cgbfa(3P)

NAME

cgbfa - 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 factorization 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