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#### 4.6 psb_norm1 — 1-Norm of Vector

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

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

psb_geasum(x, desc_a, info [,global])
psb_norm1(x, desc_a, info [,global])

asum | x | Function
Short Precision Real | Short Precision Real | psb_geasum
Long Precision Real | Long Precision Real | psb_geasum
Short Precision Real | Short Precision Complex | psb_geasum
Long Precision Real | Long Precision Complex | psb_geasum

Table 6: Data types

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 6.
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 1-norm of vector x.
  Scope: global unless the optional variable global=.false. has been specified
  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_geasum(x1,desc_a,info,global=.false.)
   vres(2) = psb_geasum(x2,desc_a,info,global=.false.)
   vres(3) = psb_geasum(x3,desc_a,info,global=.false.)
   call psb_sum(ictxt,vres(1:3))

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

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