sspsl(l) — SunSoft Performance Library

NAME

sspsl - solve the linear system Ax = b for a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA, and vectors b and x.

SYNOPSIS

CALL DSPSL (DA, N, IPIVOT, DB)

CALL SSPSL (SA, N, IPIVOT, SB)

CALL ZSPSL (ZA, N, IPIVOT, ZB)

CALL CSPSL (CA, N, IPIVOT, CB)

ARGUMENTS

xAUDU factorization of the matrix A, as computed by xSPCO or xSPFA.

NOrder of the matrix A. N >= 0.

IPIVOTPivot vector as computed by xSPCO or xSPFA.

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 = 3)
      PARAMETER        (LENGTA = (N ∗ N + N) / 2)
C
      DOUBLE PRECISION A(LENGTA), B(N), RCOND, WORK(N)
      INTEGER           IPIVOT(N)
C
      EXTERNAL          DSPCO, DSPSL
C
C     Initialize the array A to store in packed symmetric format
C     the matrix A shown below. Initialize the array B to store
C     the vector b shown below.
C
C         1 0 4        15
C     A = 0 2 0    b = 12
C         4 0 1        15
C
      DATA A / 1.0D0, 0.0D0, 2.0D0, 4.0D0, 0.0D0, 1.0D0 /
      DATA B / 1.5D1, 1.2D1, 1.5D1 /
C
      PRINT 1000
      PRINT 1010, A(1), A(2), A(4)
      PRINT 1010, A(2), A(3), A(5)
      PRINT 1010, A(4), A(5), A(6)
      PRINT 1020
      PRINT 1030, B
      CALL DSPCO (A, N, IPIVOT, RCOND, WORK)
      IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
        PRINT 1040
      END IF
      CALL DSPSL (A, N, IPIVOT, B)
      PRINT 1050
      PRINT 1030, B
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (3(3X, F4.1))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, F4.1)
1040 FORMAT (1X, ’A may be singular to working precision.’)
1050 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
C
      END

SAMPLE OUTPUT

A:
    1.0    0.0    4.0
    0.0    2.0    0.0
    4.0    0.0    1.0

b:
   15.0
   12.0
   15.0

A∗∗(-1) ∗ b:
    3.0
    6.0
    3.0