dppcon


NAME

dppcon - estimate the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF


SYNOPSIS

  SUBROUTINE DPPCON( UPLO, N, A, ANORM, RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, INFO
  INTEGER WORK2(*)
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION A(*), WORK(*)
 
  SUBROUTINE DPPCON_64( UPLO, N, A, ANORM, RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, INFO
  INTEGER*8 WORK2(*)
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION A(*), WORK(*)
 

F95 INTERFACE

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

C INTERFACE

#include <sunperf.h>

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

void dppcon_64(char uplo, long n, double *a, double anorm, double *rcond, long *info);


PURPOSE

dppcon estimates the reciprocal of the condition number (in the 1-norm) of a real symmetric positive definite packed matrix using the Cholesky factorization A = U**T*U or A = L*L**T computed by SPPTRF.

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**T*U or A = L*L**T, 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 symmetric 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)