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## man page of LAPACK-3

### LAPACK-3: computes the reciprocal pivot growth factor norm(A)/norm(U)

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## NAME

LAPACK-3 - computes the reciprocal pivot growth factor norm(A)/norm(U)## SYNOPSIS

DOUBLE PRECISION FUNCTION ZLA_GBRPVGRW( N, KL, KU, NCOLS, AB, LDAB, AFB, LDAFB ) IMPLICIT NONE INTEGER N, KL, KU, NCOLS, LDAB, LDAFB COMPLEX*16 AB( LDAB, * ), AFB( LDAFB, * )## PURPOSE

ZLA_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.## ARGUMENTS

N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. KL (input) INTEGER The number of subdiagonals within the band of A. KL >= 0. KU (input) INTEGER The number of superdiagonals within the band of A. KU >= 0. NCOLS (input) INTEGER The number of columns of the matrix A. NCOLS >= 0. AB (input) COMPLEX*16 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 (input) INTEGER The leading dimension of the array AB. LDAB >= KL+KU+1. AFB (input) COMPLEX*16 array, dimension (LDAFB,N) Details of the LU factorization of the band matrix A, as computed by ZGBTRF. 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 (input) INTEGER The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. LAPACK routine (version 3.2.2)March 2011 LAPACK-3(3)

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