• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

csycon - estimate the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF

SYNOPSIS

  SUBROUTINE CSYCON( UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK, 
 *      INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*), WORK(*)
  INTEGER N, LDA, INFO
  INTEGER IPIVOT(*)
  REAL ANORM, RCOND

  SUBROUTINE CSYCON_64( UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK, 
 *      INFO)
  CHARACTER * 1 UPLO
  COMPLEX A(LDA,*), WORK(*)
  INTEGER*8 N, LDA, INFO
  INTEGER*8 IPIVOT(*)
  REAL ANORM, RCOND

F95 INTERFACE

  SUBROUTINE SYCON( UPLO, [N], A, [LDA], IPIVOT, ANORM, RCOND, [WORK], 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER :: N, LDA, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL :: ANORM, RCOND

  SUBROUTINE SYCON_64( UPLO, [N], A, [LDA], IPIVOT, ANORM, RCOND, 
 *       [WORK], [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER(8) :: N, LDA, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL :: ANORM, RCOND

C INTERFACE

#include <sunperf.h>

void csycon(char uplo, int n, complex *a, int lda, int *ipivot, float anorm, float *rcond, int *info);

void csycon_64(char uplo, long n, complex *a, long lda, long *ipivot, float anorm, float *rcond, long *info);

PURPOSE

csycon estimates the reciprocal of the condition number (in the 1-norm) of a complex symmetric matrix A using the factorization A = U*D*U**T or A = L*D*L**T computed by CSYTRF.

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 triangular, form is A = U*D*U**T;

   = 'L':  Lower triangular, form is A  = L*D*L**T.

• 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 CSYTRF.

• 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 CSYTRF.

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

• RCOND (output)
  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)
  dimension(2*N)

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value