Contents

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

NAME

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

SYNOPSIS

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

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

     SUBROUTINE CPPCON_64(UPLO, N, A, ANORM, RCOND, WORK, WORK2, INFO)

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

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

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

     SUBROUTINE PPCON_64(UPLO, [N], A, ANORM, RCOND, [WORK], [WORK2], [INFO])

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

  C INTERFACE
     #include <sunperf.h>

     void cppcon(char uplo, int n, complex *a, float anorm, float
               *rcond, int *info);
     void cppcon_64(char uplo, long n, complex *a,  float  anorm,
               float *rcond, long *info);

PURPOSE

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

     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) COMPLEX array, dimension (N*(N+1)/2)
               The triangular factor U or  L  from  the  Cholesky
               factorization  A  =  U**H*U  or A = L*L**H, packed
               columnwise in a linear array.  The j-th column  of
               U  or  L  is stored in the array A as follows:  if
               UPLO = 'U', A(i + (j-1)*j/2) = U(i,j) for 1<=i<=j;
               if  UPLO = 'L', A(i + (j-1)*(2n-j)/2) = L(i,j) for
               j<=i<=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)
               COMPLEX array, dimension(2*N)

     WORK2 (workspace)
               REAL array, dimension(N)
     INFO (output)
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille-
               gal value