• NAME
• SYNOPSIS
• F95 INTERFACE
• C INTERFACE
• PURPOSE
• ARGUMENTS

NAME

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

SYNOPSIS

  SUBROUTINE ZTBCON( NORM, UPLO, DIAG, N, NDIAG, A, LDA, RCOND, WORK, 
 *      WORK2, INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  DOUBLE COMPLEX A(LDA,*), WORK(*)
  INTEGER N, NDIAG, LDA, INFO
  DOUBLE PRECISION RCOND
  DOUBLE PRECISION WORK2(*)

  SUBROUTINE ZTBCON_64( NORM, UPLO, DIAG, N, NDIAG, A, LDA, RCOND, 
 *      WORK, WORK2, INFO)
  CHARACTER * 1 NORM, UPLO, DIAG
  DOUBLE COMPLEX A(LDA,*), WORK(*)
  INTEGER*8 N, NDIAG, LDA, INFO
  DOUBLE PRECISION RCOND
  DOUBLE PRECISION WORK2(*)

F95 INTERFACE

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

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

C INTERFACE

#include <sunperf.h>

void ztbcon(char norm, char uplo, char diag, int n, int ndiag, doublecomplex *a, int lda, double *rcond, int *info);

void ztbcon_64(char norm, char uplo, char diag, long n, long ndiag, doublecomplex *a, long lda, double *rcond, long *info);

PURPOSE

ztbcon 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:

   = '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.

• 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)
  dimension(N)

• INFO (output)
  

   = 0:  successful exit

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