VecCheckOrthogonality#

Checks (or prints) the level of (bi-)orthogonality of a set of vectors.

Synopsis#

#include "slepcvec.h" 
PetscErrorCode VecCheckOrthogonality(Vec V[],PetscInt nv,Vec W[],PetscInt nw,Mat B,PetscViewer viewer,PetscReal *lev)

Collective

Input Parameters#

V - a set of vectors
nv - number of V vectors
W - an alternative set of vectors (optional)
nw - number of W vectors
B - Hermitian matrix defining the inner product (optional)
viewer - optional visualization context

Output Parameter#

lev - level of orthogonality (optional)

Notes#

This function computes \(W^*V\) and prints the result. It is intended to check the level of bi-orthogonality of the vectors in the two sets. If \(W\) is equal to NULL then \(V\) is used, thus checking the orthogonality of the \(V\) vectors.

If matrix B is provided then the check uses the \(B\)-inner product, \(W^*BV\), where \(B\) is assumed to be Hermitian.

If V, W represent eigenvectors computed by SLEPc, this function will not work correctly if one of the eigenvalues is complex when running with real scalars.

If lev is not NULL, it will contain the maximum entry of matrix \(W^*V - I\) (in absolute value) omitting the diagonal. Otherwise, the matrix \(W^*V\) is printed.

Level#

developer

Location#

src/sys/vec/vecutil.c

Examples#

src/eps/tutorials/ex55.c
src/eps/tutorials/ex41.c

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