cppcon

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)
* 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, 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): dimension(2*N)
* WORK2 (workspace)
* INFO (output)