Contents

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

NAME

     sgbcon - 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 SGBCON(NORM, N, KL, KU, A, LDA, IPIVOT, ANORM,
           RCOND, WORK, WORK2, INFO)

     CHARACTER * 1 NORM
     INTEGER N, KL, KU, LDA, INFO
     INTEGER IPIVOT(*), WORK2(*)
     REAL ANORM, RCOND
     REAL A(LDA,*), WORK(*)

     SUBROUTINE SGBCON_64(NORM, N, KL, KU, A, LDA, IPIVOT, ANORM,
           RCOND, WORK, WORK2, INFO)

     CHARACTER * 1 NORM
     INTEGER*8 N, KL, KU, LDA, INFO
     INTEGER*8 IPIVOT(*), WORK2(*)
     REAL ANORM, RCOND
     REAL A(LDA,*), WORK(*)

  F95 INTERFACE
     SUBROUTINE GBCON(NORM, [N], KL, KU, A, [LDA], IPIVOT, ANORM,
            RCOND, [WORK], [WORK2], [INFO])

     CHARACTER(LEN=1) :: NORM
     INTEGER :: N, KL, KU, LDA, INFO
     INTEGER, DIMENSION(:) :: IPIVOT, WORK2
     REAL :: ANORM, RCOND
     REAL, DIMENSION(:) :: WORK
     REAL, DIMENSION(:,:) :: A

     SUBROUTINE GBCON_64(NORM, [N], KL, KU, A, [LDA], IPIVOT, ANORM,
            RCOND, [WORK], [WORK2], [INFO])

     CHARACTER(LEN=1) :: NORM
     INTEGER(8) :: N, KL, KU, LDA, INFO
     INTEGER(8), DIMENSION(:) :: IPIVOT, WORK2
     REAL :: ANORM, RCOND
     REAL, DIMENSION(:) :: WORK
     REAL, DIMENSION(:,:) :: A

  C INTERFACE
     #include <sunperf.h>
     void sgbcon(char norm, int n, int kl, int ku, float *a,  int
               lda,  int  *ipivot, float anorm, float *rcond, int
               *info);

     void sgbcon_64(char norm, long n, long kl,  long  ku,  float
               *a,  long  lda,  long  *ipivot, float anorm, float
               *rcond, long *info);

PURPOSE

     sgbcon 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:
               = '1' or 'O':  1-norm;
               = 'I':         Infinity-norm.

     N (input) The order of the matrix A.  N >= 0.

     KL (input)
               The number of subdiagonals within the band  of  A.
               KL >= 0.

     KU (input)
               The number of superdiagonals within the band of A.
               KU >= 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  KL+KU  superdiagonals
               in  rows  1  to  KL+KU+1, and the multipliers used
               during  the  factorization  are  stored  in   rows
               KL+KU+2 to 2*KL+KU+1.

     LDA (input)
               The leading dimension of  the  array  A.   LDA  >=
               2*KL+KU+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(3*N)

     WORK2 (workspace)
               dimension (N)

     INFO (output)
               = 0:  successful exit
               < 0: if INFO = -i, the i-th argument had an  ille-
               gal value