Contents

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

NAME

     zpocon - estimate the reciprocal of the condition number (in
     the  1-norm) of a complex Hermitian positive definite matrix
     using the Cholesky factorization A = U**H*U or  A  =  L*L**H
     computed by ZPOTRF

SYNOPSIS

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

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

     SUBROUTINE ZPOCON_64(UPLO, N, A, LDA, ANORM, RCOND, WORK, WORK2,
           INFO)

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

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

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

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

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

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

     void zpocon_64(char uplo, long  n,  doublecomplex  *a,  long
               lda, double anorm, double *rcond, long *info);

PURPOSE

     zpocon estimates the reciprocal of the condition number  (in
     the  1-norm) of a complex Hermitian positive definite matrix
     using the Cholesky factorization A = U**H*U or  A  =  L*L**H
     computed by ZPOTRF.

     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**H*U or A = L*L**H, as com-
               puted by ZPOTRF.

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

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

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