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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_HERPVGRW( UPLO, N, INFO, A, LDA, AF, LDAF, IPIV, WORK ) IMPLICIT NONE CHARACTER*1 UPLO INTEGER N, INFO, LDA, LDAF INTEGER IPIV( * ) COMPLEX*16 A( LDA, * ), AF( LDAF, * ) DOUBLE PRECISION WORK( * )## PURPOSE

ZLA_HERPVGRW 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

UPLO (input) CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored. N (input) INTEGER The number of linear equations, i.e., the order of the matrix A. N >= 0. INFO (input) INTEGER The value of INFO returned from ZHETRF, .i.e., the pivot in column INFO is exactly 0. NCOLS (input) INTEGER The number of columns of the matrix A. NCOLS >= 0. A (input) COMPLEX*16 array, dimension (LDA,N) On entry, the N-by-N matrix A. LDA (input) INTEGER The leading dimension of the array A. LDA >= max(1,N). AF (input) COMPLEX*16 array, dimension (LDAF,N) The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by ZHETRF. LDAF (input) INTEGER The leading dimension of the array AF. LDAF >= max(1,N). IPIV (input) INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZHETRF. WORK (input) COMPLEX*16 array, dimension (2*N) LAPACK routine (version 3.2.2)March 2011 LAPACK-3(3)

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