zsidi(l) — SunSoft Performance Library

NAME

zsidi - compute the determinant, inertia, and inverse of a symmetric matrix A, which has been UDU-factored by xSICO or xSIFA.

SYNOPSIS

CALL DSIDI (DA, LDA, N, IPIVOT, DDET, INERT, DWORK, JOB)

CALL SSIDI (SA, LDA, N, IPIVOT, SDET, INERT, SWORK, JOB)

CALL ZSIDI (ZA, LDA, N, IPIVOT, ZDET, ZWORK, JOB)

CALL CSIDI (CA, LDA, N, IPIVOT, CDET, CWORK, JOB)

ARGUMENTS

xAOn entry, the UDU factorization of the matrix A, as computed by
xSICO or xSIFA. On exit, if the c digit of JOB ∗ 0, then the upper triangle of A contains the upper triangle of the inverse of the original matrix A if the inverse was requested, otherwise unchanged. The strict lower triangle of A is not referenced.

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

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

IPIVOTPivot vector as computed by x SICO or xSIFA.

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 for real subroutines or bc for
complex subroutines; determines operation the subroutine will perform:
a <> 0 Compute the inertia.
b <> 0 Compute the determinant.
c <> 0 Compute the inverse.
Note that the inverse should not be computed if xSICO has set RCOND = 0 or if xSIFA has set INFO >= 0.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           IDODET, IDOINR, IDOINV, LDA, N
      PARAMETER        (IDODET = 10)
      PARAMETER        (IDOINR = 100)
      PARAMETER        (IDOINV = 1)
      PARAMETER        (N = 4)
      PARAMETER        (LDA = N)
C
      DOUBLE PRECISION A(LDA,N), DET(2), WORK(N)
      INTEGER           ICOL, INERT(3), INFO, IPIVOT(N), IROW, JOB
C
      EXTERNAL DSIFA, DSIDI
C
C     Initialize the array A to store the matrix A shown below.
C
C         -.5   -.5   -.5   -.5
C     A = -.5 -1.5 -1.5 -1.5
C         -.5 -1.5 -2.5 -2.5
C         -.5 -1.5 -2.5 -3.5
C
      DATA A / -5.0D-1, 3∗8D8, -5.0D-1, -1.5D0, 2∗8D8, -5.0D-1,
     $         -1.5D0, -2.5D0, 8D8, -5.0D-1, -1.5D0, -2.5D0, -3.5D0 /
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)
      CALL DSIFA (A, LDA, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        JOB = IDOINR + IDODET + IDOINV
        CALL DSIDI (A, LDA, N, IPIVOT, DET, INERT, WORK, JOB)
        PRINT 1030, DET(1) ∗ (10.0D0 ∗∗ DET(2))
        PRINT 1040, INERT
        PRINT 1050
      DO 110, IROW = 1, N
        PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),
     $              (A(IROW,ICOL), ICOL = IROW + 1, N)
110 CONTINUE
      ELSE
        PRINT 1060
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(3X, F5.1))
1020 FORMAT (/1X, ’A in symmetric form: (∗ in unused elements)’)
1030 FORMAT (/1X, ’Determinant of A: ’, F6.3)
1040 FORMAT (1X, ’Inertia of A: <’, I1, ’,’, I1, ’,’, I1, ’>’)
1050 FORMAT (/1X, ’A∗∗(-1):’)
1060 FORMAT (/1X, ’A is too poorly conditioned.’)
C
      END

SAMPLE OUTPUT

A in full form:
    -0.5    -0.5    -0.5    -0.5
    -0.5    -1.5    -1.5    -1.5
    -0.5    -1.5    -2.5    -2.5
    -0.5    -1.5    -2.5    -3.5

A in symmetric form: (∗ in unused elements)
    -0.5    -0.5    -0.5    -0.5
   ∗∗∗∗∗    -1.5    -1.5    -1.5
   ∗∗∗∗∗   ∗∗∗∗∗    -2.5    -2.5
   ∗∗∗∗∗   ∗∗∗∗∗   ∗∗∗∗∗    -3.5

Determinant of A: 0.500
Inertia of A: <0,4,0>

A∗∗(-1):
    -3.0     1.0     0.0     0.0
     1.0    -2.0     1.0     0.0
     0.0     1.0    -2.0     1.0
     0.0     0.0     1.0    -1.0