4.8 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:

else if x is a complex vector then it computes 2-norm as:

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 psb_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 psb_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:
       vres(1) = psb_genrm2(x1,desc_a,info,global=.false.) 
       vres(2) = psb_genrm2(x2,desc_a,info,global=.false.) 
       vres(3) = psb_genrm2(x3,desc_a,info,global=.false.) 
       call psb_nrm2(ctxt,vres(1:3))

   In this way the global communication, which for small sizes is a latency-bound operation, is invoked only once.