ctbcon

NAME

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

SYNOPSIS

  SUBROUTINE CTBCON( NORM, UPLO, DIAG, N, NDIAG, A, LDA, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  COMPLEX A(LDA,*), WORK(*)
  INTEGER N, NDIAG, LDA, INFO
  REAL RCOND
  REAL WORK2(*)
 
  SUBROUTINE CTBCON_64( NORM, UPLO, DIAG, N, NDIAG, A, LDA, RCOND, 
 *      WORK, WORK2, INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  COMPLEX A(LDA,*), WORK(*)
  INTEGER*8 N, NDIAG, LDA, INFO
  REAL RCOND
  REAL WORK2(*)

F95 INTERFACE

  SUBROUTINE TBCON( NORM, UPLO, DIAG, [N], NDIAG, A, [LDA], RCOND, 
 *       [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM, UPLO, DIAG
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER :: N, NDIAG, LDA, INFO
  REAL :: RCOND
  REAL, DIMENSION(:) :: WORK2
 
  SUBROUTINE TBCON_64( NORM, UPLO, DIAG, [N], NDIAG, A, [LDA], RCOND, 
 *       [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM, UPLO, DIAG
  COMPLEX, DIMENSION(:) :: WORK
  COMPLEX, DIMENSION(:,:) :: A
  INTEGER(8) :: N, NDIAG, LDA, INFO
  REAL :: RCOND
  REAL, DIMENSION(:) :: WORK2

C INTERFACE

#include <sunperf.h>

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

void ctbcon_64(char norm, char uplo, char diag, long n, long ndiag, complex *a, long lda, float *rcond, long *info);

PURPOSE

ctbcon estimates the reciprocal of the condition number of a triangular band 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.
* NDIAG (input): The number of superdiagonals or subdiagonals of the triangular band matrix A. NDIAG >= 0.
* A (input): The upper or lower triangular band matrix A, stored in the first kd+1 rows of the array. The j-th column of A is stored in the j-th column of the array A as follows: if UPLO = 'U', A(kd+1+i-j,j) = A(i,j) for max(1,j-kd)<=i<=j; if UPLO = 'L', A(1+i-j,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal elements of A are not referenced and are assumed to be 1.
* LDA (input): The leading dimension of the array A. LDA >= NDIAG+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(2*N)
* WORK2 (workspace)
* INFO (output)