?la_gbrpvgrw

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_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; ldab≥`kl`+`ku`+1.
ldafb	INTEGER. The leading dimension of afb; ldafb≥ 2*`kl`+`ku`+1.

Parent topic: LAPACK Auxiliary Routines

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?la_gbrpvgrw

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