# sla_gbrpvgrw.f - Man Page

SRC/sla_gbrpvgrw.f

## Synopsis

### Functions/Subroutines

real function **sla_gbrpvgrw** (n, kl, ku, ncols, ab, ldab, afb, ldafb)**SLA_GBRPVGRW** computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

## Function/Subroutine Documentation

### real function sla_gbrpvgrw (integer n, integer kl, integer ku, integer ncols, real, dimension( ldab, * ) ab, integer ldab, real, dimension( ldafb, * ) afb, integer ldafb)

**SLA_GBRPVGRW** computes the reciprocal pivot growth factor norm(A)/norm(U) for a general banded matrix.

**Purpose:**

SLA_GBRPVGRW 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.

**Parameters***N*N is INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0.

*KL*KL is INTEGER The number of subdiagonals within the band of A. KL >= 0.

*KU*KU is INTEGER The number of superdiagonals within the band of A. KU >= 0.

*NCOLS*NCOLS is INTEGER The number of columns of the matrix A. NCOLS >= 0.

*AB*AB is REAL array, dimension (LDAB,N) On entry, the matrix A in band storage, in rows 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)

*LDAB*LDAB is INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1.

*AFB*AFB is REAL array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by SGBTRF. 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.

*LDAFB*LDAFB is INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **115** of file **sla_gbrpvgrw.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sla_gbrpvgrw(3) is an alias of sla_gbrpvgrw.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK