spocon

NAME

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

SYNOPSIS

  SUBROUTINE SPOCON( UPLO, N, A, LDA, ANORM, RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 UPLO
  INTEGER N, LDA, INFO
  INTEGER WORK2(*)
  REAL ANORM, RCOND
  REAL A(LDA,*), WORK(*)
 
  SUBROUTINE SPOCON_64( UPLO, N, A, LDA, ANORM, RCOND, WORK, WORK2, 
 *      INFO)
  CHARACTER * 1 UPLO
  INTEGER*8 N, LDA, INFO
  INTEGER*8 WORK2(*)
  REAL ANORM, RCOND
  REAL A(LDA,*), WORK(*)

F95 INTERFACE

  SUBROUTINE POCON( UPLO, [N], A, [LDA], ANORM, RCOND, [WORK], [WORK2], 
 *       [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER :: N, LDA, INFO
  INTEGER, DIMENSION(:) :: WORK2
  REAL :: ANORM, RCOND
  REAL, DIMENSION(:) :: WORK
  REAL, DIMENSION(:,:) :: A
 
  SUBROUTINE POCON_64( UPLO, [N], A, [LDA], ANORM, RCOND, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: UPLO
  INTEGER(8) :: N, LDA, INFO
  INTEGER(8), DIMENSION(:) :: WORK2
  REAL :: ANORM, RCOND
  REAL, DIMENSION(:) :: WORK
  REAL, DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void spocon(char uplo, int n, float *a, int lda, float anorm, float *rcond, int *info);

void spocon_64(char uplo, long n, float *a, long lda, float anorm, float *rcond, long *info);

PURPOSE

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

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, as computed by SPOTRF.
* LDA (input): The leading dimension of the array A. LDA >= max(1,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(3*N)
* WORK2 (workspace)
* INFO (output)