psb_spsm -- Triangular System Solve

This subroutine computes the Triangular System Solve:

$$\begin{eqnarray*} y &\leftarrow& \alpha P_r T^{-1} P_c x + \beta y\\ y &\leftar... ...\beta y\\ y &\leftarrow& \alpha P_r T^{-H} P_c D x + \beta y\\ \end{eqnarray*}$$

where:

$x$

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

$y$

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

$T$

is the global sparse block triangular submatrix $T$

$D$

is the scaling diagonal matrix.

$P_r, P_c$

are the permutation matrices.

call psb_spsm(alpha, t, x, beta, y, desc_a, info)
call psb_spsm(alpha, t, x, beta, y, desc_a, info,&
             & trans, unit, choice, diag, work)

Table 12: Data types

$T$, $x$, $y$, $D$, $\alpha$, $\beta$	Subroutine
Short Precision Real	psb_spsm
Long Precision Real	psb_spsm
Short Precision Complex	psb_spsm
Long Precision Complex	psb_spsm

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 12.

t

the global portion of the sparse matrix $T$.
Scope: local
Type: required
Intent: in.
Specified as: a structured data type specified in § 3.

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 12. 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 12.

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 12. 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

specify with unitd the operation to perform.

trans = 'N'

the operation is with no transposed matrix

trans = 'T'

the operation is with transposed matrix.

trans = 'C'

the operation is with conjugate transposed matrix.

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

unitd

specify with trans the operation to perform.

unitd = 'U'

the operation is with no scaling

unitd = 'L'

the operation is with left scaling

unitd = 'R'

the operation is with right scaling.

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

choice

specifies the update of overlap elements to be performed on exit:

psb_none_

psb_sum_

psb_avg_

psb_square_root_

Scope: global
Type: optional
Intent: in.
Default: psb_avg_
Specified as: an integer variable.

diag

the diagonal scaling matrix.
Scope: local
Type: optional
Intent: in.
Default: $diag(1) = 1 (no scaling)$
Specified as: a rank one array containing numbers of the type indicated in Table 12.

work

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

On Return

y

the local portion of global dense matrix $y$.
Scope: local
Type: required
Intent: inout.
Specified as: an array of rank one or two containing numbers of type specified in Table 12.

info

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