NAME

dsycon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF

SYNOPSIS

SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIV, ANORM, RCOND, WORK, IWORK, INFO )

CHARACTER UPLO

INTEGER INFO, LDA, N

DOUBLE PRECISION ANORM, RCOND

INTEGER IPIV( ∗ ), IWORK( ∗ )

DOUBLE PRECISION A( LDA, ∗ ), WORK( ∗ )

#include <sunperf.h>

void dsycon(char uplo, int n, double ∗da, int lda, int ∗ipivot, double anorm, double ∗drcond, int ∗info);

PURPOSE

DSYCON estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric matrix A using the factorization A = U∗D∗U∗∗T or A = L∗D∗L∗∗T computed by DSYTRF. 
 
An estimate is obtained for norm(inv(A)), and the reciprocal of the condition number is computed as RCOND = 1 / (ANORM ∗ norm(inv(A))).
 

ARGUMENTS

UPLO (input) CHARACTER∗1
Specifies whether the details of the factorization are stored as an upper or lower triangular matrix. = ’U’:  Upper triangular, form is A = U∗D∗U∗∗T;
= ’L’:  Lower triangular, form is A = L∗D∗L∗∗T.

N (input) INTEGER
The order of the matrix A.  N >= 0.

A (input) DOUBLE PRECISION array, dimension (LDA,N)
The block diagonal matrix D and the multipliers used to obtain the factor U or L as computed by DSYTRF.

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

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

ANORM (input) DOUBLE PRECISION
The 1-norm of the original matrix A.

RCOND (output) DOUBLE PRECISION
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(ANORM ∗ AINVNM), where AINVNM is an estimate of the 1-norm of inv(A) computed in this routine.

WORK (workspace) DOUBLE PRECISION array, dimension (2∗N)

IWORK (workspace) INTEGER array, dimension (N)

INFO (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

SunOS 5.0  —  Last change: 10 Dec 1998