# IPOrthogonalize

Orthogonalize a vector with respect to a set of vectors.

### Synopsis

    #include "slepcip.h"
    PetscErrorCode IPOrthogonalize(IP ip,PetscInt nds,Vec *defl,PetscInt n,PetscBool *which,Vec *V,Vec v,PetscScalar *H,PetscReal *norm,PetscBool *lindep)

Collective on IP and Vec

### Input Parameters

| ip | - the inner product (IP) context
| nds | - number of columns of defl
| defl | - first set of vectors
| n | - number of columns of V
| which | - logical array indicating columns of V to be used
| V | - second set of vectors

### Input/Output Parameter

v - (input) vector to be orthogonalized and (output) result of orthogonalization

### Output Parameter

| H | - coefficients computed during orthogonalization with V
| norm | - norm of the vector after being orthogonalized
| lindep | - flag indicating that refinement did not improve the quality of orthogonalization

### Notes

This function applies an orthogonal projector to project vector v onto the orthogonal complement of the span of the columns of defl and V. The columns of defl and V are assumed to be mutually orthonormal.

On exit, v = v0 - V*H, where v0 is the original vector v.

This routine does not normalize the resulting vector.

### See Also

IPSetOrthogonalization(), IPBiOrthogonalize()

Location: src/ip/iporthog.c
Index of all IP routines
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