cpbsl(3P)

NAME

cpbsl - section solve the linear system Ax = b for a symmetric positive definite matrix A in banded storage, which has been Cholesky-factored by xPBCO or xPBFA, and vectors b and x.

SYNOPSIS

CALL DPBSL (DA, LDA, N, NDIAG, DB)

CALL SPBSL (SA, LDA, N, NDIAG, SB)

CALL ZPBSL (ZA, LDA, N, NDIAG, ZB)

CALL CPBSL (CA, LDA, N, NDIAG, CB)

void dpbsl(double ∗abd, long int lda, long int n, long int m,
double ∗b)

void spbsl(float ∗abd, long int lda, long int n, long int m, float
∗b)

void zpbsl(doublecomplex ∗abd, long int lda, long int n,
long int m, doublecomplex ∗b)

void cpbsl(complex ∗abd, long int lda, long int n,
long int m, complex ∗b)

ARGUMENTS

xACholesky factorization of the matrix A, as computed by xPBCO or xPBFA.

LDALeading dimension of the array A as specified in a dimension or type
statement. LDA >= NDIAG + 1.

NOrder of the matrix A. N >= 0.

NDIAGNumber of diagonals of matrix A. N-1 >= NDIAG >= 0 but if
N = 0 then NDIAG = 0.

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

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           LDA, N, NDIAG
      PARAMETER        (N = 4)
      PARAMETER        (NDIAG = 1)
      PARAMETER        (LDA = NDIAG + 1)
C
      DOUBLE PRECISION A(LDA,N), B(N)
      INTEGER           ICOL, INFO, IROW
C
      EXTERNAL          DPBFA, DPBSL
C
C     Initialize the array A to store in banded storage mode
C     the matrix A shown below. Initialize the array B to
C     store the vector B shown below.
C
C          2 -1   0   0         60
C     A = -1   2 -1   0    b = 120
C          0 -1   2 -1        120
C          0   0 -1   2         60
C
      DATA A / 8D8, 2.0D0, -1.0D0, 2.0D0, -1.0D0, 2.0D0, -1.0D0, 2.0D0 /
      DATA B / 6.0D1, 1.2D1, 1.2D1, 6.0D1 /
C
      PRINT 1000
      PRINT 1010, A(2,1), A(1,2)
      PRINT 1010, A(3,1), A(2,2), A(1,3)
      PRINT 1020,         A(3,2), A(2,3), A(1,4)
      PRINT 1030,                 A(3,3), A(2,4)
      PRINT 1040
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, LDA)
      PRINT 1050
      PRINT 1060, B
      CALL DPBFA (A, LDA, N, NDIAG, INFO)
      IF (INFO .EQ. 0) THEN
        CALL DPBSL (A, LDA, N, NDIAG, B)
        PRINT 1070
        PRINT 1060, B
      ELSE
        PRINT 1080
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(3X, F5.1))
1020 FORMAT (8X, 3(3X, F5.1))
1030 FORMAT (16X, 3(3X, F5.1))
1040 FORMAT (/1X, ’A in banded form: (∗ in unused entries)’)
1050 FORMAT (/1X, ’b:’)
1060 FORMAT (3X, F5.1)
1070 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
1080 FORMAT (/1X, ’A is not positive definite.’)
C
      END

SAMPLE OUTPUT

A in full form:
     2.0    -1.0
    -1.0     2.0    -1.0
            -1.0     2.0    -1.0
                    -1.0     2.0

A in banded form: (∗ in unused entries)
   ∗∗∗∗∗    -1.0    -1.0    -1.0
     2.0     2.0     2.0     2.0

b:
    60.0
    12.0
    12.0
    60.0

A∗∗(-1) ∗ b:
    72.0
    84.0
    84.0
    72.0