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@ -10,14 +10,14 @@
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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 $x_{:, jx:jx+n-1}$
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\item[$y$] represents the global dense submatrix $y_{:, jy:jy+n-1}$
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\end{description}
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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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%% \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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@ -44,7 +44,7 @@ Specified as: a number of the data type indicated in Table~\ref{tab:f90axpby}.
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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 with the POINTER attribute
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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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@ -55,30 +55,29 @@ Specified as: a number of the data type indicated in Table~\ref{tab:f90axpby}.
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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 with the POINTER
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attributecontaining numbers of the type
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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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%% \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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@ -111,14 +110,14 @@ 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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%% 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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%% \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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@ -136,37 +135,39 @@ Long Precision Complex & psb\_gedot \\
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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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$x$.\\
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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: a pointer to array of rank one or two
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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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$y$. 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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$y$. \\
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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: a pointer to array of rank one or two
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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[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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@ -213,14 +214,14 @@ Long Precision Complex & psb\_gedot \\
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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 pointer to array of rank one or two
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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: a pointer to array of rank one or two
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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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@ -232,7 +233,7 @@ Specified as: a structured data of type \descdata.
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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] the local portion of result submatrix $y$.\\
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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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@ -254,13 +255,13 @@ 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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%% 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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%% \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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@ -280,30 +281,31 @@ Long Precision Real&Long Precision Complex & psb\_geamax \\
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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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$x$. %% 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 with the POINTER attribute
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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[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 number of the data type indicated in Table~\ref{tab:f90amax}.
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\item[info] the local portion of result submatrix $y$.\\
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Scope: {\bf local} \\
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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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@ -340,7 +342,7 @@ Long Precision Real &Long Precision Complex & psb\_geamax\\
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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 with the POINTER attribute
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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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@ -350,9 +352,8 @@ 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 the data type indicated
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in Table~\ref{tab:f90amax}.
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\item[info] the local portion of result submatrix $y$.\\
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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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@ -373,22 +374,18 @@ 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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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\_geasum}{x, desc\_a, info}
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\syntax*{psb\_geasum}{x, desc\_a, info, jx}
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|
|
|
\begin{table}[h]
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|
|
\begin{center}
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|
|
|
|
\begin{tabular}{ll}
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|
|
\begin{tabular}{lll}
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|
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\hline
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|
$dot$, $x$, $y$ & {\bf Function}\\
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$asum$ & $x$ & {\bf Function}\\
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\hline
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Long Precision Real & psb\_geasum \\
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|
Long Precision Complex & psb\_geasum \\
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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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@ -398,29 +395,24 @@ Long Precision Complex & psb\_geasum \\
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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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|
$x$. %% 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 with the POINTER attribute
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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[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 1-norm of subvector $x$.\\
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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 number of the data type indicated in Table~\ref{tab:f90asum}.
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\item[info] the local portion of result submatrix $y$.\\
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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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|
@ -442,19 +434,19 @@ 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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|
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|
|
\begin{description}
|
|
|
|
|
\item[$x$] represents the global subvector $x_{:,jx}$
|
|
|
|
|
\end{description}
|
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|
|
%% where:
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|
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|
|
%% \begin{description}
|
|
|
|
|
%% \item[$x$] represents the global subvector $x_{:,jx}$
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|
|
%% \end{description}
|
|
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|
|
|
|
|
|
|
\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}
|
|
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|
|
@ -462,34 +454,35 @@ Long Precision Complex & psb\_genrm2 \\
|
|
|
|
|
\end{table}
|
|
|
|
|
|
|
|
|
|
\syntax{psb\_genrm2}{x, desc\_a, info}
|
|
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|
|
\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}.
|
|
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\item[x] the local portion of global dense matrix
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$x$. This subroutine 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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$x$. %% This subroutine 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 with the POINTER attribute
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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:f90spsm}. The rank of $x$ must be the same of $y$.
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\item[beta] the scalar $\beta$.\\
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@ -763,11 +760,12 @@ 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:f90spsm}.
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\item[y] the local portion of global dense matrix
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$y$. This subroutine computes the location of the first element of
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local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . \\
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$y$. %% This subroutine computes the location of the first element of
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%% local subarray used, based on $jy$ 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 with the POINTER attribute
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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:f90spsm}. 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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@ -794,57 +792,41 @@ Scope: {\bf global} \\
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Type: {\bf optional}\\
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Default: $unitd = U$\\
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Specified as: a character variable.
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\item[choice] specify whether a cleanup of the overlapped elements is
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required on exit.
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\item[choice] specifies the update of overlap elements to be performed
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on exit:
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\begin{description}
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\item[choice = .false.] no cleanup on exit
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\item[choice = .true.] cleanup on exit.\\
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\item \verb|psb_none_|
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\item \verb|psb_sum_|
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\item \verb|psb_avg_|
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\item \verb|psb_square_root_|
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\end{description}
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Scope: {\bf global} \\
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Type: {\bf optional}\\
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Default: $choice = .true.$\\
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Specified as: a logical variable.
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Default: \verb|psb_avg_|\\
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Specified as: an integer variable.
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\item[diag] the diagonal scaling matrix.\\
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Scope: {\bf local} \\
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Type: {\bf optional}\\
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Default: $diag(1) = 1 (no scaling)$\\
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Specified as: a rank one array containing numbers of the type
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indicated in Table~\ref{tab:f90spsm}.
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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}\\
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Default: \verb|min(size(x,2)-jx+1,size(y,2)-jy+1)|\\
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Specified as: an integer variable $ n \ge 0$.
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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[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 $y$ is 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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Scope: {\bf global} \\
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Specified as: a number of the data type indicated in Table~\ref{tab:f90spsm}.
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\item[work] the work array. \\
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\item[work] a work array. \\
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Scope: {\bf local} \\
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Type: {\bf optional}\\
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Specified as: a rank one array of the same type of $x$ with the
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POINTER attribute.
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TARGET attribute.
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\item[\bf On Return]
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\item[y] the local portion of global dense matrix
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$y$. This subroutine computes the location of the first element of
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local subarray used, based on $jy$ and the field $matrix\_data$ of $desc\_a$ . \\
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|
|
$y$. %% This subroutine computes the location of the first element of
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|
%% local subarray used, based on $jy$ 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 pointer to array of rank one or two
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|
|
containing numbers of type specified in
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|
Table~\ref{tab:f90spsm}.
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\item[info] the local portion of result submatrix $y$.\\
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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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Salvatore Filippone
19 years ago