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:
```
 = '1' or 'O':  1-norm;
```
```
 = 'I':         Infinity-norm.
```

UPLO (input)

 = 'U':  A is upper triangular;

 = 'L':  A is lower triangular.

DIAG (input)

 = 'N':  A is non-unit triangular;

 = 'U':  A is unit triangular.

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)

 = 0:  successful exit

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