Contents

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

NAME

     zgecon - estimate the reciprocal of the condition number  of
     a  general  complex  matrix  A,  in either the 1-norm or the
     infinity-norm, using the LU factorization computed by CGETRF

SYNOPSIS

     SUBROUTINE ZGECON(NORM, N, A, LDA, ANORM, RCOND, WORK, WORK2, INFO)

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

     SUBROUTINE ZGECON_64(NORM, N, A, LDA, ANORM, RCOND, WORK, WORK2,
           INFO)

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

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

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

     SUBROUTINE GECON_64(NORM, [N], A, [LDA], ANORM, RCOND, [WORK], [WORK2],
            [INFO])

     CHARACTER(LEN=1) :: NORM
     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 zgecon(char norm, int n,  doublecomplex  *a,  int  lda,
               double anorm, double *rcond, int *info);

     void zgecon_64(char norm, long  n,  doublecomplex  *a,  long
               lda, double anorm, double *rcond, long *info);

PURPOSE

     zgecon estimates the reciprocal of the condition number of a
     general  complex  matrix  A,  in  either  the  1-norm or the
     infinity-norm,  using  the  LU  factorization  computed   by
     CGETRF.

     An estimate is obtained for norm(inv(A)), and the reciprocal
     of the condition number is computed as
        RCOND = 1 / ( norm(A) * norm(inv(A)) ).

ARGUMENTS

     NORM (input)
               Specifies whether the 1-norm condition  number  or
               the infinity-norm condition number is required:
               = '1' or 'O':  1-norm;
               = 'I':         Infinity-norm.

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

     A (input) The factors L and U from  the  factorization  A  =
               P*L*U as computed by CGETRF.

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

     ANORM (input)
               If NORM = '1' or 'O', the 1-norm of  the  original
               matrix A.  If NORM = 'I', the infinity-norm of the
               original matrix A.

     RCOND (output)
               The reciprocal of  the  condition  number  of  the
               matrix   A,  computed  as  RCOND  =  1/(norm(A)  *
               norm(inv(A))).

     WORK (workspace)
               dimension(2*N)

     WORK2 (workspace)
               dimension(2*N)

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