zposl(l) — SunSoft Performance Library

NAME

zposl - solve the linear system Ax = b for a symmetric positive definite matrix A, which has been Cholesky-factored by xPOCO or xPOFA, and vectors b and x.

SYNOPSIS

CALL DPOSL (DA, LDA, N, DB)

CALL SPOSL (SA, LDA, N, SB)

CALL ZPOSL (ZA, LDA, N, ZB)

CALL CPOSL (CA, LDA, N, CB)

ARGUMENTS

xACholesky factorization of the matrix A, as computed by xPOCO or xPOFA.

LDALeading dimension of the array A as specified in a dimension
or type statement. LDA >= max(1,N).

NOrder of the matrix A. N >= 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
      PARAMETER        (N = 4)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), B(N), RCOND, WORK(N)
      INTEGER           ICOL, INFO, IROW
C
      EXTERNAL          DPOCO, DPOSL
C
C     Initialize the array A to store in symmetric storage mode
C     the matrix A shown below. Initialize the array B to store
C     the vector B shown below.
C
C         4 3 2 1        20
C     A = 3 4 3 2    b = 20
C         2 3 4 3        20
C         1 2 3 4        20
C
      DATA A / 4.0D0, 3∗8D8, 3.0D0, 4.0D0, 2∗8D8, 2.0D0, 3.0D0, 4.0D0,
     $         8D8, 1.0D0, 2.0D0, 3.0D0, 4.0D0 /
      DATA B / 4∗2.0D1 /
C
      PRINT 1000
      DO 100, IROW = 1, N
        PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
     $              (A(IROW,ICOL), ICOL = IROW + 1, N)
100 CONTINUE
      PRINT 1020
      PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
      PRINT 1030
      PRINT 1040, B
      CALL DPOCO (A, LDA, N, RCOND, WORK, INFO)
      IF ((RCOND + 1.0D0) .EQ. 1.0D0) THEN
        PRINT 1050
      END IF
      CALL DPOSL (A, LDA, N, B)
      PRINT 1060
      PRINT 1040, B
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(3X, F7.3))
1020 FORMAT (/1X, ’A in symmetric form: (∗ in unused entries)’)
1030 FORMAT (/1X, ’b:’)
1040 FORMAT (3X, F7.3)
1050 FORMAT (/1X, ’A may be singular to working precision.’)
1060 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
C
      END

SAMPLE OUTPUT

A in full form:
     4.000     3.000     2.000     1.000
     3.000     4.000     3.000     2.000
     2.000     3.000     4.000     3.000
     1.000     2.000     3.000     4.000

A in symmetric form: (∗ in unused entries)
     4.000     3.000     2.000     1.000
   ∗∗∗∗∗∗∗     4.000     3.000     2.000
   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗     4.000     3.000
   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗   ∗∗∗∗∗∗∗     4.000

b:
    20.000
    20.000
    20.000
    20.000

A∗∗(-1) ∗ b:
     4.000
     0.000
     0.000
     4.000