BVMatProject#

Computes the projection of a matrix onto a subspace.

Synopsis#

#include "slepcbv.h" 
PetscErrorCode BVMatProject(BV X,Mat A,BV Y,Mat M)

Collective

Input Parameters#

X - basis vectors
A - (optional) matrix to be projected
Y - left basis vectors, can be equal to X

Output Parameter#

M - the resulting matrix

Notes#

If A=NULL, then it is assumed that X already contains \(AX\).

This operation is similar to BVDot(), with important differences. The goal is to compute the matrix resulting from the orthogonal projection of A onto the subspace spanned by the columns of X, \(M = X^*AX\), or the oblique projection onto X along Y, \(M = Y^*AX\).

A difference with respect to BVDot() is that the standard inner product is always used, regardless of a non-standard inner product being specified with BVSetMatrix().

On entry, M must be a sequential dense Mat with dimensions ky,kx at least, where ky (resp. kx) is the number of active columns of Y (resp. X). Another difference with respect to BVDot() is that all entries of M are computed except the leading ly,lx part, where ly (resp. lx) is the number of leading columns of Y (resp. X). Hence, the leading columns of X and Y participate in the computation, as opposed to BVDot(). The leading part of M is assumed to be already available from previous computations.

In the orthogonal projection case, Y=X, some computation can be saved if A is real symmetric (or complex Hermitian). In order to exploit this property, the symmetry flag of A must be set with MatSetOption().

Level#

intermediate

Location#

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

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