_geasum \\ +Long Precision Real&Long Precision Complex & psb\_geasum \\ \hline \end{tabular} \end{center} @@ -398,29 +395,24 @@ Long Precision Complex & psb\_geasum \\ \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 $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ +$x$. %% 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 with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90asum}. \item[desc\_a] contains data structures for communications.\\ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a structured data of type \descdata. -\item[jx] the column index of global dense matrix $x$, -identifying the column of subvector $x$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ -Default: $jx = 1$\\ -Specified as: an integer variable $jx\ge 1$. \item[\bf On Return] -\item[Function value] is the 1-norm of subvector $x$.\\ +\item[Function value] is the 1-norm of vector $x$.\\ Scope: {\bf global} \\ -Specified as: a number of the data type indicated in Table~\ref{tab:f90asum}. -\item[info] the local portion of result submatrix $y$.\\ +Specified as: a long precision real number. +\item[info] Scope: {\bf local} \\ Type: {\bf required} \\ An integer value that contains an error code. @@ -442,19 +434,19 @@ computes 2-norm as: \[ nrm2 \leftarrow \sqrt{x^T x}\] else if $x$ is double precision complex vector then computes 2-norm as: \[ nrm2 \leftarrow \sqrt{x^H x}\] -where: -\begin{description} -\item[$x$] represents the global subvector $x_{:,jx}$ -\end{description} +%% where: +%% \begin{description} +%% \item[$x$] represents the global subvector $x_{:,jx}$ +%% \end{description} \begin{table}[h] \begin{center} -\begin{tabular}{ll} +\begin{tabular}{lll} \hline -$nrm2$, $x$ & {\bf Function}\\ +$nrm2$ & $x$ & {\bf Function}\\ \hline -Long Precision Real & psb\_genrm2 \\ -Long Precision Complex & psb\_genrm2 \\ +Long Precision Real&Long Precision Real & psb\_genrm2 \\ +Long Precision Real&Long Precision Complex & psb\_genrm2 \\ \hline \end{tabular} \end{center} @@ -462,34 +454,35 @@ Long Precision Complex & psb\_genrm2 \\ \end{table} \syntax{psb\_genrm2}{x, desc\_a, info} -\syntax*{psb\_genrm2}{x, desc\_a, info, jx} +%% \syntax*{psb\_genrm2}{x, desc\_a, info, jx} \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 $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ +$x$.%% This function computes the location of the first element of +%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . +\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90nrm2}. \item[desc\_a] contains data structures for communications.\\ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a structured data of type \descdata. -\item[jx] the column index of global dense matrix $x$, -identifying the column of subvector $x$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ -Default: $jx = 1$\\ -Specified as: an integer variable $jx\ge 1$. +%% \item[jx] the column index of global dense matrix $x$, +%% identifying the column of subvector $x$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ +%% Default: $jx = 1$\\ +%% Specified as: an integer variable $jx\ge 1$. \item[\bf On Return] \item[Function Value] is the 2-norm of subvector $x$.\\ Scope: {\bf global} \\ Type: {\bf required} \\ -Specified as: a number of the data type indicated in Table~\ref{tab:f90nrm2}. -\item[info] the local portion of result submatrix $y$.\\ +Specified as: a long precision real number. +\item[info] Scope: {\bf local} \\ Type: {\bf required} \\ An integer value that contains an error code. @@ -516,7 +509,7 @@ where: \begin{center} \begin{tabular}{ll} \hline -$nrmi$, $A$ & {\bf Function}\\ +$A$ & {\bf Function}\\ \hline Long Precision Real & psb\_spnrmi \\ Long Precision Complex & psb\_spnrmi \\ @@ -542,8 +535,8 @@ Specified as: a structured data of type \descdata. \item[\bf On Return] \item[Function value] is the infinity-norm of sparse submatrix $A$.\\ Scope: {\bf global} \\ -Specified as: a number of the data type indicated in Table~\ref{tab:f90nrmi}. -\item[info] the local portion of result submatrix $y$.\\ +Specified as: a long precision real number. +\item[info] Scope: {\bf local} \\ Type: {\bf required} \\ An integer value that contains an error code. @@ -576,8 +569,8 @@ y \leftarrow \alpha P_r A^H P_c x + \beta y where: \begin{description} -\item[$x$] is the global dense submatrix $x_{:, jx:jx+k-1}$ -\item[$y$] is the global dense submatrix $y_{:, jy:jy+k-1}$ +\item[$x$] is the global dense submatrix $x_{:, :}$ +\item[$y$] is the global dense submatrix $y_{:, :}$ \item[$A$] is the global sparse submatrix $A$ \item[$P_r, P_c$] are the permutation matrices. \end{description} @@ -598,7 +591,7 @@ Long Precision Complex & psb\_spmm \\ \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, k, jx, jy, work} +trans, work} \begin{description} \item[\bf On Entry] @@ -613,11 +606,12 @@ Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: a structured data of type \spdata. \item[x] the local portion of global dense matrix -$x$. This subroutine computes the location of the first element of -local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ +$x$. %% This subroutine computes the location of the first element of +%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . +\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90spmm}. The rank of $x$ must be the same of $y$. \item[beta] the scalar $\beta$.\\ @@ -625,11 +619,12 @@ Scope: {\bf global} \\ Type: {\bf required} \\ Specified as: a number of the data type indicated in Table~\ref{tab:f90spmm}. \item[y] the local portion of global dense matrix -$y$. This subroutine computes the location of the first element of -local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . \\ +$y$. %% This subroutine computes the location of the first element of +%% local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . +\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90spmm}. The rank of $y$ must be the same of $x$. \item[desc\_a] contains data structures for communications.\\ @@ -648,37 +643,38 @@ Scope: {\bf global} \\ Type: {\bf optional}\\ Default: $trans = N$\\ Specified as: a character variable. -\item[k] number of columns in dense submatrices $x$ and $y$. \\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: \verb|min(size(x,2)-jx+1,size(y,2)-jy+1)|\\ -Specified as: an integer variable $ k \ge 1$. -\item[jx] the column index of global dense matrix $x$, -identifying the column of subvector $x$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ -Default: $iy = 1$\\ -Specified as: an integer variable $jx\ge 1$. -\item[jy] the column index of global dense matrix $y$, -identifying the column of subvector $y$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $y$ is of rank 2.\\ -Default: $jy = 1$\\ -Specified as: an integer variable $jy\ge 1$. - -\item[work] the work array.\\ +%% \item[k] number of columns in dense submatrices $x$ and $y$. \\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}\\ +%% Default: \verb|min(size(x,2)-jx+1,size(y,2)-jy+1)|\\ +%% Specified as: an integer variable $ k \ge 1$. +%% \item[jx] the column index of global dense matrix $x$, +%% identifying the column of subvector $x$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ +%% Default: $iy = 1$\\ +%% Specified as: an integer variable $jx\ge 1$. +%% \item[jy] the column index of global dense matrix $y$, +%% identifying the column of subvector $y$.\\ +%% Scope: {\bf global} \\ +%% Type: {\bf optional}; can only be present if $y$ is of rank 2.\\ +%% Default: $jy = 1$\\ +%% Specified as: an integer variable $jy\ge 1$. + +\item[work] work array.\\ Scope: {\bf local} \\ +Type: {\bf optional}\\ Specified as: a rank one array of the same type of $x$ and $y$ with -the POINTER attribute. +the TARGET attribute. \item[\bf On Return] \item[y] the local portion of result submatrix $y$.\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a pointer to array of rank one or two +Specified as: an array of rank one or two containing numbers of type specified in Table~\ref{tab:f90spmm}. -\item[info] the local portion of result submatrix $y$.\\ +\item[info] Scope: {\bf local} \\ Type: {\bf required} \\ An integer value that contains an error code. @@ -710,8 +706,8 @@ y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\ where: \begin{description} -\item[$x$] is the global dense submatrix $x_{:, jx:jx+n-1}$ -\item[$y$] is the global dense submatrix $y_{:, jy:jy+n-1}$ +\item[$x$] is the global dense submatrix $x_{:, :}$ +\item[$y$] is the global dense submatrix $y_{:, :}$ \item[$T$] is the global sparse block triangular submatrix $T$ \item[$D$] is the scaling diagonal matrix. \item[$P_r, P_c$] are the permutation matrices. @@ -719,7 +715,7 @@ where: \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, n, jx, jy, work} +trans, unit, choice, diag, work} \begin{table}[h] \begin{center} @@ -751,11 +747,12 @@ Type: {\bf required}\\ Specified as: a structured data type specified in \S~\ref{sec:datastruct}. \item[x] the local portion of global dense matrix -$x$. This subroutine computes the location of the first element of -local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ +$x$. %% This subroutine computes the location of the first element of +%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . +\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90spsm}. The rank of $x$ must be the same of $y$. \item[beta] the scalar $\beta$.\\ @@ -763,11 +760,12 @@ Scope: {\bf global} \\ Type: {\bf required} \\ Specified as: a number of the data type indicated in Table~\ref{tab:f90spsm}. \item[y] the local portion of global dense matrix -$y$. This subroutine computes the location of the first element of -local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . \\ +$y$. %% This subroutine computes the location of the first element of +%% local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . +\\ Scope: {\bf local} \\ Type: {\bf required} \\ -Specified as: a rank one or two array with the POINTER attribute +Specified as: a rank one or two array containing numbers of type specified in Table~\ref{tab:f90spsm}. The rank of $y$ must be the same of $x$. \item[desc\_a] contains data structures for communications.\\ @@ -794,57 +792,41 @@ Scope: {\bf global} \\ Type: {\bf optional}\\ Default: $unitd = U$\\ Specified as: a character variable. -\item[choice] specify whether a cleanup of the overlapped elements is -required on exit. +\item[choice] specifies the update of overlap elements to be performed + on exit: \begin{description} -\item[choice = .false.] no cleanup on exit -\item[choice = .true.] cleanup on exit.\\ +\item \verb|psb_none_| +\item \verb|psb_sum_| +\item \verb|psb_avg_| +\item \verb|psb_square_root_| \end{description} Scope: {\bf global} \\ Type: {\bf optional}\\ -Default: $choice = .true.$\\ -Specified as: a logical variable. +Default: \verb|psb_avg_|\\ +Specified as: an integer variable. \item[diag] the diagonal scaling matrix.\\ Scope: {\bf local} \\ Type: {\bf optional}\\ Default: $diag(1) = 1 (no scaling)$\\ Specified as: a rank one array containing numbers of the type indicated in Table~\ref{tab:f90spsm}. -\item[n] number of columns in dense submatrices $x$ and $y$. \\ -Scope: {\bf global} \\ -Type: {\bf optional}\\ -Default: \verb|min(size(x,2)-jx+1,size(y,2)-jy+1)|\\ -Specified as: an integer variable $ n \ge 0$. -\item[jx] the column index of global dense matrix $x$, -identifying the column of subvector $x$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $x$ is of rank 2.\\ -Default: $jx = 1 $\\ -Specified as: an integer variable $jx\ge 1$. -\item[jy] the column index of global dense matrix $y$, -identifying the column of subvector $y$.\\ -Scope: {\bf global} \\ -Type: {\bf optional}; can only be present if $y$ is of rank 2.\\ -Default: $jy = 1 $\\ -Specified as: an integer variable $jy\ge 1$. \\ -Scope: {\bf global} \\ -Specified as: a number of the data type indicated in Table~\ref{tab:f90spsm}. -\item[work] the work array. \\ +\item[work] a work array. \\ Scope: {\bf local} \\ Type: {\bf optional}\\ Specified as: a rank one array of the same type of $x$ with the -POINTER attribute. +TARGET attribute. \item[\bf On Return] \item[y] the local portion of global dense matrix -$y$. This subroutine computes the location of the first element of -local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . \\ +$y$. %% This subroutine computes the location of the first element of +%% local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . +\\ Scope: {\bf local} \\ Type: {\bf required} \\ Specified as: a pointer to array of rank one or two containing numbers of type specified in Table~\ref{tab:f90spsm}. -\item[info] the local portion of result submatrix $y$.\\ +\item[info] Scope: {\bf local} \\ Type: {\bf required} \\ An integer value that contains an error code. diff --git a/docs/pdf/toolsrout.tex b/docs/pdf/toolsrout.tex index 395c4e32..76474464 100644 --- a/docs/pdf/toolsrout.tex +++ b/docs/pdf/toolsrout.tex @@ -1,291 +1,116 @@ \section{Data management and initialization routines} \label{sec:toolsrout} -% -%% psb_alloc %% -% -\subroutine{psb\_geall}{Allocates a dense matrix} -\syntax{call psb\_geall}{m, n, x, desc\_a, info, js} - -\begin{description} -\item[\bf On Entry] -\item[m] The number of rows of the dense matrix to be allocated.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar. -\item[n] The number of columns of the dense matrix to be allocated.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar. -\item[desc\_a] The communication descriptor.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a variable of type \descdata.\\ -\item[js] The starting column.\\ -Scope: {\bf local} \\ -Type: {\bf optional}\\ -Specified as: Integer scalar. -\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 one or two dimensional array.\\ -\item[info] Error code. -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar. -\end{description} % -%% psb_asb %% -% -\subroutine{psb\_geasb}{Assembly a dense matrix} - -\syntax{call psb\_geasb}{x, desc\_a, info} - -\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.\\ -\end{description} - -\begin{description} -\item[\bf On Return] -\item[x] The dense matrix to be assembled.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a one or two dimensional array.\\ -\item[info] Error code.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ -\end{description} - - -% -%% psb_csrp %% -% -\subroutine{psb\_csrp}{Applies a right permutation to a sparse matrix} - -\syntax{call psb\_csrp}{trans, iperm, a, desc\_a, info} - -\begin{description} -\item[\bf On Entry] -\item[trans] A character that specifies whether to permute $A$ or $A^T$.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$.\\ -\item[iperm] An integer array containing permutation information.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer one-dimensional array.\\ -\item[a] The sparse matrix to be permuted.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a \spdata variable.\\ -\item[desc\_a] The communication descriptor of type \descdata.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a variable of type \descdata.\\ -\end{description} - -\begin{description} -\item[\bf On Return] -\item[info] Error code.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ -\end{description} - - -% -%% psb_descprt %% -% -\subroutine{psb\_cdprt}{Prints a descriptor} - -\syntax{call psb\_cdprt}{iout, desc\_a, glob, short} - -\begin{description} -\item[\bf On Entry] -\item[iout] An integer that defines the output unit. -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ -\item[desc\_a] The communication descriptor of type \descdata that - must be printed.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a variable of type \descdata.\\ -\end{description} - -\begin{description} -\item[\bf On Return] -\item[glob] ?????? -\item[short] ?????? -\end{description} - - -% -%% psb_free %% -% -\subroutine{psb\_gefree}{Frees a dense matrix} - -\syntax{call psb\_gefree}{x, desc\_a, info} - -\begin{description} -\item[\bf On Entry] -\item[x] The dense matrix to - be freed.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a one or two dimensional array. -\item[desc\_a] The communication descriptor.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a variable of type \descdata.\\ -\end{description} - -\begin{description} -\item[\bf On Return] -\item[info] Error code.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ -\end{description} - - -% -%% psb_gelp %% +%% psb_cdall %% % -\subroutine{psb\_gelp}{Applies a left permutation to a dense matrix} - -\syntax{call psb\_gelp}{trans, iperm, x, desc\_a, info} +\subroutine{psb\_cdall}{Allocates a communication descriptor} -\begin{description} -\item[\bf On Entry] -\item[trans] A character that specifies whether to permute $A$ or $A^T$.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$.\\ -\item[iperm] An integer array containing permutation information.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer one-dimensional array.\\ -\item[x] The dense matrix to be permuted.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a one or two dimensional array.\\ -\item[desc\_a] The communication descriptor.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a variable of type \descdata.\\ -\end{description} +\syntax{call psb\_cdall}{m, n, parts, icontxt, desc\_a, info} +\syntax*{call psb\_cdall}{m, v, icontxt, desc\_a, info, flag} +This subroutine initializes the communication descriptor associated +with an index space. It takes two forms depending on whether the user +specifies the domain partitioning through a subroutine or through a vector \begin{description} -\item[\bf On Return] -\item[info] Error code.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: Integer scalar.\\ +\item[\bf First Form: On Entry ] +\item[m] the number of rows of the problem.\\ +Scope:{\bf global}.\\ +Type:{\bf required}.\\ +Specified as: an integer value. +\item[n] the number of columns of the problem.\\ +Scope:{\bf global}.\\ +Type:{\bf required}.\\ +Specified as: an integer value. Currently constrained to be $m=n$. +\item[parts] the subroutine that defines the partitioning scheme.\\ +Scope:{\bf global}.\\ +Type:{\bf required}.\\ +Specified as: a subroutine. +\item[icontxt] the communication context.\\ +Scope:{\bf global}.\\ +Type:{\bf required}.\\ +Specified as: an integer value. \end{description} - -% -%% psb_spins %% -% -\subroutine{psb\_spins}{Insert a cloud of elements into a sparse matrix} - -\syntax{call psb\_spins}{nz, ia, ja, val, a, desc\_a, info, is, js} - \begin{description} -\item[\bf On Entry] -\item[nz] the number of elements to be inserted.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: an integer scalar. -\item[ia] the row indices of the elements to be inserted.\\ -Scope:{\bf local}.\\ +\item[\bf Second Form: On Entry ] +\item[m] the size of the index space.\\ +Scope:{\bf global}.\\ Type:{\bf required}.\\ -Specified as: an integer array of size $nz$. -\item[ja] the column indices of the elements to be inserted.\\ -Scope:{\bf local}.\\ +Specified as: an integer value $m>0$. +\item[v] Data allocation: each index $i\in \{1\dots m\}$ is allocated + to process $v(i)$. +Scope:{\bf global}.\\ Type:{\bf required}.\\ -Specified as: an integer array of size $nz$. -\item[val] the elements to be inserted.\\ -Scope:{\bf local}.\\ +Specified as: an integer array of size $m$. +\item[icontxt] the communication context.\\ +Scope:{\bf global}.\\ Type:{\bf required}.\\ -Specified as: an array of size $nz$. -\item[desc\_a] The communication descriptor.\\ -Scope: {\bf local}. \\ -Type: {\bf required}.\\ -Specified as: a variable of type \descdata.\\ -\item[is] the starting row on matrix $a$.\\ -Scope:{\bf local}.\\ +Specified as: an integer value. +\item[flag] Specifies whether entries in $v$ are zero- or one-based. +Scope:{\bf global}.\\ Type:{\bf optional}.\\ -Specified as: an integer vaule. -\item[js] the starting column on matrix $a$.\\ -Scope:{\bf local}.\\ -Type:{\bf optional}\\ -Specified as: an integer value +Specified as: an integer value $0,1$, default $0$. \end{description} \begin{description} \item[\bf On Return] -\item[a] the matrix into which elements will be inserted.\\ -Scope:{\bf local}\\ -Type:{\bf required}\\ -Specified as: a structured data of type \spdata. -\item[info] Error code.\\ +\item[desc\_a] the communication descriptor.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: a structured data of type \descdata. +\item[info] Error code. Scope: {\bf local} \\ Type: {\bf required}\\ +Specified as: an integer variable.\\ \end{description} % -%% psb_cdall %% +%% psb_cdins %% % -\subroutine{psb\_cdall}{Allocates a communication descriptor} +\subroutine{psb\_cdins}{Communication descriptor insert routine} -\syntax{call psb\_cdall}{m, n, parts, icontxt, desc\_a, info} -\syntax*{call psb\_cdall}{m, v, icontxt, desc\_a, info, flag} +\syntax{call psb\_cdins}{nz, ia, ja, desc\_a, info} \begin{description} \item[\bf On Entry] -\item[m] the number of rows of the problem.\\ -Scope:{\bf global}.\\ -Type:{\bf required}.\\ -Specified as: an integer value. -\item[n] the number of columns of the problem.\\ -Scope:{\bf global}.\\ -Type:{\bf required}.\\ -Specified as: an integer value. -\item[parts] the subroutine that defines the partitioning scheme.\\ -Scope:{\bf global}.\\ -Type:{\bf required}.\\ -Specified as: a subroutine as described in ??? -\item[icontxt] the communication context.\\ -Scope:{\bf global}.\\ -Type:{\bf required}.\\ +\item[nz] the number of points being inserted.\\ +Scope: {\bf local}.\\ +Type: {\bf required}.\\ Specified as: an integer value. +\item[ia] the row indices of the points being inserted.\\ +Scope: {\bf local}.\\ +Type: {\bf required}.\\ +Specified as: an integer array of length $nz$. +\item[ja] the column indices of the points being inserted.\\ +Scope: {\bf local}.\\ +Type: {\bf required}.\\ +Specified as: an integer array of length $nz$. +%% \item[is] the row offset.\\ +%% Scope:{\bf local}.\\ +%% Type:{\bf optional}.\\ +%% Specified as: an integer value. +%% \item[js] the column offset.\\ +%% Scope: {\bf local}.\\ +%% Type: {\bf optional}.\\ +%% Specified as: an integer value. \end{description} \begin{description} \item[\bf On Return] -\item[desc\_a] the communication descriptor.\\ +\item[desc\_a] the communication descriptor to be freed.\\ Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: a structured data of type \descdata. \item[info] Error code. Scope: {\bf local} \\ Type: {\bf required}\\ -Specified as: an integer variable.\\ +Specified as: an integer variable. \end{description} + % %% psb_cdasb %% % @@ -307,7 +132,7 @@ Specified as: a structured data of type \descdata. Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: an integer variable. -\item[arg] +%\item[arg] \end{description} @@ -365,76 +190,96 @@ Specified as: an integer variable. \end{description} +%% % +%% %% psb_cdren %% +%% % +%% \subroutine{psb\_cdren}{Applies a renumeration to a communication descriptor} + +%% \syntax{call psb\_cdren}{trans, iperm, desc\_a, info} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[trans] A character that specifies whether to permute $A$ or $A^T$.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$.\\ +%% \item[iperm] An integer array containing permutation information.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: an integer one-dimensional array.\\ +%% \item[desc\_a] 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[info] Error code. +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: an integer variable. +%% \end{description} + + + + % -%% psb_cdins %% +%% psb_descprt %% % -\subroutine{psb\_cdins}{Comunnication descriptor insert routine} +%% \subroutine{psb\_cdprt}{Prints a descriptor} -\syntax{call psb\_cdins}{nz, ia, ja, desc\_a, info, is, js} +%% \syntax{call psb\_cdprt}{iout, desc\_a, glob, short} -\begin{description} -\item[\bf On Entry] -\item[nz] the number of points being inserted.\\ -Scope: {\bf local}.\\ -Type: {\bf required}.\\ -Specified as: an integer value. -\item[ia] the row indices of the points being inserted.\\ -Scope: {\bf local}.\\ -Type: {\bf required}.\\ -Specified as: an integer array of length $nz$. -\item[ja] the column indices of the points being inserted.\\ -Scope: {\bf local}.\\ -Type: {\bf required}.\\ -Specified as: an integer array of length $nz$. -\item[is] the row offset.\\ -Scope:{\bf local}.\\ -Type:{\bf optional}.\\ -Specified as: an integer value. -\item[js] the column offset.\\ -Scope: {\bf local}.\\ -Type: {\bf optional}.\\ -Specified as: an integer value. -\end{description} +%% \begin{description} +%% \item[\bf On Entry] +%% \item[iout] An integer that defines the output unit. +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: Integer scalar.\\ +%% \item[desc\_a] The communication descriptor of type \descdata that +%% must be printed.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a variable of type \descdata.\\ +%% \end{description} -\begin{description} -\item[\bf On Return] -\item[desc\_a] the communication descriptor to be freed.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. -\item[info] Error code. -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer variable. -\end{description} +%% \begin{description} +%% \item[\bf On Return] +%% \item[glob] ?????? +%% \item[short] ?????? +%% \end{description} % -%% psb_cdren %% +%% psb_spalloc %% % -\subroutine{psb\_cdren}{Applies a renumeration to a communication descriptor} +\subroutine{psb\_spall}{Allocates a sparse matrix} -\syntax{call psb\_cdren}{trans, iperm, desc\_a, info} +\syntax{call psb\_spall}{a, desc\_a, info, nnz} \begin{description} \item[\bf On Entry] -\item[trans] A character that specifies whether to permute $A$ or $A^T$.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$.\\ -\item[iperm] An integer array containing permutation information.\\ -Scope: {\bf local} \\ -Type: {\bf required}\\ -Specified as: an integer one-dimensional array.\\ \item[desc\_a] the communication descriptor.\\ Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: a structured data of type \descdata. +\item[nnz] the number of nonzeroes in the local part of the assembled matrix.\\ +Scope: {\bf global}.\\ +Type: {\bf optional}.\\ +Specified as: an integer value. Note: a good estimate for the number +of nonzeroes in the assembled matrix may substantially improve +performance in the matrix build phase, as it will reduce or eliminate +the need for multiple data allocation. \end{description} \begin{description} \item[\bf On Return] +\item[a] the matrix to be allocated.\\ +Scope:{\bf local}\\ +Type:{\bf required}\\ +Specified as: a structured data of type \spdata. \item[info] Error code. Scope: {\bf local} \\ Type: {\bf required}\\ @@ -444,44 +289,66 @@ Specified as: an integer variable. % -%% psb_spalloc %% +%% psb_spins %% % -\subroutine{psb\_spall}{Allocates a sparse matrix} +\subroutine{psb\_spins}{Insert a cloud of elements into a sparse matrix} -\syntax{call psb\_spall}{a, desc\_a, info, nnz} +\syntax{call psb\_spins}{nz, ia, ja, val, a, desc\_a, info} \begin{description} \item[\bf On Entry] -\item[desc\_a] the communication descriptor.\\ +\item[nz] the number of elements to be inserted.\\ Scope:{\bf local}.\\ Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. -\item[nnz] the number of nonzeroes in the matrix.\\ -Scope: {\bf global}.\\ -Type: {\bf optional}.\\ -Specified as: an integer value. +Specified as: an integer scalar. +\item[ia] the row indices of the elements to be inserted.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: an integer array of size $nz$. +\item[ja] the column indices of the elements to be inserted.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: an integer array of size $nz$. +\item[val] the elements to be inserted.\\ +Scope:{\bf local}.\\ +Type:{\bf required}.\\ +Specified as: an array of size $nz$. +\item[desc\_a] The communication descriptor.\\ +Scope: {\bf local}. \\ +Type: {\bf required}.\\ +Specified as: a variable of type \descdata.\\ +%% \item[is] the starting row on matrix $a$.\\ +%% Scope:{\bf local}.\\ +%% Type:{\bf optional}.\\ +%% Specified as: an integer vaule. +%% \item[js] the starting column on matrix $a$.\\ +%% Scope:{\bf local}.\\ +%% Type:{\bf optional}\\ +%% Specified as: an integer value \end{description} \begin{description} \item[\bf On Return] -\item[a] the matrix to be allocated.\\ +\item[a] the matrix into which elements will be inserted.\\ Scope:{\bf local}\\ Type:{\bf required}\\ Specified as: a structured data of type \spdata. -\item[info] Error code. +\item[desc\_a] The communication descriptor.\\ +Scope: {\bf local}. \\ +Type: {\bf required}.\\ +Specified as: a variable of type \descdata.\\ +\item[info] Error code.\\ Scope: {\bf local} \\ Type: {\bf required}\\ -Specified as: an integer variable. \end{description} - % %% psb_spasb %% % \subroutine{psb\_spasb}{Sparse matrix assembly routine} -\syntax{call psb\_spasb}{a, desc\_a, info, afmt, up, dup} +\syntax{call psb\_spasb}{a, desc\_a, info, afmt, upd, dupl} \begin{description} \item[\bf On Entry] @@ -492,15 +359,16 @@ Specified as: a structured data of type \descdata. \item[afmt] the storage format for the sparse matrix.\\ Scope: {\bf global}.\\ Type: {\bf optional}.\\ -Specified as: an array of characters. If not specified 'CSR' will be assumed. -\item[up] ???.\\ +Specified as: an array of characters. Defalt: 'CSR'. +\item[upd] Provide for updates to the matrix coefficients.\\ Scope: {\bf global}.\\ Type: {\bf optional}.\\ -Specified as: . -\item[dup] ???.\\ +Specified as: integer, possible values: \verb|psb_upd_srch_|, \verb|psb_upd_perm_| +\item[dupl] How to handle duplicate coefficients.\\ Scope: {\bf global}.\\ Type: {\bf optional}.\\ -Specified as: +Specified as: integer, possible values: \verb|psb_dupl_ovwrt_|, +\verb|psb_dupl_add_|, \verb|psb_dupl_err_|. \end{description} \begin{description} @@ -517,16 +385,49 @@ Specified as: an integer variable. +%% % +%% %% psb_spcnv %% +%% % +%% \subroutine{psb\_spcnv}{Converts a sparse matrix storage format} + +%% \syntax{call psb\_spcnv}{a, b, desc\_a, info} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[a] the matrix to be converted.\\ +%% Scope:{\bf local}\\ +%% Type:{\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[desc\_a] 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[b] the converted matrix.\\ +%% Scope:{\bf local}\\ +%% Type:{\bf required}\\ +%% Specified as: a structured data of type \spdata. +%% \item[info] Error code. +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: an integer variable. +%% \end{description} + + + % -%% psb_spcnv %% +%% psb_spfree %% % -\subroutine{psb\_spcnv}{Converts a sparse matrix storage format} +\subroutine{psb\_spfree}{Frees a sparse matrix} -\syntax{call psb\_spcnv}{a, b, desc\_a, info} +\syntax{call psb\_spfree}{a, desc\_a, info} \begin{description} \item[\bf On Entry] -\item[a] the matrix to be converted.\\ +\item[a] the matrix to be freed.\\ Scope:{\bf local}\\ Type:{\bf required}\\ Specified as: a structured data of type \spdata. @@ -538,10 +439,6 @@ Specified as: a structured data of type \descdata. \begin{description} \item[\bf On Return] -\item[b] the converted matrix.\\ -Scope:{\bf local}\\ -Type:{\bf required}\\ -Specified as: a structured data of type \spdata. \item[info] Error code. Scope: {\bf local} \\ Type: {\bf required}\\ @@ -550,16 +447,17 @@ Specified as: an integer variable. + % -%% psb_spfree %% +%% psb_sprn %% % -\subroutine{psb\_spfree}{Frees a sparse matrix} +\subroutine{psb\_sprn}{Reinit sparse matrix structure for psblas routines.} -\syntax{call psb\_spfree}{a, desc\_a, info} +\syntax{call psb\_sprn}{a, decsc\_a, info} \begin{description} \item[\bf On Entry] -\item[a] the matrix to be freed.\\ +\item[a] the matrix to be reinitialized.\\ Scope:{\bf local}\\ Type:{\bf required}\\ Specified as: a structured data of type \spdata. @@ -577,6 +475,88 @@ Type: {\bf required}\\ Specified as: an integer variable. \end{description} +% +%% psb_spupdate %% +% +%% \subroutine{psb\_spupdate}{Updates a sparse matrix.} + +%% \syntax{call psb\_spupdate}{a, ia, ja, blck, desc\_a, info, ix, jx, updflag} + +%% \begin{description} +%% \item[\bf On Entry] +%% \end{description} + +%% \begin{description} +%% \item[\bf On Return] +%% \end{description} +%% % +%% %% psb_csrp %% +%% % +%% \subroutine{psb\_csrp}{Applies a right permutation to a sparse matrix} + +%% \syntax{call psb\_csrp}{trans, iperm, a, desc\_a, info} + +%% \begin{description} +%% \item[\bf On Entry] +%% \item[trans] A character that specifies whether to permute $A$ or $A^T$.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$.\\ +%% \item[iperm] An integer array containing permutation information.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: an integer one-dimensional array.\\ +%% \item[a] The sparse matrix to be permuted.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a \spdata variable.\\ +%% \item[desc\_a] The communication descriptor of type \descdata.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: a variable of type \descdata.\\ +%% \end{description} + +%% \begin{description} +%% \item[\bf On Return] +%% \item[info] Error code.\\ +%% Scope: {\bf local} \\ +%% Type: {\bf required}\\ +%% Specified as: Integer scalar.\\ +%% \end{description} + + +% +%% psb_alloc %% +% +\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 POINTER +attribute, of type real, complex or integer.\\ +\item[info] Error code. +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: Integer scalar. +\end{description} % @@ -584,7 +564,8 @@ Specified as: an integer variable. % \subroutine{psb\_geins}{Dense matrix insertion routine} -\syntax{call psb\_geins}{m, n, x, ix, jx, blck, desc\_a, info, iblck, jblck} +\syntax{call psb\_geins}{m, n, blck, x, ix, jx, desc\_a, info,dupl} +\syntax*{call psb\_geins}{m, blck, x, ix, desc\_a, info,dupl} \begin{description} \item[\bf On Entry] @@ -592,15 +573,8 @@ Specified as: an integer variable. Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: an integer value. -\item[n] columns number of submatrix belonging to blck to be inserted.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: an integer value. -\item[ix] x global-row corresponding to position at which blck submatrix must be inserted.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: an integer value. -\item[jx] x global-col corresponding to position at which blck submatrix must be inserted.\\ +\item[n] columns number of submatrix belonging to blck to be inserted + (only when $x$ is of rank 2).\\ Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: an integer value. @@ -608,18 +582,23 @@ Specified as: an integer value. Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: a one or two dimensional array. -\item[desc\_a] the communication descriptor.\\ +\item[ix] x global-row corresponding to position at which blck submatrix must be inserted.\\ Scope:{\bf local}.\\ Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. -\item[iblck] first row of submatrix belonging to blck to be inserted.\\ +Specified as: an integer value. +\item[jx] x global-col corresponding to position at which blck submatrix must be inserted (only when $x$ is of rank 2).\\ Scope:{\bf local}.\\ Type:{\bf required}.\\ Specified as: an integer value. -\item[jblck] first column of submatrix belonging to blck to be inserted.\\ +\item[desc\_a] the communication descriptor.\\ Scope:{\bf local}.\\ Type:{\bf required}.\\ -Specified as: an integer value. +Specified as: a structured data of type \descdata. +\item[dupl] How to handle duplicate coefficients.\\ +Scope: {\bf global}.\\ +Type: {\bf optional}.\\ +Specified as: integer, possible values: \verb|psb_dupl_ovwrt_|, +\verb|psb_dupl_add_|, \verb|psb_dupl_err_|. \end{description} \begin{description} @@ -627,57 +606,106 @@ Specified as: an integer value. \item[x] the output dense matrix.\\ Scope: {\bf local} \\ Type: {\bf required}\\ -Specified as: a one or two dimensional array.\\ +Specified as: a rank one or two array with the POINTER +attribute, of type real, complex or integer.\\ \item[info] Error code. Scope: {\bf local} \\ Type: {\bf required}\\ Specified as: an integer variable. \end{description} +% +%% psb_asb %% +% +\subroutine{psb\_geasb}{Assembly a dense matrix} + +\syntax{call psb\_geasb}{x, desc\_a, info} +\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.\\ +\end{description} +\begin{description} +\item[\bf On Return] +\item[x] The dense matrix to be assembled.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a rank one or two array with the POINTER +attribute, of type real, complex or integer.\\ +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: Integer scalar.\\ +\end{description} % -%% psb_sprn %% +%% psb_free %% % -\subroutine{psb\_sprn}{Reinit sparse matrix structure for psblas routines.} +\subroutine{psb\_gefree}{Frees a dense matrix} -\syntax{call psb\_sprn}{a, decsc\_a, info} +\syntax{call psb\_gefree}{x, desc\_a, info} \begin{description} \item[\bf On Entry] -\item[a] the matrix to be reinitialized.\\ -Scope:{\bf local}\\ -Type:{\bf required}\\ -Specified as: a structured data of type \spdata. -\item[desc\_a] the communication descriptor.\\ -Scope:{\bf local}.\\ -Type:{\bf required}.\\ -Specified as: a structured data of type \descdata. +\item[x] The dense matrix to + be freed.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a rank one or two array with the POINTER +attribute, of type real, complex or integer.\\ + +\item[desc\_a] The communication descriptor.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a variable of type \descdata.\\ \end{description} \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. +Specified as: Integer scalar.\\ \end{description} + % -%% psb_spupdate %% +%% psb_gelp %% % -%% \subroutine{psb\_spupdate}{Updates a sparse matrix.} - -%% \syntax{call psb\_spupdate}{a, ia, ja, blck, desc\_a, info, ix, jx, updflag} +\subroutine{psb\_gelp}{Applies a left permutation to a dense matrix} -%% \begin{description} -%% \item[\bf On Entry] -%% \end{description} +\syntax{call psb\_gelp}{trans, iperm, x, desc\_a, info} -%% \begin{description} -%% \item[\bf On Return] -%% \end{description} +\begin{description} +\item[\bf On Entry] +\item[trans] A character that specifies whether to permute $A$ or $A^T$.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$.\\ +\item[iperm] An integer array containing permutation information.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: an integer one-dimensional array.\\ +\item[x] The dense matrix to be permuted.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a one or two dimensional array.\\ +\item[desc\_a] The communication descriptor.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: a variable of type \descdata.\\ +\end{description} +\begin{description} +\item[\bf On Return] +\item[info] Error code.\\ +Scope: {\bf local} \\ +Type: {\bf required}\\ +Specified as: Integer scalar.\\ +\end{description} % diff --git a/docs/userguide.pdf b/docs/userguide.pdf index ff5b2326..a954a88f 100644 --- a/docs/userguide.pdf +++ b/docs/userguide.pdf @@ -30,352 +30,370 @@ endobj (3.1 Sparse Matrix data structure) endobj 25 0 obj -<< /S /GoTo /D (subsection.3.2) >> +<< /S /GoTo /D (subsubsection.3.1.1) >> endobj 28 0 obj -(3.2 Descriptor data structure) +(3.1.1 Named Constants) endobj 29 0 obj -<< /S /GoTo /D (subsection.3.3) >> +<< /S /GoTo /D (subsection.3.2) >> endobj 32 0 obj -(3.3 Preconditioner data structure) +(3.2 Descriptor data structure) endobj 33 0 obj -<< /S /GoTo /D (section.4) >> +<< /S /GoTo /D (subsubsection.3.2.1) >> endobj 36 0 obj -(4 Algebraic routines) +(3.2.1 Named Constants) endobj 37 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543.505 cm -0 g 0 G -1 0 0 1 -328.767 -12.21 cm +1 0 0 1 114.839 531.295 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -114.839 -531.295 cm BT @@ -671,11 +650,11 @@ S Q 1 0 0 1 -130.436 -531.295 cm BT -/F8 9.963 Tf 133.425 531.295 Td[(geam)-1(ax)]TJ +/F8 9.963 Tf 133.425 531.295 Td[(geaxpb)29(y)]TJ ET -1 0 0 1 166.357 531.295 cm +1 0 0 1 169.125 531.295 cm 0 g 0 G -1 0 0 1 -166.357 -531.295 cm +1 0 0 1 -169.125 -531.295 cm BT /F8 9.963 Tf 172.123 531.295 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET @@ -683,7 +662,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -531.295 cm BT -/F8 9.963 Tf 433.644 531.295 Td[(16)]TJ +/F8 9.963 Tf 433.644 531.295 Td[(12)]TJ ET 1 0 0 1 443.606 531.295 cm 0 g 0 G @@ -704,19 +683,19 @@ S Q 1 0 0 1 -130.436 -519.085 cm BT -/F8 9.963 Tf 133.425 519.085 Td[(geam)-1(ax)]TJ +/F8 9.963 Tf 133.425 519.085 Td[(gedot)]TJ ET -1 0 0 1 166.357 519.085 cm +1 0 0 1 157.225 519.085 cm 0 g 0 G -1 0 0 1 -166.357 -519.085 cm +1 0 0 1 -157.225 -519.085 cm BT -/F8 9.963 Tf 172.123 519.085 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 164.375 519.085 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 433.644 519.085 cm 0 g 0 G 1 0 0 1 -433.644 -519.085 cm BT -/F8 9.963 Tf 433.644 519.085 Td[(18)]TJ +/F8 9.963 Tf 433.644 519.085 Td[(14)]TJ ET 1 0 0 1 443.606 519.085 cm 0 g 0 G @@ -737,19 +716,19 @@ S Q 1 0 0 1 -130.436 -506.876 cm BT -/F8 9.963 Tf 133.425 506.876 Td[(geas)-1(u)1(m)]TJ +/F8 9.963 Tf 133.425 506.876 Td[(gedot)]TJ ET -1 0 0 1 165.582 506.876 cm +1 0 0 1 157.225 506.876 cm 0 g 0 G -1 0 0 1 -165.582 -506.876 cm +1 0 0 1 -157.225 -506.876 cm BT -/F8 9.963 Tf 172.123 506.876 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 164.375 506.876 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 433.644 506.876 cm 0 g 0 G 1 0 0 1 -433.644 -506.876 cm BT -/F8 9.963 Tf 433.644 506.876 Td[(19)]TJ +/F8 9.963 Tf 433.644 506.876 Td[(16)]TJ ET 1 0 0 1 443.606 506.876 cm 0 g 0 G @@ -770,11 +749,11 @@ S Q 1 0 0 1 -130.436 -494.666 cm BT -/F8 9.963 Tf 133.425 494.666 Td[(genrm2)]TJ +/F8 9.963 Tf 133.425 494.666 Td[(geam)-1(ax)]TJ ET -1 0 0 1 165.555 494.666 cm +1 0 0 1 166.357 494.666 cm 0 g 0 G -1 0 0 1 -165.555 -494.666 cm +1 0 0 1 -166.357 -494.666 cm BT /F8 9.963 Tf 172.123 494.666 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET @@ -782,7 +761,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -494.666 cm BT -/F8 9.963 Tf 433.644 494.666 Td[(21)]TJ +/F8 9.963 Tf 433.644 494.666 Td[(18)]TJ ET 1 0 0 1 443.606 494.666 cm 0 g 0 G @@ -803,11 +782,11 @@ S Q 1 0 0 1 -130.436 -482.457 cm BT -/F8 9.963 Tf 133.425 482.457 Td[(spnr)1(mi)]TJ +/F8 9.963 Tf 133.425 482.457 Td[(geam)-1(ax)]TJ ET -1 0 0 1 163.396 482.457 cm +1 0 0 1 166.357 482.457 cm 0 g 0 G -1 0 0 1 -163.396 -482.457 cm +1 0 0 1 -166.357 -482.457 cm BT /F8 9.963 Tf 172.123 482.457 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET @@ -815,7 +794,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -482.457 cm BT -/F8 9.963 Tf 433.644 482.457 Td[(23)]TJ +/F8 9.963 Tf 433.644 482.457 Td[(19)]TJ ET 1 0 0 1 443.606 482.457 cm 0 g 0 G @@ -836,19 +815,19 @@ S Q 1 0 0 1 -130.436 -470.247 cm BT -/F8 9.963 Tf 133.425 470.247 Td[(spmm)]TJ +/F8 9.963 Tf 133.425 470.247 Td[(geas)-1(u)1(m)]TJ ET -1 0 0 1 159.494 470.247 cm +1 0 0 1 165.582 470.247 cm 0 g 0 G -1 0 0 1 -159.494 -470.247 cm +1 0 0 1 -165.582 -470.247 cm BT -/F8 9.963 Tf 164.375 470.247 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 172.123 470.247 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET 1 0 0 1 433.644 470.247 cm 0 g 0 G 1 0 0 1 -433.644 -470.247 cm BT -/F8 9.963 Tf 433.644 470.247 Td[(24)]TJ +/F8 9.963 Tf 433.644 470.247 Td[(20)]TJ ET 1 0 0 1 443.606 470.247 cm 0 g 0 G @@ -869,41 +848,29 @@ S Q 1 0 0 1 -130.436 -458.038 cm BT -/F8 9.963 Tf 133.425 458.038 Td[(spsm)]TJ +/F8 9.963 Tf 133.425 458.038 Td[(genrm2)]TJ ET -1 0 0 1 155.122 458.038 cm +1 0 0 1 165.555 458.038 cm 0 g 0 G -1 0 0 1 -155.122 -458.038 cm +1 0 0 1 -165.555 -458.038 cm BT -/F8 9.963 Tf 164.375 458.038 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 172.123 458.038 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET 1 0 0 1 433.644 458.038 cm 0 g 0 G 1 0 0 1 -433.644 -458.038 cm BT -/F8 9.963 Tf 433.644 458.038 Td[(27)]TJ +/F8 9.963 Tf 433.644 458.038 Td[(21)]TJ ET 1 0 0 1 443.606 458.038 cm 0 g 0 G -1 0 0 1 -343.711 -22.342 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -99.895 -435.696 cm -BT -/F29 9.963 Tf 99.895 435.696 Td[(5)-925(Co)1(m)-1(m)32(unicat)-1(ion)-383(routines)]TJ -ET -1 0 0 1 238.328 435.696 cm -0 g 0 G -1 0 0 1 -238.328 -435.696 cm -BT -/F29 9.963 Tf 432.149 435.696 Td[(31)]TJ -ET -1 0 0 1 114.839 423.486 cm +1 0 0 1 -328.767 -12.21 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -423.486 cm +1 0 0 1 -114.839 -445.828 cm BT -/F8 9.963 Tf 114.839 423.486 Td[(psb)]TJ +/F8 9.963 Tf 114.839 445.828 Td[(psb)]TJ ET -1 0 0 1 130.436 423.486 cm +1 0 0 1 130.436 445.828 cm q []0 d 0 J @@ -912,31 +879,31 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -423.486 cm +1 0 0 1 -130.436 -445.828 cm BT -/F8 9.963 Tf 133.425 423.486 Td[(hal)1(o)]TJ +/F8 9.963 Tf 133.425 445.828 Td[(spnr)1(mi)]TJ ET -1 0 0 1 151.69 423.486 cm +1 0 0 1 163.396 445.828 cm 0 g 0 G -1 0 0 1 -151.69 -423.486 cm +1 0 0 1 -163.396 -445.828 cm BT -/F8 9.963 Tf 156.626 423.486 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 172.123 445.828 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET -1 0 0 1 433.644 423.486 cm +1 0 0 1 433.644 445.828 cm 0 g 0 G -1 0 0 1 -433.644 -423.486 cm +1 0 0 1 -433.644 -445.828 cm BT -/F8 9.963 Tf 433.644 423.486 Td[(32)]TJ +/F8 9.963 Tf 433.644 445.828 Td[(22)]TJ ET -1 0 0 1 443.606 423.486 cm +1 0 0 1 443.606 445.828 cm 0 g 0 G 1 0 0 1 -328.767 -12.209 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -411.277 cm +1 0 0 1 -114.839 -433.619 cm BT -/F8 9.963 Tf 114.839 411.277 Td[(psb)]TJ +/F8 9.963 Tf 114.839 433.619 Td[(psb)]TJ ET -1 0 0 1 130.436 411.277 cm +1 0 0 1 130.436 433.619 cm q []0 d 0 J @@ -945,31 +912,31 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -411.277 cm +1 0 0 1 -130.436 -433.619 cm BT -/F8 9.963 Tf 133.425 411.277 Td[(o)28(vrl)]TJ +/F8 9.963 Tf 133.425 433.619 Td[(spmm)]TJ ET -1 0 0 1 150.057 411.277 cm +1 0 0 1 159.494 433.619 cm 0 g 0 G -1 0 0 1 -150.057 -411.277 cm +1 0 0 1 -159.494 -433.619 cm BT -/F8 9.963 Tf 156.626 411.277 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 164.375 433.619 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET -1 0 0 1 433.644 411.277 cm +1 0 0 1 433.644 433.619 cm 0 g 0 G -1 0 0 1 -433.644 -411.277 cm +1 0 0 1 -433.644 -433.619 cm BT -/F8 9.963 Tf 433.644 411.277 Td[(34)]TJ +/F8 9.963 Tf 433.644 433.619 Td[(23)]TJ ET -1 0 0 1 443.606 411.277 cm +1 0 0 1 443.606 433.619 cm 0 g 0 G 1 0 0 1 -328.767 -12.21 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -399.067 cm +1 0 0 1 -114.839 -421.409 cm BT -/F8 9.963 Tf 114.839 399.067 Td[(psb)]TJ +/F8 9.963 Tf 114.839 421.409 Td[(psb)]TJ ET -1 0 0 1 130.436 399.067 cm +1 0 0 1 130.436 421.409 cm q []0 d 0 J @@ -978,25 +945,37 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -399.067 cm +1 0 0 1 -130.436 -421.409 cm BT -/F8 9.963 Tf 133.425 399.067 Td[(gath)1(e)-1(r)]TJ +/F8 9.963 Tf 133.425 421.409 Td[(spsm)]TJ ET -1 0 0 1 161.127 399.067 cm +1 0 0 1 155.122 421.409 cm 0 g 0 G -1 0 0 1 -161.127 -399.067 cm +1 0 0 1 -155.122 -421.409 cm BT -/F8 9.963 Tf 164.375 399.067 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 164.375 421.409 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET -1 0 0 1 433.644 399.067 cm +1 0 0 1 433.644 421.409 cm 0 g 0 G -1 0 0 1 -433.644 -399.067 cm +1 0 0 1 -433.644 -421.409 cm BT -/F8 9.963 Tf 433.644 399.067 Td[(36)]TJ +/F8 9.963 Tf 433.644 421.409 Td[(25)]TJ ET -1 0 0 1 443.606 399.067 cm +1 0 0 1 443.606 421.409 cm 0 g 0 G -1 0 0 1 -328.767 -12.209 cm +1 0 0 1 -343.711 -22.342 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.895 -399.067 cm +BT +/F29 9.963 Tf 99.895 399.067 Td[(5)-925(Co)1(m)-1(m)32(unicat)-1(ion)-383(routines)]TJ +ET +1 0 0 1 238.328 399.067 cm +0 g 0 G +1 0 0 1 -238.328 -399.067 cm +BT +/F29 9.963 Tf 432.149 399.067 Td[(28)]TJ +ET +1 0 0 1 114.839 386.858 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -114.839 -386.858 cm BT @@ -1013,41 +992,29 @@ S Q 1 0 0 1 -130.436 -386.858 cm BT -/F8 9.963 Tf 133.425 386.858 Td[(sc)-1(atter)]TJ +/F8 9.963 Tf 133.425 386.858 Td[(hal)1(o)]TJ ET -1 0 0 1 162.843 386.858 cm +1 0 0 1 151.69 386.858 cm 0 g 0 G -1 0 0 1 -162.843 -386.858 cm +1 0 0 1 -151.69 -386.858 cm BT -/F8 9.963 Tf 172.123 386.858 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ +/F8 9.963 Tf 156.626 386.858 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 386.858 cm 0 g 0 G 1 0 0 1 -433.644 -386.858 cm BT -/F8 9.963 Tf 433.644 386.858 Td[(38)]TJ +/F8 9.963 Tf 433.644 386.858 Td[(29)]TJ ET 1 0 0 1 443.606 386.858 cm 0 g 0 G -1 0 0 1 -343.711 -22.342 cm -0 0 1 rg 0 0 1 RG -1 0 0 1 -99.895 -364.516 cm -BT -/F29 9.963 Tf 99.895 364.516 Td[(6)-925(Data)-383(m)-1(anagemen)32(t)-383(and)-383(i)-1(niti)-1(ali)-1(zation)-384(r)1(outi)-1(nes)]TJ -ET -1 0 0 1 339.407 364.516 cm -0 g 0 G -1 0 0 1 -339.407 -364.516 cm -BT -/F29 9.963 Tf 432.149 364.516 Td[(40)]TJ -ET -1 0 0 1 114.839 352.307 cm +1 0 0 1 -328.767 -12.21 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -352.307 cm +1 0 0 1 -114.839 -374.648 cm BT -/F8 9.963 Tf 114.839 352.307 Td[(psb)]TJ +/F8 9.963 Tf 114.839 374.648 Td[(psb)]TJ ET -1 0 0 1 130.436 352.307 cm +1 0 0 1 130.436 374.648 cm q []0 d 0 J @@ -1056,31 +1023,31 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -352.307 cm +1 0 0 1 -130.436 -374.648 cm BT -/F8 9.963 Tf 133.425 352.307 Td[(geall)]TJ +/F8 9.963 Tf 133.425 374.648 Td[(o)28(vrl)]TJ ET -1 0 0 1 153.351 352.307 cm +1 0 0 1 150.057 374.648 cm 0 g 0 G -1 0 0 1 -153.351 -352.307 cm +1 0 0 1 -150.057 -374.648 cm BT -/F8 9.963 Tf 156.626 352.307 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 156.626 374.648 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET -1 0 0 1 433.644 352.307 cm +1 0 0 1 433.644 374.648 cm 0 g 0 G -1 0 0 1 -433.644 -352.307 cm +1 0 0 1 -433.644 -374.648 cm BT -/F8 9.963 Tf 433.644 352.307 Td[(41)]TJ +/F8 9.963 Tf 433.644 374.648 Td[(31)]TJ ET -1 0 0 1 443.606 352.307 cm +1 0 0 1 443.606 374.648 cm 0 g 0 G -1 0 0 1 -328.767 -12.21 cm +1 0 0 1 -328.767 -12.209 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -340.097 cm +1 0 0 1 -114.839 -362.439 cm BT -/F8 9.963 Tf 114.839 340.097 Td[(psb)]TJ +/F8 9.963 Tf 114.839 362.439 Td[(psb)]TJ ET -1 0 0 1 130.436 340.097 cm +1 0 0 1 130.436 362.439 cm q []0 d 0 J @@ -1089,31 +1056,31 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -340.097 cm +1 0 0 1 -130.436 -362.439 cm BT -/F8 9.963 Tf 133.425 340.097 Td[(geas)-1(b)]TJ +/F8 9.963 Tf 133.425 362.439 Td[(gath)1(e)-1(r)]TJ ET -1 0 0 1 157.28 340.097 cm +1 0 0 1 161.127 362.439 cm 0 g 0 G -1 0 0 1 -157.28 -340.097 cm +1 0 0 1 -161.127 -362.439 cm BT -/F8 9.963 Tf 164.375 340.097 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 164.375 362.439 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET -1 0 0 1 433.644 340.097 cm +1 0 0 1 433.644 362.439 cm 0 g 0 G -1 0 0 1 -433.644 -340.097 cm +1 0 0 1 -433.644 -362.439 cm BT -/F8 9.963 Tf 433.644 340.097 Td[(42)]TJ +/F8 9.963 Tf 433.644 362.439 Td[(33)]TJ ET -1 0 0 1 443.606 340.097 cm +1 0 0 1 443.606 362.439 cm 0 g 0 G 1 0 0 1 -328.767 -12.21 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -114.839 -327.887 cm +1 0 0 1 -114.839 -350.229 cm BT -/F8 9.963 Tf 114.839 327.887 Td[(psb)]TJ +/F8 9.963 Tf 114.839 350.229 Td[(psb)]TJ ET -1 0 0 1 130.436 327.887 cm +1 0 0 1 130.436 350.229 cm q []0 d 0 J @@ -1122,25 +1089,37 @@ q 2.989 0.199 l S Q -1 0 0 1 -130.436 -327.887 cm +1 0 0 1 -130.436 -350.229 cm BT -/F8 9.963 Tf 133.425 327.887 Td[(cs)-1(rp)]TJ +/F8 9.963 Tf 133.425 350.229 Td[(sc)-1(atter)]TJ ET -1 0 0 1 151.22 327.887 cm +1 0 0 1 162.843 350.229 cm 0 g 0 G -1 0 0 1 -151.22 -327.887 cm +1 0 0 1 -162.843 -350.229 cm BT -/F8 9.963 Tf 156.626 327.887 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 172.123 350.229 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ ET -1 0 0 1 433.644 327.887 cm +1 0 0 1 433.644 350.229 cm 0 g 0 G -1 0 0 1 -433.644 -327.887 cm +1 0 0 1 -433.644 -350.229 cm BT -/F8 9.963 Tf 433.644 327.887 Td[(43)]TJ +/F8 9.963 Tf 433.644 350.229 Td[(35)]TJ ET -1 0 0 1 443.606 327.887 cm +1 0 0 1 443.606 350.229 cm 0 g 0 G -1 0 0 1 -328.767 -12.209 cm +1 0 0 1 -343.711 -22.342 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -99.895 -327.887 cm +BT +/F29 9.963 Tf 99.895 327.887 Td[(6)-925(Data)-383(m)-1(anagemen)32(t)-383(and)-383(i)-1(niti)-1(ali)-1(zation)-384(r)1(outi)-1(nes)]TJ +ET +1 0 0 1 339.407 327.887 cm +0 g 0 G +1 0 0 1 -339.407 -327.887 cm +BT +/F29 9.963 Tf 432.149 327.887 Td[(37)]TJ +ET +1 0 0 1 114.839 315.678 cm 0 0 1 rg 0 0 1 RG 1 0 0 1 -114.839 -315.678 cm BT @@ -1157,19 +1136,19 @@ S Q 1 0 0 1 -130.436 -315.678 cm BT -/F8 9.963 Tf 133.425 315.678 Td[(cdpr)1(t)]TJ +/F8 9.963 Tf 133.425 315.678 Td[(geall)]TJ ET -1 0 0 1 156.699 315.678 cm +1 0 0 1 153.351 315.678 cm 0 g 0 G -1 0 0 1 -156.699 -315.678 cm +1 0 0 1 -153.351 -315.678 cm BT -/F8 9.963 Tf 164.375 315.678 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 156.626 315.678 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 315.678 cm 0 g 0 G 1 0 0 1 -433.644 -315.678 cm BT -/F8 9.963 Tf 433.644 315.678 Td[(44)]TJ +/F8 9.963 Tf 433.644 315.678 Td[(38)]TJ ET 1 0 0 1 443.606 315.678 cm 0 g 0 G @@ -1190,11 +1169,11 @@ S Q 1 0 0 1 -130.436 -303.468 cm BT -/F8 9.963 Tf 133.425 303.468 Td[(gefree)]TJ +/F8 9.963 Tf 133.425 303.468 Td[(geas)-1(b)]TJ ET -1 0 0 1 158.636 303.468 cm +1 0 0 1 157.28 303.468 cm 0 g 0 G -1 0 0 1 -158.636 -303.468 cm +1 0 0 1 -157.28 -303.468 cm BT /F8 9.963 Tf 164.375 303.468 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1202,7 +1181,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -303.468 cm BT -/F8 9.963 Tf 433.644 303.468 Td[(45)]TJ +/F8 9.963 Tf 433.644 303.468 Td[(39)]TJ ET 1 0 0 1 443.606 303.468 cm 0 g 0 G @@ -1223,11 +1202,11 @@ S Q 1 0 0 1 -130.436 -291.259 cm BT -/F8 9.963 Tf 133.425 291.259 Td[(gelp)]TJ +/F8 9.963 Tf 133.425 291.259 Td[(cs)-1(rp)]TJ ET -1 0 0 1 151.137 291.259 cm +1 0 0 1 151.22 291.259 cm 0 g 0 G -1 0 0 1 -151.137 -291.259 cm +1 0 0 1 -151.22 -291.259 cm BT /F8 9.963 Tf 156.626 291.259 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET @@ -1235,7 +1214,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -291.259 cm BT -/F8 9.963 Tf 433.644 291.259 Td[(46)]TJ +/F8 9.963 Tf 433.644 291.259 Td[(40)]TJ ET 1 0 0 1 443.606 291.259 cm 0 g 0 G @@ -1256,11 +1235,11 @@ S Q 1 0 0 1 -130.436 -279.049 cm BT -/F8 9.963 Tf 133.425 279.049 Td[(spin)1(s)]TJ +/F8 9.963 Tf 133.425 279.049 Td[(cdpr)1(t)]TJ ET -1 0 0 1 155.122 279.049 cm +1 0 0 1 156.699 279.049 cm 0 g 0 G -1 0 0 1 -155.122 -279.049 cm +1 0 0 1 -156.699 -279.049 cm BT /F8 9.963 Tf 164.375 279.049 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1268,7 +1247,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -279.049 cm BT -/F8 9.963 Tf 433.644 279.049 Td[(47)]TJ +/F8 9.963 Tf 433.644 279.049 Td[(41)]TJ ET 1 0 0 1 443.606 279.049 cm 0 g 0 G @@ -1289,19 +1268,19 @@ S Q 1 0 0 1 -130.436 -266.84 cm BT -/F8 9.963 Tf 133.425 266.84 Td[(cdall)]TJ +/F8 9.963 Tf 133.425 266.84 Td[(gefree)]TJ ET -1 0 0 1 153.904 266.84 cm +1 0 0 1 158.636 266.84 cm 0 g 0 G -1 0 0 1 -153.904 -266.84 cm +1 0 0 1 -158.636 -266.84 cm BT -/F8 9.963 Tf 156.626 266.84 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ +/F8 9.963 Tf 164.375 266.84 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET 1 0 0 1 433.644 266.84 cm 0 g 0 G 1 0 0 1 -433.644 -266.84 cm BT -/F8 9.963 Tf 433.644 266.84 Td[(49)]TJ +/F8 9.963 Tf 433.644 266.84 Td[(42)]TJ ET 1 0 0 1 443.606 266.84 cm 0 g 0 G @@ -1322,19 +1301,19 @@ S Q 1 0 0 1 -130.436 -254.63 cm BT -/F8 9.963 Tf 133.425 254.63 Td[(cdasb)]TJ +/F8 9.963 Tf 133.425 254.63 Td[(gelp)]TJ ET -1 0 0 1 157.834 254.63 cm +1 0 0 1 151.137 254.63 cm 0 g 0 G -1 0 0 1 -157.834 -254.63 cm +1 0 0 1 -151.137 -254.63 cm BT -/F8 9.963 Tf 164.375 254.63 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 156.626 254.63 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 254.63 cm 0 g 0 G 1 0 0 1 -433.644 -254.63 cm BT -/F8 9.963 Tf 433.644 254.63 Td[(50)]TJ +/F8 9.963 Tf 433.644 254.63 Td[(43)]TJ ET 1 0 0 1 443.606 254.63 cm 0 g 0 G @@ -1355,11 +1334,11 @@ S Q 1 0 0 1 -130.436 -242.421 cm BT -/F8 9.963 Tf 133.425 242.421 Td[(cdcp)28(y)]TJ +/F8 9.963 Tf 133.425 242.421 Td[(spin)1(s)]TJ ET -1 0 0 1 158.332 242.421 cm +1 0 0 1 155.122 242.421 cm 0 g 0 G -1 0 0 1 -158.332 -242.421 cm +1 0 0 1 -155.122 -242.421 cm BT /F8 9.963 Tf 164.375 242.421 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1367,7 +1346,7 @@ ET 0 g 0 G 1 0 0 1 -433.644 -242.421 cm BT -/F8 9.963 Tf 433.644 242.421 Td[(51)]TJ +/F8 9.963 Tf 433.644 242.421 Td[(44)]TJ ET 1 0 0 1 443.606 242.421 cm 0 g 0 G @@ -1388,19 +1367,19 @@ S Q 1 0 0 1 -130.436 -230.211 cm BT -/F8 9.963 Tf 133.425 230.211 Td[(cdfr)1(e)-1(e)]TJ +/F8 9.963 Tf 133.425 230.211 Td[(cdall)]TJ ET -1 0 0 1 159.19 230.211 cm +1 0 0 1 153.904 230.211 cm 0 g 0 G -1 0 0 1 -159.19 -230.211 cm +1 0 0 1 -153.904 -230.211 cm BT -/F8 9.963 Tf 164.375 230.211 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ +/F8 9.963 Tf 156.626 230.211 Td[(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ ET 1 0 0 1 433.644 230.211 cm 0 g 0 G 1 0 0 1 -433.644 -230.211 cm BT -/F8 9.963 Tf 433.644 230.211 Td[(52)]TJ +/F8 9.963 Tf 433.644 230.211 Td[(46)]TJ ET 1 0 0 1 443.606 230.211 cm 0 g 0 G @@ -1421,11 +1400,11 @@ S Q 1 0 0 1 -130.436 -218.002 cm BT -/F8 9.963 Tf 133.425 218.002 Td[(cdin)1(s)]TJ +/F8 9.963 Tf 133.425 218.002 Td[(cdasb)]TJ ET -1 0 0 1 155.62 218.002 cm +1 0 0 1 157.834 218.002 cm 0 g 0 G -1 0 0 1 -155.62 -218.002 cm +1 0 0 1 -157.834 -218.002 cm BT /F8 9.963 Tf 164.375 218.002 Td[(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-499(.)]TJ ET @@ -1433,7 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Td[(A)-384(list)-384(of)-384(th)1(e)-385(h)1(alo)-384(and)-384(b)-27(oun)1(dar)1(y)-384(e)-1(l)1(e)-1(me)-1(n)29(ts)-385(f)1(or)-384(the)-384(c)-1(u)1(rren)28(t)-384(p)1(ro)-28(ce)-1(ss)]TJ -32.255 -11.955 Td[(to)-347(b)-27(e)-348(exc)27(h)1(anged)-347(with)-346(other)-347(p)1(ro)-28(ce)-1(ss)-1(es;)-354(for)-346(e)-1(ac)28(h)-347(pr)1(o)-28(ce)-1(ss)-1(es)-348(with)-346(whic)28(h)-347(it)-347(is)]TJ 0 -11.956 Td[(nece)-1(ss)-1(ar)1(y)-333(to)-334(comm)27(u)1(nicate:)]TJ -ET -1 0 0 1 175.611 453.576 cm -0 g 0 G -1 0 0 1 -175.611 -453.576 cm +1 0 0 1 -184.912 -343.891 cm BT -/F8 9.963 Tf 184.799 453.576 Td[(1.)]TJ +/F29 9.963 Tf 188.349 343.891 Td[(data)]TJ ET -1 0 0 1 192.548 453.576 cm +1 0 0 1 210.308 343.891 cm 0 g 0 G -1 0 0 1 -192.548 -453.576 cm +1 0 0 1 -210.308 -343.891 cm BT -/F8 9.963 Tf 197.529 453.576 Td[(Pr)1(o)-28(ce)-1(ss)-334(id)1(e)-1(n)28(t)1(i\014er;)]TJ +/F8 9.963 Tf 215.29 343.891 Td[(in)1(c)-1(l)1(udes)-223(general)-222(i)1(nf)1(ormation)-222(ab)-27(out)-222(matri)1(x)-222(and)-222(BLA)28(CS)-222(gri)1(d.)-407(Mor)1(e)]TJ -39.679 -11.956 Td[(pr)1(e)-1(cise)-1(l)1(y:)]TJ ET -1 0 0 1 175.611 437.138 cm +1 0 0 1 170.63 310.15 cm 0 g 0 G -1 0 0 1 -175.611 -437.138 cm +1 0 0 1 -170.63 -310.15 cm BT -/F8 9.963 Tf 184.799 437.138 Td[(2.)]TJ +/F29 9.963 Tf 175.611 310.15 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 192.548 437.138 cm -0 g 0 G -1 0 0 1 -192.548 -437.138 cm +1 0 0 1 209.819 310.15 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -209.819 -310.15 cm BT -/F8 9.963 Tf 197.529 437.138 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(p)-27(oin)29(ts)-334(to)-333(b)-28(e)-333(rec)-1(eiv)28(ed;)]TJ +/F29 9.963 Tf 213.256 310.15 Td[(data[psb)]TJ ET -1 0 0 1 175.611 420.699 cm -0 g 0 G -1 0 0 1 -175.611 -420.699 cm +1 0 0 1 256.334 310.15 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -256.334 -310.15 cm BT -/F8 9.963 Tf 184.799 420.699 Td[(3.)]TJ +/F29 9.963 Tf 259.771 310.15 Td[(dec)]TJ ET -1 0 0 1 192.548 420.699 cm -0 g 0 G -1 0 0 1 -192.548 -420.699 cm +1 0 0 1 277.167 310.15 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -277.167 -310.15 cm BT -/F8 9.963 Tf 197.529 420.699 Td[(Ind)1(ice)-1(s)-334(of)-332(p)-28(oin)29(ts)-334(to)-333(b)-27(e)-334(rec)-1(eiv)28(ed;)]TJ +/F29 9.963 Tf 280.604 310.15 Td[(t)32(yp)-32(e)]TJ ET -1 0 0 1 175.611 404.261 cm -0 g 0 G -1 0 0 1 -175.611 -404.261 cm +1 0 0 1 303.409 310.15 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -303.409 -310.15 cm BT -/F8 9.963 Tf 184.799 404.261 Td[(4.)]TJ +/F29 9.963 Tf 306.847 310.15 Td[(])]TJ ET -1 0 0 1 192.548 404.261 cm +1 0 0 1 310.029 310.15 cm 0 g 0 G -1 0 0 1 -192.548 -404.261 cm +1 0 0 1 -310.029 -310.15 cm BT -/F8 9.963 Tf 197.529 404.261 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(p)-27(oin)29(ts)-334(to)-333(b)-28(e)-333(s)-1(en)28(t;)]TJ +/F8 9.963 Tf 315.01 310.15 Td[(Iden)28(ti\014)1(es)-223(the)-222(dec)-1(omp)-27(os)-1(i)1(tion)-222(t)28(yp)-27(e)-223(\050)1(global)1(\051;)]TJ -117.481 -11.955 Td[(th)1(e)-356(ac)-1(t)1(ual)-355(v)56(alues)-356(ar)1(e)-356(in)28(t)1(e)-1(rn)1(ally)-355(d)1(e)-1(\014)1(ned,)-360(s)-1(o)-355(th)1(e)-1(y)-355(shou)1(ld)-355(n)1(e)-1(v)28(er)-355(b)-28(e)-355(ac)-1(-)]TJ 0 -11.956 Td[(ce)-1(ss)-1(ed)-333(di)1(rec)-1(tl)1(y)83(.)]TJ ET -1 0 0 1 175.611 387.823 cm +1 0 0 1 170.63 269.369 cm 0 g 0 G -1 0 0 1 -175.611 -387.823 cm +1 0 0 1 -170.63 -269.369 cm BT -/F8 9.963 Tf 184.799 387.823 Td[(5.)]TJ +/F29 9.963 Tf 175.611 269.369 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 192.548 387.823 cm -0 g 0 G -1 0 0 1 -192.548 -387.823 cm +1 0 0 1 209.819 269.369 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -209.819 -269.369 cm BT -/F8 9.963 Tf 197.529 387.823 Td[(Ind)1(ice)-1(s)-334(of)-332(p)-28(oin)29(ts)-334(to)-333(b)-27(e)-334(s)-1(en)28(t;)]TJ -21.918 -20.922 Td[(The)-313(li)1(s)-1(t)-312(m)-1(a)28(y)-312(c)-1(on)28(t)1(ain)-312(an)-313(ar)1(bitr)1(ary)-312(n)28(um)28(b)-27(e)-1(r)-312(of)-312(group)1(s)-1(;)-319(its)-313(end)-312(is)-313(mark)28(ed)-312(b)28(y)]TJ 0 -11.955 Td[(a)-333(-)-1(1.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(p)-28(oi)1(n)28(ter)-333(to)-334(an)-332(in)28(tege)-1(r)-333(ar)1(ra)28(y)-333(of)-333(ran)1(k)-333(one.)]TJ +/F29 9.963 Tf 213.256 269.369 Td[(data[psb)]TJ ET -1 0 0 1 145.724 322.069 cm -0 g 0 G -1 0 0 1 -145.724 -322.069 cm +1 0 0 1 256.334 269.369 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -256.334 -269.369 cm BT -/F29 9.963 Tf 150.705 322.069 Td[(o)32(vrlap)]TJ +/F29 9.963 Tf 259.771 269.369 Td[(ctxt)]TJ ET -1 0 0 1 182.684 322.069 cm +1 0 0 1 280.508 269.369 cm q []0 d 0 J @@ -4281,83 +4448,125 @@ q 3.437 0.199 l S Q -1 0 0 1 -182.684 -322.069 cm +1 0 0 1 -280.508 -269.369 cm BT -/F29 9.963 Tf 186.122 322.069 Td[(index)]TJ +/F29 9.963 Tf 283.945 269.369 Td[(])]TJ ET -1 0 0 1 213.332 322.069 cm +1 0 0 1 287.128 269.369 cm 0 g 0 G -1 0 0 1 -213.332 -322.069 cm +1 0 0 1 -287.128 -269.369 cm BT -/F8 9.963 Tf 218.313 322.069 Td[(A)-320(list)-320(of)-319(the)-320(o)28(v)28(e)-1(r)1(lap)-320(elem)-1(en)28(ts)-320(for)-319(the)-320(c)-1(u)1(rr)1(e)-1(n)28(t)-319(pro)-27(c)-1(es)-1(s,)-323(or)1(gani)1(z)-1(ed)]TJ -42.702 -11.955 Td[(in)-333(gr)1(oup)1(s)-334(lik)28(e)-333(the)-334(p)1(reviou)1(s)-334(v)28(ec)-1(tor)1(:)]TJ +/F8 9.963 Tf 292.109 269.369 Td[(Com)-1(m)28(un)1(ication)-222(con)28(text)-222(as)-223(r)1(e)-1(tu)1(rn)1(e)-1(d)-222(b)29(y)-222(the)-222(B)-1(LA)28(CS)]TJ -94.58 -11.955 Td[(\050glob)1(al\051.)]TJ ET -1 0 0 1 175.611 289.192 cm +1 0 0 1 170.63 240.543 cm 0 g 0 G -1 0 0 1 -175.611 -289.192 cm +1 0 0 1 -170.63 -240.543 cm BT -/F8 9.963 Tf 184.799 289.192 Td[(1.)]TJ +/F29 9.963 Tf 175.611 240.543 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 192.548 289.192 cm -0 g 0 G -1 0 0 1 -192.548 -289.192 cm +1 0 0 1 209.819 240.543 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -209.819 -240.543 cm BT -/F8 9.963 Tf 197.529 289.192 Td[(Pr)1(o)-28(ce)-1(ss)-334(id)1(e)-1(n)28(t)1(i\014er;)]TJ +/F29 9.963 Tf 213.256 240.543 Td[(data[psb)]TJ ET -1 0 0 1 175.611 272.754 cm -0 g 0 G -1 0 0 1 -175.611 -272.754 cm +1 0 0 1 256.334 240.543 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -256.334 -240.543 cm BT -/F8 9.963 Tf 184.799 272.754 Td[(2.)]TJ +/F29 9.963 Tf 259.771 240.543 Td[(m)]TJ ET -1 0 0 1 192.548 272.754 cm -0 g 0 G -1 0 0 1 -192.548 -272.754 cm +1 0 0 1 270.006 240.543 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -270.006 -240.543 cm BT -/F8 9.963 Tf 197.529 272.754 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(p)-27(oin)29(ts)-334(to)-333(b)-28(e)-333(rec)-1(eiv)28(ed;)]TJ +/F29 9.963 Tf 273.443 240.543 Td[(])]TJ ET -1 0 0 1 175.611 256.316 cm +1 0 0 1 276.626 240.543 cm 0 g 0 G -1 0 0 1 -175.611 -256.316 cm +1 0 0 1 -276.626 -240.543 cm BT -/F8 9.963 Tf 184.799 256.316 Td[(3.)]TJ +/F8 9.963 Tf 281.607 240.543 Td[(T)83(otal)-333(n)28(u)1(m)27(b)-27(er)-333(of)-333(e)-1(q)1(uation)1(s)-334(\050gl)1(obal\051.)]TJ ET -1 0 0 1 192.548 256.316 cm +1 0 0 1 170.63 223.673 cm 0 g 0 G -1 0 0 1 -192.548 -256.316 cm +1 0 0 1 -170.63 -223.673 cm BT -/F8 9.963 Tf 197.529 256.316 Td[(Ind)1(ice)-1(s)-334(of)-332(p)-28(oin)29(ts)-334(to)-333(b)-27(e)-334(rec)-1(eiv)28(ed;)]TJ +/F29 9.963 Tf 175.611 223.673 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 175.611 239.877 cm -0 g 0 G -1 0 0 1 -175.611 -239.877 cm +1 0 0 1 209.819 223.673 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -209.819 -223.673 cm BT -/F8 9.963 Tf 184.799 239.877 Td[(4.)]TJ +/F29 9.963 Tf 213.256 223.673 Td[(data[psb)]TJ ET -1 0 0 1 192.548 239.877 cm -0 g 0 G -1 0 0 1 -192.548 -239.877 cm +1 0 0 1 256.334 223.673 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -256.334 -223.673 cm BT -/F8 9.963 Tf 197.529 239.877 Td[(Num)28(b)-27(e)-1(r)-333(of)-333(p)-27(oin)29(ts)-334(to)-333(b)-28(e)-333(s)-1(en)28(t;)]TJ +/F29 9.963 Tf 259.771 223.673 Td[(n)]TJ ET -1 0 0 1 175.611 223.439 cm -0 g 0 G -1 0 0 1 -175.611 -223.439 cm +1 0 0 1 266.824 223.673 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -266.824 -223.673 cm BT -/F8 9.963 Tf 184.799 223.439 Td[(5.)]TJ +/F29 9.963 Tf 270.261 223.673 Td[(])]TJ ET -1 0 0 1 192.548 223.439 cm +1 0 0 1 273.443 223.673 cm 0 g 0 G -1 0 0 1 -192.548 -223.439 cm +1 0 0 1 -273.443 -223.673 cm BT -/F8 9.963 Tf 197.529 223.439 Td[(Ind)1(ice)-1(s)-334(of)-332(p)-28(oin)29(ts)-334(to)-333(b)-27(e)-334(s)-1(en)28(t;)]TJ -21.918 -20.922 Td[(The)-313(li)1(s)-1(t)-312(m)-1(a)28(y)-312(c)-1(on)28(t)1(ain)-312(an)-313(ar)1(bitr)1(ary)-312(n)28(um)28(b)-27(e)-1(r)-312(of)-312(group)1(s)-1(;)-319(its)-313(end)-312(is)-313(mark)28(ed)-312(b)28(y)]TJ 0 -11.955 Td[(a)-333(-)-1(1.)]TJ 0 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(p)-28(oi)1(n)28(ter)-333(to)-334(an)-332(in)28(tege)-1(r)-333(ar)1(ra)28(y)-333(of)-333(ran)1(k)-333(one.)]TJ +/F8 9.963 Tf 278.424 223.673 Td[(T)83(otal)-333(n)28(u)1(m)27(b)-27(er)-333(of)-333(v)56(ariab)1(le)-1(s)-333(\050glob)1(al\051.)]TJ ET -1 0 0 1 145.724 157.686 cm +1 0 0 1 170.63 206.802 cm 0 g 0 G -1 0 0 1 -145.724 -157.686 cm +1 0 0 1 -170.63 -206.802 cm BT -/F29 9.963 Tf 150.705 157.686 Td[(o)32(vrlap)]TJ +/F29 9.963 Tf 175.611 206.802 Td[(mat)-1(r)1(i)-1(x)]TJ ET -1 0 0 1 182.684 157.686 cm +1 0 0 1 209.819 206.802 cm q []0 d 0 J @@ -4366,119 +4575,167 @@ q 3.437 0.199 l S Q -1 0 0 1 -182.684 -157.686 cm -BT -/F29 9.963 Tf 186.122 157.686 Td[(index)]TJ -ET -1 0 0 1 213.332 157.686 cm -0 g 0 G -1 0 0 1 -213.332 -157.686 cm +1 0 0 1 -209.819 -206.802 cm BT -/F8 9.963 Tf 218.313 157.686 Td[(F)84(or)-333(all)-333(o)28(v)28(e)-1(rl)1(ap)-333(p)-27(oin)28(ts)-334(b)-27(elongi)1(ng)-333(to)-333(th)-333(e)-1(cur)1(ren)28(t)-333(pr)1(o)-28(c)-1(ess)-1(:)]TJ +/F29 9.963 Tf 213.256 206.802 Td[(data[psb)]TJ ET -1 0 0 1 175.611 136.764 cm -0 g 0 G -1 0 0 1 -175.611 -136.764 cm +1 0 0 1 256.334 206.802 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -256.334 -206.802 cm BT -/F8 9.963 Tf 184.799 136.764 Td[(1.)]TJ +/F29 9.963 Tf 259.771 206.802 Td[(n)]TJ ET -1 0 0 1 192.548 136.764 cm -0 g 0 G -1 0 0 1 -192.548 -136.764 cm +1 0 0 1 266.824 206.802 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -266.824 -206.802 cm BT -/F8 9.963 Tf 197.529 136.764 Td[(Ov)28(erlap)-332(p)-28(oin)29(t)-333(ind)1(e)-1(x;)]TJ +/F29 9.963 Tf 270.261 206.802 Td[(ro)32(w)]TJ ET -1 0 0 1 175.611 120.326 cm -0 g 0 G -1 0 0 1 -175.611 -120.326 cm +1 0 0 1 289.351 206.802 cm +q +[]0 d +0 J +0.398 w +0 0.199 m +3.437 0.199 l +S +Q +1 0 0 1 -289.351 -206.802 cm BT -/F8 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14.346 Tf 180.814 680.539 Td[(geax)1(pb)31(y|Ge)-1(neral)-375(Dense)-375(M)-1(a)1(trix)-375(Sum)]TJ/F8 9.963 Tf -30.109 -29.479 Td[(Thi)1(s)-437(subr)1(outi)1(ne)-436(is)-437(an)-435(in)28(terf)1(ac)-1(e)-436(to)-436(the)-436(c)-1(omp)1(utati)1(onal)-436(k)28(ern)1(e)-1(l)-436(f)1(or)-436(dense)-436(m)-1(atr)1(ix)]TJ 0 -11.955 Td[(sum:)]TJ/F11 9.963 Tf 142.537 -11.955 Td[(y)]TJ/F14 9.963 Tf 8.009 0 Td[(\040)]TJ/F11 9.963 Tf 12.73 0 Td[(\013)-226(x)]TJ/F8 9.963 Tf 16.532 0 Td[(+)]TJ/F11 9.963 Tf 9.963 0 Td[(\014)-52(y)]TJ/F18 14.346 Tf -189.771 -32.879 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 66.835 -21.821 Td[(call)-333(psb)]TJ ET -1 0 0 1 260.42 430.22 cm +1 0 0 1 251.401 572.451 cm q []0 d 0 J @@ -5440,11 +6397,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -260.42 -430.22 cm +1 0 0 1 -251.401 -572.451 cm BT -/F8 9.963 Tf 263.409 430.22 Td[(gedot)-333(\050)]TJ/F19 9.963 Tf 30.995 0 Td[(x,)-357(y,)-357(desc)]TJ +/F8 9.963 Tf 254.39 572.451 Td[(geaxpb)29(y)-334(\050)]TJ/F19 9.963 Tf 42.895 0 Td[(alpha,)-357(x,)-358(b)52(et)-1(a,)-357(y,)-357(desc)]TJ ET -1 0 0 1 336.044 430.22 cm +1 0 0 1 392.137 572.451 cm q []0 d 0 J @@ -5453,42 +6410,42 @@ q 3.055 0.199 l S Q -1 0 0 1 -336.044 -430.22 cm +1 0 0 1 -392.137 -572.451 cm BT -/F19 9.963 Tf 339.1 430.22 Td[(a,)-357(info,)-357(jx,)-357(jy)]TJ/F8 9.963 Tf 57.323 0 Td[(\051)]TJ +/F19 9.963 Tf 395.192 572.451 Td[(a,)-357(info)]TJ/F8 9.963 Tf 28.515 0 Td[(\051)]TJ ET -1 0 0 1 150.705 403.557 cm +1 0 0 1 150.705 546.206 cm 0 g 0 G -1 0 0 1 79.839 -21.021 cm +1 0 0 1 74.163 -21.021 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.982 20.623 cm +1 0 0 1 4.981 20.622 cm q []0 d 0 J 0.398 w 0 0.199 m -174.069 0.199 l +185.423 0.199 l S Q -1 0 0 1 -235.526 -403.159 cm +1 0 0 1 -229.849 -545.807 cm BT -/F11 9.963 Tf 241.503 394.79 Td[(dot)]TJ/F8 9.963 Tf 13.612 0 Td[(,)]TJ/F11 9.963 Tf 6.089 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(,)]TJ/F11 9.963 Tf 6.088 0 Td[(y)]TJ/F29 9.963 Tf 86.824 0 Td[(F)96(un)1(c)-1(tion)]TJ +/F11 9.963 Tf 235.827 537.439 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(,)]TJ/F11 9.963 Tf 6.088 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(,)]TJ/F11 9.963 Tf 6.088 0 Td[(\013)]TJ/F8 9.963 Tf 6.41 0 Td[(,)]TJ/F11 9.963 Tf 6.088 0 Td[(\014)]TJ/F29 9.963 Tf 82.696 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 235.526 390.805 cm +1 0 0 1 229.849 533.454 cm q []0 d 0 J 0.398 w 0 0.199 m -174.069 0.199 l +185.423 0.199 l S Q -1 0 0 1 -235.526 -390.805 cm +1 0 0 1 -229.849 -533.454 cm BT -/F8 9.963 Tf 241.503 382.436 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ +/F8 9.963 Tf 235.827 525.085 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ ET -1 0 0 1 375.407 382.436 cm +1 0 0 1 369.73 525.085 cm q []0 d 0 J @@ -5497,11 +6454,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -375.407 -382.436 cm +1 0 0 1 -369.73 -525.085 cm BT -/F8 9.963 Tf 378.396 382.436 Td[(gedot)]TJ -136.893 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ +/F8 9.963 Tf 372.719 525.085 Td[(geaxpb)29(y)]TJ -136.892 -11.955 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ ET -1 0 0 1 375.407 370.481 cm +1 0 0 1 369.73 513.13 cm q []0 d 0 J @@ -5510,136 +6467,195 @@ q 2.989 0.199 l S Q -1 0 0 1 -375.407 -370.481 cm +1 0 0 1 -369.73 -513.13 cm BT -/F8 9.963 Tf 378.396 370.481 Td[(gedot)]TJ +/F8 9.963 Tf 372.719 513.13 Td[(geaxpb)29(y)]TJ ET -1 0 0 1 235.526 366.496 cm +1 0 0 1 229.849 509.145 cm q []0 d 0 J 0.398 w 0 0.199 m -174.069 0.199 l +185.423 0.199 l S Q -1 0 0 1 43.351 -27.84 cm +1 0 0 1 49.028 -27.84 cm 0 g 0 G -1 0 0 1 -278.877 -338.656 cm +1 0 0 1 -278.877 -481.305 cm BT -/F8 9.963 Tf 278.877 338.656 Td[(T)83(ab)1(le)-334(2:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ +/F8 9.963 Tf 278.877 481.305 Td[(T)83(ab)1(le)-334(1:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ ET -1 0 0 1 366.244 338.656 cm +1 0 0 1 366.244 481.305 cm 0 g 0 G 1 0 0 1 -215.539 -1.937 cm 0 g 0 G -1 0 0 1 -4.981 -32.036 cm +1 0 0 1 -4.981 -30.835 cm 0 g 0 G -1 0 0 1 -145.724 -304.683 cm +1 0 0 1 -145.724 -448.533 cm BT -/F29 9.963 Tf 150.705 304.683 Td[(On)-383(En)33(t)-1(r)1(y)]TJ +/F29 9.963 Tf 150.705 448.533 Td[(On)-383(En)33(t)-1(r)1(y)]TJ ET -1 0 0 1 198.29 304.683 cm +1 0 0 1 198.29 448.533 cm 0 g 0 G -1 0 0 1 -52.566 -20.447 cm +1 0 0 1 -52.566 -19.769 cm 0 g 0 G -1 0 0 1 -145.724 -284.236 cm +1 0 0 1 -145.724 -428.764 cm BT -/F29 9.963 Tf 150.705 284.236 Td[(x)]TJ +/F29 9.963 Tf 150.705 428.764 Td[(alpha)]TJ ET -1 0 0 1 156.752 284.236 cm +1 0 0 1 177.756 428.764 cm 0 g 0 G -1 0 0 1 -156.752 -284.236 cm +1 0 0 1 -177.756 -428.764 cm BT -/F8 9.963 Tf 161.733 284.236 Td[(th)1(e)-331(lo)-28(cal)-330(p)-27(ortion)-330(of)-329(global)-330(d)1(e)-1(n)1(s)-1(e)-330(m)-1(atr)1(ix)]TJ/F11 9.963 Tf 175.908 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)-443(This)-330(fun)1(ction)-330(com)-1(p)1(utes)-331(th)1(e)-331(lo)-27(c)-1(a-)]TJ -167.723 -11.956 Td[(tion)-339(of)-340(th)1(e)-341(\014)1(rst)-340(e)-1(l)1(e)-1(men)28(t)-340(of)-340(l)1(o)-28(c)-1(al)-339(s)-1(u)1(barr)1(a)28(y)-340(use)-1(d)1(,)-342(b)1(as)-1(ed)-340(on)]TJ/F11 9.963 Tf 250.121 0 Td[(j)-57(x)]TJ/F8 9.963 Tf 13.755 0 Td[(and)-339(th)1(e)-341(\014)1(e)-1(ld)]TJ/F11 9.963 Tf -263.876 -11.955 Td[(matr)-28(i)1(x)]TJ +/F8 9.963 Tf 182.737 428.764 Td[(th)1(e)-334(s)-1(calar)]TJ/F11 9.963 Tf 45.469 0 Td[(\013)]TJ/F8 9.963 Tf 6.41 0 Td[(.)]TJ -59.005 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(n)28(um)28(b)-27(e)-1(r)-333(of)-333(th)1(e)-334(d)1(ata)-334(t)28(y)1(p)-28(e)-333(ind)1(ic)-1(at)1(e)-1(d)-333(i)1(n)-333(T)83(abl)1(e)]TJ ET -1 0 0 1 207.718 260.325 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -2.989 0.199 l -S -Q -1 0 0 1 -207.718 -260.325 cm +1 0 0 1 433.893 392.898 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -433.893 -392.898 cm +BT +/F8 9.963 Tf 433.893 392.898 Td[(1)]TJ +ET +1 0 0 1 438.875 392.898 cm +0 g 0 G +1 0 0 1 -438.875 -392.898 cm +BT +/F8 9.963 Tf 438.875 392.898 Td[(.)]TJ +ET +1 0 0 1 145.724 373.129 cm +0 g 0 G +1 0 0 1 -145.724 -373.129 cm +BT +/F29 9.963 Tf 150.705 373.129 Td[(x)]TJ +ET +1 0 0 1 156.752 373.129 cm +0 g 0 G +1 0 0 1 -156.752 -373.129 cm +BT +/F8 9.963 Tf 161.733 373.129 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(o)1(rtion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -167.934 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-363(as:)-503(a)-363(ran)1(k)-363(on)1(e)-364(or)-362(t)28(w)27(o)-362(arra)28(y)-363(wi)1(th)-363(th)1(e)-363(POINTE)1(R)-363(attri)1(but)1(e)-364(con-)]TJ 0 -11.956 Td[(tain)1(ing)-356(n)28(um)28(b)-28(ers)-357(of)-357(t)28(y)1(p)-28(e)-357(s)-1(p)-27(ec)-1(i\014)1(e)-1(d)-356(in)-356(T)83(abl)1(e)]TJ +ET +1 0 0 1 364.199 325.308 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -364.199 -325.308 cm +BT +/F8 9.963 Tf 364.199 325.308 Td[(1)]TJ +ET +1 0 0 1 369.18 325.308 cm +0 g 0 G +1 0 0 1 -369.18 -325.308 cm +BT +/F8 9.963 Tf 369.18 325.308 Td[(.)-515(The)-357(ran)1(k)-357(of)]TJ/F11 9.963 Tf 63.432 0 Td[(x)]TJ/F8 9.963 Tf 9.25 0 Td[(m)27(u)1(s)-1(t)-356(b)-28(e)-357(th)1(e)]TJ -266.251 -11.955 Td[(sam)-1(e)-334(of)]TJ/F11 9.963 Tf 36.309 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ +ET +1 0 0 1 145.724 293.584 cm +0 g 0 G +1 0 0 1 -145.724 -293.584 cm BT -/F11 9.963 Tf 210.707 260.325 Td[(data)]TJ/F8 9.963 Tf 22.636 0 Td[(of)]TJ/F11 9.963 Tf 11.346 0 Td[(d)-1(e)1(sc)]TJ +/F29 9.963 Tf 150.705 293.584 Td[(b)-32(eta)]TJ ET -1 0 0 1 264.093 260.325 cm +1 0 0 1 172.664 293.584 cm +0 g 0 G +1 0 0 1 -172.664 -293.584 cm +BT +/F8 9.963 Tf 177.645 293.584 Td[(th)1(e)-334(s)-1(calar)]TJ/F11 9.963 Tf 45.469 0 Td[(\014)]TJ/F8 9.963 Tf 6.161 0 Td[(.)]TJ -53.664 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(n)28(um)28(b)-27(e)-1(r)-333(of)-333(th)1(e)-334(d)1(ata)-334(t)28(y)1(p)-28(e)-333(ind)1(ic)-1(at)1(e)-1(d)-333(i)1(n)-333(T)83(abl)1(e)]TJ +ET +1 0 0 1 433.893 257.719 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -433.893 -257.719 cm +BT +/F8 9.963 Tf 433.893 257.719 Td[(1)]TJ +ET +1 0 0 1 438.875 257.719 cm +0 g 0 G +1 0 0 1 -438.875 -257.719 cm +BT +/F8 9.963 Tf 438.875 257.719 Td[(.)]TJ +ET +1 0 0 1 145.724 237.95 cm +0 g 0 G +1 0 0 1 -145.724 -237.95 cm +BT +/F29 9.963 Tf 150.705 237.95 Td[(y)]TJ +ET +1 0 0 1 156.752 237.95 cm +0 g 0 G +1 0 0 1 -156.752 -237.95 cm +BT +/F8 9.963 Tf 161.733 237.95 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(o)1(rtion)-333(of)-332(the)-334(gl)1(obal)-333(dense)-334(matri)1(x)]TJ/F11 9.963 Tf 193.276 0 Td[(y)]TJ/F8 9.963 Tf 5.241 0 Td[(.)]TJ -184.639 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-393(as:)-564(a)-393(ran)1(k)-393(one)-393(or)-393(t)28(w)28(o)-393(arra)28(y)-393(wit)1(h)-393(th)1(e)-394(PO)1(INT)-1(E)1(R)-393(attri)1(bu)1(te)-1(con-)]TJ 0 -11.955 Td[(tain)1(ing)-341(n)29(um)28(b)-28(ers)-341(of)-341(th)1(e)-342(t)28(yp)-27(e)-341(ind)1(icate)-1(d)-340(in)-341(T)83(ab)1(le)]TJ +ET +1 0 0 1 383.313 190.129 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -383.313 -190.129 cm +BT +/F8 9.963 Tf 383.313 190.129 Td[(1)]TJ +ET +1 0 0 1 388.294 190.129 cm +0 g 0 G +1 0 0 1 -388.294 -190.129 cm +BT +/F8 9.963 Tf 388.294 190.129 Td[(.)-467(T)-1(h)1(e)-342(r)1(ank)-341(of)]TJ/F11 9.963 Tf 62.48 0 Td[(y)]TJ/F8 9.963 Tf 8.64 0 Td[(m)27(u)1(s)-1(t)-340(b)-28(e)]TJ -283.803 -11.955 Td[(th)1(e)-334(s)-1(ame)-334(of)]TJ/F11 9.963 Tf 53.467 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ +ET +1 0 0 1 145.724 158.405 cm +0 g 0 G +1 0 0 1 -145.724 -158.405 cm +BT +/F29 9.963 Tf 150.705 158.405 Td[(desc)]TJ +ET +1 0 0 1 172.619 158.405 cm q []0 d 0 J 0.398 w 0 0.199 m -2.989 0.199 l +3.437 0.199 l S Q -1 0 0 1 -264.093 -260.325 cm -BT -/F11 9.963 Tf 267.082 260.325 Td[(a)]TJ/F8 9.963 Tf 8.587 0 Td[(.)]TJ -100.058 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 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9.963 Tf 6.276 -4.113 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(\050:)]TJ/F11 9.963 Tf 6.642 0 Td[(;)-166(i)]TJ/F8 9.963 Tf 7.86 0 Td[(\051)]TJ -215.343 -19.079 Td[(If)-245(t)1(he)-245(m)-1(at)1(rice)-1(s)-245(are)-245(com)-1(p)1(lex,)-263(t)1(hen)-245(th)1(e)-246(u)1(s)-1(u)1(al)-245(con)28(v)28(en)28(tion)-244(app)1(lies)-1(,)-262(i.e.)-415(th)1(e)-245(c)-1(on)1(jugat)1(e)]TJ 0 -11.955 Td[(tran)1(sp)-28(ose)-324(of)]TJ/F11 9.963 Tf 55.836 0 Td[(x)]TJ/F8 9.963 Tf 8.913 0 Td[(is)-323(use)-1(d)1(.)-441(If)]TJ/F11 9.963 Tf 46.365 0 Td[(x)]TJ/F8 9.963 Tf 8.913 0 Td[(and)]TJ/F11 9.963 Tf 19.27 0 Td[(y)]TJ/F8 9.963 Tf 8.461 0 Td[(are)-323(of)-323(r)1(ank)-323(on)1(e)-1(,)-325(th)1(e)-1(n)]TJ/F11 9.963 Tf 94.211 0 Td[(r)-28(es)]TJ/F8 9.963 Tf 17.3 0 Td[(is)-323(a)-323(s)-1(calar,)-324(e)-1(lse)-324(i)1(t)-323(is)]TJ -259.269 -11.956 Td[(a)-333(ran)1(k)-334(on)1(e)-334(ar)1(ra)28(y)83(.)]TJ/F18 14.346 Tf 0 -34.973 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 99.039 -22.15 Td[(psb)]TJ ET -1 0 0 1 268.839 463.837 cm +1 0 0 1 265.341 522.262 cm q []0 d 0 J @@ -6329,11 +7234,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -268.839 -463.837 cm +1 0 0 1 -265.341 -522.262 cm BT -/F8 9.963 Tf 271.828 463.837 Td[(geam)-1(ax)-333(\050)]TJ/F19 9.963 Tf 40.127 0 Td[(x,)-357(desc)]TJ +/F8 9.963 Tf 268.33 522.262 Td[(gedot)-333(\050)]TJ/F19 9.963 Tf 30.995 0 Td[(r)52(es,)-358(x,)-357(y,)-357(desc)]TJ ET -1 0 0 1 342.138 463.837 cm +1 0 0 1 359.932 522.262 cm q []0 d 0 J @@ -6342,42 +7247,42 @@ q 3.055 0.199 l S Q -1 0 0 1 -342.138 -463.837 cm +1 0 0 1 -359.932 -522.262 cm BT -/F19 9.963 Tf 345.193 463.837 Td[(a,)-358(i)1(nfo,)-358(j)1(x)]TJ/F8 9.963 Tf 42.812 0 Td[(\051)]TJ +/F19 9.963 Tf 362.988 522.262 Td[(a,)-357(info)]TJ/F8 9.963 Tf 28.515 0 Td[(\051)]TJ ET -1 0 0 1 150.705 438.537 cm +1 0 0 1 150.705 495.097 cm 0 g 0 G -1 0 0 1 26.309 -21.021 cm +1 0 0 1 74.163 -21.021 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.982 20.622 cm +1 0 0 1 4.981 20.623 cm q []0 d 0 J 0.398 w 0 0.199 m -281.13 0.199 l +185.423 0.199 l S Q -1 0 0 1 -181.996 -438.138 cm +1 0 0 1 -229.849 -494.699 cm BT -/F11 9.963 Tf 187.973 429.77 Td[(ama)1(x)-7465(x)]TJ/F29 9.963 Tf 217.657 0 Td[(F)96(un)1(c)-1(tion)]TJ +/F11 9.963 Tf 235.827 486.33 Td[(r)-28(e)1(s)]TJ/F8 9.963 Tf 14.08 0 Td[(,)]TJ/F11 9.963 Tf 6.088 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(,)]TJ/F11 9.963 Tf 6.088 0 Td[(y)]TJ/F29 9.963 Tf 86.356 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 181.996 425.785 cm +1 0 0 1 229.849 482.345 cm q []0 d 0 J 0.398 w 0 0.199 m -281.13 0.199 l +185.423 0.199 l S Q -1 0 0 1 -181.996 -425.785 cm +1 0 0 1 -229.849 -482.345 cm BT -/F8 9.963 Tf 187.973 417.416 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(sb)]TJ +/F8 9.963 Tf 235.827 473.976 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ ET -1 0 0 1 421.227 417.416 cm +1 0 0 1 369.73 473.976 cm q []0 d 0 J @@ -6386,11 +7291,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -421.227 -417.416 cm +1 0 0 1 -369.73 -473.976 cm BT -/F8 9.963 Tf 424.215 417.416 Td[(geam)-1(ax)]TJ -236.242 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(sb)]TJ +/F8 9.963 Tf 372.719 473.976 Td[(gedot)]TJ -136.892 -11.955 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ ET -1 0 0 1 421.227 405.461 cm +1 0 0 1 369.73 462.021 cm q []0 d 0 J @@ -6399,94 +7304,92 @@ q 2.989 0.199 l S Q -1 0 0 1 -421.227 -405.461 cm +1 0 0 1 -369.73 -462.021 cm BT -/F8 9.963 Tf 424.215 405.461 Td[(geam)-1(ax)]TJ +/F8 9.963 Tf 372.719 462.021 Td[(gedot)]TJ ET -1 0 0 1 181.996 401.476 cm +1 0 0 1 229.849 458.036 cm q []0 d 0 J 0.398 w 0 0.199 m -281.13 0.199 l +185.423 0.199 l S Q -1 0 0 1 96.881 -27.84 cm +1 0 0 1 49.028 -27.84 cm 0 g 0 G -1 0 0 1 -278.877 -373.636 cm +1 0 0 1 -278.877 -430.196 cm BT -/F8 9.963 Tf 278.877 373.636 Td[(T)83(ab)1(le)-334(4:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ +/F8 9.963 Tf 278.877 430.196 Td[(T)83(ab)1(le)-334(3:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ ET -1 0 0 1 366.244 373.636 cm +1 0 0 1 366.244 430.196 cm 0 g 0 G 1 0 0 1 -215.539 -1.937 cm 0 g 0 G -1 0 0 1 -4.981 -27.529 cm +1 0 0 1 -4.981 -33.293 cm 0 g 0 G -1 0 0 1 -145.724 -344.17 cm +1 0 0 1 -145.724 -394.966 cm BT -/F29 9.963 Tf 150.705 344.17 Td[(On)-383(En)33(t)-1(r)1(y)]TJ +/F29 9.963 Tf 150.705 394.966 Td[(On)-383(En)33(t)-1(r)1(y)]TJ ET -1 0 0 1 198.29 344.17 cm +1 0 0 1 198.29 394.966 cm 0 g 0 G -1 0 0 1 -52.566 -18.824 cm +1 0 0 1 -52.566 -21.453 cm 0 g 0 G -1 0 0 1 -145.724 -325.346 cm +1 0 0 1 -145.724 -373.513 cm BT -/F29 9.963 Tf 150.705 325.346 Td[(x)]TJ +/F29 9.963 Tf 150.705 373.513 Td[(x)]TJ ET -1 0 0 1 156.752 325.346 cm +1 0 0 1 156.752 373.513 cm 0 g 0 G -1 0 0 1 -156.752 -325.346 cm +1 0 0 1 -156.752 -373.513 cm BT -/F8 9.963 Tf 161.733 325.346 Td[(th)1(e)-331(lo)-28(cal)-330(p)-27(ortion)-330(of)-329(global)-330(d)1(e)-1(n)1(s)-1(e)-330(m)-1(atr)1(ix)]TJ/F11 9.963 Tf 175.908 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)-443(This)-330(fun)1(ction)-330(com)-1(p)1(utes)-331(th)1(e)-331(lo)-27(c)-1(a-)]TJ -167.723 -11.955 Td[(tion)-339(of)-340(th)1(e)-341(\014)1(rst)-340(e)-1(l)1(e)-1(men)28(t)-340(of)-340(l)1(o)-28(c)-1(al)-339(s)-1(u)1(barr)1(a)28(y)-340(use)-1(d)1(,)-342(b)1(as)-1(ed)-340(on)]TJ/F11 9.963 Tf 250.121 0 Td[(j)-57(x)]TJ/F8 9.963 Tf 13.755 0 Td[(and)-339(th)1(e)-341(\014)1(e)-1(ld)]TJ/F11 9.963 Tf -263.876 -11.955 Td[(matr)-28(i)1(x)]TJ +/F8 9.963 Tf 161.733 373.513 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(o)1(rtion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -167.934 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-331(as)-1(:)-443(a)-331(p)-27(oin)28(t)1(e)-1(r)-331(t)1(o)-332(ar)1(ra)28(y)-331(of)-331(r)1(ank)-331(on)1(e)-332(or)-330(t)28(w)27(o)-331(con)28(tain)1(ing)-331(n)29(um)28(b)-28(ers)-331(of)]TJ 0 -11.955 Td[(t)28(yp)-27(e)-334(sp)-28(ec)-1(i)1(\014ed)-333(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 207.718 301.436 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -2.989 0.199 l -S -Q -1 0 0 1 -207.718 -301.436 cm +1 0 0 1 277.231 325.692 cm +0 0 1 rg 0 0 1 RG +1 0 0 1 -277.231 -325.692 cm BT -/F11 9.963 Tf 210.707 301.436 Td[(data)]TJ/F8 9.963 Tf 22.636 0 Td[(of)]TJ/F11 9.963 Tf 11.346 0 Td[(d)-1(e)1(sc)]TJ +/F8 9.963 Tf 277.231 325.692 Td[(3)]TJ ET -1 0 0 1 264.093 301.436 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -2.989 0.199 l -S -Q -1 0 0 1 -264.093 -301.436 cm +1 0 0 1 282.212 325.692 cm +0 g 0 G +1 0 0 1 -282.212 -325.692 cm +BT +/F8 9.963 Tf 282.212 325.692 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.017 0 Td[(x)]TJ/F8 9.963 Tf 9.015 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.712 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ +ET +1 0 0 1 145.724 304.238 cm +0 g 0 G +1 0 0 1 -145.724 -304.238 cm BT -/F11 9.963 Tf 267.082 301.436 Td[(a)]TJ/F8 9.963 Tf 8.587 0 Td[(.)]TJ -100.058 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-363(as:)-503(a)-363(ran)1(k)-363(on)1(e)-364(or)-362(t)28(w)27(o)-362(arra)28(y)-363(wi)1(th)-363(th)1(e)-363(POINTE)1(R)-363(attri)1(but)1(e)-364(con-)]TJ 0 -11.955 Td[(tain)1(ing)-333(n)28(u)1(m)27(b)-27(ers)-334(of)-333(t)28(yp)-27(e)-334(sp)-27(e)-1(ci\014ed)-333(in)-332(T)83(able)]TJ +/F29 9.963 Tf 150.705 304.238 Td[(y)]TJ +ET +1 0 0 1 156.752 304.238 cm +0 g 0 G +1 0 0 1 -156.752 -304.238 cm +BT +/F8 9.963 Tf 161.733 304.238 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(o)1(rtion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(y)]TJ/F8 9.963 Tf 5.242 0 Td[(.)]TJ -167.482 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-331(as)-1(:)-443(a)-331(p)-27(oin)28(t)1(e)-1(r)-331(t)1(o)-332(ar)1(ra)28(y)-331(of)-331(r)1(ank)-331(on)1(e)-332(or)-330(t)28(w)27(o)-331(con)28(tain)1(ing)-331(n)29(um)28(b)-28(ers)-331(of)]TJ 0 -11.955 Td[(t)28(yp)-27(e)-334(sp)-28(ec)-1(i)1(\014ed)-333(in)-333(T)83(ab)1(le)]TJ ET -1 0 0 1 362.55 253.615 cm +1 0 0 1 277.231 256.418 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -362.55 -253.615 cm +1 0 0 1 -277.231 -256.418 cm BT -/F8 9.963 Tf 362.55 253.615 Td[(4)]TJ +/F8 9.963 Tf 277.231 256.418 Td[(3)]TJ ET -1 0 0 1 367.531 253.615 cm +1 0 0 1 282.212 256.418 cm 0 g 0 G -1 0 0 1 -367.531 -253.615 cm +1 0 0 1 -282.212 -256.418 cm BT -/F8 9.963 Tf 367.531 253.615 Td[(.)]TJ +/F8 9.963 Tf 282.212 256.418 Td[(.)-444(The)-334(r)1(ank)-333(of)]TJ/F11 9.963 Tf 62.017 0 Td[(y)]TJ/F8 9.963 Tf 8.563 0 Td[(m)27(u)1(s)-1(t)-333(b)-27(e)-334(th)1(e)-334(sam)-1(e)-333(of)]TJ/F11 9.963 Tf 91.712 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ ET -1 0 0 1 145.724 234.791 cm +1 0 0 1 145.724 234.964 cm 0 g 0 G -1 0 0 1 -145.724 -234.791 cm +1 0 0 1 -145.724 -234.964 cm BT -/F29 9.963 Tf 150.705 234.791 Td[(desc)]TJ +/F29 9.963 Tf 150.705 234.964 Td[(desc)]TJ ET -1 0 0 1 172.619 234.791 cm +1 0 0 1 172.619 234.964 cm q []0 d 0 J @@ -6495,23 +7398,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -172.619 -234.791 cm +1 0 0 1 -172.619 -234.964 cm BT -/F29 9.963 Tf 176.057 234.791 Td[(a)]TJ +/F29 9.963 Tf 176.057 234.964 Td[(a)]TJ ET -1 0 0 1 181.626 234.791 cm +1 0 0 1 181.626 234.964 cm 0 g 0 G -1 0 0 1 -181.626 -234.791 cm +1 0 0 1 -181.626 -234.964 cm BT -/F8 9.963 Tf 186.607 234.791 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Td[(repr)1(e)-1(se)-1(n)29(ts)-334(th)1(e)-334(glob)1(al)-333(s)-1(u)1(b)28(v)28(e)-1(ctor)]TJ/F11 9.963 Tf 138.065 0 Td[(x)]TJ/F7 6.974 Tf 5.694 -1.494 Td[(:)]TJ/F10 6.974 Tf 2.256 0 Td[(;j)-58(x)]TJ/F18 14.346 Tf -156.691 -31.094 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 110.073 -21.821 Td[(psb)]TJ -ET -1 0 0 1 225.565 489.772 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -2.989 0.199 l -S -Q -1 0 0 1 -225.565 -489.772 cm -BT -/F8 9.963 Tf 228.554 489.772 Td[(geas)-1(u)1(m)-334(\050)]TJ/F19 9.963 Tf 39.352 0 Td[(x,)-357(desc)]TJ -ET -1 0 0 1 298.089 489.772 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -3.055 0.199 l -S -Q -1 0 0 1 -298.089 -489.772 cm +1 0 0 1 -125.163 -680.226 cm BT -/F19 9.963 Tf 301.145 489.772 Td[(a,)-357(info)]TJ/F8 9.963 Tf 28.515 0 Td[(\051)]TJ -126.84 -23.91 Td[(psb)]TJ +/F18 14.346 Tf 130.004 680.226 Td[(geam)1(ax|Gene)-1(rali)1(ze)-1(d)-375(In\014ni)1(t)32(y)-375(No)1(r)-1(m)]TJ/F8 9.963 Tf -30.109 -29.791 Td[(This)-359(s)-1(u)1(br)1(outi)1(ne)-360(compu)1(te)-1(s)-359(a)-359(s)-1(eries)-360(of)-358(in\014)1(nit)28(y)-359(n)1(orms)-360(on)-358(the)-359(c)-1(olu)1(mns)-360(of)-358(a)-359(dense)]TJ 0 -11.955 Td[(matrix)]TJ/F11 9.963 Tf 32.407 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(:)]TJ/F11 9.963 Tf 87.106 -11.955 Td[(r)-28(es)]TJ/F8 9.963 Tf 14.08 0 Td[(\050)]TJ/F11 9.963 Tf 3.874 0 Td[(i)]TJ/F8 9.963 Tf 3.433 0 Td[(\051)]TJ/F14 9.963 Tf 6.641 0 Td[(\040)]TJ/F8 9.963 Tf 12.73 0 Td[(max)]TJ/F10 6.974 Tf 7.069 -6.504 Td[(k)]TJ/F14 9.963 Tf 13.133 6.504 Td[(j)]TJ/F11 9.963 Tf 2.768 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(\050)]TJ/F11 9.963 Tf 3.874 0 Td[(k)-31(;)-167(i)]TJ/F8 9.963 Tf 13.36 0 Td[(\051)]TJ/F14 9.963 Tf 3.875 0 Td[(j)]TJ/F18 14.346 Tf -215.738 -32.946 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 100.201 -21.821 Td[(psb)]TJ ET -1 0 0 1 218.417 465.862 cm +1 0 0 1 215.694 571.758 cm q []0 d 0 J @@ -7086,11 +7926,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -218.417 -465.862 cm +1 0 0 1 -215.694 -571.758 cm BT -/F8 9.963 Tf 221.405 465.862 Td[(geas)-1(u)1(m)-334(\050)]TJ/F19 9.963 Tf 39.353 0 Td[(x,)-357(desc)]TJ +/F8 9.963 Tf 218.682 571.758 Td[(geam)-1(ax)-333(\050)]TJ/F19 9.963 Tf 40.128 0 Td[(r)51(e)1(s,)-358(x,)-357(desc)]TJ ET -1 0 0 1 290.941 465.862 cm +1 0 0 1 307.961 571.758 cm q []0 d 0 J @@ -7099,42 +7939,42 @@ q 3.055 0.199 l S Q -1 0 0 1 -290.941 -465.862 cm +1 0 0 1 -307.961 -571.758 cm BT -/F19 9.963 Tf 293.996 465.862 Td[(a,)-358(i)1(nfo,)-358(j)1(x)]TJ/F8 9.963 Tf 42.812 0 Td[(\051)]TJ +/F19 9.963 Tf 311.016 571.758 Td[(a,)-357(info)]TJ/F8 9.963 Tf 28.515 0 Td[(\051)]TJ ET -1 0 0 1 99.895 440.292 cm +1 0 0 1 99.895 545.357 cm 0 g 0 G -1 0 0 1 76.372 -21.021 cm +1 0 0 1 24.488 -21.021 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.981 20.623 cm +1 0 0 1 4.982 20.622 cm q []0 d 0 J 0.398 w 0 0.199 m -181.005 0.199 l +284.773 0.199 l S Q -1 0 0 1 -181.248 -439.894 cm +1 0 0 1 -129.365 -544.958 cm BT -/F11 9.963 Tf 187.226 431.525 Td[(dot)]TJ/F8 9.963 Tf 13.612 0 Td[(,)]TJ/F11 9.963 Tf 6.088 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(,)]TJ/F11 9.963 Tf 6.089 0 Td[(y)]TJ/F29 9.963 Tf 86.824 0 Td[(F)96(un)1(c)-1(tion)]TJ +/F11 9.963 Tf 135.342 536.59 Td[(r)-28(es)-8558(x)]TJ/F29 9.963 Tf 217.657 0 Td[(Subr)1(outi)-1(n)1(e)]TJ ET -1 0 0 1 181.248 427.54 cm +1 0 0 1 129.365 532.605 cm q []0 d 0 J 0.398 w 0 0.199 m -181.005 0.199 l +284.773 0.199 l S Q -1 0 0 1 -181.248 -427.54 cm +1 0 0 1 -129.365 -532.605 cm BT -/F8 9.963 Tf 187.226 419.171 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ +/F8 9.963 Tf 135.342 524.236 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ ET -1 0 0 1 321.13 419.171 cm +1 0 0 1 368.596 524.236 cm q []0 d 0 J @@ -7143,11 +7983,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -321.13 -419.171 cm +1 0 0 1 -368.596 -524.236 cm BT -/F8 9.963 Tf 324.119 419.171 Td[(geas)-1(u)1(m)]TJ -136.893 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ +/F8 9.963 Tf 371.585 524.236 Td[(geam)-1(ax)]TJ -236.243 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-1200(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ ET -1 0 0 1 321.13 407.216 cm +1 0 0 1 368.596 512.281 cm q []0 d 0 J @@ -7156,94 +7996,68 @@ q 2.989 0.199 l S Q -1 0 0 1 -321.13 -407.216 cm +1 0 0 1 -368.596 -512.281 cm BT -/F8 9.963 Tf 324.119 407.216 Td[(geas)-1(u)1(m)]TJ +/F8 9.963 Tf 371.585 512.281 Td[(geam)-1(ax)]TJ ET -1 0 0 1 181.248 403.231 cm +1 0 0 1 129.365 508.296 cm q []0 d 0 J 0.398 w 0 0.199 m -181.005 0.199 l +284.773 0.199 l S Q -1 0 0 1 46.819 -27.84 cm +1 0 0 1 98.702 -27.84 cm 0 g 0 G -1 0 0 1 -228.067 -375.391 cm +1 0 0 1 -228.067 -480.456 cm BT -/F8 9.963 Tf 228.067 375.391 Td[(T)83(ab)1(le)-334(6:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ +/F8 9.963 Tf 228.067 480.456 Td[(T)83(ab)1(le)-334(5:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ ET -1 0 0 1 315.434 375.391 cm +1 0 0 1 315.434 480.456 cm 0 g 0 G 1 0 0 1 -215.539 -1.937 cm 0 g 0 G -1 0 0 1 -4.981 -28.474 cm +1 0 0 1 -4.981 -31.383 cm 0 g 0 G -1 0 0 1 -94.914 -344.98 cm +1 0 0 1 -94.914 -447.136 cm BT -/F29 9.963 Tf 99.895 344.98 Td[(On)-383(En)32(tr)1(y)]TJ +/F29 9.963 Tf 99.895 447.136 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 147.481 344.98 cm +1 0 0 1 147.481 447.136 cm 0 g 0 G -1 0 0 1 -52.567 -19.094 cm +1 0 0 1 -52.567 -19.925 cm 0 g 0 G -1 0 0 1 -94.914 -325.886 cm +1 0 0 1 -94.914 -427.211 cm BT -/F29 9.963 Tf 99.895 325.886 Td[(x)]TJ +/F29 9.963 Tf 99.895 427.211 Td[(x)]TJ ET -1 0 0 1 105.942 325.886 cm +1 0 0 1 105.942 427.211 cm 0 g 0 G -1 0 0 1 -105.942 -325.886 cm -BT -/F8 9.963 Tf 110.923 325.886 Td[(th)1(e)-331(lo)-28(cal)-330(p)-28(or)1(tion)-330(of)-330(g)1(lobal)-330(d)1(e)-1(n)1(s)-1(e)-331(matr)1(ix)]TJ/F11 9.963 Tf 175.908 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)-443(This)-330(fun)1(c)-1(t)1(ion)-330(com)-1(p)1(utes)-331(th)1(e)-331(lo)-28(ca-)]TJ -167.723 -11.955 Td[(tion)-339(of)-340(th)1(e)-341(\014)1(rst)-340(e)-1(l)1(e)-1(men)28(t)-340(of)-340(l)1(o)-28(c)-1(al)-339(s)-1(u)1(barr)1(a)28(y)-340(use)-1(d)1(,)-342(b)1(as)-1(ed)-340(on)]TJ/F11 9.963 Tf 250.122 0 Td[(j)-57(x)]TJ/F8 9.963 Tf 13.754 0 Td[(and)-339(the)-340(\014eld)]TJ/F11 9.963 Tf -263.876 -11.955 Td[(matr)-28(i)1(x)]TJ -ET -1 0 0 1 156.908 301.976 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -2.989 0.199 l -S -Q -1 0 0 1 -156.908 -301.976 cm -BT -/F11 9.963 Tf 159.897 301.976 Td[(data)]TJ/F8 9.963 Tf 22.636 0 Td[(of)]TJ/F11 9.963 Tf 11.347 0 Td[(desc)]TJ -ET -1 0 0 1 213.283 301.976 cm -q -[]0 d -0 J -0.398 w -0 0.199 m -2.989 0.199 l -S -Q -1 0 0 1 -213.283 -301.976 cm +1 0 0 1 -105.942 -427.211 cm BT -/F11 9.963 Tf 216.272 301.976 Td[(a)]TJ/F8 9.963 Tf 8.587 0 Td[(.)]TJ -100.057 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.956 Td[(Sp)-27(ec)-1(i)1(\014ed)-363(as:)-503(a)-363(ran)1(k)-363(on)1(e)-364(or)-362(t)28(w)27(o)-362(arra)28(y)-362(w)-1(i)1(th)-363(th)1(e)-363(POINTE)1(R)-363(attri)1(but)1(e)-364(con-)]TJ 0 -11.955 Td[(tain)1(in)1(g)-334(n)28(u)1(m)27(b)-27(ers)-334(of)-333(t)28(y)1(p)-28(e)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(in)-332(T)83(able)]TJ +/F8 9.963 Tf 110.923 427.211 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(gl)1(obal)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -167.933 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-363(as:)-503(a)-363(ran)1(k)-363(on)1(e)-364(or)-362(t)28(w)27(o)-362(arra)28(y)-362(w)-1(i)1(th)-363(th)1(e)-363(POINTE)1(R)-363(attri)1(but)1(e)-364(con-)]TJ 0 -11.956 Td[(tain)1(in)1(g)-334(n)28(u)1(m)27(b)-27(ers)-334(of)-333(t)28(y)1(p)-28(e)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(in)-332(T)83(able)]TJ ET -1 0 0 1 311.74 254.155 cm +1 0 0 1 311.74 379.39 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -311.74 -254.155 cm +1 0 0 1 -311.74 -379.39 cm BT -/F8 9.963 Tf 311.74 254.155 Td[(6)]TJ +/F8 9.963 Tf 311.74 379.39 Td[(5)]TJ ET -1 0 0 1 316.722 254.155 cm +1 0 0 1 316.722 379.39 cm 0 g 0 G -1 0 0 1 -316.722 -254.155 cm +1 0 0 1 -316.722 -379.39 cm BT -/F8 9.963 Tf 316.722 254.155 Td[(.)]TJ +/F8 9.963 Tf 316.722 379.39 Td[(.)]TJ ET -1 0 0 1 94.914 235.061 cm +1 0 0 1 94.914 359.465 cm 0 g 0 G -1 0 0 1 -94.914 -235.061 cm +1 0 0 1 -94.914 -359.465 cm BT -/F29 9.963 Tf 99.895 235.061 Td[(desc)]TJ +/F29 9.963 Tf 99.895 359.465 Td[(desc)]TJ ET -1 0 0 1 121.81 235.061 cm +1 0 0 1 121.81 359.465 cm q []0 d 0 J @@ -7252,23 +8066,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -121.81 -235.061 cm +1 0 0 1 -121.81 -359.465 cm BT -/F29 9.963 Tf 125.247 235.061 Td[(a)]TJ +/F29 9.963 Tf 125.247 359.465 Td[(a)]TJ ET -1 0 0 1 130.816 235.061 cm +1 0 0 1 130.816 359.465 cm 0 g 0 G -1 0 0 1 -130.816 -235.061 cm +1 0 0 1 -130.816 -359.465 cm BT -/F8 9.963 Tf 135.798 235.061 Td[(con)28(tain)1(s)-334(dat)1(a)-334(stru)1(c)-1(tu)1(res)-334(fo)1(r)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 135.798 359.465 Td[(con)28(tain)1(s)-334(dat)1(a)-334(stru)1(c)-1(tu)1(res)-334(fo)1(r)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 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-576.972 cm BT -/F11 9.963 Tf 172.212 576.972 Td[(x)]TJ +/F11 9.963 Tf 121.403 576.972 Td[(x)]TJ ET -1 0 0 1 177.906 576.972 cm +1 0 0 1 127.097 576.972 cm 0 g 0 G -1 0 0 1 -177.906 -576.972 cm +1 0 0 1 -127.097 -576.972 cm BT -/F8 9.963 Tf 182.887 576.972 Td[(is)-334(t)1(he)-334(gl)1(obal)-333(s)-1(u)1(bmatr)1(ix)]TJ/F11 9.963 Tf 103.916 0 Td[(g)-36(l)-20(ob)]TJ +/F8 9.963 Tf 132.078 576.972 Td[(is)-334(t)1(he)-334(gl)1(obal)-333(submatr)1(ix)]TJ/F11 9.963 Tf 103.916 0 Td[(g)-36(l)-20(ob)]TJ ET -1 0 0 1 304.784 576.972 cm +1 0 0 1 253.974 576.972 cm q []0 d 0 J @@ -11292,17 +11921,17 @@ q 2.989 0.199 l S Q -1 0 0 1 -304.784 -576.972 cm +1 0 0 1 -253.974 -576.972 cm BT -/F11 9.963 Tf 307.773 576.972 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.495 Td[(iy)]TJ/F7 6.974 Tf 7.109 0 Td[(:)]TJ/F10 6.974 Tf 2.255 0 Td[(iy)]TJ/F7 6.974 Tf 7.11 0 Td[(+)]TJ/F10 6.974 Tf 6.116 0 Td[(m)]TJ/F13 6.974 Tf 7.069 0 Td[(\000)]TJ/F7 6.974 Tf 6.227 0 Td[(1)]TJ/F10 6.974 Tf 3.971 0 Td[(;j)-58(y)]TJ/F7 6.974 Tf 10.357 0 Td[(:)]TJ/F10 6.974 Tf 2.255 0 Td[(j)-58(y)]TJ/F7 6.974 Tf 7.991 0 Td[(+)]TJ/F10 6.974 Tf 6.116 0 Td[(n)]TJ/F13 6.974 Tf 4.924 0 Td[(\000)]TJ/F7 6.974 Tf 6.227 0 Td[(1)]TJ +/F11 9.963 Tf 256.963 576.972 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.495 Td[(iy)]TJ/F7 6.974 Tf 7.11 0 Td[(:)]TJ/F10 6.974 Tf 2.255 0 Td[(iy)]TJ/F7 6.974 Tf 7.109 0 Td[(+)]TJ/F10 6.974 Tf 6.116 0 Td[(m)]TJ/F13 6.974 Tf 7.07 0 Td[(\000)]TJ/F7 6.974 Tf 6.227 0 Td[(1)]TJ/F10 6.974 Tf 3.971 0 Td[(;j)-58(y)]TJ/F7 6.974 Tf 10.356 0 Td[(:)]TJ/F10 6.974 Tf 2.256 0 Td[(j)-57(y)]TJ/F7 6.974 Tf 7.99 0 Td[(+)]TJ/F10 6.974 Tf 6.116 0 Td[(n)]TJ/F13 6.974 Tf 4.925 0 Td[(\000)]TJ/F7 6.974 Tf 6.227 0 Td[(1)]TJ ET -1 0 0 1 145.724 557.427 cm +1 0 0 1 94.914 557.427 cm 0 g 0 G -1 0 0 1 -145.724 -557.427 cm +1 0 0 1 -94.914 -557.427 cm BT -/F11 9.963 Tf 150.705 557.427 Td[(l)-20(oc)]TJ +/F11 9.963 Tf 99.895 557.427 Td[(l)-20(oc)]TJ ET -1 0 0 1 163.701 557.427 cm +1 0 0 1 112.892 557.427 cm q []0 d 0 J @@ -11311,34 +11940,34 @@ q 3.437 0.199 l S Q -1 0 0 1 -163.701 -557.427 cm +1 0 0 1 -112.892 -557.427 cm BT -/F11 9.963 Tf 167.139 557.427 Td[(x)]TJ/F10 6.974 Tf 5.693 -1.494 Td[(i)]TJ +/F11 9.963 Tf 116.329 557.427 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ ET -1 0 0 1 176.149 557.427 cm +1 0 0 1 125.34 557.427 cm 0 g 0 G -1 0 0 1 -176.149 -557.427 cm +1 0 0 1 -125.34 -557.427 cm BT -/F8 9.963 Tf 181.131 557.427 Td[(is)-333(the)-334(l)1(o)-28(c)-1(al)-333(p)-27(orti)1(on)-333(of)-333(glob)1(al)-333(dense)-334(matrix)-333(on)-333(p)1(ro)-27(c)-1(es)-1(s)]TJ/F11 9.963 Tf 234.703 0 Td[(i)]TJ/F8 9.963 Tf 3.433 0 Td[(.)]TJ +/F8 9.963 Tf 130.321 557.427 Td[(is)-334(t)1(he)-334(l)1(o)-28(c)-1(al)-333(p)-27(orti)1(on)-333(of)-333(glob)1(al)-333(dense)-334(matrix)-333(on)-333(p)1(ro)-28(ces)-1(s)]TJ/F11 9.963 Tf 234.704 0 Td[(i)]TJ/F8 9.963 Tf 3.432 0 Td[(.)]TJ ET -1 0 0 1 145.724 537.883 cm +1 0 0 1 94.914 537.883 cm 0 g 0 G -1 0 0 1 -145.724 -537.883 cm +1 0 0 1 -94.914 -537.883 cm BT -/F11 9.963 Tf 150.705 537.883 Td[(co)1(l)-20(l)-21(e)1(ct)]TJ +/F11 9.963 Tf 99.895 537.883 Td[(co)1(l)-21(l)-20(e)1(ct)]TJ ET -1 0 0 1 178.731 537.883 cm +1 0 0 1 127.921 537.883 cm 0 g 0 G -1 0 0 1 -178.731 -537.883 cm +1 0 0 1 -127.921 -537.883 cm BT -/F8 9.963 Tf 183.712 537.883 Td[(is)-334(t)1(he)-334(collect)-334(f)1(un)1(c)-1(ti)1(on.)]TJ +/F8 9.963 Tf 132.902 537.883 Td[(is)-334(t)1(he)-334(collec)-1(t)-333(f)1(un)1(c)-1(ti)1(on.)]TJ ET -1 0 0 1 150.705 519.1 cm +1 0 0 1 99.895 519.1 cm 0 g 0 G 1 0 0 1 74.163 -21.021 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.981 20.623 cm +1 0 0 1 4.982 20.623 cm q []0 d 0 J @@ -11347,11 +11976,11 @@ q 185.423 0.199 l S Q -1 0 0 1 -229.849 -518.702 cm +1 0 0 1 -179.04 -518.702 cm BT -/F11 9.963 Tf 235.827 510.333 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F11 9.963 Tf 3.316 1.494 Td[(;)-166(y)]TJ/F29 9.963 Tf 109.296 0 Td[(Subr)1(outi)-1(ne)]TJ +/F11 9.963 Tf 185.017 510.333 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F11 9.963 Tf 3.317 1.494 Td[(;)-166(y)]TJ/F29 9.963 Tf 109.296 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 229.849 506.348 cm +1 0 0 1 179.04 506.348 cm q []0 d 0 J @@ -11360,11 +11989,11 @@ q 185.423 0.199 l S Q -1 0 0 1 -229.849 -506.348 cm +1 0 0 1 -179.04 -506.348 cm BT -/F8 9.963 Tf 235.827 497.979 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ +/F8 9.963 Tf 185.017 497.979 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ ET -1 0 0 1 369.73 497.979 cm +1 0 0 1 318.921 497.979 cm q []0 d 0 J @@ -11373,11 +12002,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -369.73 -497.979 cm +1 0 0 1 -318.921 -497.979 cm BT -/F8 9.963 Tf 372.719 497.979 Td[(gath)1(e)-1(r)]TJ -136.892 -11.955 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ +/F8 9.963 Tf 321.91 497.979 Td[(gath)1(e)-1(r)]TJ -136.893 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ ET -1 0 0 1 369.73 486.024 cm +1 0 0 1 318.921 486.024 cm q []0 d 0 J @@ -11386,11 +12015,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -369.73 -486.024 cm +1 0 0 1 -318.921 -486.024 cm BT -/F8 9.963 Tf 372.719 486.024 Td[(gath)1(e)-1(r)]TJ +/F8 9.963 Tf 321.91 486.024 Td[(gath)1(e)-1(r)]TJ ET -1 0 0 1 229.849 482.039 cm +1 0 0 1 179.04 482.039 cm q []0 d 0 J @@ -11401,19 +12030,19 @@ S Q 1 0 0 1 46.537 -27.84 cm 0 g 0 G -1 0 0 1 -276.386 -454.199 cm +1 0 0 1 -225.577 -454.199 cm BT -/F8 9.963 Tf 276.386 454.199 Td[(T)83(ab)1(le)-334(13:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ +/F8 9.963 Tf 225.577 454.199 Td[(T)83(ab)1(le)-334(13:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ ET -1 0 0 1 368.735 454.199 cm +1 0 0 1 317.925 454.199 cm 0 g 0 G 1 0 0 1 -218.03 -1.937 cm 0 g 0 G -1 0 0 1 -150.705 -452.262 cm +1 0 0 1 -99.895 -452.262 cm BT -/F18 14.346 Tf 150.705 407.906 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 5.266 -21.821 Td[(call)-333(psb)]TJ +/F18 14.346 Tf 99.895 407.906 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 5.267 -21.821 Td[(call)-333(psb)]TJ ET -1 0 0 1 189.833 386.085 cm +1 0 0 1 139.024 386.085 cm q []0 d 0 J @@ -11422,11 +12051,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -189.833 -386.085 cm +1 0 0 1 -139.024 -386.085 cm BT -/F8 9.963 Tf 192.822 386.085 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ +/F8 9.963 Tf 142.013 386.085 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ ET -1 0 0 1 245.134 386.085 cm +1 0 0 1 194.324 386.085 cm q []0 d 0 J @@ -11435,11 +12064,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -245.134 -386.085 cm +1 0 0 1 -194.324 -386.085 cm BT -/F19 9.963 Tf 248.189 386.085 Td[(x,)-357(lo)51(c)]TJ +/F19 9.963 Tf 197.38 386.085 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 271.753 386.085 cm +1 0 0 1 220.943 386.085 cm q []0 d 0 J @@ -11448,11 +12077,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -271.753 -386.085 cm +1 0 0 1 -220.943 -386.085 cm BT -/F19 9.963 Tf 274.808 386.085 Td[(x,)-357(desc)]TJ +/F19 9.963 Tf 223.998 386.085 Td[(x,)-357(desc)]TJ ET -1 0 0 1 304.991 386.085 cm +1 0 0 1 254.182 386.085 cm q []0 d 0 J @@ -11461,11 +12090,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -304.991 -386.085 cm +1 0 0 1 -254.182 -386.085 cm BT -/F19 9.963 Tf 308.046 386.085 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(jglobx)1(,)-358(il)1(o)51(cx,)-357(jlo)52(cx,)-358(k)]TJ/F8 9.963 Tf 177.229 0 Td[(\051)]TJ/F18 14.346 Tf -334.57 -29.888 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 39.421 -21.821 Td[(call)-333(psb)]TJ +/F19 9.963 Tf 257.237 386.085 Td[(a,)-357(info,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(jgl)1(o)-1(bx)1(,)-358(i)1(lo)51(cx,)-357(jl)1(o)51(cx,)-358(k)]TJ/F8 9.963 Tf 177.228 0 Td[(\051)]TJ/F18 14.346 Tf -334.57 -29.888 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 39.422 -21.821 Td[(call)-333(psb)]TJ ET -1 0 0 1 223.988 334.376 cm +1 0 0 1 173.179 334.376 cm q []0 d 0 J @@ -11474,11 +12103,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -223.988 -334.376 cm +1 0 0 1 -173.179 -334.376 cm BT -/F8 9.963 Tf 226.977 334.376 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ +/F8 9.963 Tf 176.168 334.376 Td[(gath)1(e)-1(r)-333(\050)]TJ/F19 9.963 Tf 34.897 0 Td[(glob)]TJ ET -1 0 0 1 279.289 334.376 cm +1 0 0 1 228.479 334.376 cm q []0 d 0 J @@ -11487,11 +12116,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -279.289 -334.376 cm +1 0 0 1 -228.479 -334.376 cm BT -/F19 9.963 Tf 282.344 334.376 Td[(x,)-357(lo)51(c)]TJ +/F19 9.963 Tf 231.535 334.376 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 305.908 334.376 cm +1 0 0 1 255.098 334.376 cm q []0 d 0 J @@ -11500,11 +12129,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -305.908 -334.376 cm +1 0 0 1 -255.098 -334.376 cm BT -/F19 9.963 Tf 308.963 334.376 Td[(x,)-357(desc)]TJ +/F19 9.963 Tf 258.153 334.376 Td[(x,)-357(desc)]TJ ET -1 0 0 1 339.146 334.376 cm +1 0 0 1 288.337 334.376 cm q []0 d 0 J @@ -11513,25 +12142,25 @@ q 3.055 0.199 l S Q -1 0 0 1 -339.146 -334.376 cm +1 0 0 1 -288.337 -334.376 cm BT -/F19 9.963 Tf 342.201 334.376 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(ilo)51(c)1(x)]TJ/F8 9.963 Tf 108.919 0 Td[(\051)]TJ +/F19 9.963 Tf 291.392 334.376 Td[(a,)-357(info,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(il)1(o)51(cx)]TJ/F8 9.963 Tf 108.918 0 Td[(\051)]TJ ET -1 0 0 1 145.724 310.466 cm +1 0 0 1 94.914 310.466 cm 0 g 0 G -1 0 0 1 -145.724 -310.466 cm +1 0 0 1 -94.914 -310.466 cm BT -/F29 9.963 Tf 150.705 310.466 Td[(On)-383(En)33(t)-1(r)1(y)]TJ +/F29 9.963 Tf 99.895 310.466 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 198.29 310.466 cm +1 0 0 1 147.481 310.466 cm 0 g 0 G -1 0 0 1 -52.566 -19.545 cm +1 0 0 1 -52.567 -19.545 cm 0 g 0 G -1 0 0 1 -145.724 -290.921 cm +1 0 0 1 -94.914 -290.921 cm BT -/F29 9.963 Tf 150.705 290.921 Td[(lo)-32(c)]TJ +/F29 9.963 Tf 99.895 290.921 Td[(lo)-32(c)]TJ ET -1 0 0 1 165.713 290.921 cm +1 0 0 1 114.904 290.921 cm q []0 d 0 J @@ -11540,17 +12169,17 @@ q 3.437 0.199 l S Q -1 0 0 1 -165.713 -290.921 cm +1 0 0 1 -114.904 -290.921 cm BT -/F29 9.963 Tf 169.151 290.921 Td[(x)]TJ +/F29 9.963 Tf 118.341 290.921 Td[(x)]TJ ET -1 0 0 1 175.197 290.921 cm +1 0 0 1 124.388 290.921 cm 0 g 0 G -1 0 0 1 -175.197 -290.921 cm +1 0 0 1 -124.388 -290.921 cm BT -/F8 9.963 Tf 180.179 290.921 Td[(th)1(e)-334(lo)-28(cal)-333(p)-27(ortion)-333(of)-332(global)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.117 0 Td[(g)-36(l)-20(ob)]TJ +/F8 9.963 Tf 129.369 290.921 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(gl)1(obal)-333(d)1(e)-1(n)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 176.118 0 Td[(g)-36(l)-20(ob)]TJ ET -1 0 0 1 374.277 290.921 cm +1 0 0 1 323.467 290.921 cm q []0 d 0 J @@ -11559,29 +12188,29 @@ q 2.989 0.199 l S Q -1 0 0 1 -374.277 -290.921 cm +1 0 0 1 -323.467 -290.921 cm BT -/F11 9.963 Tf 377.266 290.921 Td[(x)]TJ/F8 9.963 Tf 5.694 0 Td[(.)]TJ -207.349 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 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Td[(is)-334(t)1(he)-334(l)1(o)-28(c)-1(al)-333(p)-27(orti)1(on)-333(of)-333(glob)1(al)-333(dense)-334(matrix)-333(on)-333(p)1(ro)-28(ces)-1(s)]TJ/F11 9.963 Tf 234.704 0 Td[(i)]TJ/F8 9.963 Tf 3.432 0 Td[(.)]TJ ET -1 0 0 1 145.724 530.935 cm +1 0 0 1 94.914 530.935 cm 0 g 0 G -1 0 0 1 -145.724 -530.935 cm +1 0 0 1 -94.914 -530.935 cm BT -/F11 9.963 Tf 150.705 530.935 Td[(sc)1(atter)]TJ +/F11 9.963 Tf 99.895 530.935 Td[(sca)1(tter)]TJ ET -1 0 0 1 181.558 530.935 cm +1 0 0 1 130.748 530.935 cm 0 g 0 G -1 0 0 1 -181.558 -530.935 cm +1 0 0 1 -130.748 -530.935 cm BT -/F8 9.963 Tf 186.539 530.935 Td[(is)-334(t)1(he)-334(sc)-1(at)1(te)-1(r)-333(f)1(un)1(c)-1(ti)1(on.)]TJ +/F8 9.963 Tf 135.73 530.935 Td[(is)-334(t)1(he)-334(sc)-1(at)1(te)-1(r)-333(f)1(un)1(c)-1(ti)1(on.)]TJ ET -1 0 0 1 150.705 510.675 cm +1 0 0 1 99.895 510.675 cm 0 g 0 G 1 0 0 1 74.163 -21.021 cm 0 g 0 G 0 g 0 G -1 0 0 1 4.981 20.623 cm +1 0 0 1 4.982 20.623 cm q []0 d 0 J @@ -12098,11 +12727,11 @@ q 185.423 0.199 l S Q -1 0 0 1 -229.849 -510.277 cm +1 0 0 1 -179.04 -510.277 cm BT -/F11 9.963 Tf 235.827 501.908 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F11 9.963 Tf 3.316 1.494 Td[(;)-166(y)]TJ/F29 9.963 Tf 109.296 0 Td[(Subr)1(outi)-1(ne)]TJ +/F11 9.963 Tf 185.017 501.908 Td[(x)]TJ/F10 6.974 Tf 5.694 -1.494 Td[(i)]TJ/F11 9.963 Tf 3.317 1.494 Td[(;)-166(y)]TJ/F29 9.963 Tf 109.296 0 Td[(Subr)1(outi)-1(ne)]TJ ET -1 0 0 1 229.849 497.923 cm +1 0 0 1 179.04 497.923 cm q []0 d 0 J @@ -12111,11 +12740,11 @@ q 185.423 0.199 l S Q -1 0 0 1 -229.849 -497.923 cm +1 0 0 1 -179.04 -497.923 cm BT -/F8 9.963 Tf 235.827 489.554 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ +/F8 9.963 Tf 185.017 489.554 Td[(Long)-333(P)1(rec)-1(ision)-333(Real)-3103(p)1(s)-1(b)]TJ ET -1 0 0 1 369.73 489.554 cm +1 0 0 1 318.921 489.554 cm q []0 d 0 J @@ -12124,11 +12753,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -369.73 -489.554 cm +1 0 0 1 -318.921 -489.554 cm BT -/F8 9.963 Tf 372.719 489.554 Td[(sc)-1(atter)]TJ -136.892 -11.955 Td[(Lon)1(g)-334(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ +/F8 9.963 Tf 321.91 489.554 Td[(sc)-1(atter)]TJ -136.893 -11.955 Td[(Long)-333(P)1(rec)-1(ision)-333(Compl)1(e)-1(x)-1200(p)1(s)-1(b)]TJ ET -1 0 0 1 369.73 477.599 cm +1 0 0 1 318.921 477.599 cm q []0 d 0 J @@ -12137,11 +12766,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -369.73 -477.599 cm +1 0 0 1 -318.921 -477.599 cm BT -/F8 9.963 Tf 372.719 477.599 Td[(sc)-1(atter)]TJ +/F8 9.963 Tf 321.91 477.599 Td[(sc)-1(atter)]TJ ET -1 0 0 1 229.849 473.614 cm +1 0 0 1 179.04 473.614 cm q []0 d 0 J @@ -12152,19 +12781,19 @@ S Q 1 0 0 1 46.537 -27.84 cm 0 g 0 G -1 0 0 1 -276.386 -445.774 cm +1 0 0 1 -225.577 -445.774 cm BT -/F8 9.963 Tf 276.386 445.774 Td[(T)83(ab)1(le)-334(14:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ +/F8 9.963 Tf 225.577 445.774 Td[(T)83(ab)1(le)-334(14:)-444(Data)-333(t)28(yp)-27(e)-1(s)]TJ ET -1 0 0 1 368.735 445.774 cm +1 0 0 1 317.925 445.774 cm 0 g 0 G 1 0 0 1 -218.03 -1.937 cm 0 g 0 G -1 0 0 1 -150.705 -443.837 cm +1 0 0 1 -99.895 -443.837 cm BT -/F18 14.346 Tf 150.705 398.408 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 4.409 -21.893 Td[(call)-333(psb)]TJ +/F18 14.346 Tf 99.895 398.408 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 4.409 -21.893 Td[(call)-333(psb)]TJ ET -1 0 0 1 188.976 376.515 cm +1 0 0 1 138.166 376.515 cm q []0 d 0 J @@ -12173,11 +12802,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -188.976 -376.515 cm +1 0 0 1 -138.166 -376.515 cm BT -/F8 9.963 Tf 191.964 376.515 Td[(sc)-1(atter)-333(\050)]TJ/F19 9.963 Tf 36.613 0 Td[(glob)]TJ +/F8 9.963 Tf 141.155 376.515 Td[(sc)-1(atter)-333(\050)]TJ/F19 9.963 Tf 36.613 0 Td[(gl)1(o)-1(b)]TJ ET -1 0 0 1 245.992 376.515 cm +1 0 0 1 195.182 376.515 cm q []0 d 0 J @@ -12186,11 +12815,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -245.992 -376.515 cm +1 0 0 1 -195.182 -376.515 cm BT -/F19 9.963 Tf 249.047 376.515 Td[(x,)-357(lo)51(c)]TJ +/F19 9.963 Tf 198.237 376.515 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 272.611 376.515 cm +1 0 0 1 221.801 376.515 cm q []0 d 0 J @@ -12199,11 +12828,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -272.611 -376.515 cm +1 0 0 1 -221.801 -376.515 cm BT -/F19 9.963 Tf 275.666 376.515 Td[(x,)-357(desc)]TJ +/F19 9.963 Tf 224.856 376.515 Td[(x,)-357(desc)]TJ ET -1 0 0 1 305.849 376.515 cm +1 0 0 1 255.04 376.515 cm q []0 d 0 J @@ -12212,11 +12841,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -305.849 -376.515 cm +1 0 0 1 -255.04 -376.515 cm BT -/F19 9.963 Tf 308.904 376.515 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(jgl)1(o)-1(bx)1(,)-358(il)1(o)51(cx,)-357(jl)1(o)51(cx,)-358(k)]TJ/F8 9.963 Tf 177.229 0 Td[(\051)]TJ/F18 14.346 Tf -335.428 -29.971 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 38.564 -21.893 Td[(call)-333(psb)]TJ +/F19 9.963 Tf 258.095 376.515 Td[(a,)-357(info,)-357(r)51(o)51(ot,)-358(i)1(globx,)-357(jgl)1(o)-1(bx)1(,)-358(i)1(lo)51(cx,)-357(jl)1(o)51(cx,)-358(k)]TJ/F8 9.963 Tf 177.228 0 Td[(\051)]TJ/F18 14.346 Tf -335.428 -29.971 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 38.564 -21.893 Td[(call)-333(psb)]TJ ET -1 0 0 1 223.131 324.651 cm +1 0 0 1 172.321 324.651 cm q []0 d 0 J @@ -12225,11 +12854,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -223.131 -324.651 cm +1 0 0 1 -172.321 -324.651 cm BT -/F8 9.963 Tf 226.119 324.651 Td[(sc)-1(atter)-333(\050)]TJ/F19 9.963 Tf 36.613 0 Td[(glob)]TJ +/F8 9.963 Tf 175.31 324.651 Td[(sc)-1(atter)-333(\050)]TJ/F19 9.963 Tf 36.613 0 Td[(gl)1(o)-1(b)]TJ ET -1 0 0 1 280.147 324.651 cm +1 0 0 1 229.337 324.651 cm q []0 d 0 J @@ -12238,11 +12867,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -280.147 -324.651 cm +1 0 0 1 -229.337 -324.651 cm BT -/F19 9.963 Tf 283.202 324.651 Td[(x,)-357(lo)51(c)]TJ +/F19 9.963 Tf 232.392 324.651 Td[(x,)-357(lo)51(c)]TJ ET -1 0 0 1 306.766 324.651 cm +1 0 0 1 255.956 324.651 cm q []0 d 0 J @@ -12251,11 +12880,11 @@ q 3.055 0.199 l S Q -1 0 0 1 -306.766 -324.651 cm +1 0 0 1 -255.956 -324.651 cm BT -/F19 9.963 Tf 309.821 324.651 Td[(x,)-357(desc)]TJ +/F19 9.963 Tf 259.011 324.651 Td[(x,)-357(desc)]TJ ET -1 0 0 1 340.004 324.651 cm +1 0 0 1 289.195 324.651 cm q []0 d 0 J @@ -12264,25 +12893,25 @@ q 3.055 0.199 l S Q -1 0 0 1 -340.004 -324.651 cm +1 0 0 1 -289.195 -324.651 cm BT -/F19 9.963 Tf 343.059 324.651 Td[(a,)-358(i)1(nfo,)-358(r)52(o)51(ot,)-358(i)1(globx,)-357(ilo)52(cx)]TJ/F8 9.963 Tf 108.919 0 Td[(\051)]TJ +/F19 9.963 Tf 292.25 324.651 Td[(a,)-357(info,)-357(r)51(o)51(ot,)-358(i)1(globx,)-357(il)1(o)51(cx)]TJ/F8 9.963 Tf 108.918 0 Td[(\051)]TJ ET -1 0 0 1 145.724 300.657 cm +1 0 0 1 94.914 300.657 cm 0 g 0 G -1 0 0 1 -145.724 -300.657 cm +1 0 0 1 -94.914 -300.657 cm BT -/F29 9.963 Tf 150.705 300.657 Td[(On)-383(En)33(t)-1(r)1(y)]TJ +/F29 9.963 Tf 99.895 300.657 Td[(On)-383(En)32(tr)1(y)]TJ ET -1 0 0 1 198.29 300.657 cm +1 0 0 1 147.481 300.657 cm 0 g 0 G -1 0 0 1 -52.566 -20.26 cm +1 0 0 1 -52.567 -20.26 cm 0 g 0 G -1 0 0 1 -145.724 -280.397 cm +1 0 0 1 -94.914 -280.397 cm BT -/F29 9.963 Tf 150.705 280.397 Td[(glob)]TJ +/F29 9.963 Tf 99.895 280.397 Td[(glob)]TJ ET -1 0 0 1 172.397 280.397 cm +1 0 0 1 121.587 280.397 cm q []0 d 0 J @@ -12291,23 +12920,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -172.397 -280.397 cm +1 0 0 1 -121.587 -280.397 cm BT -/F29 9.963 Tf 175.834 280.397 Td[(x)]TJ +/F29 9.963 Tf 125.024 280.397 Td[(x)]TJ ET -1 0 0 1 181.881 280.397 cm +1 0 0 1 131.071 280.397 cm 0 g 0 G -1 0 0 1 -181.881 -280.397 cm +1 0 0 1 -131.071 -280.397 cm BT -/F8 9.963 Tf 186.862 280.397 Td[(The)-333(arra)28(y)-333(th)1(at)-334(m)28(ust)-333(b)-28(e)-333(s)-1(cattere)-1(d)-332(in)28(to)-333(lo)-28(cal)-333(pi)1(e)-1(ce)-1(s.)]TJ -11.251 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(ran)1(k)-334(on)1(e)-334(or)-333(t)28(w)28(o)-334(ar)1(ra)28(y)83(.)]TJ +/F8 9.963 Tf 136.052 280.397 Td[(The)-334(ar)1(ra)28(y)-333(that)-333(m)28(ust)-333(b)-28(e)-333(s)-1(cattere)-1(d)-332(in)28(to)-333(lo)-28(cal)-333(pi)1(e)-1(ce)-1(s.)]TJ -11.25 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(ran)1(k)-333(one)-334(or)-333(t)28(w)28(o)-334(ar)1(ra)28(y)84(.)]TJ ET -1 0 0 1 145.724 224.272 cm +1 0 0 1 94.914 224.272 cm 0 g 0 G -1 0 0 1 -145.724 -224.272 cm +1 0 0 1 -94.914 -224.272 cm BT -/F29 9.963 Tf 150.705 224.272 Td[(desc)]TJ +/F29 9.963 Tf 99.895 224.272 Td[(desc)]TJ ET -1 0 0 1 172.619 224.272 cm +1 0 0 1 121.81 224.272 cm q []0 d 0 J @@ -12316,23 +12945,23 @@ q 3.437 0.199 l S Q -1 0 0 1 -172.619 -224.272 cm +1 0 0 1 -121.81 -224.272 cm BT -/F29 9.963 Tf 176.057 224.272 Td[(a)]TJ +/F29 9.963 Tf 125.247 224.272 Td[(a)]TJ ET -1 0 0 1 181.626 224.272 cm +1 0 0 1 130.816 224.272 cm 0 g 0 G -1 0 0 1 -181.626 -224.272 cm +1 0 0 1 -130.816 -224.272 cm BT -/F8 9.963 Tf 186.607 224.272 Td[(con)28(tain)1(s)-334(data)-333(stru)1(c)-1(tu)1(res)-334(for)-333(comm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 135.798 224.272 Td[(con)28(tain)1(s)-334(dat)1(a)-334(stru)1(c)-1(tu)1(res)-334(fo)1(r)-333(c)-1(omm)27(u)1(nication)1(s)-1(.)]TJ -10.996 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 346.526 188.406 cm +1 0 0 1 295.717 188.406 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -346.526 -188.406 cm +1 0 0 1 -295.717 -188.406 cm BT -/F32 9.963 Tf 346.526 188.406 Td[(psb)]TJ +/F32 9.963 Tf 295.717 188.406 Td[(psb)]TJ ET -1 0 0 1 362.845 188.406 cm +1 0 0 1 312.036 188.406 cm q []0 d 0 J @@ -12341,11 +12970,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -362.845 -188.406 cm +1 0 0 1 -312.036 -188.406 cm BT -/F32 9.963 Tf 365.983 188.406 Td[(desc)]TJ +/F32 9.963 Tf 315.174 188.406 Td[(desc)]TJ ET -1 0 0 1 387.532 188.406 cm +1 0 0 1 336.723 188.406 cm q []0 d 0 J @@ -12354,93 +12983,93 @@ q 3.138 0.199 l S Q -1 0 0 1 -387.532 -188.406 cm +1 0 0 1 -336.723 -188.406 cm BT -/F32 9.963 Tf 390.67 188.406 Td[(type)]TJ +/F32 9.963 Tf 339.861 188.406 Td[(type)]TJ ET -1 0 0 1 411.592 188.406 cm +1 0 0 1 360.782 188.406 cm 0 g 0 G -1 0 0 1 -411.592 -188.406 cm +1 0 0 1 -360.782 -188.406 cm BT -/F8 9.963 Tf 411.592 188.406 Td[(.)]TJ +/F8 9.963 Tf 360.782 188.406 Td[(.)]TJ ET -1 0 0 1 145.724 168.146 cm +1 0 0 1 94.914 168.146 cm 0 g 0 G -1 0 0 1 -145.724 -168.146 cm +1 0 0 1 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Td[(k)]TJ/F11 9.963 Tf 4.982 0 Td[(r)]TJ/F10 6.974 Tf 4.495 -1.495 Td[(i)]TJ/F14 9.963 Tf 3.316 1.495 Td[(k)]TJ +/F8 9.963 Tf 275.131 599.126 Td[(\050)]TJ/F14 9.963 Tf 3.874 0 Td[(k)]TJ/F11 9.963 Tf 4.981 0 Td[(A)]TJ/F14 9.963 Tf 7.472 0 Td[(kk)]TJ/F11 9.963 Tf 9.963 0 Td[(x)]TJ/F14 9.963 Tf 5.694 0 Td[(k)]TJ/F8 9.963 Tf 7.195 0 Td[(+)]TJ/F14 9.963 Tf 9.963 0 Td[(k)]TJ/F11 9.963 Tf 4.981 0 Td[(b)]TJ/F14 9.963 Tf 4.276 0 Td[(k)]TJ/F8 9.963 Tf 4.981 0 Td[(\051)]TJ/F11 9.963 Tf 7.837 6.834 Td[(<)-278(e)1(ps)]TJ/F8 9.963 Tf -195.643 -21.533 Td[(or)]TJ/F14 9.963 Tf 149.166 -9.412 Td[(k)]TJ/F11 9.963 Tf 4.981 0 Td[(r)]TJ/F10 6.974 Tf 4.495 -1.495 Td[(i)]TJ/F14 9.963 Tf 3.317 1.495 Td[(k)]TJ ET -1 0 0 1 248.595 570.566 cm +1 0 0 1 299.404 570.566 cm q []0 d 0 J @@ -18213,11 +18889,11 @@ q 18.708 0.199 l S Q -1 0 0 1 -248.595 -570.566 cm +1 0 0 1 -299.404 -570.566 cm BT -/F14 9.963 Tf 248.595 561.441 Td[(k)]TJ/F11 9.963 Tf 4.981 0 Td[(b)]TJ/F14 9.963 Tf 4.276 0 Td[(k)]TJ/F7 6.974 Tf 4.981 -1.494 Td[(2)]TJ/F11 9.963 Tf 8.432 8.328 Td[(<)-278(e)1(ps)]TJ/F8 9.963 Tf -171.37 -24.715 Td[(acc)-1(ord)1(in)1(g)-334(to)-333(th)1(e)-334(v)56(alue)-333(pass)-1(ed)-333(th)1(rough)-332(the)-334(i)1(s)-1(top)-332(argumen)28(t)-333(\050s)-1(ee)-334(lat)1(e)-1(r\051)1(.)]TJ/F18 14.346 Tf 0 -34.616 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 31.341 -22.092 Td[(call)-333(psb)]TJ +/F14 9.963 Tf 299.404 561.441 Td[(k)]TJ/F11 9.963 Tf 4.982 0 Td[(b)]TJ/F14 9.963 Tf 4.275 0 Td[(k)]TJ/F7 6.974 Tf 4.981 -1.494 Td[(2)]TJ/F11 9.963 Tf 8.433 8.328 Td[(<)-277(eps)]TJ/F8 9.963 Tf -171.37 -24.715 Td[(acc)-1(or)1(din)1(g)-334(t)1(o)-334(th)1(e)-334(v)56(alu)1(e)-334(pass)-1(ed)-333(th)1(rou)1(gh)-333(the)-333(is)-1(top)-332(argumen)28(t)-333(\050s)-1(ee)-334(lat)1(e)-1(r)1(\051.)]TJ/F18 14.346 Tf 0 -34.616 Td[(Syn)31(t)1(ax)]TJ/F8 9.963 Tf 31.34 -22.092 Td[(call)-333(psb)]TJ ET -1 0 0 1 165.098 486.852 cm +1 0 0 1 215.907 486.852 cm q []0 d 0 J @@ -18226,11 +18902,11 @@ q 2.989 0.199 l S Q -1 0 0 1 -165.098 -486.852 cm +1 0 0 1 -215.907 -486.852 cm BT -/F8 9.963 Tf 168.087 486.852 Td[(cgs)-334(\050)]TJ/F19 9.963 Tf 20.534 0 Td[(a,pr)52(e)51(c,b,)1(x,eps,desc)]TJ +/F8 9.963 Tf 218.896 486.852 Td[(cgs)-334(\050)]TJ/F19 9.963 Tf 20.534 0 Td[(a,pr)52(e)51(c,b,x)1(,eps,desc)]TJ ET -1 0 0 1 268.323 486.852 cm +1 0 0 1 319.133 486.852 cm q []0 d 0 J @@ -18239,37 +18915,37 @@ q 3.055 0.199 l S Q -1 0 0 1 -268.323 -486.852 cm +1 0 0 1 -319.133 -486.852 cm BT -/F19 9.963 Tf 271.379 486.852 Td[(a,i)1(n)-1(f)1(o,itmax,)1(iter,)1(err,)1(itr)51(ac)51(e,)1(istop)]TJ/F8 9.963 Tf 137.013 0 Td[(\051)]TJ +/F19 9.963 Tf 322.188 486.852 Td[(a,i)1(n)-1(f)1(o,itmax,)1(iter,)1(err,)1(itr)51(ac)51(e,)1(istop)]TJ/F8 9.963 Tf 137.013 0 Td[(\051)]TJ ET -1 0 0 1 94.914 462.627 cm +1 0 0 1 145.724 462.627 cm 0 g 0 G -1 0 0 1 -94.914 -462.627 cm +1 0 0 1 -145.724 -462.627 cm BT -/F29 9.963 Tf 99.895 462.627 Td[(On)-383(En)32(tr)1(y)]TJ +/F29 9.963 Tf 150.705 462.627 Td[(On)-383(En)33(t)-1(r)1(y)]TJ ET -1 0 0 1 147.481 462.627 cm +1 0 0 1 198.29 462.627 cm 0 g 0 G -1 0 0 1 -52.567 -21.185 cm +1 0 0 1 -52.566 -21.185 cm 0 g 0 G -1 0 0 1 -94.914 -441.442 cm +1 0 0 1 -145.724 -441.442 cm BT -/F29 9.963 Tf 99.895 441.442 Td[(a)]TJ +/F29 9.963 Tf 150.705 441.442 Td[(a)]TJ ET -1 0 0 1 105.465 441.442 cm +1 0 0 1 156.274 441.442 cm 0 g 0 G -1 0 0 1 -105.465 -441.442 cm +1 0 0 1 -156.274 -441.442 cm BT -/F8 9.963 Tf 110.446 441.442 Td[(th)1(e)-334(lo)-28(cal)-333(p)-28(or)1(tion)-333(of)-333(g)1(lobal)-333(spar)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 178.968 0 Td[(A)]TJ/F8 9.963 Tf 7.472 0 Td[(.)]TJ -172.084 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.956 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 161.256 441.442 Td[(th)1(e)-334(lo)-28(cal)-333(p)-27(ortion)-333(of)-332(global)-333(spar)1(s)-1(e)-334(matr)1(ix)]TJ/F11 9.963 Tf 178.968 0 Td[(A)]TJ/F8 9.963 Tf 7.472 0 Td[(.)]TJ -172.085 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.956 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 295.717 405.576 cm +1 0 0 1 346.526 405.576 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -405.576 cm +1 0 0 1 -346.526 -405.576 cm BT -/F32 9.963 Tf 295.717 405.576 Td[(psb)]TJ +/F32 9.963 Tf 346.526 405.576 Td[(psb)]TJ ET -1 0 0 1 312.036 405.576 cm +1 0 0 1 362.845 405.576 cm q []0 d 0 J @@ -18278,11 +18954,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -312.036 -405.576 cm +1 0 0 1 -362.845 -405.576 cm BT -/F32 9.963 Tf 315.174 405.576 Td[(spmat)]TJ +/F32 9.963 Tf 365.983 405.576 Td[(spmat)]TJ ET -1 0 0 1 341.953 405.576 cm +1 0 0 1 392.763 405.576 cm q []0 d 0 J @@ -18291,35 +18967,35 @@ q 3.138 0.199 l S Q -1 0 0 1 -341.953 -405.576 cm +1 0 0 1 -392.763 -405.576 cm BT -/F32 9.963 Tf 345.091 405.576 Td[(type)]TJ +/F32 9.963 Tf 395.901 405.576 Td[(type)]TJ ET -1 0 0 1 366.013 405.576 cm +1 0 0 1 416.822 405.576 cm 0 g 0 G -1 0 0 1 -366.013 -405.576 cm +1 0 0 1 -416.822 -405.576 cm BT -/F8 9.963 Tf 366.013 405.576 Td[(.)]TJ +/F8 9.963 Tf 416.822 405.576 Td[(.)]TJ ET -1 0 0 1 94.914 384.392 cm +1 0 0 1 145.724 384.392 cm 0 g 0 G -1 0 0 1 -94.914 -384.392 cm +1 0 0 1 -145.724 -384.392 cm BT -/F29 9.963 Tf 99.895 384.392 Td[(pr)1(e)-1(c)]TJ +/F29 9.963 Tf 150.705 384.392 Td[(pr)1(e)-1(c)]TJ ET -1 0 0 1 121.322 384.392 cm +1 0 0 1 172.131 384.392 cm 0 g 0 G -1 0 0 1 -121.322 -384.392 cm +1 0 0 1 -172.131 -384.392 cm BT -/F8 9.963 Tf 126.303 384.392 Td[(The)-334(d)1(ata)-333(s)-1(tr)1(uctur)1(e)-334(con)28(tain)1(ing)-333(th)1(e)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ -1.501 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.956 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ +/F8 9.963 Tf 177.113 384.392 Td[(The)-333(data)-333(s)-1(t)1(ructur)1(e)-334(con)28(tain)1(ing)-333(th)1(e)-334(pr)1(e)-1(cond)1(ition)1(e)-1(r)1(.)]TJ -1.502 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.956 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(s)-1(tr)1(uctur)1(e)-1(d)-333(d)1(ata)-333(of)-333(t)28(yp)-27(e)]TJ ET -1 0 0 1 295.717 348.526 cm +1 0 0 1 346.526 348.526 cm 0 0 1 rg 0 0 1 RG -1 0 0 1 -295.717 -348.526 cm +1 0 0 1 -346.526 -348.526 cm BT -/F32 9.963 Tf 295.717 348.526 Td[(psb)]TJ +/F32 9.963 Tf 346.526 348.526 Td[(psb)]TJ ET -1 0 0 1 312.036 348.526 cm +1 0 0 1 362.845 348.526 cm q []0 d 0 J @@ -18328,11 +19004,11 @@ q 3.138 0.199 l S Q -1 0 0 1 -312.036 -348.526 cm +1 0 0 1 -362.845 -348.526 cm BT -/F32 9.963 Tf 315.174 348.526 Td[(prec)]TJ +/F32 9.963 Tf 365.983 348.526 Td[(prec)]TJ ET -1 0 0 1 336.723 348.526 cm +1 0 0 1 387.532 348.526 cm q []0 d 0 J @@ -18341,59 +19017,59 @@ q 3.138 0.199 l S Q -1 0 0 1 -336.723 -348.526 cm +1 0 0 1 -387.532 -348.526 cm BT -/F32 9.963 Tf 339.861 348.526 Td[(type)]TJ +/F32 9.963 Tf 390.67 348.526 Td[(type)]TJ ET -1 0 0 1 360.782 348.526 cm +1 0 0 1 411.592 348.526 cm 0 g 0 G -1 0 0 1 -360.782 -348.526 cm +1 0 0 1 -411.592 -348.526 cm BT -/F8 9.963 Tf 360.782 348.526 Td[(.)]TJ +/F8 9.963 Tf 411.592 348.526 Td[(.)]TJ ET -1 0 0 1 94.914 327.342 cm +1 0 0 1 145.724 327.342 cm 0 g 0 G -1 0 0 1 -94.914 -327.342 cm +1 0 0 1 -145.724 -327.342 cm BT -/F29 9.963 Tf 99.895 327.342 Td[(b)]TJ +/F29 9.963 Tf 150.705 327.342 Td[(b)]TJ ET -1 0 0 1 106.26 327.342 cm +1 0 0 1 157.07 327.342 cm 0 g 0 G -1 0 0 1 -106.26 -327.342 cm +1 0 0 1 -157.07 -327.342 cm BT -/F8 9.963 Tf 111.242 327.342 Td[(The)-333(R)-1(HS)-332(v)28(e)-1(ctor.)]TJ 13.56 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(ran)1(k)-333(one)-334(ar)1(ra)28(y)83(.)]TJ +/F8 9.963 Tf 162.051 327.342 Td[(The)-333(R)-1(HS)-332(v)28(e)-1(ctor.)]TJ 13.56 -11.956 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(ran)1(k)-334(on)1(e)-334(ar)1(ra)28(y)83(.)]TJ ET -1 0 0 1 94.914 270.291 cm +1 0 0 1 145.724 270.291 cm 0 g 0 G -1 0 0 1 -94.914 -270.291 cm +1 0 0 1 -145.724 -270.291 cm BT -/F29 9.963 Tf 99.895 270.291 Td[(x)]TJ +/F29 9.963 Tf 150.705 270.291 Td[(x)]TJ ET -1 0 0 1 105.942 270.291 cm +1 0 0 1 156.752 270.291 cm 0 g 0 G -1 0 0 1 -105.942 -270.291 cm +1 0 0 1 -156.752 -270.291 cm BT -/F8 9.963 Tf 110.923 270.291 Td[(The)-334(i)1(nit)1(ial)-333(gues)-1(s.)]TJ 13.879 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(ran)1(k)-333(one)-334(ar)1(ra)28(y)83(.)]TJ +/F8 9.963 Tf 161.733 270.291 Td[(The)-333(init)1(ial)-333(gues)-1(s.)]TJ 13.878 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(lo)-32(cal)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-28(e:)]TJ/F29 9.963 Tf 29.612 0 Td[(requ)1(i)-1(r)1(ed)]TJ/F8 9.963 Tf -29.612 -11.955 Td[(Sp)-27(ec)-1(i\014)1(ed)-333(as)-1(:)-444(a)-333(ran)1(k)-334(on)1(e)-334(ar)1(ra)28(y)83(.)]TJ ET -1 0 0 1 94.914 213.241 cm +1 0 0 1 145.724 213.241 cm 0 g 0 G -1 0 0 1 -94.914 -213.241 cm +1 0 0 1 -145.724 -213.241 cm BT -/F29 9.963 Tf 99.895 213.241 Td[(eps)]TJ +/F29 9.963 Tf 150.705 213.241 Td[(eps)]TJ ET -1 0 0 1 116.031 213.241 cm +1 0 0 1 166.84 213.241 cm 0 g 0 G -1 0 0 1 -116.031 -213.241 cm +1 0 0 1 -166.84 -213.241 cm BT -/F8 9.963 Tf 121.012 213.241 Td[(The)-333(s)-1(top)1(pin)1(g)-333(tole)-1(r)1(ance)-1(.)]TJ 3.79 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 9.963 Tf -32.379 -11.955 Td[(T)28(yp)-27(e)-1(:)]TJ/F29 9.963 Tf 29.611 0 Td[(requ)1(i)-1(r)1(e)-1(d)]TJ/F8 9.963 Tf -29.611 -11.955 Td[(Sp)-27(ec)-1(i)1(\014ed)-333(as)-1(:)-444(a)-333(real)-333(n)28(um)28(b)-28(er.)]TJ +/F8 9.963 Tf 171.821 213.241 Td[(The)-334(stop)1(pin)1(g)-334(t)1(ole)-1(r)1(ance)-1(.)]TJ 3.79 -11.955 Td[(Scop)-27(e)-1(:)]TJ/F29 9.963 Tf 32.379 0 Td[(global)]TJ/F8 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All Rights Reserved) readonly def -/FullName (CMMI7) readonly def +/FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def -/ItalicAngle -14.04 def +/ItalicAngle 0 def /isFixedPitch false def end readonly def -/FontName /PUTCYK+CMMI7 def +/FontName /HDHRKY+CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 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 120 /x put -dup 121 /y put +dup 43 /plus put +dup 49 /one put +dup 50 /two put +dup 58 /colon put readonly def -/FontBBox{0 -250 1171 750}readonly def -/UniqueID 5087382 def +/FontBBox{-27 -250 1122 750}readonly def +/UniqueID 5000790 def currentdict end currentfile eexec -ÙÖoc;„j—¶†©~E£Ðª)s™§„̾…´™;.ëÞ;Ôr·ÏTeò…ji«–íK­/df5à¶A|Ç{S/…ØÇ )¡šSïcë\^ÈŸÆÂm‰çÙäp·+ïÚ#õßv¾¯Lé17¢íŠ©×Öýó~kÍàÙ ˜d#å– -]Ÿ»L•eVèßËúìGo£oÙ¥È\šõþÙÂÝÒkÜ ™9‹ŸM×v9ß2¤Ö#:œ¯i±QßÓ?À–.¬n>¿¸­%j”zGm >Nj›S]Éñ¾Ñ)Å7uÕÖ‡‡¥Œ“ŸÕÚU±•¹QhÈ4)½-‡‚×p#êz£™É{8YãаGP¸9 ññ¼)Ü"¼­PìÆ£Æ3ГzYèYåZùõgp_P÷C߬CÄçÜ”DÎþC'šý<|”(‰£Ròÿ€l/ø³ëIÕxªXÏüMYz©”í„»è²ntÔŸlõAv·)|Ú*iQ€P3|ºTxë˜LÝ" ®ÙʃÃ?¼ÈAwõ·pŸÆÒ‹:rï÷)ˆÁ6,ç›Nœ{?åˆé‚J¼oÑA剳‘Js¤(0T9†$ø“Õ¶Ã'§î'0ÞÞj—°œ%&Æ4öLŸ„wÍQcK¦HüpöYÉ ÀBÀÖ¶ŒÑß6Ö$ób¸ZXÖZŽmýX>ù§šB# µ9Žëxôµ¨šÒ¥à6IUJ½eG#˜ÿ݆>@P1o(ýß‹UøÖc˜Cо¤"‰ø[ØD‰´.ÇÅ)Ó>çè;@Ly›ŽŒˆ—‡Í¶¸¸UxºiÕ ÒÈá*ðèYÀÊCÔ§£#¿H ©S$·íΞ -u"µYôÜF¾…SßµÇf³ÌÂþÃÜõx•ˆ¤JþÚç)ì) oTß$<¿,ï‡\¨ã7Q[éÖ–Qã Ö‘œ _&e>}©ÊyïFÂMdî0’Òk¬Vâ~åÅÄ0¸Ô{1´„ 7–Qb²‘üY{AYî È^ß’š¤+¸…ñÔj¬¸LŒZŸ€$F›!m0Ï° ¹ìÀ‚ á]&ïŽS·h Ç+iî¼²MÚÂ!‹:Þ¿lªE!ó"1p%UÉ·JzÆ¡07Êæ_I툨6¡¸]¹êŠ¸è3o]_¬½ó¥(læP9v04` -­I©ÐFœ´ùø‡ºåX_Mb¨O9ìÊî°9‹”J ½£+¢;Ê}ÞvH[!˜!ROQh),þö!µÂp}Öb ,\ú˜|yxM2©¡YˆåPuœék‚êœû £PEôÒ·kG+=…Ç𳚋R68C–)xù-ôå­-'}Ò32“FdÌ?…õpšN†Hm)Ÿ?X®ÿ…Hx(µl½WáoXºdóÛj||RM°BJºd<‡Ý´«ZÂV5ǸÜIøP#¸°·›šÙu(9ÃJÁ›ö©ú1$*A Ó€ñÅJÇíU©é9€ûšÛ+z+'ÉØ2Íͧx - =+ãPÊ*[.yF ᤅŒRòU€ØÌ/rÏZ£ÅQ뙶BÌÔÒ¡E•5072GKg3½ Q\ Jº™¢ýaÒëm¾UúsÿA¦¢Ù©ÄY0 `{SÛAðäå2lÔ±)­&¿›ŠŽ«ýt×çÇ×C#ü;ÄïÀC/ñj¹Ö î²GËày™I¾}Ö€÷+·lÙ‡îþæ¦Ê᪔ï×RN–ÓŠi›o5×Y©à*žcÐ8¿›;ÑUqïF©Ì²osÒ>uæ¥ßÐshõ3 -½/â®B"°cÆÿWÄœuøa‹¨%5’·Eé^°I•ÞPåø†àKÿ ™-nÓªç%OÇ%ûÚŒ - Z¥ü Y=j‡’™ÒÍ]«Zíñõ'Ô îqºʪ[I·‚Týù×h7 ±Aç=—ôÏÑW»øÕÓsتN -'m`ÿÉWþpfß*îKg5ãÐÙQ °‰ãf³×w/6îŠ\™Æ›ó(Å1dæö"¡Å(lhUG†í]d†øt»ï‹¹‹{¶§O …uªÍš€c?ÊÂüÕÙ¾^unÂG^BÙ"XƒÞ®k} o½F ,š:†Õ5]\(ŽµÞn˜î½°EÜž[[ê×¼>Êi-Æý¡®xÔ‰aG#m´ÿ#¾œƒ„vOÄ/ÃRAE&åŸáœ#PÒšú¸43º¹âªFe÷Ž"pÜ;\j>eèDû¡j?B{4é­Üi@LDS-±ärqí&Ô…Ðáóß`ÖÇ6d{ºcSmÒ‘÷#‹ /¢^nÙwÇsíäèÙöÑ´[ÖDÜ&H:-|UÄ)‚¿Îå#WSG Ê7‡»Íá-×’õUùy°k6ó¹ê0̪̿^75ë‚Œ™ô·@JM¶xÃ".÷"¼0Eíie+]Üt½WИ\Ço²Ï\ÙO›äÉJøðÛøÛKeÛáwç›Â¯'°ždØó¹×ƒk:U°aw/´wb™ägnH)QoÈr^Û¦*à܈¥ÇÊýoÈ¿—VǷͿع’gž‘¡Ö£âàdË–J=1á(ÅØ–EØ÷?¨“Ú%\§ý±@Òb€]3}E´ý€8m}ƒiËNâYÚ¶ö&qF-úo$ qÁJ½¤¶HDgô4vJç1 e¨Ä÷M-ü•¬Ž÷!Ì)¦áóB†ßÞZ%†Ö–JN7™/Ý@çý±µü¶=áFŽ †æ¢`ùó$+ÇkÊÖTTŸƒÚ=þ §f*£a!†ÊUQ#¦ÖǤÛÓZ92û“[ É:Ÿ§‰F[úÒB:I&j|“ÝÊ‹…ž˜}¢|bG¦ L¯K èGæzMUñì]&®´è¶žÌ|¢=8˜€Ï¨:(]žYi¶auÞhΖŒ…æ(zû½-_~¿Ïx\PjÞYŽqþ*Ãx7ißÌD ¢u%5 ~tã’•eÚæ‰TØBî8¥—cQºº“¾3_Õ•¸ô<ÏyÏL‡)š¿ß|ÍîfQ‚uÌņeoEbn¨û|•ZµÐ…‰ ¶wƒî|PÕt   Ón¡LHR÷͹ŠnK ϪL%Ú°„¾a%¹I)!.bêu/̶拸q±è^'fÚ·Jâv èÌg‡ñÃ̹&¬GÕñÍrHºiö”zNÞ÷b¥>ªíLÁÃÞÝeóÉ<óÇîR®á†L%$ݸùp -ÔÉ//L¾/zhK -\¡ŽRS À~sdÀ8¦Ä÷¦ûM›0œ\Š§’æÿÈ•hzÖ¸sð/¶O– ¤í¹[1I5?É8“ä…….¿<Ülû¬ -É“Ìœ¿R¤&Ù«„Ÿû"Äì˜Þòõávºïù*ÿÎüçƒH½ßQbŠWè«7P›T§¨ª5’{ KÿÖGÛ w©Í©…3z¯¦Ò/'1©4ê³`Qiд£ÅàT*W=gÉ2ï‚dÒÙÒbdÚœçœ$-"4õ½â¶5áô@oË7«ÎRWLÖŽáß±">úð°Ó›ÇO¨ÌÈ{À¦¶ßSæùC_—Y¿i-g•óÌtÑœPMHu·ß§ -aÕ{õbýd½•—×v®ø¥€‰—vd¶™l¶Ž9õ ÔÓ×m›1ÓªëX‹™ïô°³‚MfØ–¢OLø¬yu_(\O9yTøOÊùù¼È"<§ ‹Ô9›òú—w¡À¸{ÜÙº“ôa°Cì‚H‡Z@æMp¡Ûä\Û‚µ.»œ¤+æÂ5ºnJº¯„Èø8Ê”Ùþ?Å)kPò É“põI¥2•ì†aX9Î6m53ÉYeGRÛÆØ=ž…úá" {kª3*ã©®q¿¯B=ˆóý nç+ð|þ¥ oŽ¼OAuð í謈ðm÷b3¹Ž»‹DbCN}h€V¾J§”íìQºH’#ëñd¹8BabxËÊÙ"Ú‹}Oæ;ɧT¿@†eŠÅê¤áÌרˆ¾ú³LÛ.’ódh{¡whhNÓ„Á…NÐFè4 Á í„Oüíü– «mg²è%¡cM6‡º“¥‹þ?€&¯”†T¦… ïúò+ÛùWAìðö™œÀ4ŠaÆ#À;\¦úžôÌ1 ¸¸ˆ¼Ë+MÈÜ,¯à(Cï6Æ(x>Æb‹ÐAÛuB¨)Ö¸2WR#)Úv“°³Sèòáo£? 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin -/version (1.0) readonly def +/version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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29534495..8c0cdbd8 100644 --- a/src/comm/psb_dovrl.f90 +++ b/src/comm/psb_dovrl.f90 @@ -40,10 +40,9 @@ ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. ! work - real(optional). A working area. -! choice - logical(optional). ???. -! update_type - integer(optional). ???. +! update - integer(optional). ???. ! -subroutine psb_dovrlm(x,desc_a,info,jx,ik,work,choice,update_type) +subroutine psb_dovrlm(x,desc_a,info,jx,ik,work,update) use psb_descriptor_type use psb_const_mod use psi_mod @@ -56,15 +55,14 @@ subroutine psb_dovrlm(x,desc_a,info,jx,ik,work,choice,update_type) type(psb_desc_type), intent(in) :: desc_a integer, intent(out) :: info real(kind(1.d0)), optional, target :: work(:) - logical, intent(in), optional :: choice - integer, intent(in), optional :: update_type,jx,ik + integer, intent(in), optional :: update,jx,ik ! locals integer :: int_err(5), icontxt, nprow, npcol, myrow, mycol,& & err_act, m, n, iix, jjx, temp(2), ix, ijx, nrow, ncol, k, maxk, iupdate,& & imode, err, liwork, i real(kind(1.d0)),pointer :: iwork(:), xp(:,:) - logical :: ichoice + logical :: do_update character(len=20) :: name, ch_err name='psb_dovrlm' @@ -111,17 +109,13 @@ subroutine psb_dovrlm(x,desc_a,info,jx,ik,work,choice,update_type) k = maxk end if - if (present(choice)) then - ichoice = choice + if (present(update)) then + iupdate = update else - ichoice = .true. - endif - if (present(update_type)) then - iupdate = update_type - else - iupdate = psb_none_ + iupdate = psb_avg_ endif + do_update = (iupdate /= psb_none_) imode = IOR(psb_swap_send_,psb_swap_recv_) ! check vector correctness @@ -166,7 +160,7 @@ subroutine psb_dovrlm(x,desc_a,info,jx,ik,work,choice,update_type) end if ! exchange overlap elements - if(ichoice) then + if(do_update) then xp => x(iix:size(x,1),jjx:jjx+k-1) call psi_swapdata(imode,k,1.d0,xp,& & desc_a,iwork,info,data=psb_comm_ovr_) @@ -263,10 +257,9 @@ end subroutine psb_dovrlm ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code. ! work - real(optional). A working area. -! choice - logical(optional). ???. -! update_type - integer(optional). ???. +! update - integer(optional). ???. ! -subroutine psb_dovrlv(x,desc_a,info,work,choice,update_type) +subroutine psb_dovrlv(x,desc_a,info,work,update) use psb_descriptor_type use psi_mod use psb_const_mod @@ -279,15 +272,14 @@ subroutine psb_dovrlv(x,desc_a,info,work,choice,update_type) type(psb_desc_type), intent(in) :: desc_a integer, intent(out) :: info real(kind(1.d0)), optional, target :: work(:) - logical, intent(in), optional :: choice - integer, intent(in), optional :: update_type + integer, intent(in), optional :: update ! locals integer :: int_err(5), icontxt, nprow, npcol, myrow, mycol,& & err_act, m, n, iix, jjx, temp(2), ix, ijx, nrow, ncol, k, maxk, iupdate,& & imode, err, liwork, i real(kind(1.d0)),pointer :: iwork(:) - logical :: ichoice + logical :: do_update character(len=20) :: name, ch_err name='psb_dovrlv' @@ -320,17 +312,13 @@ subroutine psb_dovrlv(x,desc_a,info,work,choice,update_type) k = 1 - if (present(choice)) then - ichoice = choice - else - ichoice = .true. - endif - if (present(update_type)) then - iupdate = update_type + if (present(update)) then + iupdate = update else - iupdate = psb_none_ + iupdate = psb_avg_ endif + do_update = (iupdate /= psb_none_) imode = IOR(psb_swap_send_,psb_swap_recv_) ! check vector correctness @@ -375,7 +363,7 @@ subroutine psb_dovrlv(x,desc_a,info,work,choice,update_type) end if ! exchange overlap elements - if(ichoice) then + if(do_update) then call psi_swapdata(imode,1.d0,x(iix:size(x)),& & desc_a,iwork,info,data=psb_comm_ovr_) end if diff --git a/src/comm/psb_zovrl.f90 b/src/comm/psb_zovrl.f90 index 88e9f8bd..4a72e138 100644 --- a/src/comm/psb_zovrl.f90 +++ b/src/comm/psb_zovrl.f90 @@ -40,10 +40,9 @@ ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. ! work - real(optional). A working area. -! choice - logical(optional). ???. -! update_type - integer(optional). ???. +! update - integer(optional). ???. ! -subroutine psb_zovrlm(x,desc_a,info,jx,ik,work,choice,update_type) +subroutine psb_zovrlm(x,desc_a,info,jx,ik,work,update) use psb_descriptor_type use psb_const_mod use psi_mod @@ -56,15 +55,14 @@ subroutine psb_zovrlm(x,desc_a,info,jx,ik,work,choice,update_type) type(psb_desc_type), intent(in) :: desc_a integer, intent(out) :: info complex(kind(1.d0)), optional, target :: work(:) - logical, intent(in), optional :: choice - integer, intent(in), optional :: update_type,jx,ik + integer, intent(in), optional :: update,jx,ik ! locals integer :: int_err(5), icontxt, nprow, npcol, myrow, mycol,& & err_act, m, n, iix, jjx, temp(2), ix, ijx, nrow, ncol, k, maxk, iupdate,& & imode, err, liwork, i complex(kind(1.d0)),pointer :: iwork(:), xp(:,:) - logical :: ichoice + logical :: do_update character(len=20) :: name, ch_err name='psb_zovrlm' @@ -111,17 +109,13 @@ subroutine psb_zovrlm(x,desc_a,info,jx,ik,work,choice,update_type) k = maxk end if - if (present(choice)) then - ichoice = choice + if (present(update)) then + iupdate = update else - ichoice = .true. - endif - if (present(update_type)) then - iupdate = update_type - else - iupdate = psb_none_ + iupdate = psb_avg_ endif + do_update = (iupdate /= psb_none_) imode = IOR(psb_swap_send_,psb_swap_recv_) ! check vector correctness @@ -166,7 +160,7 @@ subroutine psb_zovrlm(x,desc_a,info,jx,ik,work,choice,update_type) end if ! exchange overlap elements - if(ichoice) then + if(do_update) then xp => x(iix:size(x,1),jjx:jjx+k-1) call psi_swapdata(imode,k,zone,xp,& & desc_a,iwork,info,data=psb_comm_ovr_) @@ -263,10 +257,9 @@ end subroutine psb_zovrlm ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code. ! work - real(optional). A working area. -! choice - logical(optional). ???. -! update_type - integer(optional). ???. +! update - integer(optional). ???. ! -subroutine psb_zovrlv(x,desc_a,info,work,choice,update_type) +subroutine psb_zovrlv(x,desc_a,info,work,update) use psb_descriptor_type use psi_mod use psb_const_mod @@ -279,15 +272,14 @@ subroutine psb_zovrlv(x,desc_a,info,work,choice,update_type) type(psb_desc_type), intent(in) :: desc_a integer, intent(out) :: info complex(kind(1.d0)), optional, target :: work(:) - logical, intent(in), optional :: choice - integer, intent(in), optional :: update_type + integer, intent(in), optional :: update ! locals integer :: int_err(5), icontxt, nprow, npcol, myrow, mycol,& & err_act, m, n, iix, jjx, temp(2), ix, ijx, nrow, ncol, k, maxk, iupdate,& & imode, err, liwork, i complex(kind(1.d0)),pointer :: iwork(:) - logical :: ichoice + logical :: do_update character(len=20) :: name, ch_err name='psb_zovrlv' @@ -320,17 +312,13 @@ subroutine psb_zovrlv(x,desc_a,info,work,choice,update_type) k = 1 - if (present(choice)) then - ichoice = choice - else - ichoice = .true. - endif - if (present(update_type)) then - iupdate = update_type + if (present(update)) then + iupdate = update else iupdate = psb_none_ endif + do_update = (iupdate /= psb_none_) imode = IOR(psb_swap_send_,psb_swap_recv_) ! check vector correctness @@ -376,7 +364,7 @@ subroutine psb_zovrlv(x,desc_a,info,work,choice,update_type) ! exchange overlap elements - if(ichoice) then + if(do_update) then call psi_swapdata(imode,zone,x(iix:size(x)),& & desc_a,iwork,info,data=psb_comm_ovr_) end if diff --git a/src/methd/psb_dbicg.f90 b/src/methd/psb_dbicg.f90 index e0c3a219..fbfc03f6 100644 --- a/src/methd/psb_dbicg.f90 +++ b/src/methd/psb_dbicg.f90 @@ -102,7 +102,7 @@ subroutine psb_dbicg(a,prec,b,x,eps,desc_a,info,& & r(:), p(:), zt(:), pt(:), z(:), rt(:),qt(:) integer, pointer :: iperm(:), ipnull(:), ipsave(:), int_err(:) real(kind(1.d0)) ::rerr - integer ::litmax, liter, naux, m, mglob, it, itrac,& + integer ::litmax, liter, naux, m, mglob, it, itrace_,& & nprows,npcols,me,mecol, n_row, n_col, istop_, err_act character ::diagl, diagu logical, parameter :: debug = .false. @@ -159,7 +159,7 @@ subroutine psb_dbicg(a,prec,b,x,eps,desc_a,info,& naux=4*n_col allocate(aux(naux),stat=info) - call psb_geall(mglob,9,wwrk,desc_a,info) + call psb_geall(wwrk,desc_a,info,n=9) call psb_geasb(wwrk,desc_a,info) if(info.ne.0) then info=4011 @@ -186,9 +186,9 @@ subroutine psb_dbicg(a,prec,b,x,eps,desc_a,info,& endif if (present(itrace)) then - itrac = itrace + itrace_ = itrace else - itrac = -1 + itrace_ = 0 end if diagl = 'u' @@ -241,15 +241,8 @@ subroutine psb_dbicg(a,prec,b,x,eps,desc_a,info,& if (istop_ == 1) then xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - if (me.eq.0) write(itrac,'(a,i4,5(2x,es10.4))') 'bicg: ',itx,rerr,rni,bni,& - &xni,ani - endif else if (istop_ == 2) then rerr = rni/bn2 - if (itrac /= -1) then - if (me.eq.0) write(itrac,'(a,i4,3(2x,es10.4))') 'bicg: ',itx,rerr,rni,bn2 - endif endif if(info.ne.0) then @@ -261,6 +254,11 @@ subroutine psb_dbicg(a,prec,b,x,eps,desc_a,info,& if (rerr<=eps) then exit restart end if + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'bicg: ',itx,rerr + end If + iteration: do it = it + 1 @@ -315,23 +313,25 @@ subroutine psb_dbicg(a,prec,b,x,eps,desc_a,info,& if (istop_ == 1) then xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - if (me.eq.0) write(itrac,'(a,i4,5(2x,es10.4))') 'bicg: ',itx,rerr,rni,bni,& - &xni,ani - endif else if (istop_ == 2) then rerr = rni/bn2 - if (itrac /= -1) then - if (me.eq.0) write(itrac,'(a,i4,3(2x,es10.4))') 'bicg: ',itx,rerr,rni,bn2 - endif endif if (rerr<=eps) then exit restart end if + if (itx.ge.litmax) exit restart + + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'bicg: ',itx,rerr + end If end do iteration end do restart - + If (itrace_ > 0) then + if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'bicg: ',itx,rerr + end If + if (present(err)) err=rerr if (present(iter)) iter = itx if (rerr>eps) then diff --git a/src/methd/psb_dcg.f90 b/src/methd/psb_dcg.f90 index bea4d478..39f45b47 100644 --- a/src/methd/psb_dcg.f90 +++ b/src/methd/psb_dcg.f90 @@ -102,7 +102,7 @@ Subroutine psb_dcg(a,prec,b,x,eps,desc_a,info,& real(kind(1.d0)) ::rerr real(kind(1.d0)) ::alpha, beta, rho, rho_old, rni, xni, bni, ani,bn2,& & sigma - integer :: litmax, liter, istop_, naux, m, mglob, it, itx, itrac,& + integer :: litmax, liter, istop_, naux, m, mglob, it, itx, itrace_,& & nprows,npcols,me,mecol, n_col, isvch, ich, icontxt, n_row,err_act, int_err(5) character ::diagl, diagu logical, parameter :: exchange=.true., noexchange=.false. @@ -148,7 +148,7 @@ Subroutine psb_dcg(a,prec,b,x,eps,desc_a,info,& naux=4*n_col allocate(aux(naux), stat=info) - call psb_geall(mglob,5,wwrk,desc_a,info) + call psb_geall(wwrk,desc_a,info,n=5) call psb_geasb(wwrk,desc_a,info) if (info.ne.0) then info=4011 @@ -170,9 +170,9 @@ Subroutine psb_dcg(a,prec,b,x,eps,desc_a,info,& endif if (present(itrace)) then - itrac = itrace + itrace_ = itrace else - itrac = -1 + itrace_ = 0 end if itx=0 @@ -243,23 +243,24 @@ Subroutine psb_dcg(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - If (itrac /= -1) Then - If (me.Eq.0) Write(itrac,'(a,i4,5(2x,es10.4))') 'cg: ',itx,rerr,rni,bni,& - &xni,ani - Endif - Else If (istop_ == 2) Then rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - If (itrac /= -1) Then - If (me.Eq.0) Write(itrac,'(a,i4,3(2x,es10.4)))') 'cg: ',itx,rerr,rni,bn2 - Endif Endif if (rerr<=eps) exit restart + if (itx>= litmax) exit restart + + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'cg: ',itx,rerr + end If end do iteration end do restart + If (itrace_ > 0) then + if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'cg: ',itx,rerr + end If if (present(err)) err=rerr if (present(iter)) iter = itx diff --git a/src/methd/psb_dcgs.f90 b/src/methd/psb_dcgs.f90 index d151f1b6..c8c07a1d 100644 --- a/src/methd/psb_dcgs.f90 +++ b/src/methd/psb_dcgs.f90 @@ -100,7 +100,7 @@ Subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,& & r(:), p(:), v(:), s(:), t(:), z(:), f(:), rt(:),qt(:),uv(:) Integer, Pointer :: iperm(:), ipnull(:), ipsave(:) Real(Kind(1.d0)) ::rerr - Integer ::litmax, liter, naux, m, mglob, it, itrac,int_err(5),& + Integer ::litmax, liter, naux, m, mglob, it, itrace_,int_err(5),& & nprows,npcols,me,mecol, n_row, n_col,istop_, err_act Character ::diagl, diagu Logical, Parameter :: exchange=.True., noexchange=.False. @@ -153,7 +153,7 @@ Subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,& naux=4*n_col Allocate(aux(naux),stat=info) - Call psb_geall(mglob,11,wwrk,desc_a,info) + Call psb_geall(wwrk,desc_a,info,n=11) Call psb_geasb(wwrk,desc_a,info) if (info.ne.0) Then info=4011 @@ -181,9 +181,9 @@ Subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,& Endif If (Present(itrace)) Then - itrac = itrace + itrace_ = itrace Else - itrac = -1 + itrace_ = 0 End If ! Ensure global coherence for convergence checks. @@ -227,26 +227,23 @@ Subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'cgs: ',& - & itx,rerr,rni,bni,xni,ani - endif else if (istop_ == 2) then rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr,rni,bn2 - endif endif if(info/=0)then info=4011 call psb_errpush(info,name) goto 9999 - end if - + end if If (rerr<=eps) Then Exit restart End If + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr + end If + iteration: Do it = it + 1 @@ -303,28 +300,31 @@ Subroutine psb_dcgs(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'cgs: ',& - & itx,rerr,rni,bni,xni,ani - endif - else if (istop_ == 2) then - rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'cgs: ',& - & itx,rerr,rni,bn2 - endif endif If (rerr<=eps) Then Exit restart End If + If (itx.Ge.litmax) Exit restart + + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr + end If + End Do iteration End Do restart + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr + end If + + If (Present(err)) err=rerr If (Present(iter)) iter = itx If (rerr>eps) Then diff --git a/src/methd/psb_dcgstab.f90 b/src/methd/psb_dcgstab.f90 index 018c582e..0a335280 100644 --- a/src/methd/psb_dcgstab.f90 +++ b/src/methd/psb_dcgstab.f90 @@ -100,7 +100,7 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,& & r(:), p(:), v(:), s(:), t(:), z(:), f(:) Integer, Pointer :: iperm(:), ipnull(:), ipsave(:) Real(Kind(1.d0)) ::rerr - Integer ::litmax, liter, naux, m, mglob, it,itrac,& + Integer ::litmax, liter, naux, m, mglob, it,itrace_,& & nprows,npcols,myrow,mycol, n_row, n_col Character ::diagl, diagu Logical, Parameter :: debug = .false. @@ -158,7 +158,7 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,& naux=6*n_col allocate(aux(naux),stat=info) - if (info == 0) call psb_geall(mglob,8,wwrk,desc_a,info) + if (info == 0) call psb_geall(wwrk,desc_a,info,n=8) if (info == 0) call psb_geasb(wwrk,desc_a,info) if (info /= 0) then info=4011 @@ -182,9 +182,9 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,& Endif If (Present(itrace)) Then - itrac = itrace + itrace_ = itrace Else - itrac = -1 + itrace_ = 0 End If diagl = 'U' @@ -245,8 +245,8 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,& rn0 = rni End If If (rn0 == 0.d0 ) Then - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,*) 'BiCGSTAB: ',itx,rn0 + If (itrace_ > 0 ) Then + If (myrow == 0) Write(*,*) 'BiCGSTAB: ',itx,rn0 Endif Exit restart End If @@ -254,15 +254,8 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,& If (istop_ == 1) Then xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'bicgstab: ',itx,rerr,rni,bni,& - &xni,ani - Endif Else If (istop_ == 2) Then rerr = rni/bn2 - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr,rni,bn2 - Endif Endif if (info /= 0) Then info=4011 @@ -270,10 +263,14 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,& goto 9999 End If - If (rerr<=eps) Then Exit restart End If + + If (itrace_ > 0) then + if (((itx==0).or.(mod(itx,itrace_)==0)).and.(myrow == 0)) & + & write(*,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr + Endif iteration: Do it = it + 1 @@ -357,33 +354,35 @@ Subroutine psb_dcgstab(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,5(2x,es10.4))') & - & 'bicgstab: ',itx,rerr,rni,bni,xni,ani - Endif Else If (istop_ == 2) Then rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,3(2x,es10.4)))') & - & 'bicgstab: ',itx,rerr,rni,bn2 - Endif Endif - If (rerr<=eps) Then Exit restart End If If (itx.Ge.litmax) Exit restart + + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(myrow == 0)) & + & write(*,'(a,i4,3(2x,es10.4)))') & + & 'bicgstab: ',itx,rerr + Endif + End Do iteration End Do restart + If (itrace_ > 0) then + if (myrow == 0) write(*,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr + Endif + If (Present(err)) err=rerr If (Present(iter)) iter = itx If (rerr>eps) Then - Write(0,*) 'BI-CGSTAB FAILED TO CONVERGE TO ',EPS,& - & ' IN ',ITX,' ITERATIONS ' + Write(0,*) 'BI-CGSTAB failed to converge to ',EPS,& + & ' in ',ITX,' iterations. ' End If Deallocate(aux) diff --git a/src/methd/psb_dcgstabl.f90 b/src/methd/psb_dcgstabl.f90 index 95a2260e..e8a65264 100644 --- a/src/methd/psb_dcgstabl.f90 +++ b/src/methd/psb_dcgstabl.f90 @@ -109,7 +109,7 @@ Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,& &pv1(:), pv2(:), pm1(:,:), pm2(:,:) Integer, Pointer :: iperm(:), ipnull(:), ipsave(:) Real(Kind(1.d0)) ::rerr - Integer ::litmax, liter, naux, m, mglob, it, itrac,& + Integer ::litmax, liter, naux, m, mglob, it, itrace_,& & nprows,npcols,me,mecol, n_row, n_col, nl, err_act Character ::diagl, diagu Logical, Parameter :: exchange=.True., noexchange=.False. @@ -161,9 +161,9 @@ Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,& Endif If (Present(itrace)) Then - itrac = itrace + itrace_ = itrace Else - itrac = -1 + itrace_ = 0 End If If (Present(irst)) Then @@ -183,9 +183,9 @@ Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,& call psb_errpush(info,name) goto 9999 End If - Call psb_geall(mglob,10,wwrk,desc_a,info) - Call psb_geall(mglob,nl+1,uh,desc_a,info,js=0) - Call psb_geall(mglob,nl+1,rh,desc_a,info,js=0) + Call psb_geall(wwrk,desc_a,info,n=10) + Call psb_geall(uh,desc_a,info,n=nl+1) + Call psb_geall(rh,desc_a,info,n=nl+1) Call psb_geasb(wwrk,desc_a,info) Call psb_geasb(uh,desc_a,info) Call psb_geasb(rh,desc_a,info) @@ -255,17 +255,9 @@ Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'bicgstab(l): ',& - & itx,rerr,rni,bni,xni,ani - endif else if (istop_ == 2) then rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',& - & itx,rerr,rni,bn2 - endif endif if (info.ne.0) Then info=4011 @@ -276,6 +268,10 @@ Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,& If (rerr<=eps) Then Exit restart End If + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',itx,rerr + end If iteration: Do it = it + nl @@ -364,29 +360,27 @@ Subroutine psb_dcgstabl(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(rh(:,0),desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'bicgstab(l): ',& - & itx,rerr,rni,bni,xni,ani - endif - else if (istop_ == 2) then - rni = psb_genrm2(rh(:,0),desc_a,info) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',& - & itx,rerr,rni,bn2 - endif endif If (rerr<=eps) Then Exit restart End If - If (itx.Ge.litmax) Exit restart + + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',itx,rerr + end If + End Do iteration End Do restart + If (itrace_ > 0) then + if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'bicgstab(l): ',itx,rerr + end If If (Present(err)) err=rerr If (Present(iter)) iter = itx If (rerr>eps) Then diff --git a/src/methd/psb_dgmresr.f90 b/src/methd/psb_dgmresr.f90 index e1c5730b..a0e87f47 100644 --- a/src/methd/psb_dgmresr.f90 +++ b/src/methd/psb_dgmresr.f90 @@ -111,7 +111,7 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& &pv1(:), pv2(:), pm1(:,:), rr(:,:) Integer, Pointer :: iperm(:), ipnull(:), ipsave(:), ierrv(:) Real(Kind(1.d0)) :: rerr, scal, gm - Integer ::litmax, liter, naux, m, mglob, it,k, itrac,& + Integer ::litmax, liter, naux, m, mglob, it,k, itrace_,& & nprows,npcols,me,mecol, n_row, n_col, nl, int_err(5) Character ::diagl, diagu Logical, Parameter :: exchange=.True., noexchange=.False. @@ -164,9 +164,9 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& Endif If (Present(itrace)) Then - itrac = itrace + itrace_ = itrace Else - itrac = -1 + itrace_ = 0 End If If (Present(irst)) Then @@ -188,8 +188,8 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& goto 9999 End If - Call psb_geall(mglob,nl+1,v,desc_a,info) - Call psb_geall(mglob,w,desc_a,info) + Call psb_geall(v,desc_a,info,n=nl+1) + Call psb_geall(w,desc_a,info) Call psb_geasb(v,desc_a,info) Call psb_geasb(w,desc_a,info) if (info.ne.0) Then @@ -247,17 +247,9 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(v(:,1),desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'gmresr(l): ',& - & itx,rerr,rni,bni,xni,ani - endif else if (istop_ == 2) then rni = psb_genrm2(v(:,1),desc_a,info) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'gmresr(l): ',& - & itx,rerr,rni,bn2 - endif endif if (info.ne.0) Then info=4011 @@ -268,6 +260,10 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& If (rerr<=eps) Then Exit restart End If + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr + end If If (itx.Ge.litmax) Exit restart @@ -304,17 +300,9 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& rni = abs(rs(i+1)) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'gmresr(l): ',& - & itx,rerr,rni,bni,xni,ani - endif else if (istop_ == 2) then rni = abs(rs(i+1)) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'gmresr(l): ',& - & itx,rerr,rni,bn2 - endif endif if (rerr < eps ) then @@ -325,6 +313,10 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& end do exit restart end if + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr + end If end Do inner if (debug) write(0,*) 'Before DTRSM :',rs(1:nl) @@ -335,6 +327,9 @@ Subroutine psb_dgmresr(a,prec,b,x,eps,desc_a,info,& end do End Do restart + If (itrace_ > 0) then + if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'gmres(l): ',itx,rerr + end If If (Present(err)) err=rerr If (Present(iter)) iter = itx diff --git a/src/methd/psb_zcgs.f90 b/src/methd/psb_zcgs.f90 index 9714067a..ea6fffaa 100644 --- a/src/methd/psb_zcgs.f90 +++ b/src/methd/psb_zcgs.f90 @@ -100,7 +100,7 @@ Subroutine psb_zcgs(a,prec,b,x,eps,desc_a,info,& & r(:), p(:), v(:), s(:), t(:), z(:), f(:), rt(:),qt(:),uv(:) Integer, Pointer :: iperm(:), ipnull(:), ipsave(:) Real(Kind(1.d0)) ::rerr - Integer ::litmax, liter, naux, m, mglob, it, itrac,int_err(5),& + Integer ::litmax, liter, naux, m, mglob, it, itrace_,int_err(5),& & nprows,npcols,me,mecol, n_row, n_col,istop_, err_act Character ::diagl, diagu Logical, Parameter :: exchange=.True., noexchange=.False. @@ -153,7 +153,7 @@ Subroutine psb_zcgs(a,prec,b,x,eps,desc_a,info,& naux=4*n_col Allocate(aux(naux),stat=info) - Call psb_geall(mglob,11,wwrk,desc_a,info) + Call psb_geall(wwrk,desc_a,info,n=11) Call psb_geasb(wwrk,desc_a,info) if (info.ne.0) Then info=4011 @@ -181,9 +181,9 @@ Subroutine psb_zcgs(a,prec,b,x,eps,desc_a,info,& Endif If (Present(itrace)) Then - itrac = itrace + itrace_ = itrace Else - itrac = -1 + itrace_ = 0 End If ! Ensure global coherence for convergence checks. @@ -227,16 +227,9 @@ Subroutine psb_zcgs(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'cgs: ',& - & itx,rerr,rni,bni,xni,ani - endif else if (istop_ == 2) then rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr,rni,bn2 - endif endif if(info/=0)then info=4011 @@ -247,6 +240,10 @@ Subroutine psb_zcgs(a,prec,b,x,eps,desc_a,info,& If (rerr<=eps) Then Exit restart End If + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr + end If iteration: Do it = it + 1 @@ -303,27 +300,26 @@ Subroutine psb_zcgs(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'cgs: ',& - & itx,rerr,rni,bni,xni,ani - endif - else if (istop_ == 2) then - rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - if (itrac /= -1) then - If (me == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'cgs: ',& - & itx,rerr,rni,bn2 - endif endif If (rerr<=eps) Then Exit restart End If If (itx.Ge.litmax) Exit restart + + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(me == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr + end If + End Do iteration End Do restart + If (itrace_ > 0) then + if (me == 0) write(*,'(a,i4,3(2x,es10.4))') 'cgs: ',itx,rerr + end If If (Present(err)) err=rerr If (Present(iter)) iter = itx diff --git a/src/methd/psb_zcgstab.f90 b/src/methd/psb_zcgstab.f90 index 6e7004c9..f7d04cb5 100644 --- a/src/methd/psb_zcgstab.f90 +++ b/src/methd/psb_zcgstab.f90 @@ -100,7 +100,7 @@ Subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,& & r(:), p(:), v(:), s(:), t(:), z(:), f(:) Integer, Pointer :: iperm(:), ipnull(:), ipsave(:) Real(Kind(1.d0)) :: rerr - Integer :: litmax, liter, naux, m, mglob, it,itrac,& + Integer :: litmax, liter, naux, m, mglob, it,itrace_,& & nprows,npcols,myrow,mycol, n_row, n_col Character ::diagl, diagu Logical, Parameter :: debug = .false. @@ -158,7 +158,7 @@ Subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,& naux=6*n_col allocate(aux(naux),stat=info) - call psb_geall(mglob,8,wwrk,desc_a,info) + call psb_geall(wwrk,desc_a,info,n=8) call psb_geasb(wwrk,desc_a,info) if (info /= 0) then info=4011 @@ -182,9 +182,9 @@ Subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,& Endif If (Present(itrace)) Then - itrac = itrace + itrace_ = itrace Else - itrac = -1 + itrace_ = 0 End If diagl = 'U' @@ -245,24 +245,14 @@ Subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,& rn0 = rni End If If (rn0 == 0.d0 ) Then - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,*) 'BiCGSTAB: ',itx,rn0 - Endif Exit restart End If If (istop_ == 1) Then xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,5(2x,es10.4))') 'bicgstab: ',itx,rerr,rni,bni,& - &xni,ani - Endif Else If (istop_ == 2) Then rerr = rni/bn2 - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr,rni,bn2 - Endif Endif if (info /= 0) Then info=4011 @@ -270,11 +260,15 @@ Subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,& goto 9999 End If - If (rerr<=eps) Then Exit restart End If + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(myrow == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr + end If + iteration: Do it = it + 1 itx = itx + 1 @@ -356,18 +350,9 @@ Subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,& rni = psb_geamax(r,desc_a,info) xni = psb_geamax(x,desc_a,info) rerr = rni/(ani*xni+bni) - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,5(2x,es10.4))') & - & 'bicgstab: ',itx,rerr,rni,bni,xni,ani - Endif - Else If (istop_ == 2) Then rni = psb_genrm2(r,desc_a,info) rerr = rni/bn2 - If (itrac /= -1) Then - If (myrow == 0) Write(itrac,'(a,i4,3(2x,es10.4)))') & - & 'bicgstab: ',itx,rerr,rni,bn2 - Endif Endif If (rerr<=eps) Then @@ -375,14 +360,22 @@ Subroutine psb_zcgstab(a,prec,b,x,eps,desc_a,info,& End If If (itx.Ge.litmax) Exit restart + If (itrace_ > 0) then + if ((mod(itx,itrace_)==0).and.(myrow == 0))& + & write(*,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr + end If + End Do iteration End Do restart + If (itrace_ > 0) then + if (myrow == 0) write(*,'(a,i4,3(2x,es10.4))') 'bicgstab: ',itx,rerr + end If If (Present(err)) err=rerr If (Present(iter)) iter = itx If (rerr>eps) Then - Write(0,*) 'BI-CGSTAB FAILED TO CONVERGE TO ',EPS,& - & ' IN ',ITX,' ITERATIONS ' + Write(0,*) 'BI-cgstab failed to converge to ',eps,& + & ' in ',itx,' iterations. ' End If Deallocate(aux) diff --git a/src/prec/psb_dbaseprc_aply.f90 b/src/prec/psb_dbaseprc_aply.f90 index 52e7f8e9..945a2fc2 100644 --- a/src/prec/psb_dbaseprc_aply.f90 +++ b/src/prec/psb_dbaseprc_aply.f90 @@ -234,11 +234,11 @@ subroutine psb_dbaseprc_aply(prec,x,beta,y,desc_data,trans,work,info) case(psb_none_) ! Would work anyway, but since it's supposed to do nothing... - ! call f90_psovrl(ty,prec%desc_data,update_type=prec%a_restrict) + ! call f90_psovrl(ty,prec%desc_data,update=prec%a_restrict) case(psb_sum_,psb_avg_) call psb_ovrl(ty,prec%desc_data,info,& - & update_type=prec%iprcparm(prol_),work=aux) + & update=prec%iprcparm(prol_),work=aux) if(info /=0) then info=4010 ch_err='psb_ovrl' diff --git a/src/prec/psb_dslu_bld.f90 b/src/prec/psb_dslu_bld.f90 index fb381504..16235056 100644 --- a/src/prec/psb_dslu_bld.f90 +++ b/src/prec/psb_dslu_bld.f90 @@ -89,7 +89,7 @@ subroutine psb_dslu_bld(a,desc_a,p,info) call blacs_barrier(icontxt,'All') endif - call psb_dcsdp(a,atmp,info) + call psb_csdp(a,atmp,info) if(info /= 0) then info=4010 ch_err='psb_dcsdp' diff --git a/src/prec/psb_zbaseprc_aply.f90 b/src/prec/psb_zbaseprc_aply.f90 index 19a26a3b..d879ac84 100644 --- a/src/prec/psb_zbaseprc_aply.f90 +++ b/src/prec/psb_zbaseprc_aply.f90 @@ -234,11 +234,11 @@ subroutine psb_zbaseprc_aply(prec,x,beta,y,desc_data,trans,work,info) case(psb_none_) ! Would work anyway, but since it's supposed to do nothing... - ! call f90_psovrl(ty,prec%desc_data,update_type=prec%a_restrict) + ! call f90_psovrl(ty,prec%desc_data,update=prec%a_restrict) case(psb_sum_,psb_avg_) call psb_ovrl(ty,prec%desc_data,info,& - & update_type=prec%iprcparm(prol_),work=aux) + & update=prec%iprcparm(prol_),work=aux) if(info /=0) then info=4010 ch_err='psb_ovrl' diff --git a/src/prec/psb_zbldaggrmat.f90 b/src/prec/psb_zbldaggrmat.f90 index 09cea289..be8aa6e8 100644 --- a/src/prec/psb_zbldaggrmat.f90 +++ b/src/prec/psb_zbldaggrmat.f90 @@ -624,7 +624,7 @@ contains if (debug) write(0,*) me,'Done NUMBMM 2' if (p%iprcparm(smth_kind_) == smth_omg_) then - call psb_transp(am1,am2,fmt='COO') + call psb_transc(am1,am2,fmt='COO') nzl = am2%infoa(psb_nnz_) i=0 ! @@ -643,7 +643,7 @@ contains am2%infoa(psb_nnz_) = i call psb_ipcoo2csr(am2,info) else - call psb_transp(am1,am2) + call psb_transc(am1,am2) endif if (debug) write(0,*) me,'starting sphalo/ rwxtd' diff --git a/src/prec/psb_zslu_bld.f90 b/src/prec/psb_zslu_bld.f90 index 28339157..54f4fd81 100644 --- a/src/prec/psb_zslu_bld.f90 +++ b/src/prec/psb_zslu_bld.f90 @@ -51,7 +51,7 @@ subroutine psb_zslu_bld(a,desc_a,p,info) character(len=5) :: fmt character :: upd='F' integer :: i,j,nza,nzb,nzt,icontxt, me,mycol,nprow,npcol,err_act - logical, parameter :: debug=.false. + logical, parameter :: debug=.true. character(len=20) :: name, ch_err interface psb_asmatbld @@ -85,14 +85,14 @@ subroutine psb_zslu_bld(a,desc_a,p,info) atmp%fida='COO' if (Debug) then - write(0,*) me, 'SPLUBLD: Calling csdp' + write(0,*) me, 'ZSLUBLD: Calling csdp' call blacs_barrier(icontxt,'All') endif - call psb_zcsdp(a,atmp,info) + call psb_csdp(a,atmp,info) if(info /= 0) then info=4010 - ch_err='psb_zcsdp' + ch_err='psb_csdp' call psb_errpush(info,name,a_err=ch_err) goto 9999 end if diff --git a/src/psblas/psb_dspmm.f90 b/src/psblas/psb_dspmm.f90 index ab61482f..b52de478 100644 --- a/src/psblas/psb_dspmm.f90 +++ b/src/psblas/psb_dspmm.f90 @@ -188,26 +188,26 @@ subroutine psb_dspmm(alpha,a,x,beta,y,desc_a,info,& liwork= 2*ncol if (a%pr(1) /= 0) liwork = liwork + n * ik if (a%pl(1) /= 0) liwork = liwork + m * ik -if (present(work)) then + if (present(work)) then if (size(work) >= liwork) then - aliw =.false. + aliw =.false. else - aliw=.true. + aliw=.true. endif else - aliw=.true. + aliw=.true. end if if (aliw) then - call psb_realloc(liwork,iwork,info) - if(info.ne.0) then - info=4010 - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if + call psb_realloc(liwork,iwork,info) + if(info.ne.0) then + info=4010 + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if else - iwork => work + iwork => work endif iwork(1)=dzero diff --git a/src/psblas/psb_dspsm.f90 b/src/psblas/psb_dspsm.f90 index 38746cf6..cbdcd3b4 100644 --- a/src/psblas/psb_dspsm.f90 +++ b/src/psblas/psb_dspsm.f90 @@ -196,26 +196,26 @@ subroutine psb_dspsm(alpha,a,x,beta,y,desc_a,info,& liwork= 2*ncol if (a%pr(1) /= 0) llwork = liwork + m * ik if (a%pl(1) /= 0) llwork = llwork + m * ik - if (present(work)) then + if (present(work)) then if (size(work) >= liwork) then - aliw =.false. + aliw =.false. else - aliw=.true. + aliw=.true. endif else - aliw=.true. + aliw=.true. end if if (aliw) then - call psb_realloc(liwork,iwork,info) - if(info.ne.0) then - info=4010 - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if + call psb_realloc(liwork,iwork,info) + if(info.ne.0) then + info=4010 + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if else - iwork => work + iwork => work endif iwork(1)=0.d0 @@ -490,27 +490,27 @@ subroutine psb_dspsv(alpha,a,x,beta,y,desc_a,info,& liwork= 2*ncol if (a%pr(1) /= 0) llwork = liwork + m * ik if (a%pl(1) /= 0) llwork = llwork + m * ik - + if (present(work)) then if (size(work) >= liwork) then - aliw =.false. + aliw =.false. else - aliw=.true. + aliw=.true. endif else - aliw=.true. + aliw=.true. end if - + if (aliw) then - call psb_realloc(liwork,iwork,info) - if(info.ne.0) then - info=4010 - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if + call psb_realloc(liwork,iwork,info) + if(info.ne.0) then + info=4010 + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if else - iwork => work + iwork => work endif iwork(1)=0.d0 @@ -596,7 +596,7 @@ subroutine psb_dspsv(alpha,a,x,beta,y,desc_a,info,& end select end if - if (aliw) deallocate(iwork) + if (aliw) deallocate(iwork) if(.not.present(d)) deallocate(id) call psb_erractionrestore(err_act) diff --git a/src/psblas/psb_zspmm.f90 b/src/psblas/psb_zspmm.f90 index 4fef1b64..2f8d477a 100644 --- a/src/psblas/psb_zspmm.f90 +++ b/src/psblas/psb_zspmm.f90 @@ -183,26 +183,26 @@ subroutine psb_zspmm(alpha,a,x,beta,y,desc_a,info,& liwork= 2*ncol if (a%pr(1) /= 0) liwork = liwork + n * ik if (a%pl(1) /= 0) liwork = liwork + m * ik -if (present(work)) then + if (present(work)) then if (size(work) >= liwork) then - aliw =.false. + aliw =.false. else - aliw=.true. + aliw=.true. endif else - aliw=.true. + aliw=.true. end if if (aliw) then - call psb_realloc(liwork,iwork,info) - if(info.ne.0) then - info=4010 - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if + call psb_realloc(liwork,iwork,info) + if(info.ne.0) then + info=4010 + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if else - iwork => work + iwork => work endif iwork(1)=zzero @@ -315,7 +315,7 @@ if (present(work)) then y(iiy+nrow+1-1:iiy+ncol,1:ik)=zzero ! local Matrix-vector product - + call psb_csmm(alpha,a,x(iix:lldx,jjx:jjx+ik-1),& & beta,y(iiy:lldy,jjy:jjy+ik-1),info,trans=itrans) diff --git a/src/psblas/psb_zspsm.f90 b/src/psblas/psb_zspsm.f90 index a57ec8d9..4ee88a12 100644 --- a/src/psblas/psb_zspsm.f90 +++ b/src/psblas/psb_zspsm.f90 @@ -199,26 +199,26 @@ subroutine psb_zspsm(alpha,a,x,beta,y,desc_a,info,& liwork= 2*ncol if (a%pr(1) /= 0) llwork = liwork + m * ik if (a%pl(1) /= 0) llwork = llwork + m * ik - if (present(work)) then + if (present(work)) then if (size(work) >= liwork) then - aliw =.false. + aliw =.false. else - aliw=.true. + aliw=.true. endif else - aliw=.true. + aliw=.true. end if if (aliw) then - call psb_realloc(liwork,iwork,info) - if(info.ne.0) then - info=4010 - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if + call psb_realloc(liwork,iwork,info) + if(info.ne.0) then + info=4010 + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if else - iwork => work + iwork => work endif iwork(1)=0.d0 @@ -428,14 +428,14 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& ! check on blacs grid call blacs_gridinfo(icontxt, nprow, npcol, myrow, mycol) if (nprow == -1) then - info = 2010 - call psb_errpush(info,name) - goto 9999 + info = 2010 + call psb_errpush(info,name) + goto 9999 else if (npcol /= 1) then - info = 2030 - int_err(1) = npcol - call psb_errpush(info,name) - goto 9999 + info = 2030 + int_err(1) = npcol + call psb_errpush(info,name) + goto 9999 endif ! just this case right now @@ -469,7 +469,7 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& goto 9999 end if else - itrans = 'N' + itrans = 'N' endif m = desc_a%matrix_data(psb_m_) @@ -479,9 +479,9 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& lldy = size(y) if((lldx.lt.ncol).or.(lldy.lt.ncol)) then - info=3010 - call psb_errpush(info,name) - goto 9999 + info=3010 + call psb_errpush(info,name) + goto 9999 end if iwork => null() @@ -489,38 +489,38 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& liwork= 2*ncol if (a%pr(1) /= 0) llwork = liwork + m * ik if (a%pl(1) /= 0) llwork = llwork + m * ik - + if (present(work)) then if (size(work) >= liwork) then - aliw =.false. + aliw =.false. else - aliw=.true. + aliw=.true. endif else - aliw=.true. + aliw=.true. end if - + if (aliw) then - call psb_realloc(liwork,iwork,info) - if(info.ne.0) then - info=4010 - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if + call psb_realloc(liwork,iwork,info) + if(info.ne.0) then + info=4010 + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if else - iwork => work + iwork => work endif iwork(1)=0.d0 if(present(d)) then - lld = size(d) - id => d + lld = size(d) + id => d else - lld=1 - allocate(id(1)) - id=1.d0 + lld=1 + allocate(id(1)) + id=1.d0 end if ! checking for matrix correctness @@ -529,25 +529,25 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& call psb_chkvect(m,ik,size(x),ix,jx,desc_a%matrix_data,info,iix,jjx) call psb_chkvect(m,ik,size(y),iy,jy,desc_a%matrix_data,info,iiy,jjy) if(info.ne.0) then - info=4010 - ch_err='psb_chkvect/mat' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info=4010 + ch_err='psb_chkvect/mat' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if if(ja.ne.ix) then - ! this case is not yet implemented - info = 3030 + ! this case is not yet implemented + info = 3030 end if if((iix.ne.1).or.(iiy.ne.1)) then - ! this case is not yet implemented - info = 3040 + ! this case is not yet implemented + info = 3040 end if if(info.ne.0) then - call psb_errpush(info,name) - goto 9999 + call psb_errpush(info,name) + goto 9999 end if ! Perform local triangular system solve @@ -556,46 +556,46 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& call psb_cssm(alpha,a,xp,beta,yp,info,unitd=lunitd,d=id,trans=itrans) if(info.ne.0) then - info = 4010 - ch_err='dcssm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 + info = 4010 + ch_err='dcssm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 end if ! update overlap elements if(lchoice.gt.0) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & zone,yp,desc_a,iwork,info) - - i=0 - ! switch on update type - select case (lchoice) - case(psb_square_root_) - do while(desc_a%ovrlap_elem(i).ne.-ione) - y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_)) =& - & y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_))/& - & sqrt(real(desc_a%ovrlap_elem(i+psb_n_dom_ovr_))) - i = i+2 - end do - case(psb_avg_) - do while(desc_a%ovrlap_elem(i).ne.-ione) - y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_)) =& - & y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_))/& - & real(desc_a%ovrlap_elem(i+psb_n_dom_ovr_)) - i = i+2 - end do - case(psb_sum_) - ! do nothing - case default - ! wrong value for choice argument - info = 70 - int_err=(/10,lchoice,0,0,0/) - call psb_errpush(info,name,i_err=int_err) - goto 9999 - end select + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & zone,yp,desc_a,iwork,info) + + i=0 + ! switch on update type + select case (lchoice) + case(psb_square_root_) + do while(desc_a%ovrlap_elem(i).ne.-ione) + y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_)) =& + & y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_))/& + & sqrt(real(desc_a%ovrlap_elem(i+psb_n_dom_ovr_))) + i = i+2 + end do + case(psb_avg_) + do while(desc_a%ovrlap_elem(i).ne.-ione) + y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_)) =& + & y(desc_a%ovrlap_elem(i+psb_ovrlp_elem_))/& + & real(desc_a%ovrlap_elem(i+psb_n_dom_ovr_)) + i = i+2 + end do + case(psb_sum_) + ! do nothing + case default + ! wrong value for choice argument + info = 70 + int_err=(/10,lchoice,0,0,0/) + call psb_errpush(info,name,i_err=int_err) + goto 9999 + end select end if - if (aliw) deallocate(iwork) + if (aliw) deallocate(iwork) if(.not.present(d)) deallocate(id) call psb_erractionrestore(err_act) @@ -605,8 +605,8 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& call psb_erractionrestore(err_act) if (err_act.eq.act_abort) then - call psb_error(icontxt) - return + call psb_error(icontxt) + return end if return end subroutine psb_zspsv diff --git a/src/serial/psb_dcsdp.f90 b/src/serial/psb_dcsdp.f90 index 397044d0..dc0dbcb9 100644 --- a/src/serial/psb_dcsdp.f90 +++ b/src/serial/psb_dcsdp.f90 @@ -118,8 +118,7 @@ subroutine psb_dcsdp(a, b,info,ifc,check,trans,unitd,upd,dupl) if (check_=='R') then allocate(work(max(size(a%aspk),size(b%aspk))+1000),stat=info) else - allocate(work(max(size(a%ia1),size(b%ia1),& - & size(a%ia2),size(b%ia2))+max(a%m,b%m)+1000),stat=info) + allocate(work(max(size(a%ia1),size(a%ia2))+max(a%m,b%m)+1000),stat=info) endif if (info /= 0) then @@ -196,13 +195,20 @@ subroutine psb_dcsdp(a, b,info,ifc,check,trans,unitd,upd,dupl) call psb_errpush(info,name,a_err=ch_err) goto 9999 endif - if ((size(b%aspk) < aspk_size) .or.& + if (.not.associated(b%aspk).or.& + &.not.associated(b%ia1).or.& + &.not.associated(b%ia2).or.& + &.not.associated(b%pl).or.& + &.not.associated(b%pr)) then + call psb_sp_reall(b,ia1_size,ia2_size,aspk_size,info) + else if ((size(b%aspk) < aspk_size) .or.& &(size(b%ia1) < ia1_size) .or.& &(size(b%ia2) < ia2_size) .or.& &(size(b%pl) < b%m) .or.& &(size(b%pr) < b%k )) then call psb_sp_reall(b,ia1_size,ia2_size,aspk_size,info) endif + if (info /= no_err) then info=4010 ch_err='psb_sp_reall' diff --git a/src/serial/psb_zcsdp.f90 b/src/serial/psb_zcsdp.f90 index 0a28c1d3..f3ea0422 100644 --- a/src/serial/psb_zcsdp.f90 +++ b/src/serial/psb_zcsdp.f90 @@ -67,7 +67,7 @@ subroutine psb_zcsdp(a, b,info,ifc,check,trans,unitd,upd,dupl) & ipc, i, count, err_act, ierrv(5), i1, i2, ia character :: check_,trans_,unitd_, up Integer, Parameter :: maxtry=8 - logical, parameter :: debug=.false. + logical, parameter :: debug=.true. character(len=20) :: name, ch_err interface psb_cest @@ -114,11 +114,11 @@ subroutine psb_zcsdp(a, b,info,ifc,check,trans,unitd,upd,dupl) unitd_ = 'U' endif + if (check_=='R') then allocate(work(max(size(a%aspk),size(b%aspk))+1000),stat=info) else - allocate(work(max(size(a%ia1),size(b%ia1),& - & size(a%ia2),size(b%ia2))+max(a%m,b%m)+1000),stat=info) + allocate(work(max(size(a%ia1),size(a%ia2))+max(a%m,b%m)+1000),stat=info) endif if (info /= 0) then @@ -127,7 +127,7 @@ subroutine psb_zcsdp(a, b,info,ifc,check,trans,unitd,upd,dupl) goto 9999 end if if (ifc_<1) then - write(0,*) 'dcsdp90 Error: invalid ifc ',ifc_ + write(0,*) 'csdp90 Error: invalid ifc ',ifc_ info = -4 call psb_errpush(info,name) goto 9999 @@ -181,13 +181,15 @@ subroutine psb_zcsdp(a, b,info,ifc,check,trans,unitd,upd,dupl) b%m=a%m b%k=a%k call psb_spinfo(psb_nztotreq_,a,size_req,info) - if (debug) write(0,*) 'DCSDP : size_req 1:',size_req + if (debug) write(0,*) 'DCSDP : size_req 1:',size_req,a%m,a%k ! n_row=b%m n_col=b%k call psb_cest(b%fida, n_row,n_col,size_req,& & ia1_size, ia2_size, aspk_size, upd_,info) +!!$ write(0,*) size(b%aspk),size(b%ia1),size(b%ia2),size(b%pl),size(b%pr),& +!!$ & ia1_size, ia2_size, aspk_size,b%fida,b%m,b%k if (info /= no_err) then info=4010 @@ -195,13 +197,20 @@ subroutine psb_zcsdp(a, b,info,ifc,check,trans,unitd,upd,dupl) call psb_errpush(info,name,a_err=ch_err) goto 9999 endif - if ((size(b%aspk) < aspk_size) .or.& + if (.not.associated(b%aspk).or.& + &.not.associated(b%ia1).or.& + &.not.associated(b%ia2).or.& + &.not.associated(b%pl).or.& + &.not.associated(b%pr)) then + call psb_sp_reall(b,ia1_size,ia2_size,aspk_size,info) + else if ((size(b%aspk) < aspk_size) .or.& &(size(b%ia1) < ia1_size) .or.& &(size(b%ia2) < ia2_size) .or.& &(size(b%pl) < b%m) .or.& &(size(b%pr) < b%k )) then call psb_sp_reall(b,ia1_size,ia2_size,aspk_size,info) endif + if (info /= no_err) then info=4010 ch_err='psb_sp_reall' diff --git a/src/serial/psb_ztransc.f90 b/src/serial/psb_ztransc.f90 new file mode 100644 index 00000000..b8fb3f63 --- /dev/null +++ b/src/serial/psb_ztransc.f90 @@ -0,0 +1,92 @@ +!!$ +!!$ Parallel Sparse BLAS v2.0 +!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata +!!$ Alfredo Buttari University of Rome Tor Vergata +!!$ +!!$ Redistribution and use in source and binary forms, with or without +!!$ modification, are permitted provided that the following conditions +!!$ are met: +!!$ 1. Redistributions of source code must retain the above copyright +!!$ notice, this list of conditions and the following disclaimer. +!!$ 2. Redistributions in binary form must reproduce the above copyright +!!$ notice, this list of conditions, and the following disclaimer in the +!!$ documentation and/or other materials provided with the distribution. +!!$ 3. The name of the PSBLAS group or the names of its contributors may +!!$ not be used to endorse or promote products derived from this +!!$ software without specific written permission. +!!$ +!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS +!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +!!$ POSSIBILITY OF SUCH DAMAGE. +!!$ +!!$ +! File: psb_ztransc.f90 +! Subroutine: +! Parameters: + +subroutine psb_ztransc(a,b,c,fmt) + use psb_spmat_type + use psb_tools_mod + use psb_string_mod + use psb_serial_mod, only : psb_ipcoo2csr, psb_ipcsr2coo, psb_fixcoo + implicit none + + type(psb_zspmat_type) :: a,b + integer, optional :: c + character(len=*), optional :: fmt + + character(len=5) :: fmt_ + integer ::c_, info, nz, i + integer, pointer :: itmp(:) + if (present(c)) then + c_=c + else + c_=1 + endif + if (present(fmt)) then + fmt_ = toupper(fmt) + else + fmt_='CSR' + endif + if (associated(b%aspk)) call psb_sp_free(b,info) + call psb_sp_clone(a,b,info) + + if (b%fida=='CSR') then + call psb_ipcsr2coo(b,info) + else if (b%fida=='COO') then + ! do nothing + else + write(0,*) 'Unimplemented case in TRANSC ' + endif + itmp => b%ia1 + b%ia1 => b%ia2 + b%ia2 => itmp + + b%m = a%k + b%k = a%m + + do i=1, b%infoa(psb_nnz_) + b%aspk(i) = conjg(b%aspk(i)) + end do + +!!$ write(0,*) 'Calling IPCOO2CSR from transc90 ',b%m,b%k + if (fmt_=='CSR') then + call psb_ipcoo2csr(b,info) + b%fida='CSR' + else if (fmt_=='COO') then + call psb_fixcoo(b,info) + b%fida='COO' + else + write(0,*) 'Unknown FMT in TRANSC : "',fmt_,'"' + endif + + return +end subroutine psb_ztransc diff --git a/src/serial/psb_ztransp.f90 b/src/serial/psb_ztransp.f90 index dd86896d..f1aada5f 100644 --- a/src/serial/psb_ztransp.f90 +++ b/src/serial/psb_ztransp.f90 @@ -45,7 +45,7 @@ subroutine psb_ztransp(a,b,c,fmt) character(len=5) :: fmt_ integer ::c_, info, nz - integer, pointer :: itmp(:)=>null() + integer, pointer :: itmp(:) if (present(c)) then c_=c else diff --git a/src/tools/psb_dallc.f90 b/src/tools/psb_dallc.f90 index 79359dbe..d7f241aa 100644 --- a/src/tools/psb_dallc.f90 +++ b/src/tools/psb_dallc.f90 @@ -35,13 +35,11 @@ ! Allocates dense matrix for PSBLAS routines ! ! Parameters: -! m - number of rows. -! n - number of columns. ! x - the matrix to be allocated. ! desc_a - the communication descriptor. -! info - eventually returns an error code -! js - (optional) the starting column -subroutine psb_dalloc(m, n, x, desc_a, info, js) +! info - possibly returns an error code +! n - optional number of columns. +subroutine psb_dalloc(x, desc_a, info, n) !....allocate dense matrix for psblas routines..... use psb_descriptor_type use psb_const_mod @@ -50,18 +48,17 @@ subroutine psb_dalloc(m, n, x, desc_a, info, js) implicit none !....parameters... - integer, intent(in) :: m,n real(kind(1.d0)), pointer :: x(:,:) type(psb_desc_type), intent(in) :: desc_a integer :: info - integer, optional, intent(in) :: js + integer, optional, intent(in) :: n + !locals integer :: nprow,npcol,myrow,mycol,err,n_col,n_row,i,j,jj,err_act - integer :: icontxt,dectype + integer :: icontxt,dectype,n_ integer :: int_err(5),temp(1),exch(3) real(kind(1.d0)) :: real_err(5) - integer, allocatable:: prc_v(:) character(len=20) :: name, ch_err name='psb_dallc' @@ -88,88 +85,56 @@ subroutine psb_dalloc(m, n, x, desc_a, info, js) dectype=desc_a%matrix_data(psb_dec_type_) !... check m and n parameters.... - if (m.lt.0) then - info = 10 - int_err(1) = 1 - int_err(2) = m - call psb_errpush(info,name,int_err) - goto 9999 - else if (n.lt.0) then - info = 10 - int_err(1) = 2 - int_err(2) = n - call psb_errpush(info,name,int_err) - else if (.not.psb_is_ok_dec(dectype)) then + if (.not.psb_is_ok_dec(dectype)) then info = 3110 call psb_errpush(info,name) goto 9999 - else if (m.ne.desc_a%matrix_data(psb_n_)) then - info = 300 - int_err(1) = 1 - int_err(2) = m - int_err(3) = 4 - int_err(4) = psb_n_ - int_err(5) = desc_a%matrix_data(psb_n_) - call psb_errpush(info,name,int_err) - goto 9999 endif - if (present(js)) then - j=js + if (present(n)) then + n_ = n else - j=1 + n_ = 1 endif - !global check on m and n parameters + !global check on n parameters if (myrow.eq.psb_root_) then - exch(1)=m - exch(2)=n - exch(3)=j - call igebs2d(icontxt,psb_all_,psb_topdef_, ithree,ione, exch, ithree) + exch(1)=n_ + call igebs2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione) else - call igebr2d(icontxt,psb_all_,psb_topdef_, ithree,ione, exch, ithree, psb_root_, 0) - if (exch(1).ne.m) then + call igebr2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione, psb_root_, 0) + if (exch(1).ne.n_) then info=550 int_err(1)=1 call psb_errpush(info,name,int_err) goto 9999 - else if (exch(2).ne.n) then - info=550 - int_err(1)=2 - call psb_errpush(info,name,int_err) - goto 9999 - else if (exch(3).ne.j) then - info=550 - int_err(1)=3 - call psb_errpush(info,name,int_err) - goto 9999 endif endif !....allocate x ..... if (psb_is_asb_dec(dectype).or.psb_is_upd_dec(dectype)) then n_col = max(1,desc_a%matrix_data(psb_n_col_)) - allocate(x(n_col,j:j+n-1),stat=info) + allocate(x(n_col,n_),stat=info) if (info.ne.0) then info=4010 ch_err='allocate' call psb_errpush(info,name,a_err=ch_err) goto 9999 endif - do jj=j,j+n-1 + do j=1,n_ do i=1,n_col x(i,j) = 0.0d0 end do end do else if (psb_is_bld_dec(dectype)) then n_row = max(1,desc_a%matrix_data(psb_n_row_)) - allocate(x(n_row,j:j+n-1),stat=info) + allocate(x(n_row,n_),stat=info) if (info.ne.0) then info=4010 ch_err='allocate' call psb_errpush(info,name,a_err=ch_err) goto 9999 endif - do jj=j,j+n-1 + do j = 1, n_ do i=1,n_row x(i,j) = 0.0d0 end do @@ -224,11 +189,10 @@ end subroutine psb_dalloc ! Allocates dense matrix for PSBLAS routines ! ! Parameters: -! m - number of rows. ! x - the matrix to be allocated. ! desc_a - the communication descriptor. -! info - eventually returns an error code -subroutine psb_dallocv(m, x, desc_a,info) +! info - possibly returns an error code +subroutine psb_dallocv(x, desc_a,info,n) !....allocate sparse matrix structure for psblas routines..... use psb_descriptor_type use psb_const_mod @@ -238,14 +202,14 @@ subroutine psb_dallocv(m, x, desc_a,info) implicit none !....parameters... - integer, intent(in) :: m - real(kind(1.d0)), pointer :: x(:) - type(psb_desc_type), intent(in):: desc_a - integer :: info + real(kind(1.d0)), pointer :: x(:) + type(psb_desc_type), intent(in) :: desc_a + integer :: info + integer, optional, intent(in) :: n !locals integer :: nprow,npcol,myrow,mycol,err,n_col,n_row,dectype,i,err_act - integer :: icontxt + integer :: icontxt, n_ integer :: int_err(5),temp(1),exch real(kind(1.d0)) :: real_err(5) logical, parameter :: debug=.false. @@ -275,40 +239,13 @@ subroutine psb_dallocv(m, x, desc_a,info) if (debug) write(0,*) 'dall: dectype',dectype if (debug) write(0,*) 'dall: is_ok? dectype',psb_is_ok_dec(dectype) !... check m and n parameters.... - if (m.lt.0) then - info = 10 - int_err(1) = 1 - int_err(2) = m - call psb_errpush(info,name,int_err) - goto 9999 - else if (.not.psb_is_ok_dec(dectype)) then + if (.not.psb_is_ok_dec(dectype)) then info = 3110 call psb_errpush(info,name) goto 9999 - else if (m.ne.desc_a%matrix_data(psb_n_)) then - info = 300 - int_err(1) = 1 - int_err(2) = m - int_err(3) = 4 - int_err(4) = psb_n_ - int_err(5) = desc_a%matrix_data(psb_n_) - call psb_errpush(info,name,int_err) - goto 9999 endif - !global check on m and n parameters - if (myrow.eq.psb_root_) then - exch = m - call igebs2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione) - else - call igebr2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione, psb_root_, 0) - if (exch .ne. m) then - info = 550 - int_err(1) = 1 - call psb_errpush(info,name,int_err) - goto 9999 - endif - endif + ! As this is a rank-1 array, optional parameter N is actually ignored. !....allocate x ..... if (psb_is_asb_dec(dectype).or.psb_is_upd_dec(dectype)) then diff --git a/src/tools/psb_dins.f90 b/src/tools/psb_dins.f90 index 9f60ab86..f49d1e65 100644 --- a/src/tools/psb_dins.f90 +++ b/src/tools/psb_dins.f90 @@ -44,7 +44,7 @@ ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. ! jblck - integer(optional). First col of submatrix belonging to blck to be inserted. -subroutine psb_dins(m, n, x, ix, jx, blck, desc_a, info,& +subroutine psb_dins(m, n, blck, x, ix, jx, desc_a, info,& & iblck, jblck,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type @@ -270,7 +270,7 @@ end subroutine psb_dins ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. -subroutine psb_dinsvm(m, x, ix, jx, blck, desc_a,info,& +subroutine psb_dinsvm(m, blck, x, ix, jx, desc_a,info,& & iblck,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type @@ -485,7 +485,7 @@ end subroutine psb_dinsvm ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. ! insflag - integer(optional). ??? -subroutine psb_dinsvv(m, x, ix, blck, desc_a, info,& +subroutine psb_dinsvv(m, blck, x, ix, desc_a, info,& & iblck,insflag,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type diff --git a/src/tools/psb_ialloc.f90 b/src/tools/psb_ialloc.f90 index 85f94ecc..16a4e0db 100644 --- a/src/tools/psb_ialloc.f90 +++ b/src/tools/psb_ialloc.f90 @@ -34,13 +34,11 @@ ! Allocates dense integer matrix for PSBLAS routines ! ! Parameters: -! m - integer. The number of rows. -! n - integer. The number of columns. -! x - integer,dimension(:,:). The matrix to be allocated. -! desc_a - type(). The communication descriptor. -! info - integer. Eventually returns an error code -! js - integer(optional). The starting column -subroutine psb_ialloc(m, n, x, desc_a, info,js) +! x - the matrix to be allocated. +! desc_a - the communication descriptor. +! info - possibly returns an error code +! n - optional number of columns. +subroutine psb_ialloc(x, desc_a, info, n) !....allocate dense matrix for psblas routines..... use psb_descriptor_type use psb_const_mod @@ -48,19 +46,18 @@ subroutine psb_ialloc(m, n, x, desc_a, info,js) implicit none !....parameters... - integer, intent(in) :: m,n - integer, pointer :: x(:,:) - type(psb_desc_type), intent(inout) :: desc_a - integer, intent(out) :: info - integer, optional, intent(in) :: js + integer, pointer :: x(:,:) + type(psb_desc_type), intent(in) :: desc_a + integer, intent(out) :: info + integer, optional, intent(in) :: n + !locals - integer :: j,nprow,npcol,myrow,mypcol,& - & n_col,n_row, err_act - integer :: icontxt,dectype + integer :: nprow,npcol,myrow,mypcol,err,n_col,n_row,i,j,jj,err_act + integer :: icontxt,dectype,n_ integer :: int_err(5),temp(1),exch(3) real(kind(1.d0)) :: real_err(5) - character(len=20) :: name, char_err + character(len=20) :: name, ch_err if(psb_get_errstatus().ne.0) return info=0 @@ -84,97 +81,70 @@ subroutine psb_ialloc(m, n, x, desc_a, info,js) dectype=desc_a%matrix_data(psb_dec_type_) !... check m and n parameters.... - if (m.lt.0) then - info = 10 - int_err(1) = 1 - int_err(2) = m - call psb_errpush(info,name,int_err) - goto 9999 - else if (n.lt.0) then - info = 10 - int_err(1) = 2 - int_err(2) = n - call psb_errpush(info,name,int_err) - goto 9999 - else if (.not.psb_is_ok_dec(dectype)) then - info = 3110 - call psb_errpush(info,name) - goto 9999 - else if (m.ne.desc_a%matrix_data(psb_n_)) then - info = 300 - int_err(1) = 1 - int_err(2) = m - int_err(3) = 4 - int_err(4) = psb_n_ - int_err(5) = desc_a%matrix_data(psb_n_) - call psb_errpush(info,name,int_err) - goto 9999 + if (.not.psb_is_ok_dec(dectype)) then + info = 3110 + call psb_errpush(info,name) + goto 9999 endif - - if (present(js)) then - j=js + + if (present(n)) then + n_ = n else - j=1 + n_ = 1 endif - !global check on m and n parameters + !global check on n parameters if (myrow.eq.psb_root_) then - exch(1)=m - exch(2)=n - exch(3)=j - call igebs2d(icontxt,psb_all_,psb_topdef_, ithree,ione, exch, ithree) + exch(1)=n_ + call igebs2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione) else - call igebr2d(icontxt,psb_all_,psb_topdef_, ithree,ione, exch, ithree, psb_root_, 0) - if (exch(1).ne.m) then - info=550 - int_err(1)=1 - call psb_errpush(info,name,int_err) - goto 9999 - else if (exch(2).ne.n) then - info=550 - int_err(1)=2 - call psb_errpush(info,name,int_err) - goto 9999 - else if (exch(3).ne.j) then - info=550 - int_err(1)=3 - call psb_errpush(info,name,int_err) - goto 9999 - endif + call igebr2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione, psb_root_, 0) + if (exch(1).ne.n_) then + info=550 + int_err(1)=1 + call psb_errpush(info,name,int_err) + goto 9999 + endif endif !....allocate x ..... if (psb_is_asb_dec(dectype).or.psb_is_upd_dec(dectype)) then - n_col = max(1,desc_a%matrix_data(psb_n_col_)) - allocate(x(n_col,j:j+n-1),stat=info) - if (info.ne.0) then - info=2025 - int_err(1)=n_col - call psb_errpush(info,name,int_err) - goto 9999 - endif + n_col = max(1,desc_a%matrix_data(psb_n_col_)) + allocate(x(n_col,n_),stat=info) + if (info.ne.0) then + info=4010 + ch_err='allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + endif + do j=1,n_ + do i=1,n_col + x(i,j) = 0 + end do + end do else if (psb_is_bld_dec(dectype)) then - n_row = max(1,desc_a%matrix_data(psb_n_row_)) - allocate(x(n_row,j:j+n-1),stat=info) - if (info.ne.0) then - info=2025 - int_err(1)=n_row - call psb_errpush(info,name,int_err) - goto 9999 - endif + n_row = max(1,desc_a%matrix_data(psb_n_row_)) + allocate(x(n_row,n_),stat=info) + if (info.ne.0) then + info=4010 + ch_err='allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + endif + do j = 1, n_ + do i=1,n_row + x(i,j) = 0 + end do + end do endif - - x = 0 call psb_erractionrestore(err_act) return 9999 continue call psb_erractionrestore(err_act) - - if (err_act.eq.act_ret) then - return - else - call psb_error(icontxt) + if (err_act.eq.act_abort) then + call psb_error(icontxt) + return end if return @@ -220,26 +190,28 @@ end subroutine psb_ialloc ! x - integer,dimension(:). The matrix to be allocated. ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code -subroutine psb_iallocv(m, x, desc_a, info) +subroutine psb_iallocv(x, desc_a, info,n) !....allocate sparse matrix structure for psblas routines..... use psb_descriptor_type use psb_const_mod + use psb_realloc_mod use psb_error_mod + implicit none !....parameters... - integer, intent(in) :: m - integer, pointer :: x(:) - type(psb_desc_type), intent(in) :: desc_a - integer, intent(out) :: info + integer, pointer :: x(:) + type(psb_desc_type), intent(in) :: desc_a + integer, intent(out) :: info + integer, optional, intent(in) :: n !locals - integer :: nprow,npcol,myrow,mypcol,err,n_col,n_row,dectype,err_act - integer :: icontxt - integer :: int_err(5),temp(1),exch(2) + integer :: nprow,npcol,myrow,mycol,err,n_col,n_row,dectype,i,err_act + integer :: icontxt, n_ + integer :: int_err(5),temp(1),exch real(kind(1.d0)) :: real_err(5) logical, parameter :: debug=.false. - character(len=20) :: name, char_err + character(len=20) :: name, ch_err if(psb_get_errstatus().ne.0) return info=0 @@ -247,59 +219,31 @@ subroutine psb_iallocv(m, x, desc_a, info) call psb_erractionsave(err_act) icontxt=desc_a%matrix_data(psb_ctxt_) - - call blacs_gridinfo(icontxt, nprow, npcol, myrow, mypcol) + + call blacs_gridinfo(icontxt, nprow, npcol, myrow, mycol) ! ....verify blacs grid correctness.. if (nprow.eq.-1) then - info = 2010 - call psb_errpush(info,name) - goto 9999 + info = 2010 + call psb_errpush(info,name) + goto 9999 else if (npcol.ne.1) then - info = 2030 - int_err(1) = npcol - call psb_errpush(info,name,int_err) - goto 9999 + info = 2030 + int_err(1) = npcol + call psb_errpush(info,name,int_err) + goto 9999 endif dectype=desc_a%matrix_data(psb_dec_type_) if (debug) write(0,*) 'dall: dectype',dectype if (debug) write(0,*) 'dall: is_ok? dectype',psb_is_ok_dec(dectype) !... check m and n parameters.... - if (m.lt.0) then - info = 10 - int_err(1) = 1 - int_err(2) = m - call psb_errpush(info,name,int_err) - goto 9999 - else if (.not.psb_is_ok_dec(dectype)) then - info = 3110 - call psb_errpush(info,name) - goto 9999 - else if (m.ne.desc_a%matrix_data(psb_n_)) then - info = 300 - int_err(1) = 1 - int_err(2) = m - int_err(3) = 4 - int_err(4) = psb_n_ - int_err(5) = desc_a%matrix_data(psb_n_) - call psb_errpush(info,name,int_err) - goto 9999 - endif - - !global check on m and n parameters - if (myrow.eq.psb_root_) then - exch(1) = m - call igebs2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione) - else - call igebr2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione, psb_root_, 0) - if (exch(1) .ne. m) then - info = 550 - int_err(1) = 1 - call psb_errpush(info,name,int_err) - goto 9999 - endif + if (.not.psb_is_ok_dec(dectype)) then + info = 3110 + call psb_errpush(info,name) + goto 9999 endif + ! As this is a rank-1 array, optional parameter N is actually ignored. !....allocate x ..... if (psb_is_asb_dec(dectype).or.psb_is_upd_dec(dectype)) then @@ -329,11 +273,9 @@ subroutine psb_iallocv(m, x, desc_a, info) 9999 continue call psb_erractionrestore(err_act) - - if (err_act.eq.act_ret) then - return - else - call psb_error(icontxt) + if (err_act.eq.act_abort) then + call psb_error(icontxt) + return end if return diff --git a/src/tools/psb_iins.f90 b/src/tools/psb_iins.f90 index 629753a4..de211546 100644 --- a/src/tools/psb_iins.f90 +++ b/src/tools/psb_iins.f90 @@ -44,7 +44,7 @@ ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. ! jblck - integer(optional). First col of submatrix belonging to blck to be inserted. -subroutine psb_iins(m, n, x, ix, jx, blck, desc_a, info,& +subroutine psb_iins(m, n, blck, x, ix, jx, desc_a, info,& & iblck, jblck,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type @@ -266,7 +266,7 @@ end subroutine psb_iins ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. -subroutine psb_iinsvm(m, x, ix, jx, blck, desc_a, info,& +subroutine psb_iinsvm(m, blck, x, ix, jx, desc_a, info,& & iblck,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type @@ -413,7 +413,7 @@ end subroutine psb_iinsvm ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. -subroutine psb_iinsvv(m, x, ix, blck, desc_a, info,& +subroutine psb_iinsvv(m, blck, x, ix, desc_a, info,& & iblck,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type diff --git a/src/tools/psb_zallc.f90 b/src/tools/psb_zallc.f90 index 258084fd..edd2e314 100644 --- a/src/tools/psb_zallc.f90 +++ b/src/tools/psb_zallc.f90 @@ -35,13 +35,11 @@ ! Allocates dense matrix for PSBLAS routines ! ! Parameters: -! m - number of rows. -! n - number of columns. ! x - the matrix to be allocated. ! desc_a - the communication descriptor. -! info - eventually returns an error code -! js - (optional) the starting column -subroutine psb_zalloc(m, n, x, desc_a, info, js) +! info - possibly returns an error code +! n - optional number of columns. +subroutine psb_zalloc(x, desc_a, info, n) !....allocate dense matrix for psblas routines..... use psb_descriptor_type use psb_const_mod @@ -50,18 +48,16 @@ subroutine psb_zalloc(m, n, x, desc_a, info, js) implicit none !....parameters... - integer, intent(in) :: m,n - complex(kind(1.d0)), pointer :: x(:,:) + complex(kind(1.d0)), pointer :: x(:,:) type(psb_desc_type), intent(in) :: desc_a integer :: info - integer, optional, intent(in) :: js + integer, optional, intent(in) :: n !locals integer :: nprow,npcol,myrow,mycol,err,n_col,n_row,i,j,jj,err_act - integer :: icontxt,dectype + integer :: icontxt,dectype,n_ integer :: int_err(5),temp(1),exch(3) real(kind(1.d0)) :: real_err(5) - integer, allocatable:: prc_v(:) character(len=20) :: name, ch_err name='psb_zallc' @@ -88,88 +84,56 @@ subroutine psb_zalloc(m, n, x, desc_a, info, js) dectype=desc_a%matrix_data(psb_dec_type_) !... check m and n parameters.... - if (m.lt.0) then - info = 10 - int_err(1) = 1 - int_err(2) = m - call psb_errpush(info,name,int_err) - goto 9999 - else if (n.lt.0) then - info = 10 - int_err(1) = 2 - int_err(2) = n - call psb_errpush(info,name,int_err) - else if (.not.psb_is_ok_dec(dectype)) then + if (.not.psb_is_ok_dec(dectype)) then info = 3110 call psb_errpush(info,name) goto 9999 - else if (m.ne.desc_a%matrix_data(psb_n_)) then - info = 300 - int_err(1) = 1 - int_err(2) = m - int_err(3) = 4 - int_err(4) = psb_n_ - int_err(5) = desc_a%matrix_data(psb_n_) - call psb_errpush(info,name,int_err) - goto 9999 endif - if (present(js)) then - j=js + if (present(n)) then + n_ = n else - j=1 + n_ = 1 endif - !global check on m and n parameters + !global check on n parameters if (myrow.eq.psb_root_) then - exch(1)=m - exch(2)=n - exch(3)=j - call igebs2d(icontxt,psb_all_,psb_topdef_, ithree,ione, exch, ithree) + exch(1)=n_ + call igebs2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione) else - call igebr2d(icontxt,psb_all_,psb_topdef_, ithree,ione, exch, ithree, psb_root_, 0) - if (exch(1).ne.m) then + call igebr2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione, psb_root_, 0) + if (exch(1).ne.n_) then info=550 int_err(1)=1 call psb_errpush(info,name,int_err) goto 9999 - else if (exch(2).ne.n) then - info=550 - int_err(1)=2 - call psb_errpush(info,name,int_err) - goto 9999 - else if (exch(3).ne.j) then - info=550 - int_err(1)=3 - call psb_errpush(info,name,int_err) - goto 9999 endif endif !....allocate x ..... if (psb_is_asb_dec(dectype).or.psb_is_upd_dec(dectype)) then n_col = max(1,desc_a%matrix_data(psb_n_col_)) - allocate(x(n_col,j:j+n-1),stat=info) + allocate(x(n_col,n_),stat=info) if (info.ne.0) then info=4010 ch_err='allocate' call psb_errpush(info,name,a_err=ch_err) goto 9999 endif - do jj=j,j+n-1 + do j=1,n_ do i=1,n_col x(i,j) = 0.0d0 end do end do else if (psb_is_bld_dec(dectype)) then n_row = max(1,desc_a%matrix_data(psb_n_row_)) - allocate(x(n_row,j:j+n-1),stat=info) + allocate(x(n_row,n_),stat=info) if (info.ne.0) then info=4010 ch_err='allocate' call psb_errpush(info,name,a_err=ch_err) goto 9999 endif - do jj=j,j+n-1 + do j = 1, n_ do i=1,n_row x(i,j) = 0.0d0 end do @@ -224,11 +188,10 @@ end subroutine psb_zalloc ! Allocates dense matrix for PSBLAS routines ! ! Parameters: -! m - number of rows. ! x - the matrix to be allocated. ! desc_a - the communication descriptor. -! info - eventually returns an error code -subroutine psb_zallocv(m, x, desc_a,info) +! info - possibly returns an error code +subroutine psb_zallocv(x, desc_a,info,n) !....allocate sparse matrix structure for psblas routines..... use psb_descriptor_type use psb_const_mod @@ -238,14 +201,14 @@ subroutine psb_zallocv(m, x, desc_a,info) implicit none !....parameters... - integer, intent(in) :: m - complex(kind(1.d0)), pointer :: x(:) - type(psb_desc_type), intent(in):: desc_a - integer :: info + complex(kind(1.d0)), pointer :: x(:) + type(psb_desc_type), intent(in) :: desc_a + integer :: info + integer, optional, intent(in) :: n !locals integer :: nprow,npcol,myrow,mycol,err,n_col,n_row,dectype,i,err_act - integer :: icontxt + integer :: icontxt, n_ integer :: int_err(5),temp(1),exch real(kind(1.d0)) :: real_err(5) logical, parameter :: debug=.false. @@ -275,40 +238,13 @@ subroutine psb_zallocv(m, x, desc_a,info) if (debug) write(0,*) 'dall: dectype',dectype if (debug) write(0,*) 'dall: is_ok? dectype',psb_is_ok_dec(dectype) !... check m and n parameters.... - if (m.lt.0) then - info = 10 - int_err(1) = 1 - int_err(2) = m - call psb_errpush(info,name,int_err) - goto 9999 - else if (.not.psb_is_ok_dec(dectype)) then + if (.not.psb_is_ok_dec(dectype)) then info = 3110 call psb_errpush(info,name) goto 9999 - else if (m.ne.desc_a%matrix_data(psb_n_)) then - info = 300 - int_err(1) = 1 - int_err(2) = m - int_err(3) = 4 - int_err(4) = psb_n_ - int_err(5) = desc_a%matrix_data(psb_n_) - call psb_errpush(info,name,int_err) - goto 9999 endif - !global check on m and n parameters - if (myrow.eq.psb_root_) then - exch = m - call igebs2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione) - else - call igebr2d(icontxt,psb_all_,psb_topdef_, ione,ione, exch, ione, psb_root_, 0) - if (exch .ne. m) then - info = 550 - int_err(1) = 1 - call psb_errpush(info,name,int_err) - goto 9999 - endif - endif + ! As this is a rank-1 array, optional parameter N is actually ignored. !....allocate x ..... if (psb_is_asb_dec(dectype).or.psb_is_upd_dec(dectype)) then diff --git a/src/tools/psb_zins.f90 b/src/tools/psb_zins.f90 index c05d7245..712958c1 100644 --- a/src/tools/psb_zins.f90 +++ b/src/tools/psb_zins.f90 @@ -44,7 +44,7 @@ ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. ! jblck - integer(optional). First col of submatrix belonging to blck to be inserted. -subroutine psb_zins(m, n, x, ix, jx, blck, desc_a, info,& +subroutine psb_zins(m, n, blck, x, ix, jx, desc_a, info,& & iblck, jblck,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type @@ -268,7 +268,7 @@ end subroutine psb_zins ! desc_a - type(). The communication descriptor. ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. -subroutine psb_zinsvm(m, x, ix, jx, blck, desc_a,info,& +subroutine psb_zinsvm(m, blck, x, ix, jx, desc_a,info,& & iblck,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type @@ -483,7 +483,7 @@ end subroutine psb_zinsvm ! info - integer. Eventually returns an error code ! iblck - integer(optional). First row of submatrix belonging to blck to be inserted. ! insflag - integer(optional). ??? -subroutine psb_zinsvv(m, x, ix, blck, desc_a, info,& +subroutine psb_zinsvv(m, blck, x, ix, desc_a, info,& & iblck,insflag,dupl) !....insert dense submatrix to dense matrix ..... use psb_descriptor_type diff --git a/src/tools/psb_zspasb.f90 b/src/tools/psb_zspasb.f90 index d50d8670..684d3e52 100644 --- a/src/tools/psb_zspasb.f90 +++ b/src/tools/psb_zspasb.f90 @@ -162,6 +162,7 @@ subroutine psb_zspasb(a,desc_a, info, afmt, upd, dupl) ! Do the real conversion into the requested storage format ! result is put in A + write(0,*) 'Calling csdp from SPASB' call psb_csdp(atemp,a,info,ifc=2,upd=upd_,dupl=dupl_) IF (debug) WRITE (*, *) myrow,' ASB: From DCSDP',info,' ',A%FIDA diff --git a/test/Fileread/df_sample.f90 b/test/Fileread/df_sample.f90 index 8bca8d95..7deb0828 100644 --- a/test/Fileread/df_sample.f90 +++ b/test/Fileread/df_sample.f90 @@ -208,10 +208,10 @@ program df_sample & desc_a,b_col_glob,b_col,info,fmt=afmt) end if - call psb_geall(m_problem,x_col,desc_a,info) + call psb_geall(x_col,desc_a,info) x_col(:) =0.0 call psb_geasb(x_col,desc_a,info) - call psb_geall(m_problem,r_col,desc_a,info) + call psb_geall(r_col,desc_a,info) r_col(:) =0.0 call psb_geasb(r_col,desc_a,info) t2 = mpi_wtime() - t1 diff --git a/test/Fileread/dhb2mm.f90 b/test/Fileread/dhb2mm.f90 index 1ee48667..b5dddd5b 100644 --- a/test/Fileread/dhb2mm.f90 +++ b/test/Fileread/dhb2mm.f90 @@ -1,13 +1,46 @@ +!!$ +!!$ Parallel Sparse BLAS v2.0 +!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata +!!$ Alfredo Buttari University of Rome Tor Vergata +!!$ +!!$ Redistribution and use in source and binary forms, with or without +!!$ modification, are permitted provided that the following conditions +!!$ are met: +!!$ 1. Redistributions of source code must retain the above copyright +!!$ notice, this list of conditions and the following disclaimer. +!!$ 2. Redistributions in binary form must reproduce the above copyright +!!$ notice, this list of conditions, and the following disclaimer in the +!!$ documentation and/or other materials provided with the distribution. +!!$ 3. The name of the PSBLAS group or the names of its contributors may +!!$ not be used to endorse or promote products derived from this +!!$ software without specific written permission. +!!$ +!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS +!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +!!$ POSSIBILITY OF SUCH DAMAGE. +!!$ +!!$ +! +! Storage conversion filter: reads from standar input a sparse matrix +! stored in Harwell-Boeing format, and writes to standard output in MatrixMarket +! format +! program dhb2mm use psb_sparse_mod use mmio use hbio type(psb_dspmat_type) :: a - integer n, nnz,info,i,j,k - INTEGER :: iwflag,IOUT,NCOL,NELTVL,NNZERO,NRHS,NRHSIX,NROW,& - & iter - CHARACTER :: RHSDATATYPE,DATATYPE*3,KEY*8,OUTFILE*20,MTITLE*72 + integer :: info + character(len=72) :: mtitle call hb_read(a,info,mtitle=mtitle) diff --git a/test/Fileread/dmm2hb.f90 b/test/Fileread/dmm2hb.f90 index 0d24e6b1..b87c9d35 100644 --- a/test/Fileread/dmm2hb.f90 +++ b/test/Fileread/dmm2hb.f90 @@ -1,14 +1,45 @@ +!!$ +!!$ Parallel Sparse BLAS v2.0 +!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata +!!$ Alfredo Buttari University of Rome Tor Vergata +!!$ +!!$ Redistribution and use in source and binary forms, with or without +!!$ modification, are permitted provided that the following conditions +!!$ are met: +!!$ 1. Redistributions of source code must retain the above copyright +!!$ notice, this list of conditions and the following disclaimer. +!!$ 2. Redistributions in binary form must reproduce the above copyright +!!$ notice, this list of conditions, and the following disclaimer in the +!!$ documentation and/or other materials provided with the distribution. +!!$ 3. The name of the PSBLAS group or the names of its contributors may +!!$ not be used to endorse or promote products derived from this +!!$ software without specific written permission. +!!$ +!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS +!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +!!$ POSSIBILITY OF SUCH DAMAGE. +!!$ +!!$ +! +! Storage conversion filter: reads from standar input a sparse matrix +! stored in MatrixMarket format, and writes to standard output in Harwell-Boeing +! format +! program dmm2hb use psb_sparse_mod use mmio use hbio type(psb_dspmat_type) :: a - integer n, nnz,info,i,j,k - - - nrhs = 0 - nrhsix = 0 + integer info call mm_mat_read(a,info) diff --git a/test/Fileread/mat_dist.f90 b/test/Fileread/mat_dist.f90 index 4205fcd7..b38f644f 100644 --- a/test/Fileread/mat_dist.f90 +++ b/test/Fileread/mat_dist.f90 @@ -211,7 +211,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geall(nrow,b,desc_a,info) + call psb_geall(b,desc_a,info) if(info/=0) then info=4010 ch_err='psb_psdsall' @@ -272,7 +272,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:j_count-1),& + call psb_geins(nnr,b_glob(i_count:j_count-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -318,7 +318,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:i_count+nnr-1),& + call psb_geins(nnr,b_glob(i_count:i_count+nnr-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -354,7 +354,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(1,b,i_count,b_glob(i_count:i_count),& + call psb_geins(1,b_glob(i_count:i_count),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -385,7 +385,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(1,b,i_count,b_glob(i_count:i_count),& + call psb_geins(1,b_glob(i_count:i_count),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -633,7 +633,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geall(nrow,b,desc_a,info) + call psb_geall(b,desc_a,info) if(info/=0) then info=4010 ch_err='psb_psdsall' @@ -699,7 +699,7 @@ contains goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:j_count-1),& + call psb_geins(nnr,b_glob(i_count:j_count-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -745,7 +745,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:i_count+nnr-1),& + call psb_geins(nnr,b_glob(i_count:i_count+nnr-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -994,7 +994,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geall(nrow,b,desc_a,info) + call psb_geall(b,desc_a,info) if(info/=0) then info=4010 ch_err='psb_psdsall' @@ -1055,7 +1055,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:j_count-1),& + call psb_geins(nnr,b_glob(i_count:j_count-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -1101,7 +1101,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:i_count+nnr-1),& + call psb_geins(nnr,b_glob(i_count:i_count+nnr-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -1137,7 +1137,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(1,b,i_count,b_glob(i_count:i_count),& + call psb_geins(1,b_glob(i_count:i_count),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -1168,7 +1168,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(1,b,i_count,b_glob(i_count:i_count),& + call psb_geins(1,b_glob(i_count:i_count),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -1416,7 +1416,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geall(nrow,b,desc_a,info) + call psb_geall(b,desc_a,info) if(info/=0) then info=4010 ch_err='psb_psdsall' @@ -1482,7 +1482,7 @@ contains goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:j_count-1),& + call psb_geins(nnr,b_glob(i_count:j_count-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 @@ -1528,7 +1528,7 @@ contains call psb_errpush(info,name,a_err=ch_err) goto 9999 end if - call psb_geins(nnr,b,i_count,b_glob(i_count:i_count+nnr-1),& + call psb_geins(nnr,b_glob(i_count:i_count+nnr-1),b,i_count,& &desc_a,info) if(info/=0) then info=4010 diff --git a/test/Fileread/zf_sample.f90 b/test/Fileread/zf_sample.f90 index 1ea01758..d0e5c389 100644 --- a/test/Fileread/zf_sample.f90 +++ b/test/Fileread/zf_sample.f90 @@ -209,10 +209,10 @@ program zf_sample & desc_a,b_col_glob,b_col,info,fmt=afmt) end if - call psb_geall(m_problem,x_col,desc_a,info) + call psb_geall(x_col,desc_a,info) x_col(:) =0.0 call psb_geasb(x_col,desc_a,info) - call psb_geall(m_problem,r_col,desc_a,info) + call psb_geall(r_col,desc_a,info) r_col(:) =0.0 call psb_geasb(r_col,desc_a,info) t2 = mpi_wtime() - t1 diff --git a/test/Fileread/zhb2mm.f90 b/test/Fileread/zhb2mm.f90 index b6251650..61ccaa85 100644 --- a/test/Fileread/zhb2mm.f90 +++ b/test/Fileread/zhb2mm.f90 @@ -1,13 +1,46 @@ +!!$ +!!$ Parallel Sparse BLAS v2.0 +!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata +!!$ Alfredo Buttari University of Rome Tor Vergata +!!$ +!!$ Redistribution and use in source and binary forms, with or without +!!$ modification, are permitted provided that the following conditions +!!$ are met: +!!$ 1. Redistributions of source code must retain the above copyright +!!$ notice, this list of conditions and the following disclaimer. +!!$ 2. Redistributions in binary form must reproduce the above copyright +!!$ notice, this list of conditions, and the following disclaimer in the +!!$ documentation and/or other materials provided with the distribution. +!!$ 3. The name of the PSBLAS group or the names of its contributors may +!!$ not be used to endorse or promote products derived from this +!!$ software without specific written permission. +!!$ +!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS +!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +!!$ POSSIBILITY OF SUCH DAMAGE. +!!$ +!!$ +! +! Storage conversion filter: reads from standar input a sparse matrix +! stored in Harwell-Boeing format, and writes to standard output in MatrixMarket +! format +! program zhb2mm use psb_sparse_mod use mmio use hbio type(psb_zspmat_type) :: a - integer n, nnz,info,i,j,k - INTEGER :: iwflag,IOUT,NCOL,NELTVL,NNZERO,NRHS,NRHSIX,NROW,& - & iter - CHARACTER :: RHSDATATYPE,DATATYPE*3,KEY*8,OUTFILE*20,MTITLE*72 + integer :: info + character(len=72) :: mtitle call hb_read(a,info,mtitle=mtitle) diff --git a/test/Fileread/zmm2hb.f90 b/test/Fileread/zmm2hb.f90 index 8cf7d915..aa152513 100644 --- a/test/Fileread/zmm2hb.f90 +++ b/test/Fileread/zmm2hb.f90 @@ -1,14 +1,45 @@ +!!$ +!!$ Parallel Sparse BLAS v2.0 +!!$ (C) Copyright 2006 Salvatore Filippone University of Rome Tor Vergata +!!$ Alfredo Buttari University of Rome Tor Vergata +!!$ +!!$ Redistribution and use in source and binary forms, with or without +!!$ modification, are permitted provided that the following conditions +!!$ are met: +!!$ 1. Redistributions of source code must retain the above copyright +!!$ notice, this list of conditions and the following disclaimer. +!!$ 2. Redistributions in binary form must reproduce the above copyright +!!$ notice, this list of conditions, and the following disclaimer in the +!!$ documentation and/or other materials provided with the distribution. +!!$ 3. The name of the PSBLAS group or the names of its contributors may +!!$ not be used to endorse or promote products derived from this +!!$ software without specific written permission. +!!$ +!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS +!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS +!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +!!$ POSSIBILITY OF SUCH DAMAGE. +!!$ +!!$ +! +! Storage conversion filter: reads from standar input a sparse matrix +! stored in MatrixMarket format, and writes to standard output in Harwell-Boeing +! format +! program zmm2hb use psb_sparse_mod use mmio use hbio type(psb_zspmat_type) :: a - integer n, nnz,info,i,j,k - - - nrhs = 0 - nrhsix = 0 + integer info call mm_mat_read(a,info) diff --git a/test/pargen/ppde90.f90 b/test/pargen/ppde90.f90 index cce97926..e920f5b1 100644 --- a/test/pargen/ppde90.f90 +++ b/test/pargen/ppde90.f90 @@ -489,8 +489,8 @@ contains call psb_cdall(n,n,parts,icontxt,desc_a,info) call psb_spall(a,desc_a,info,nnz=nnz) ! define rhs from boundary conditions; also build initial guess - call psb_geall(n,b,desc_a,info) - call psb_geall(n,t,desc_a,info) + call psb_geall(b,desc_a,info) + call psb_geall(t,desc_a,info) if(info.ne.0) then info=4010 ch_err='allocation rout.' @@ -644,10 +644,10 @@ contains call psb_spins(element-1,irow,icol,val,a,desc_a,info) if(info.ne.0) exit tins = tins + (mpi_wtime()-t3) - call psb_geins(1,b,ia,zt(1:1),desc_a,info) + call psb_geins(1,zt(1:1),b,ia,desc_a,info) if(info.ne.0) exit zt(1)=0.d0 - call psb_geins(1,t,ia,zt(1:1),desc_a,info) + call psb_geins(1,zt(1:1),t,ia,desc_a,info) if(info.ne.0) exit end if end do