Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

ID 766686
Date 11/07/2023
Public

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?la_gbrpvgrw

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

Syntax

call sla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )

call dla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )

call cla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )

call zla_gbrpvgrw( n, kl, ku, ncols, ab, ldab, afb, ldafb )

Include Files

  • mkl.fi

Description

The ?la_gbrpvgrw 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.

kl

INTEGER. The number of subdiagonals within the band of A; kl 0.

ku

INTEGER. The number of superdiagonals within the band of A; ku 0.

ncols

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

ab, afb

REAL for sla_gbrpvgrw

DOUBLE PRECISION for dla_gbrpvgrw

COMPLEX for cla_gbrpvgrw

DOUBLE COMPLEX for zla_gbrpvgrw.

Arrays: ab(ldab,*), afb(ldafb,*).

ab contains the original band matrix A (see Matrix Storage Schemes) stored in rows from 1 to kl + ku + 1. The j-th column of A is stored in the j-th column of the array ab as follows:

ab(ku+1+i-j,j) = A(i,j)

for

max(1,j-ku) i min(n,j+kl)

afb contains details of the LU factorization of the band matrix A, as returned by ?gbtrf. U is stored as an upper triangular band matrix with kl+ku superdiagonals in rows 1 to kl+ku+1, and the multipliers used during the factorization are stored in rows kl+ku+2 to 2*kl+ku+1.

ldab

INTEGER. The leading dimension of ab; ldabkl+ku+1.

ldafb

INTEGER. The leading dimension of afb; ldafb 2*kl+ku+1.

See Also