NAME

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

SYNOPSIS

  SUBROUTINE DTPCON( NORM, UPLO, DIAG, N, A, RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  INTEGER N, INFO
  INTEGER WORK2(*)
  DOUBLE PRECISION RCOND
  DOUBLE PRECISION A(*), WORK(*)

  SUBROUTINE DTPCON_64( NORM, UPLO, DIAG, N, A, RCOND, WORK, WORK2, 
 *      INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  INTEGER*8 N, INFO
  INTEGER*8 WORK2(*)
  DOUBLE PRECISION RCOND
  DOUBLE PRECISION A(*), WORK(*)

F95 INTERFACE

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

  SUBROUTINE TPCON_64( NORM, UPLO, DIAG, N, A, RCOND, [WORK], [WORK2], 
 *       [INFO])
  CHARACTER(LEN=1) :: NORM, UPLO, DIAG
  INTEGER(8) :: N, INFO
  INTEGER(8), DIMENSION(:) :: WORK2
  REAL(8) :: RCOND
  REAL(8), DIMENSION(:) :: A, WORK

C INTERFACE

#include <sunperf.h>

void dtpcon(char norm, char uplo, char diag, int n, double *a, double *rcond, int *info);

void dtpcon_64(char norm, char uplo, char diag, long n, double *a, double *rcond, long *info);

PURPOSE

dtpcon estimates the reciprocal of the condition number of a packed 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 upper or lower triangular matrix A, packed columnwise in a linear array. The j-th column of A is stored in the array A as follows: if UPLO = 'U', A(i + (j-1)*j/2) = A(i,j) for 1 < =i < =j; if UPLO = 'L', A(i + (j-1)*(2n-j)/2) = A(i,j) for j < =i < =n. If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
RCOND (output)
The reciprocal of the condition number of the matrix A, computed as RCOND = 1/(norm(A) * norm(inv(A))).
WORK (workspace)
dimension(3*N)
WORK2 (workspace)
dimension(N)

INFO (output)

 = 0:  successful exit

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