psb_spmm -- Sparse Matrix by Dense Matrix Product

This subroutine computes the Sparse Matrix by Dense Matrix Product:

$$y \leftarrow \alpha P_r A P_c x + \beta y$$ (1)

$$y \leftarrow \alpha P_r A^T P_c x + \beta y$$ (2)

$$y \leftarrow \alpha P_r A^H P_c x + \beta y$$ (3)

where:

$x$

is the global dense submatrix $x_{:, :}$

$y$

is the global dense submatrix $y_{:, :}$

$A$

is the global sparse submatrix $A$

$P_r, P_c$

are the permutation matrices.

Table 11: Data types

$A$, $x$, $y$, $\alpha$, $\beta$	Subroutine
Short Precision Real	psb_spmm
Long Precision Real	psb_spmm
Short Precision Complex	psb_spmm
Long Precision Complex	psb_spmm

call psb_spmm(alpha, a, x, beta, y, desc_a, info)
call psb_spmm(alpha, a, x, beta, y,desc_a, info, &
             & trans, work)

Type:

Synchronous.

On Entry

alpha

the scalar $\alpha$.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 11.

a

the local portion of the sparse matrix $A$.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type spdatapsb_spmat_type.

x

the local portion of global dense matrix $x$.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array containing numbers of type specified in Table 11. The rank of $x$ must be the same of $y$.

beta

the scalar $\beta$.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 11.

y

the local portion of global dense matrix $y$.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array containing numbers of type specified in Table 11. The rank of $y$ must be the same of $x$.

desc_a

contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type descdatapsb_desc_type.

trans

indicate what kind of operation to perform.

trans = N

the operation is specified by equation 1

trans = T

the operation is specified by equation 2

trans = C

the operation is specified by equation 3

Scope: global
Type: optional
Intent: in.
Default: $trans = N$
Specified as: a character variable.

work

work array.
Scope: local
Type: optional
Intent: inout.
Specified as: a rank one array of the same type of $x$ and $y$ with the TARGET attribute.

On Return

y

the local portion of result submatrix $y$.
Scope: local
Type: required
Intent: inout.
Specified as: an array of rank one or two containing numbers of type specified in Table 11.

info

Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.