BVOrthogonalizeColumn#

Orthogonalize one of the column vectors with respect to the previous ones.

Synopsis#

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

Collective

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

Notes#

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]’BV[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()

Level#

advanced

Location#

src/sys/classes/bv/interface/bvorthog.c

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