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

NAME

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

  SUBROUTINE ZPPCON_64( UPLO, N, A, ANORM, RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  DOUBLE COMPLEX A(*), WORK(*)
  INTEGER*8 N, INFO
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION WORK2(*)

F95 INTERFACE

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

  SUBROUTINE PPCON_64( UPLO, N, A, ANORM, RCOND, [WORK], [WORK2], 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  COMPLEX(8), DIMENSION(:) :: A, WORK
  INTEGER(8) :: N, INFO
  REAL(8) :: ANORM, RCOND
  REAL(8), DIMENSION(:) :: WORK2

C INTERFACE

#include <sunperf.h>

void zppcon(char uplo, int n, doublecomplex *a, double anorm, double *rcond, int *info);

void zppcon_64(char uplo, long n, doublecomplex *a, double anorm, double *rcond, long *info);

PURPOSE

zppcon 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)
  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)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

   < 0:  if INFO  = -i, the i-th argument had an illegal value