ctrcon

NAME

ctrcon - estimate the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm

SYNOPSIS

  SUBROUTINE CTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, WORK2, 
 *      INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  COMPLEX A(LDA,*), WORK(*)
  INTEGER N, LDA, INFO
  REAL RCOND
  REAL WORK2(*)
 
  SUBROUTINE CTRCON_64( NORM, UPLO, DIAG, N, A, LDA, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  COMPLEX A(LDA,*), WORK(*)
  INTEGER*8 N, LDA, INFO
  REAL RCOND
  REAL WORK2(*)

F95 INTERFACE

  SUBROUTINE TRCON( NORM, UPLO, DIAG, [N], A, [LDA], RCOND, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM, UPLO, DIAG
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER :: N, LDA, INFO
  REAL :: RCOND
  REAL, DIMENSION(:) :: WORK2
 
  SUBROUTINE TRCON_64( NORM, UPLO, DIAG, [N], A, [LDA], RCOND, [WORK], 
 *       [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM, UPLO, DIAG
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER(8) :: N, LDA, INFO
  REAL :: RCOND
  REAL, DIMENSION(:) :: WORK2

C INTERFACE

#include <sunperf.h>

void ctrcon(char norm, char uplo, char diag, int n, complex *a, int lda, float *rcond, int *info);

void ctrcon_64(char norm, char uplo, char diag, long n, complex *a, long lda, float *rcond, long *info);

PURPOSE

ctrcon estimates the reciprocal of the condition number of a triangular matrix A, in either the 1-norm or the infinity-norm.

The norm of A is computed and an estimate is obtained for norm(inv(A)), then the reciprocal of the condition number is computed as

   RCOND = 1 / ( norm(A) * norm(inv(A)) ).

ARGUMENTS

* NORM (input): Specifies whether the 1-norm condition number or the infinity-norm condition number is required:
* UPLO (input)
* DIAG (input)
* N (input): The order of the matrix A. N >= 0.
* A (input): The triangular matrix A. If UPLO = 'U', the leading N-by-N upper triangular part of the array A contains the upper triangular matrix, and the strictly lower triangular part of A is not referenced. If UPLO = 'L', the leading N-by-N lower triangular part of the array A contains the lower triangular matrix, and the strictly upper triangular part of A is not referenced. If DIAG = 'U', the diagonal elements of A are also not referenced and are assumed to be 1.
* LDA (input): The leading dimension of the array A. LDA >= max(1,N).
* RCOND (output): The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
* WORK (workspace): dimension(2*N)
* WORK2 (workspace): dimension(N)
* INFO (output)