slepc-3.21.1 2024-04-26
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Orthogonalize one of the column vectors with respect to the previous ones.


#include "slepcbv.h"   
PetscErrorCode BVOrthogonalizeColumn(BV bv,PetscInt j,PetscScalar *H,PetscReal *norm,PetscBool *lindep)

Input Parameters

bv  - the basis vectors context
j  - index of column to be orthogonalized

Output Parameters

H  - (optional) coefficients computed during orthogonalization
norm  - (optional) norm of the vector after being orthogonalized
lindep  - (optional) flag indicating that refinement did not improve the quality of orthogonalization


This function applies an orthogonal projector to project vector V[j] onto the orthogonal complement of the span of the columns V[0..j-1], where V[.] are the vectors of BV. The columns V[0..j-1] are assumed to be mutually orthonormal.

Leading columns V[0..l-1] also participate in the orthogonalization, as well as the constraints. If H is given, it must have enough space to store j-l+1 coefficients (the last coefficient will contain the value norm, unless the norm argument is NULL).

If a non-standard inner product has been specified with BVSetMatrix(), then the vector is B-orthogonalized, using the non-standard inner product defined by matrix B. The output vector satisfies V[j]'*B*V[0..j-1] = 0.

This routine does not normalize the resulting vector, see BVOrthonormalizeColumn().

In the case of an indefinite inner product, the lindep parameter is not computed (set to false).

See Also

BVSetOrthogonalization(), BVSetMatrix(), BVSetActiveColumns(), BVOrthogonalize(), BVOrthogonalizeVec(), BVGetNumConstraints(), BVOrthonormalizeColumn()





Index of all BV routines
Table of Contents for all manual pages
Index of all manual pages