dgbsl(3P)

NAME

dgbsl - solve the linear system Ax = b for a matrix A in banded storage, which has been LU-factored by xGBCO or xGBFA, and vectors b and x.

SYNOPSIS

CALL DGBSL (DA, LDA, N, NSUB, NSUPER, IPIVOT, DB, JOB)

CALL SGBSL (SA, LDA, N, NSUB, NSUPER, IPIVOT, SB, JOB)

CALL ZGBSL (ZA, LDA, N, NSUB, NSUPER, IPIVOT, ZB, JOB)

CALL CGBSL (CA, LDA, N, NSUB, NSUPER, IPIVOT, CB, JOB)

void dgbsl(double ∗abd, long int lda, long int n, long int ml,
long int mu, long int ∗ipivot, double ∗db, long int job)

void sgbsl(float ∗abd, long int lda, long int n, long int ml, long
int mu, long int ∗ipivot, float ∗sb, long int job)

void zgbsl(doublecomplex ∗abd, long int lda, long int n,
long int ml, long int mu, long int ∗ipivot, doublecomplex ∗zb, long int job)

void cgbsl(complex ∗abd, long int lda, long int n,
long int ml, long int mu, long int ∗ipivot, complex ∗cb, long int job)

ARGUMENTS

xALU factorization of the matrix A, as computed by xGBCO or xGBFA.

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

NOrder of the matrix A. N >= 0.

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

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

IPIVOTPivot vector as computed by xGBCO or xGBFA.

xBOn entry, the right-hand side vector b.
On exit, the solution vector x.

JOBDetermines which operation this subroutine will perform:
0 solve the system Ax = b
not 0 solve the linear system AHx = b Note that ATx = AHx for real matrices.

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), RCOND, WORK(N)
      INTEGER           ICOL, IPIVOT(N), IROW, IROWB, I1, I2, JOB
C
      EXTERNAL          DGBCO, 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 DGBCO (AB, LDA, N, NSUB, NSUPER, IPIVOT, RCOND, WORK)
      PRINT 1050, RCOND
      IF ((RCOND + 1.0D0) .EQ. 1.0D0) THEN
        PRINT 1070
      END IF
      JOB = IAXEQB
      CALL DGBSL (AB, LDA, N, NSUB, NSUPER, IPIVOT, B, JOB)
      PRINT 1060
      PRINT 1040, B
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, ’Reciprocal of the condition number: ’, F5.2)
1060 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1070 FORMAT (1X, ’A may be 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

Reciprocal of the condition number: 0.08

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