dgbcon

NAME

dgbcon - estimate the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm,

SYNOPSIS

  SUBROUTINE DGBCON( NORM, N, NSUB, NSUPER, A, LDA, IPIVOT, ANORM, 
 *      RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 NORM
  INTEGER N, NSUB, NSUPER, LDA, INFO
  INTEGER IPIVOT(*), WORK2(*)
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION A(LDA,*), WORK(*)
 
  SUBROUTINE DGBCON_64( NORM, N, NSUB, NSUPER, A, LDA, IPIVOT, ANORM, 
 *      RCOND, WORK, WORK2, INFO)
  CHARACTER * 1 NORM
  INTEGER*8 N, NSUB, NSUPER, LDA, INFO
  INTEGER*8 IPIVOT(*), WORK2(*)
  DOUBLE PRECISION ANORM, RCOND
  DOUBLE PRECISION A(LDA,*), WORK(*)

F95 INTERFACE

  SUBROUTINE GBCON( NORM, [N], NSUB, NSUPER, A, [LDA], IPIVOT, ANORM, 
 *       RCOND, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM
  INTEGER :: N, NSUB, NSUPER, LDA, INFO
  INTEGER, DIMENSION(:) :: IPIVOT, WORK2
  REAL(8) :: ANORM, RCOND
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A
 
  SUBROUTINE GBCON_64( NORM, [N], NSUB, NSUPER, A, [LDA], IPIVOT, 
 *       ANORM, RCOND, [WORK], [WORK2], [INFO])
  CHARACTER(LEN=1) :: NORM
  INTEGER(8) :: N, NSUB, NSUPER, LDA, INFO
  INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
  REAL(8) :: ANORM, RCOND
  REAL(8), DIMENSION(:) :: WORK
  REAL(8), DIMENSION(:,:) :: A

C INTERFACE

#include <sunperf.h>

void dgbcon(char norm, int n, int nsub, int nsuper, double *a, int lda, int *ipivot, double anorm, double *rcond, int *info);

void dgbcon_64(char norm, long n, long nsub, long nsuper, double *a, long lda, long *ipivot, double anorm, double *rcond, long *info);

PURPOSE

dgbcon estimates the reciprocal of the condition number of a real general band matrix A, in either the 1-norm or the infinity-norm, using the LU factorization computed by SGBTRF.

An estimate is obtained for norm(inv(A)), and 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:
* N (input): The order of the matrix A. N >= 0.
* NSUB (input): The number of subdiagonals within the band of A. NSUB >= 0.
* NSUPER (input): The number of superdiagonals within the band of A. NSUPER >= 0.
* A (input): Details of the LU factorization of the band matrix A, as computed by SGBTRF. U is stored as an upper triangular band matrix with NSUB+NSUPER superdiagonals in rows 1 to NSUB+NSUPER+1, and the multipliers used during the factorization are stored in rows NSUB+NSUPER+2 to 2*NSUB+NSUPER+1.
* LDA (input): The leading dimension of the array A. LDA >= 2*NSUB+NSUPER+1.
* IPIVOT (input): The pivot indices; for 1 <= i <= N, row i of the matrix was interchanged with row IPIVOT(i).
* 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/(norm(A) * norm(inv(A))).
* WORK (workspace): dimension(2*N)
* WORK2 (workspace)
* INFO (output)