?la_syrpvgrw

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 12/16/2022

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?la_syrpvgrw

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

Syntax

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

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

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

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

Include Files

mkl.fi

Description

The ?la_syrpvgrw 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 ?sytrf, that is, the pivot in column info is exactly 0.
a, af	REAL for sla_syrpvgrw DOUBLE PRECISION for dla_syrpvgrw COMPLEX for cla_syrpvgrw DOUBLE COMPLEX for zla_syrpvgrw. 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 block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ?sytrf.	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)`.
ipiv	INTEGER. Array, DIMENSION`n`. Details of the interchanges and the block structure of D as determined by ?sytrf.
work	REAL for sla_syrpvgrw and cla_syrpvgrw DOUBLE PRECISION for dla_syrpvgrw and zla_syrpvgrw. 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_syrpvgrw

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