# zla_syrpvgrw.f - Man Page

SRC/zla_syrpvgrw.f

## Synopsis

### Functions/Subroutines

double precision function **zla_syrpvgrw** (uplo, n, info, a, lda, af, ldaf, ipiv, work)**ZLA_SYRPVGRW** computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

## Function/Subroutine Documentation

### double precision function zla_syrpvgrw (character*1 uplo, integer n, integer info, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldaf, * ) af, integer ldaf, integer, dimension( * ) ipiv, double precision, dimension( * ) work)

**ZLA_SYRPVGRW** computes the reciprocal pivot growth factor norm(A)/norm(U) for a symmetric indefinite matrix.

**Purpose:**

ZLA_SYRPVGRW 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***UPLO*UPLO is CHARACTER*1 = 'U': Upper triangle of A is stored; = 'L': Lower triangle of A is stored.

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

*INFO*INFO is INTEGER The value of INFO returned from ZSYTRF, .i.e., the pivot in column INFO is exactly 0.

*A*A is COMPLEX*16 array, dimension (LDA,N) On entry, the N-by-N matrix A.

*LDA*LDA is INTEGER The leading dimension of the array A. LDA >= max(1,N).

*AF*AF is 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 ZSYTRF.

*LDAF*LDAF is INTEGER The leading dimension of the array AF. LDAF >= max(1,N).

*IPIV*IPIV is INTEGER array, dimension (N) Details of the interchanges and the block structure of D as determined by ZSYTRF.

*WORK*WORK is DOUBLE PRECISION array, dimension (2*N)

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **121** of file **zla_syrpvgrw.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

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