chpsl(l) — SunSoft Performance Library

NAME

chpsl - solve the linear system Ax = b for a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA, and vectors b and x.

SYNOPSIS

CALL ZHPSL (ZA, N, IPIVOT, ZB)

CALL CHPSL (CA, N, IPIVOT, CB)

ARGUMENTS

xAOn entry, the UDU factorization of the matrix A, as computed xHPCO or xHPFA.

NOrder of the matrix A. N >= 0.

IPIVOTPivot vector as computed by xHPCO or xHPFA.

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
      REAL       RCOND
      COMPLEX    A(LENGTA), B(N), WORK(N)
      INTEGER    IPIVOT(N)
C
      EXTERNAL   CHPCO, CHPSL
      INTRINSIC CONJG
C
C     Initialize the array A to store the matrix A shown below.
C     Initialize the array B to store the vector b shown below.
C
C          1    1+2i 1+2i         95-180i
C     A = 1+2i   6   -2+6i    b = 545-118i
C         1+2i -2+6i   11         865+ 62i
C
C
      DATA A / (1.0,0.0), (1.0,-2.0), (6.0,0.0),
     $         (1.0,-2.0), (6.0,-2.0), (11.0,0.0) /
      DATA B / (95.0,-180.0), (545.0,-118.0), (865.0,62.0) /
C
      PRINT 1000
      PRINT 1010, A(1), A(2), A(4)
      PRINT 1010, CONJG(A(2)), A(3), A(5)
      PRINT 1010, CONJG(A(4)), CONJG(A(5)), A(6)
      PRINT 1020
      PRINT 1030, B
      CALL CHPCO (A, N, IPIVOT, RCOND, WORK)
      PRINT 1040, RCOND
      IF ((RCOND + 1.0) .EQ. 1.0) THEN
        PRINT 1050
      END IF
      CALL CHPSL (A, N, IPIVOT, B)
      PRINT 1060
      PRINT 1030, B
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (3(3X, ’(’, F4.1, ’,’, F4.1, ’)’))
1020 FORMAT (/1X, ’b:’)
1030 FORMAT (3X, ’(’, F6.1, ’,’, F6.1, ’)’)
1040 FORMAT (/1X, ’Reciprocal condition number of A:’, F6.3)
1050 FORMAT (1X, ’A may be singular to working precision.’)
1060 FORMAT (/1X, ’A∗∗(-1) ∗ b:’)
C
      END

SAMPLE OUTPUT

A in full form:
   ( 1.0, 0.0)   ( 1.0,-2.0)   ( 1.0,-2.0)
   ( 1.0, 2.0)   ( 6.0, 0.0)   ( 6.0,-2.0)
   ( 1.0, 2.0)   ( 6.0, 2.0)   (11.0, 0.0)

b:
   ( 95.0,-180.0)
   ( 545.0,-118.0)
   ( 865.0, 62.0)

Reciprocal condition number of A: 0.001

A∗∗(-1) ∗ b:
   (   5.0,   0.0)
   ( 26.0,   0.0)
   ( 64.0,   0.0)