zhecon(3P) Sun Performance Library zhecon(3P)NAMEzhecon - estimate the reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
computed by ZHETRF
SYNOPSIS
SUBROUTINE ZHECON(UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK, INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER N, LDA, INFO
INTEGER IPIVOT(*)
DOUBLE PRECISION ANORM, RCOND
SUBROUTINE ZHECON_64(UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK,
INFO)
CHARACTER * 1 UPLO
DOUBLE COMPLEX A(LDA,*), WORK(*)
INTEGER*8 N, LDA, INFO
INTEGER*8 IPIVOT(*)
DOUBLE PRECISION ANORM, RCOND
F95 INTERFACE
SUBROUTINE HECON(UPLO, [N], A, [LDA], IPIVOT, ANORM, RCOND, [WORK],
[INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER :: N, LDA, INFO
INTEGER, DIMENSION(:) :: IPIVOT
REAL(8) :: ANORM, RCOND
SUBROUTINE HECON_64(UPLO, [N], A, [LDA], IPIVOT, ANORM, RCOND, [WORK],
[INFO])
CHARACTER(LEN=1) :: UPLO
COMPLEX(8), DIMENSION(:) :: WORK
COMPLEX(8), DIMENSION(:,:) :: A
INTEGER(8) :: N, LDA, INFO
INTEGER(8), DIMENSION(:) :: IPIVOT
REAL(8) :: ANORM, RCOND
C INTERFACE
#include <sunperf.h>
void zhecon(char uplo, int n, doublecomplex *a, int lda, int *ipivot,
double anorm, double *rcond, int *info);
void zhecon_64(char uplo, long n, doublecomplex *a, long lda, long
*ipivot, double anorm, double *rcond, long *info);
PURPOSEzhecon estimates the reciprocal of the condition number of a complex
Hermitian matrix A using the factorization A = U*D*U**H or A = L*D*L**H
computed by ZHETRF.
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)
Specifies whether the details of the factorization are stored
as an upper or lower triangular matrix. = 'U': Upper trian‐
gular, form is A = U*D*U**H;
= 'L': Lower triangular, form is A = L*D*L**H.
N (input) The order of the matrix A. N >= 0.
A (input) The block diagonal matrix D and the multipliers used to
obtain the factor U or L as computed by ZHETRF.
LDA (input)
The leading dimension of the array A. LDA >= max(1,N).
IPIVOT (input)
Details of the interchanges and the block structure of D as
determined by ZHETRF.
ANORM (input)
The 1-norm of the original matrix A.
RCOND (output)
The reciprocal of the condition number of the matrix A, com‐
puted as RCOND = 1/(ANORM * AINVNM), where AINVNM is an esti‐
mate of the 1-norm of inv(A) computed in this routine.
WORK (workspace)
dimension(2*N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
6 Mar 2009 zhecon(3P)