Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 3/31/2023
Public

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?la_gerpvgrw

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

Syntax

call sla_gerpvgrw( n, ncols, a, lda, af, ldaf )

call dla_gerpvgrw( n, ncols, a, lda, af, ldaf )

call cla_gerpvgrw( n, ncols, a, lda, af, ldaf )

call zla_gerpvgrw( n, ncols, a, lda, af, ldaf )

Include Files
  • mkl.fi
Description

The ?la_gerpvgrw 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

n

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

ncols

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

a, af

REAL for sla_gerpvgrw

DOUBLE PRECISION for dla_gerpvgrw

COMPLEX for cla_gerpvgrw

DOUBLE COMPLEX for zla_gerpvgrw.

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 factors L and U from the factorization triangular factor L or U from the Cholesky factorization A = P*L*U as computed by ?getrf. 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).

See Also