# IPQRDecomposition

Compute the QR factorization of a set of vectors.

### Synopsis

    #include "slepcip.h"
    PetscErrorCode IPQRDecomposition(IP ip,Vec *V,PetscInt m,PetscInt n,PetscScalar *R,PetscInt ldr)

Collective on IP and Vec

### Input Parameters

| ip | - the eigenproblem solver context
| V | - set of vectors
| m | - starting column
| n | - ending column
| ldr | - leading dimension of R

### Output Parameter

R - triangular matrix of QR factorization

### Notes

This routine orthonormalizes the columns of V so that V'*V=I up to working precision. It assumes that the first m columns (from 0 to m-1) are already orthonormal. The coefficients of the orthogonalization are stored in R so that V*R is equal to the original V.

In some cases, this routine makes V B-orthonormal, that is, V'*B*V=I.

If one of the vectors is linearly dependent wrt the rest (at working precision) then it is replaced by a random vector.

### See Also

IPOrthogonalize(), IPNorm(), IPInnerProduct().

Location: src/ip/iporthog.c
Index of all IP routines
Table of Contents for all manual pages
Index of all manual pages