VecNorm#

Computes the vector norm.

Synopsis#

#include "petscvec.h"   
PetscErrorCode VecNorm(Vec x, NormType type, PetscReal *val)

Collective

Input Parameters#

x - the vector
type - the type of the norm requested

Output Parameter#

val - the norm

Values of NormType#

NORM_1 - sum_i |x[i]|
NORM_2 - sqrt(sum_i |x[i]|^2)
NORM_INFINITY - max_i |x[i]|
NORM_1_AND_2 - computes efficiently both NORM_1 and NORM_2 and stores them each in an output array

Notes#

For complex numbers NORM_1 will return the traditional 1 norm of the 2 norm of the complex numbers; that is the 1 norm of the absolute values of the complex entries. In PETSc 3.6 and earlier releases it returned the 1 norm of the 1 norm of the complex entries (what is returned by the BLAS routine asum()). Both are valid norms but most people expect the former.

This routine stashes the computed norm value, repeated calls before the vector entries are changed are then rapid since the precomputed value is immediately available. Certain vector operations such as VecSet() store the norms so the value is immediately available and does not need to be explicitly computed. VecScale() updates any stashed norm values, thus calls after VecScale() do not need to explicitly recompute the norm.

Performance Issues#

per- processor memory bandwidth - limits the speed of the computation of local portion of the norm
interprocessor latency - limits the accumulation of the result across ranks, .i.e. MPI_Allreduce() time
number of ranks - the time for the result will grow with the log base 2 of the number of ranks sharing the vector
work load imbalance - the rank with the largest number of vector entries will limit the speed up