?la_herpvgrw

Computes the reciprocal pivot growth factor norm(A)/norm(U) for a Hermitian indefinite matrix.

Syntax

FORTRAN 77:

call cla_herpvgrw( uplo, n, info, a, lda, af, ldaf, ipiv, work )

call zla_herpvgrw( uplo, n, info, a, lda, af, ldaf, ipiv, work )

Include Files

  • Fortran: mkl.fi
  • C: mkl.h

Description

The ?la_herpvgrw routine computes the reciprocal pivot growth factor norm(A)/norm(U). The max absolute element norm is used. If this is much less than 1, the stability of the LU factorization of the equilibrated matrix A could be poor. This also means that the solution X, estimated condition numbers, and error bounds could be unreliable.

Input Parameters

uplo

CHARACTER*1. Must be 'U' or 'L'.

Specifies the triangle of A to store:

If uplo = 'U', the upper triangle of A is stored,

If uplo = 'L', the lower triangle of A is stored.

n

INTEGER. The number of linear equations, the order of the matrix A; n 0.

info

INTEGER. The value of INFO returned from ?hetrf, that is, the pivot in column info is exactly 0.

a, af

COMPLEX for cla_herpvgrw

DOUBLE COMPLEX for zla_herpvgrw.

Arrays: a(lda,*), af(ldaf,*).

a contains the n-by-n matrix A. The second dimension of a must be at least max(1,n).

af contains the block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ?hetrf. The second dimension of af must be at least max(1,n).

lda

INTEGER. The leading dimension of array a; lda max(1,n).

ldaf

INTEGER. The leading dimension of array af; ldaf max(1,n).

ipiv

INTEGER.

Array, DIMENSION n. Details of the interchanges and the block structure of D as determined by ?hetrf.

work

REAL for cla_herpvgrw

DOUBLE PRECISION for zla_herpvgrw.

Array, DIMENSION 2*n. Workspace.

For more complete information about compiler optimizations, see our Optimization Notice.