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NAME
     sgbfa - compute the LU factorization of a matrix A in banded
     storage.   It  is  typical  to follow a call to xGBFA with a
     call to xGBSL to solve Ax = b or to  xGBDI  to  compute  the
     determinant of A.

SYNOPSIS
     SUBROUTINE DGBFA (DA, LDA, N, NSUB, NSUPER, IPIVOT, INFO)

     SUBROUTINE SGBFA (SA, LDA, N, NSUB, NSUPER, IPIVOT, INFO)

     SUBROUTINE ZGBFA (ZA, LDA, N, NSUB, NSUPER, IPIVOT, INFO)

     SUBROUTINE CGBFA (CA, LDA, N, NSUB, NSUPER, IPIVOT, INFO)



     #include <sunperf.h>

     void dgbfa(double *abd, int lda, int n, int ml, int mu,  int
               *ipivot, int *info) ;

     void sgbfa(float *abd, int lda, int n, int ml, int  mu,  int
               *ipivot, int *info) ;

     void zgbfa(doublecomplex *abd, int lda, int n, int  ml,  int
               mu, int *ipivot, int *info) ;

     void cgbfa(complex *abd, int lda, int n, int ml, int mu, int
               *ipivot, int *info) ;

ARGUMENTS
     xA        On entry, the matrix A.  On exit, an LU factoriza-
               tion of the matrix A.

     LDA       Leading dimension of the array A as specified in a
               dimension  or  type  statement.  LDA >= 2 * NSUB +
               NSUPER + 1.

     N         Order of the matrix A.  N >= 0.

     NSUB      Number of subdiagonals of A.  N-1 >= NSUB >= 0 but
               if N = 0 then NSUB = 0.

     NSUPER    Number of superdiagonals of A.  N-1 >= NSUPER >= 0
               but if N = 0 then NSUPER = 0.

     IPIVOT    On exit, a vector of pivot indices.

     INFO      On exit:
               INFO = 0  Subroutine completed normally.
               INFO * 0  Returns a value  k  if  U(k,k)  =  0  to
               indicate that xGESL will divide by zero if called.

SAMPLE PROGRAM
           PROGRAM TEST
           IMPLICIT NONE
     C
           INTEGER           IAXEQB, LDA, LDAB, N, NDIAG, NSUB, NSUPER
           PARAMETER        (IAXEQB = 0)
           PARAMETER        (N = 4)
           PARAMETER        (LDA = N)
           PARAMETER        (NSUB = 1)
           PARAMETER        (NSUPER = 1)
           PARAMETER        (NDIAG = NSUB + 1 + NSUPER)
           PARAMETER        (LDAB = 2 * NSUB + 1 + NSUPER)
     C
           DOUBLE PRECISION  AB(LDAB,N), AG(LDA,N), B(N)
           INTEGER           ICOL, INFO, IPIVOT(N), IROW, IROWB, I1, I2, JOB
     C
           EXTERNAL          DGBFA, DGBSL
           INTRINSIC         MAX0, MIN0
     C
     C     Initialize the array AG to store the 4x4 matrix A with one
     C     subdiagonal and one superdiagonal shown below.  Initialize
     C     the array B to store the vector b shown below.
     C
     C           2  -1                5
     C     AG = -1   2  -1        b = 5
     C              -1   2  -1        5
     C                  -1   2        5
     C
           DATA AB / 16*8D8 /
           DATA AG /  2.0D0, -1.0D0,  2*0D0, -1.0D0,  2.0D0, -1.0D0,
          $           2*0D0, -1.0D0,  2.0D0, -1.0D0,  2*0D0, -1.0D0,
          $           2.0D0 /
           DATA B / N*5.0D0 /
     C
     C     Copy the matrix A from the array AG to the array AB.  The
     C     matrix is stored in general storage mode in AG and it will
     C     be stored in banded storage mode in AB.  The code to copy
     C     from general to banded storage mode is taken from the
     C     comment block in the original DGBFA by Cleve Moler.
     C
           DO 10, ICOL = 1, N
             I1 = MAX0 (1, ICOL - NSUPER)
             I2 = MIN0 (N, ICOL + NSUB)
             DO 10, IROW = I1, I2
               IROWB = IROW - ICOL + NDIAG
               AB(IROWB,ICOL) = AG(IROW,ICOL)
        10   CONTINUE
        20 CONTINUE
     C
     C     Print the initial values of the arrays.
     C
           PRINT 1000
           PRINT 1010, ((AG(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
           PRINT 1020
           PRINT 1010, ((AB(IROW,ICOL), ICOL = 1, N),
          $             IROW = 2 * NSUB, 2 * NSUB + 1 + NSUPER)
           PRINT 1030
           PRINT 1040, B
     C
     C     Factor the matrix in banded form.
     C
           CALL DGBFA (AB, LDA, N, NSUB, NSUPER, IPIVOT, INFO)
           IF (INFO .EQ. 0) THEN
             JOB = IAXEQB
             CALL DGBSL (AB, LDA, N, NSUB, NSUPER, IPIVOT, B, JOB)
             PRINT 1050
             PRINT 1040, B
           ELSE
             PRINT 1060
           END IF
     C
      1000 FORMAT (1X, 'A in full form:')
      1010 FORMAT (4(3X, F4.1))
      1020 FORMAT (/1X, 'A in banded form:  (* in unused elements)')
      1030 FORMAT (/1X, 'b:')
      1040 FORMAT (3X, F4.1)
      1050 FORMAT (/1X, 'A**(-1) * b:')
      1060 FORMAT (1X, 'A is singular to working precision.')
     C
           END

SAMPLE OUTPUT
      A in full form:
         2.0   -1.0    0.0    0.0
        -1.0    2.0   -1.0    0.0
         0.0   -1.0    2.0   -1.0
         0.0    0.0   -1.0    2.0

      A in banded form:  (* in unused elements)
        ****   -1.0   -1.0   -1.0
         2.0    2.0    2.0    2.0
        -1.0   -1.0   -1.0   ****

      b:
         5.0
         5.0
         5.0
         5.0

      A**(-1) * b:
        10.0
        15.0
        15.0
        10.0

Партнёры:

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