?la_gbrpvgrw

Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

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ID 766686

Date 4/28/2026

Version

Public

?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.

NOTE:

?gbtrf

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Developer Reference for Intel® oneAPI Math Kernel Library for Fortran

?la_gbrpvgrw

Syntax

Include Files

Description

Input Parameters