psb_geasums -- Generalized 1-Norm of Vector

This subroutine computes a series of 1-norms on the columns of a dense matrix $x$:

$$res(i) \leftarrow \max_k \vert x(k,i)\vert$$

This function computes the 1-norm of a vector $x$.
If $x$ is a real vector it computes 1-norm as:

$$res(i) \leftarrow \Vert x_i\Vert$$

else if $x$ is a complex vector then it computes 1-norm as:

$$res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1$$

call psb_geasums(res, x, desc_a, info)

Table 7: Data types

$res$	$x$	Subroutine
Short Precision Real	Short Precision Real	psb_geasums
Long Precision Real	Long Precision Real	psb_geasums
Short Precision Real	Short Precision Complex	psb_geasums
Long Precision Real	Long Precision Complex	psb_geasums

Type:

Synchronous.

On Entry

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 7.

desc_a

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

On Return

res

contains the 1-norm of (the columns of) $x$.
Scope: global
Intent: out.
Short as: a long precision real number. Specified as: a long precision real number.

info

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

ifstarsubroutinesubroutinepsb_genrm22-Norm of Vector

This function computes the 2-norm of a vector $x$.
If $x$ is a double precision real vector it computes 2-norm as:

$$nrm2 \leftarrow \sqrt{x^T x}$$

else if $x$ is double precision complex vector then it computes 2-norm as:

$$nrm2 \leftarrow \sqrt{x^H x}$$

Table 8: Data types

$nrm2$	$x$	Function
Short Precision Real	Short Precision Real	psb_genrm2
Long Precision Real	Long Precision Real	psb_genrm2
Short Precision Real	Short Precision Complex	psb_genrm2
Long Precision Real	Long Precision Complex	psb_genrm2

psb_genrm2(x, desc_a, info)

Type:

Synchronous.

On Entry

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 8.

desc_a

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

On Return

Function Value

is the 2-norm of subvector $x$.
Scope: global
Type: required
Specified as: a long precision real number.

info

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