?la_porpvgrw

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 3/31/2023

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?la_porpvgrw

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

Syntax

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

mkl.fi

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 = U^TU` or `A = LL^T` for real flavors, `A = U^HU` or `A = LL^H` 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.

Parent topic: LAPACK Auxiliary Routines

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?la_porpvgrw

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