Contents

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

NAME

     spocon - estimate the reciprocal of the condition number (in
     the  1-norm)  of  a  real symmetric positive definite matrix
     using the Cholesky factorization A = U**T*U or  A  =  L*L**T
     computed by SPOTRF

SYNOPSIS

     SUBROUTINE SPOCON(UPLO, N, A, LDA, ANORM, RCOND, WORK, WORK2, INFO)

     CHARACTER * 1 UPLO
     INTEGER N, LDA, INFO
     INTEGER WORK2(*)
     REAL ANORM, RCOND
     REAL A(LDA,*), WORK(*)

     SUBROUTINE SPOCON_64(UPLO, N, A, LDA, ANORM, RCOND, WORK, WORK2,
           INFO)

     CHARACTER * 1 UPLO
     INTEGER*8 N, LDA, INFO
     INTEGER*8 WORK2(*)
     REAL ANORM, RCOND
     REAL A(LDA,*), WORK(*)

  F95 INTERFACE
     SUBROUTINE POCON(UPLO, [N], A, [LDA], ANORM, RCOND, [WORK], [WORK2],
            [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER :: N, LDA, INFO
     INTEGER, DIMENSION(:) :: WORK2
     REAL :: ANORM, RCOND
     REAL, DIMENSION(:) :: WORK
     REAL, DIMENSION(:,:) :: A

     SUBROUTINE POCON_64(UPLO, [N], A, [LDA], ANORM, RCOND, [WORK], [WORK2],
            [INFO])

     CHARACTER(LEN=1) :: UPLO
     INTEGER(8) :: N, LDA, INFO
     INTEGER(8), DIMENSION(:) :: WORK2
     REAL :: ANORM, RCOND
     REAL, DIMENSION(:) :: WORK
     REAL, DIMENSION(:,:) :: A

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

     void spocon_64(char uplo, long n, float *a, long lda,  float
               anorm, float *rcond, long *info);

PURPOSE

     spocon estimates the reciprocal of the condition number  (in
     the  1-norm)  of  a  real symmetric positive definite matrix
     using the Cholesky factorization A = U**T*U or  A  =  L*L**T
     computed by SPOTRF.

     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)
               = 'U':  Upper triangle of A is stored;
               = 'L':  Lower triangle of A is stored.

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

     A (input) The triangular factor U or  L  from  the  Cholesky
               factorization  A  =  U**T*U or A = L*L**T, as com-
               puted by SPOTRF.

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

     ANORM (input)
               The 1-norm (or  infinity-norm)  of  the  symmetric
               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(3*N)
     WORK2 (workspace)
               dimension(N)

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