Contents

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

NAME

     ssycon - estimate the reciprocal of the condition number (in
     the  1-norm) of a real symmetric matrix A using the factori-
     zation A = U*D*U**T or A = L*D*L**T computed by SSYTRF

SYNOPSIS

     SUBROUTINE SSYCON(UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK,
           IWORK2, INFO)

     CHARACTER * 1 UPLO
     INTEGER N, LDA, INFO
     INTEGER IPIVOT(*), IWORK2(*)
     REAL ANORM, RCOND
     REAL A(LDA,*), WORK(*)

     SUBROUTINE SSYCON_64(UPLO, N, A, LDA, IPIVOT, ANORM, RCOND, WORK,
           IWORK2, INFO)

     CHARACTER * 1 UPLO
     INTEGER*8 N, LDA, INFO
     INTEGER*8 IPIVOT(*), IWORK2(*)
     REAL ANORM, RCOND
     REAL 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 :: ANORM, RCOND
     REAL, DIMENSION(:) :: WORK
     REAL, 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 :: ANORM, RCOND
     REAL, DIMENSION(:) :: WORK
     REAL, DIMENSION(:,:) :: A

  C INTERFACE
     #include <sunperf.h>
     void ssycon(char  uplo,  int  n,  float  *a,  int  lda,  int
               *ipivot, float anorm, float *rcond, int *info);

     void ssycon_64(char uplo, long n, float *a, long  lda,  long
               *ipivot, float anorm, float *rcond, long *info);

PURPOSE

     ssycon estimates the reciprocal of the condition number  (in
     the  1-norm) of a real symmetric matrix A using the factori-
     zation 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  struc-
               ture 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 ille-
               gal value