?la_porpvgrw

Computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric or Hermitian positive-definite matrix.

Syntax

FORTRAN 77:

call sla_porpvgrw( uplo, ncols, a, lda, af, ldaf, work )

call dla_porpvgrw( uplo, ncols, a, lda, af, ldaf, work )

call cla_porpvgrw( uplo, ncols, a, lda, af, ldaf, work )

call zla_porpvgrw( uplo, ncols, a, lda, af, ldaf, work )

Include Files

  • Fortran: mkl.fi
  • C: mkl.h

Description

The ?la_porpvgrw 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.

ncols

INTEGER. The number of columns of the matrix A; ncols 0.

a, af

REAL for sla_porpvgrw

DOUBLE PRECISION for dla_porpvgrw

COMPLEX for cla_porpvgrw

DOUBLE COMPLEX for zla_porpvgrw.

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

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

The array af contains the triangular factor L or U from the Cholesky factorization as computed by ?potrf:

A = UT*U or A = L*LT for real flavors,

A = UH*U or A = L*LH for complex flavors.

The second dimension of af must be at least max(1,n).

lda

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

ldaf

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

work

REAL for sla_porpvgrw and cla_porpvgrw

DOUBLE PRECISION for dla_porpvgrw and zla_porpvgrw.

Workspace array, dimension 2*n.

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