psb_norm2 -- 2-Norm of Vector

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

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

else if $x$ is a 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 [,global])
psb_norm2(x, desc_a, info [,global])

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 or an object of type vdatapsb_T_vect_type containing numbers of type specified in Table 8.

desc_a

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

global

Specifies whether the computation should include the global reduction across all processes.
Scope: global
Type: optional.
Intent: in.
Specified as: a logical scalar. Default: global=.true.

On Return

Function Value

is the 2-norm of vector $x$.
Scope: global unless the optional variable global=.false. has been specified
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.

Notes

1. The computation of a global result requires a global communication, which entails a significant overhead. It may be necessary and/or advisable to compute multiple norms at the same time; in this case, it is possible to improve the runtime efficiency by using the following scheme:
   
   In this way the global communication, which for small sizes is a latency-bound operation, is invoked only once.