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

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 SSYTRF

SYNOPSIS

  SUBROUTINE DSYCON( UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK, 
 *      IWORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, LDA, INFO
  INTEGER IPIVOT(*), IWORK2(*)
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION A(LDA,*), WORK(*)

  SUBROUTINE DSYCON_64( UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK, 
 *      IWORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, LDA, INFO
  INTEGER*8 IPIVOT(*), IWORK2(*)
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION A(LDA,*), WORK(*)

F95 INTERFACE

  SUBROUTINE SYCON( UPLO, [N], A, [LDA], IPIVOT, ANORM, RCOND, [WORK], 
 *       [IWORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, LDA, INFO
  INTEGER, DIMENSION(:) :: IPIVOT, IWORK2
  REAL(8) :: ANORM, RCOND
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A

  SUBROUTINE SYCON_64( UPLO, [N], A, [LDA], IPIVOT, ANORM, RCOND, 
 *       [WORK], [IWORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, LDA, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT, IWORK2
  REAL(8) :: ANORM, RCOND
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void dsycon(char uplo, int n, double *a, int lda, int *ipivot, double anorm, double *rcond, int *info);

void dsycon_64(char uplo, long n, double *a, long lda, long *ipivot, double anorm, double *rcond, long *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 SSYTRF.

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 SSYTRF.

• 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 SSYTRF.

• 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)

• IWORK2 (workspace)
  
• INFO (output)
  

   = 0:  successful exit

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