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842 lines
25 KiB
TeX
842 lines
25 KiB
TeX
\section{Computational routines}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% DENSE MATRIX SUM
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_geaxpby}{General Dense Matrix Sum}
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This subroutine is an interface to the computational kernel for
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dense matrix sum:
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\[ y \leftarrow \alpha\> x+ \beta y \]
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%% where:
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%% \begin{description}
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%% \item[$x$] represents the global dense submatrix $x_{:, :1}$
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%% \item[$y$] represents the global dense submatrix $y_{:, :}$
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%% \end{description}
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\syntax{call psb\_geaxpby}{alpha, x, beta, y, desc\_a, info}
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%% \syntax*{call psb\_geaxpby}{alpha, x, beta, y, desc\_a, info, n, jx, jy}
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%( calculating y <- alpha*x+beta*y )
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{ll}
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\hline
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$x$, $y$, $\alpha$, $\beta$ & {\bf Subroutine}\\
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\hline
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Long Precision Real & psb\_geaxpby \\
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Long Precision Complex & psb\_geaxpby \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90axpby}}
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\end{table}
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\begin{description}
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\item[\bf On Entry]
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\item[alpha] the scalar $\alpha$.\\
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Scope: {\bf global} \\
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Type: {\bf required} \\
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Specified as: a number of the data type indicated in Table~\ref{tab:f90axpby}.
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\item[x] the local portion of global dense matrix
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$x$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: a rank one or two array
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containing numbers of type
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specified in Table~\ref{tab:f90axpby}. The rank of $x$ must be the same of $y$.
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\item[beta] the scalar $\beta$.\\
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Scope: {\bf global} \\
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Type: {\bf required} \\
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Specified as: a number of the data type indicated in Table~\ref{tab:f90axpby}.
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\item[y] the local portion of the global dense matrix
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$y$. \\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: a rank one or two array containing numbers of the type
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indicated in Table~\ref{tab:f90axpby}. The rank of $y$ must be the same of $x$.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: a structured data of type \descdata.
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%% \item[n] number of columns in dense submatrices $x$ and $y$.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\
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%% Default: \verb|min(size(x,2),size(y,2))|.\\
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%% Specified as: an integer variable $n\ge 0$.
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%% \item[jx] the column index of the global dense matrix $x$,
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%% identifying the first column of the submatrix $x$.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\
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%% Default: $jx = 1$.\\
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%% Specified as: an integer variable $jx\ge 1$.
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%% \item[jy] the column index of the global dense matrix $y$,
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%% identifying the first column of the submatrix $y$.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\
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%% Default: $jy = 1$.\\
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%% Specified as: an integer variable $jy\ge 1$.
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\end{description}
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\begin{description}
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\item[\bf On Return]
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\item[y] the local portion of result submatrix $y$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: a rank one or two array containing numbers of the type
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indicated in Table~\ref{tab:f90axpby}.
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\item[info] the local portion of result submatrix $y$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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An integer value that contains an error code.
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\end{description}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% F90DOT PRODUCT
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_gedot}{Dot Product}
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This function computes dot product between two vectors $x$ and
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$y$.\\
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If $x$ and $y$ are double precision real vectors
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computes dot-product as:
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\[dot \leftarrow x^T y\]
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Else if $x$ and $y$ are double precision complex vectors then computes dot-product as:
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\[dot \leftarrow x^H y\]
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%% where:
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%% \begin{description}
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%% \item[$x$] represents the global subvector $x_{:,jx}$
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%% \item[$y$] represents the global subvector $y_{:,jy}$
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%% \end{description}
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\syntax{psb\_gedot}{x, y, desc\_a, info}
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%% \syntax*{psb\_gedot}{x, y, desc\_a, info, jx, jy}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{ll}
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\hline
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$dot$, $x$, $y$ & {\bf Function}\\
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\hline
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Long Precision Real & psb\_gedot \\
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Long Precision Complex & psb\_gedot \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90dot}}
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\end{table}
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\begin{description}
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\item[\bf On Entry]
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\item[x] the local portion of global dense matrix
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$x$.\\
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%% This function computes the location of the first element of
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%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . \\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: an array of rank one or two
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containing numbers of type specified in
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Table~\ref{tab:f90dot}. The rank of $x$ must be the same of $y$.
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\item[y] the local portion of global dense matrix
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$y$. \\
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%% This function computes the location of the first element of
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%% local subarray used, based on $iy, jy$ and the field $matrix\_data$ of $desc\_a$ . \\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: an array of rank one or two
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containing numbers of type specified in
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Table~\ref{tab:f90dot}. The rank of $y$ must be the same of $x$.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: a structured data of type \descdata.
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%% \item[jx] the column index of global dense matrix $x$,
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%% identifying the column of subvector $x$.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\
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%% Default: $jx = 1$.\\
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%% \item[jy] the column index of global dense matrix $y$,
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%% identifying the column of subvector $y$.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}; can only be present if $x$ and $y$ are of rank 2.\\
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%% Default: $jy = 1$.\\
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%% Specified as: an integer variable $jy\ge 1$.
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\item[\bf On Return]
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\item[Function value] is the dot product of subvectors $x$ and $y$.\\
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Scope: {\bf global} \\
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Specified as: a number of the data type indicated in Table~\ref{tab:f90dot}.
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\item[info] the local portion of result submatrix $y$.\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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An integer value that contains an error code.
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\end{description}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% F90DOT PRODUCT
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_gedot}{Generalized Dot Product}
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This subroutine computes a series of dot products among the columns of
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two dense matrices $x$ and $y$:
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\[ res(i) \leftarrow x(:,i)^T y(:,i)\]
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If the matrices are complex, then the
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usual convention applies, i.e. the conjugate transpose of $x$ is
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used. If $x$ and $y$ are of rank one, then $res$ is a scalar, else it
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is a rank one array.
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\syntax{psb\_gedot}{res, x, y, desc\_a, info}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{ll}
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\hline
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$res$, $x$, $y$ & {\bf Subroutine}\\
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\hline
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Long Precision Real & psb\_gedot \\
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Long Precision Complex & psb\_gedot \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90mdot}}
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\end{table}
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\begin{description}
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\item[\bf On Entry]
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\item[x] the local portion of global dense matrix
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$x$. \\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: an array of rank one or two
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containing numbers of type specified in
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Table~\ref{tab:f90mdot}. The rank of $x$ must be the same of $y$.
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\item[y] the local portion of global dense matrix
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$y$. \\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: an array of rank one or two
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containing numbers of type specified in
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Table~\ref{tab:f90mdot}. The rank of $y$ must be the same of $x$.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: a structured data of type \descdata.
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\item[\bf On Return]
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\item[res] is the dot product of subvectors $x$ and $y$.\\
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Scope: {\bf global} \\
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Specified as: a number or a rank-one array of the data type indicated
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in Table~\ref{tab:f90dot}.
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\item[info]
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Scope: {\bf local} \\
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Type: {\bf required} \\
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An integer value that contains an error code.
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\end{description}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% VECTOR INFINITY-NORM
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_geamax}{Infinity-Norm of Vector}
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This function computes
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the infinity-norm of a vector $x$.\\
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If $x$ is a double precision real vector
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computes infinity norm as:
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\[ amax \leftarrow \max_i |x_i|\]
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else if $x$ is a double precision complex vector then computes infinity-norm as:
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\[ amax \leftarrow \max_i {(|re(x_i)| + |im(x_i)|)}\]
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%% where:
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%% \begin{description}
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%% \item[$x$] represents the global subvector $x_{:,jx}$
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%% \end{description}
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\syntax{psb\_geamax}{x, desc\_a, info}
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%% \syntax*{psb\_geamax}{x, desc\_a, info, jx}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{lll}
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\hline
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$amax$ & $x$ & {\bf Function}\\
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\hline
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Long Precision Real&Long Precision Real & psb\_geamax \\
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Long Precision Real&Long Precision Complex & psb\_geamax \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90amax}}
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\end{table}
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\begin{description}
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\item[\bf On Entry]
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\item[x] the local portion of global dense matrix
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$x$. %% This function computes the location of the first element of
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%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ .
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\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: a rank one or two array
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containing numbers of type specified in
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Table~\ref{tab:f90amax}.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: a structured data of type \descdata.
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%% \item[jx] the column index of global dense matrix $x$,
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%% identifying the column of subvector $x$.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}; can only be present if $x$ is of rank 2.\\
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%% Default: $jx = 1$\\
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%% Specified as: an integer variable $jx\ge 1$.
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\item[\bf On Return]
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\item[Function value] is the infinity norm of subvector $x$.\\
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Scope: {\bf global} \\
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Specified as: a long precision real number.
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\item[info]
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Scope: {\bf global} \\
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Type: {\bf required} \\
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An integer value that contains an error code.
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\end{description}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% Infinity norm
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_geamax}{Generalized Infinity Norm}
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This subroutine computes a series of infinity norms on the columns of
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a dense matrix $x$:
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\[ res(i) \leftarrow \max_k |x(k,i)| \]
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\syntax{psb\_geamax}{res, x, desc\_a, info}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{lll}
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\hline
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$res$& $x$& {\bf Subroutine}\\
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\hline
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Long Precision Real &Long Precision Real & psb\_geamax\\
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Long Precision Real &Long Precision Complex & psb\_geamax\\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90mamax}}
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\end{table}
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\begin{description}
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\item[\bf On Entry]
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\item[x] the local portion of global dense matrix
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$x$. \\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: a rank one or two array
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containing numbers of type specified in
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Table~\ref{tab:f90mamax}.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: a structured data of type \descdata.
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\item[\bf On Return]
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\item[res] is the infinity norm of the columns of $x$.\\
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Scope: {\bf global} \\
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Specified as: a number or a rank-one array of long precision real numbers.
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\item[info]
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Scope: {\bf local} \\
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Type: {\bf required} \\
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An integer value that contains an error code.
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\end{description}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% 1-NORM OF A VECTOR
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine{psb\_geasum}{1-Norm of Vector}
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This function computes the 1-norm of a vector $x$.\\
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If $x$ is a double precision real vector
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computes 1-norm as:
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\[ asum \leftarrow \|x_i\|\]
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else if $x$ ic double precision complex vector then computes 1-norm as:
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\[ asum \leftarrow \|re(x)\|_1 + \|im(x)\|_1\]
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\syntax{psb\_geasum}{x, desc\_a, info}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{lll}
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\hline
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$asum$ & $x$ & {\bf Function}\\
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\hline
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Long Precision Real&Long Precision Real & psb\_geasum \\
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Long Precision Real&Long Precision Complex & psb\_geasum \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90asum}}
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\end{table}
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\begin{description}
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\item[\bf On Entry]
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\item[x] the local portion of global dense matrix
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$x$. %% This function computes the location of the first element of
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%% local subarray used, based on the field $matrix\_data$ of $desc\_a$ .
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\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: a rank one or two array
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containing numbers of type specified in
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Table~\ref{tab:f90asum}.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: a structured data of type \descdata.
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\item[\bf On Return]
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\item[Function value] is the 1-norm of vector $x$.\\
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Scope: {\bf global} \\
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Specified as: a long precision real number.
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\item[info]
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Scope: {\bf local} \\
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Type: {\bf required} \\
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An integer value that contains an error code.
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\end{description}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%
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% 2-NORM OF A VECTOR
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%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subroutine {psb\_genrm2}{2-Norm of Vector}
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This function computes the 2-norm of a vector $x$.\\
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If $x$ is a double precision real vector
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computes 2-norm as:
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\[ nrm2 \leftarrow \sqrt{x^T x}\]
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else if $x$ is double precision complex vector then computes 2-norm as:
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\[ nrm2 \leftarrow \sqrt{x^H x}\]
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%% where:
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%% \begin{description}
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%% \item[$x$] represents the global subvector $x_{:,jx}$
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%% \end{description}
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\begin{table}[h]
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\begin{center}
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\begin{tabular}{lll}
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\hline
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$nrm2$ & $x$ & {\bf Function}\\
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\hline
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Long Precision Real&Long Precision Real & psb\_genrm2 \\
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Long Precision Real&Long Precision Complex & psb\_genrm2 \\
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\hline
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\end{tabular}
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\end{center}
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\caption{Data types\label{tab:f90nrm2}}
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\end{table}
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\syntax{psb\_genrm2}{x, desc\_a, info}
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%% \syntax*{psb\_genrm2}{x, desc\_a, info, jx}
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\begin{description}
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\item[\bf On Entry]
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\item[x] the local portion of global dense matrix
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$x$.%% This function computes the location of the first element of
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%% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ .
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\\
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Scope: {\bf local} \\
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Type: {\bf required} \\
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Specified as: a rank one or two array
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containing numbers of type specified in
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Table~\ref{tab:f90nrm2}.
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\item[desc\_a] contains data structures for communications.\\
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Scope: {\bf local} \\
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Type: {\bf required}\\
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Specified as: a structured data of type \descdata.
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%% \item[jx] the column index of global dense matrix $x$,
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%% identifying the column of subvector $x$.\\
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%% Scope: {\bf global} \\
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%% Type: {\bf optional}; can only be present if $x$ is of rank 2.\\
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%% Default: $jx = 1$\\
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%% Specified as: an integer variable $jx\ge 1$.
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\item[\bf On Return]
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\item[Function Value] is the 2-norm of subvector $x$.\\
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Scope: {\bf global} \\
|
|
Type: {\bf required} \\
|
|
Specified as: a long precision real number.
|
|
\item[info]
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
An integer value that contains an error code.
|
|
\end{description}
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%
|
|
% INFINITY-NORM OF A MATRIX
|
|
%
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
|
|
\subroutine{psb\_spnrmi}{Infinity Norm of Sparse Matrix}
|
|
|
|
This function computes the infinity-norm of a matrix $A$:\\
|
|
|
|
\[ nrmi \leftarrow \|A\|_\infty \]
|
|
where:
|
|
\begin{description}
|
|
\item[$A$] represents the global matrix $A$
|
|
\end{description}
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\begin{tabular}{ll}
|
|
\hline
|
|
$A$ & {\bf Function}\\
|
|
\hline
|
|
Long Precision Real & psb\_spnrmi \\
|
|
Long Precision Complex & psb\_spnrmi \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{Data types\label{tab:f90nrmi}}
|
|
\end{table}
|
|
|
|
\syntax{psb\_spnrmi}{A, desc\_a, info}
|
|
|
|
\begin{description}
|
|
\item[\bf On Entry]
|
|
\item[a] the local portion of the global sparse matrix
|
|
$A$. \\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required}\\
|
|
Specified as: a structured data of type \spdata.
|
|
\item[desc\_a] contains data structures for communications.\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required}\\
|
|
Specified as: a structured data of type \descdata.
|
|
\item[\bf On Return]
|
|
\item[Function value] is the infinity-norm of sparse submatrix $A$.\\
|
|
Scope: {\bf global} \\
|
|
Specified as: a long precision real number.
|
|
\item[info]
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
An integer value that contains an error code.
|
|
\end{description}
|
|
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%
|
|
% SPARSE MATRIX by DENSE MATRIX PRODUCT
|
|
%
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
|
|
\subroutine{psb\_spmm}{Sparse Matrix by Dense Matrix Product}
|
|
|
|
This subroutine computes the Sparse Matrix by Dense Matrix Product:
|
|
|
|
\begin{equation}
|
|
y \leftarrow \alpha P_r A P_c x + \beta y
|
|
\label{eq:f90spmm_no_tra}
|
|
\end{equation}
|
|
\begin{equation}
|
|
y \leftarrow \alpha P_r A^T P_c x + \beta y
|
|
\label{eq:f90spmm_tra}
|
|
\end{equation}
|
|
\begin{equation}
|
|
y \leftarrow \alpha P_r A^H P_c x + \beta y
|
|
\label{eq:f90spmm_con}
|
|
\end{equation}
|
|
|
|
where:
|
|
\begin{description}
|
|
\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}
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\begin{tabular}{ll}
|
|
\hline
|
|
$A$, $x$, $y$, $\alpha$, $\beta$ & {\bf Subroutine}\\
|
|
\hline
|
|
Long Precision Real & psb\_spmm \\
|
|
Long Precision Complex & psb\_spmm \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{Data types\label{tab:f90spmm}}
|
|
\end{table}
|
|
|
|
\syntax{CALL psb\_spmm}{alpha, a, x, beta, y, desc\_a, info}
|
|
\syntax*{CALL psb\_spmm}{alpha, a, x, beta, y,desc\_a, info,
|
|
trans, work}
|
|
|
|
\begin{description}
|
|
\item[\bf On Entry]
|
|
\item[alpha] the scalar $\alpha$.\\
|
|
Scope: {\bf global} \\
|
|
Type: {\bf required}\\
|
|
Specified as: a number of the data type indicated in
|
|
Table~\ref{tab:f90spmm}.
|
|
\item[a] the local portion of the sparse matrix
|
|
$A$. \\
|
|
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 $desc\_a$ .
|
|
\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
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 $\beta$.\\
|
|
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 $desc\_a$ .
|
|
\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
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.\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required}\\
|
|
Specified as: a structured data of type \descdata.
|
|
\item[trans] indicate what kind of operation to perform.
|
|
\begin{description}
|
|
\item[trans = N] the operation is specified by equation \ref{eq:f90spmm_no_tra}
|
|
\item[trans = T] the operation is specified by equation
|
|
\ref{eq:f90spmm_tra}
|
|
\item[trans = C] the operation is specified by equation
|
|
\ref{eq:f90spmm_con}
|
|
\end{description}
|
|
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] work array.\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf optional}\\
|
|
Specified as: a rank one array of the same type of $x$ and $y$ with
|
|
the TARGET attribute.
|
|
|
|
\item[\bf On Return]
|
|
\item[y] the local portion of result submatrix $y$.\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
Specified as: an array of rank one or two
|
|
containing numbers of type specified in
|
|
Table~\ref{tab:f90spmm}.
|
|
\item[info]
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
An integer value that contains an error code.
|
|
\end{description}
|
|
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
%
|
|
% TRIANGULAR SYSTEM SOLVE
|
|
%
|
|
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|
|
|
|
|
|
\subroutine{psb\_spsm}{Triangular System Solve}
|
|
|
|
This subroutine computes the Triangular System Solve:
|
|
|
|
\begin{eqnarray*}
|
|
y &\leftarrow& \alpha P_r T^{-1} P_c x + \beta y\\
|
|
y &\leftarrow& \alpha D P_r T^{-1} P_c x + \beta y\\
|
|
y &\leftarrow& \alpha P_r T^{-1} P_c D x + \beta y\\
|
|
y &\leftarrow& \alpha P_r T^{-T} P_c x + \beta y\\
|
|
y &\leftarrow& \alpha D P_r T^{-T} P_c x + \beta y\\
|
|
y &\leftarrow& \alpha P_r T^{-T} P_c D x + \beta y\\
|
|
y &\leftarrow& \alpha P_r T^{-H} P_c x + \beta y\\
|
|
y &\leftarrow& \alpha D P_r T^{-H} P_c x + \beta y\\
|
|
y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\
|
|
\end{eqnarray*}
|
|
|
|
|
|
where:
|
|
\begin{description}
|
|
\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.
|
|
\end{description}
|
|
|
|
\syntax{CALL psb\_spsm}{alpha, t, x, beta, y, desc\_a, info}
|
|
\syntax*{CALL psb\_spsm}{alpha, t, x, beta, y, desc\_a, info,
|
|
trans, unit, choice, diag, work}
|
|
|
|
\begin{table}[h]
|
|
\begin{center}
|
|
\begin{tabular}{ll}
|
|
\hline
|
|
$T$, $x$, $y$, $D$, $\alpha$, $\beta$ & {\bf Subroutine}\\
|
|
\hline
|
|
Long Precision Real & psb\_spsm \\
|
|
Long Precision Complex & psb\_spsm \\
|
|
\hline
|
|
\end{tabular}
|
|
\end{center}
|
|
\caption{Data types\label{tab:f90spsm}}
|
|
\end{table}
|
|
|
|
|
|
|
|
\begin{description}
|
|
\item[\bf On Entry]
|
|
\item[alpha] the scalar $\alpha$.\\
|
|
Scope: {\bf global} \\
|
|
Type: {\bf required}\\
|
|
Specified as: a number of the data type indicated in
|
|
Table~\ref{tab:f90spsm}.
|
|
\item[t] the global portion of the sparse matrix
|
|
$T$. \\
|
|
Scope: {\bf local} \\
|
|
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 $desc\_a$ .
|
|
\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
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 $\beta$.\\
|
|
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 $desc\_a$ .
|
|
\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
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.\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required}\\
|
|
Specified as: a structured data of type \descdata.
|
|
\item[trans] specify with {\em unitd} the operation to perform.
|
|
\begin{description}
|
|
\item[trans = 'N'] the operation is with no transposed matrix
|
|
\item[trans = 'T'] the operation is with transposed matrix.
|
|
\item[trans = 'C'] the operation is with conjugate transposed matrix.
|
|
\end{description}
|
|
Scope: {\bf global} \\
|
|
Type: {\bf optional}\\
|
|
Default: $trans = N$\\
|
|
Specified as: a character variable.
|
|
\item[unitd] specify with {\em trans} the operation to perform.
|
|
\begin{description}
|
|
\item[unitd = 'U'] the operation is with no scaling
|
|
\item[unitd = 'L'] the operation is with left scaling
|
|
\item[unitd = 'R'] the operation is with right scaling.
|
|
\end{description}
|
|
Scope: {\bf global} \\
|
|
Type: {\bf optional}\\
|
|
Default: $unitd = U$\\
|
|
Specified as: a character variable.
|
|
\item[choice] specifies the update of overlap elements to be performed
|
|
on exit:
|
|
\begin{description}
|
|
\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: \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[work] a work array. \\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf optional}\\
|
|
Specified as: a rank one array of the same type of $x$ with the
|
|
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 $desc\_a$ .
|
|
\\
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
Specified as: an array of rank one or two
|
|
containing numbers of type specified in
|
|
Table~\ref{tab:f90spsm}.
|
|
\item[info]
|
|
Scope: {\bf local} \\
|
|
Type: {\bf required} \\
|
|
An integer value that contains an error code.
|
|
\end{description}
|
|
|
|
|
|
|
|
|
|
%%% Local Variables:
|
|
%%% mode: latex
|
|
%%% TeX-master: "userguide"
|
|
%%% End:
|