chpdi(l) — SunSoft Performance Library

NAME

chpdi - compute the determinant, inertia, and inverse of a Hermitian matrix A in packed storage, which has been UDU-factored by xHPCO or xHPFA.

SYNOPSIS

CALL ZHPDI (ZA, N, IPIVOT, DDET, INERT, ZWORK, JOB)

CALL CHPDI (CA, N, IPIVOT, SDET, INERT, CWORK, JOB)

ARGUMENTS

xAOn entry, the UDU factorization of the matrix, as computed by
xHPCO or xHPFA. On exit, if the c digit of JOB <> 0, then A contains the upper triangle of the inverse of the original matrix A; otherwise unchanged.

NOrder of the original matrix A. N >= 0.

IPIVOTPivot vector as computed by xHPCO or xHPFA.

xDETOn exit, if the b digit of JOB <> 0, then DET contains the
determinant of the matrix A. The determinant is stored as b ∗ (10 ∗∗ expon) where b is stored in DET(1) and expon is stored in DET(2). 1.0 <= |DET(1)| <= 10.0 or DET(1) = 0.0. If the b digit of JOB = 0, DET is not referenced.

INERTOn exit, if the a digit of JOB <> 0, then INERT contains an
integer triplet where:
INERT(1) = number of positive eigenvalues
INERT(2) = number of negative eigenvalues
INERT(3) = number of zero eigenvalues
If the a digit of JOB = 0 then INERT is not referenced.

xWORKScratch array with a dimension of N.

JOBInteger in the form abc; determines operation subroutine will perform:
a <> 0 Compute the inertia.
b <> 0 Compute the determinant.
c <> 0 Compute the inverse.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER    IDODET, IDOINR, IDOINV, LENGTA, N
      PARAMETER (IDODET = 10)
      PARAMETER (IDOINR = 100)
      PARAMETER (IDOINV = 1)
      PARAMETER (N = 3)
      PARAMETER (LENGTA = (N ∗ N + N) / 2)
C
      REAL       DET(2), RCOND
      COMPLEX    A(LENGTA), WORK(N)
      INTEGER    INERT(3), IPIVOT(N), JOB
C
      EXTERNAL   CHPCO, CHPDI
C
C     Initialize the array A to store the matrix A shown below.
C
C          1    1+2i 1+2i
C     A = 1+2i   6   -2+6i
C         1+2i -2+6i   11
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) /
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)
      CALL CHPCO (A, N, IPIVOT, RCOND, WORK)
      PRINT 1020, RCOND
      IF ((RCOND + 1.0) .EQ. 1.0) THEN
        PRINT 1030
      END IF
      JOB = IDOINR + IDODET + IDOINV
      CALL CHPDI (A, N, IPIVOT, DET, INERT, WORK, JOB)
      PRINT 1040, DET(1) ∗ (10.0D0 ∗∗ DET(2))
      PRINT 1050, INERT
      PRINT 1060
      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)
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(: 3X, ’(’, F5.1, ’,’, F5.1, ’)’))
1020 FORMAT (/1X, ’Reciprocal condition number of A:’, F6.3)
1030 FORMAT (1X, ’A may be singular to working precision.’)
1040 FORMAT (/1X, ’Determinant of A: ’, F6.3)
1050 FORMAT (1X, ’Inertia of A: <’, I1, ’,’, I1, ’,’, I1, ’>’)
1060 FORMAT (/1X, ’A∗∗(-1):’)
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)

Reciprocal condition number of A: 0.001

Determinant of A: 0.008
Inertia of A: <3,0,0>

A∗∗(-1):
   ( 26.0, 0.0)   ( -1.0, 12.0)   ( -4.0, -2.0)
   ( -1.0,-12.0)   ( 6.0, 0.0)   ( -1.0, 2.0)
   ( -4.0, 2.0)   ( -1.0, -2.0)   ( 1.0, 0.0)