NAME

cgtcon - estimate the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF

SYNOPSIS

  SUBROUTINE CGTCON( NORM, N, LOW, DIAG, UP1, UP2, IPIVOT, ANORM, 
 *      RCOND, WORK, INFO)
  CHARACTER * 1 NORM
  COMPLEX LOW(*), DIAG(*), UP1(*), UP2(*), WORK(*)
  INTEGER N, INFO
  INTEGER IPIVOT(*)
  REAL ANORM, RCOND

  SUBROUTINE CGTCON_64( NORM, N, LOW, DIAG, UP1, UP2, IPIVOT, ANORM, 
 *      RCOND, WORK, INFO)
  CHARACTER * 1 NORM
  COMPLEX LOW(*), DIAG(*), UP1(*), UP2(*), WORK(*)
  INTEGER*8 N, INFO
  INTEGER*8 IPIVOT(*)
  REAL ANORM, RCOND

F95 INTERFACE

  SUBROUTINE GTCON( NORM, [N], LOW, DIAG, UP1, UP2, IPIVOT, ANORM, 
 *       RCOND, [WORK], [INFO])
  CHARACTER(LEN=1) :: NORM
  COMPLEX, DIMENSION(:) :: LOW, DIAG, UP1, UP2, WORK
  INTEGER :: N, INFO
  INTEGER, DIMENSION(:) :: IPIVOT
  REAL :: ANORM, RCOND

  SUBROUTINE GTCON_64( NORM, [N], LOW, DIAG, UP1, UP2, IPIVOT, ANORM, 
 *       RCOND, [WORK], [INFO])
  CHARACTER(LEN=1) :: NORM
  COMPLEX, DIMENSION(:) :: LOW, DIAG, UP1, UP2, WORK
  INTEGER(8) :: N, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT
  REAL :: ANORM, RCOND

C INTERFACE

#include <sunperf.h>

void cgtcon(char norm, int n, complex *low, complex *diag, complex *up1, complex *up2, int *ipivot, float anorm, float *rcond, int *info);

void cgtcon_64(char norm, long n, complex *low, complex *diag, complex *up1, complex *up2, long *ipivot, float anorm, float *rcond, long *info);

PURPOSE

cgtcon estimates the reciprocal of the condition number of a complex tridiagonal matrix A using the LU factorization as computed by CGTTRF.

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

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.
```
N (input)
The order of the matrix A. N > = 0.
LOW (input)
The (n-1) multipliers that define the matrix L from the LU factorization of A as computed by CGTTRF.
DIAG (input)
The n diagonal elements of the upper triangular matrix U from the LU factorization of A.
UP1 (input)
The (n-1) elements of the first superdiagonal of U.
UP2 (input)
The (n-2) elements of the second superdiagonal of U.
IPIVOT (input)
The pivot indices; for 1 < = i < = n, row i of the matrix was interchanged with row IPIVOT(i). IPIVOT(i) will always be either i or i+1; IPIVOT(i) = i indicates a row interchange was not required.
ANORM (input)
If NORM = '1' or 'O', the 1-norm of the original matrix A. If NORM = 'I', the infinity-norm of the original 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)

INFO (output)

 = 0:  successful exit

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