zppsl(l) — SunSoft Performance Library

NAME

zppsl - solve the linear system Ax = b for a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA, and vectors b and x.

SYNOPSIS

CALL DPPSL (DA, N, DB)

CALL SPPSL (SA, N, SB)

CALL ZPPSL (ZA, N, ZB)

CALL CPPSL (CA, N, CB)

ARGUMENTS

xACholesky factorization of the matrix A, as computed by xPPCO or xPPFA.

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           LENGTA, N
      PARAMETER        (N = 4)
      PARAMETER        (LENGTA = (N ∗ N + N) / 2)
C
      DOUBLE PRECISION A(LENGTA), B(N), RCOND, WORK(N)
      INTEGER           INFO
C
      EXTERNAL          DPPCO, DPPSL
C
C     Initialize the array A to store in packed symmetric storage
C     mode the matrix A shown below. Initialize the array B to store
C     the matrix 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, 3.0D0, 4.0D0, 2.0D0, 3.0D0, 4.0D0,
     $         1.0D0, 2.0D0, 3.0D0, 4.0D0 /
      DATA B / 4∗2.0D1 /
C
      PRINT 1000
      PRINT 1010, A(1), A(2), A(4), A(7)
      PRINT 1010, A(2), A(3), A(5), A(8)
      PRINT 1010, A(4), A(5), A(6), A(9)
      PRINT 1010, A(7), A(8), A(9), A(10)
      PRINT 1020
      PRINT 1030, B
      CALL DPPCO (A, N, RCOND, WORK, INFO)
      IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
        PRINT 1040
      END IF
      CALL DPPSL (A, N, B)
      PRINT 1050
      PRINT 1030, B
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (5(3X, F7.3))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, F7.3)
1040 FORMAT (1X, ’A may be singular to working precision.’)
1050 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

b:
    20.000
    20.000
    20.000
    20.000

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