cspdi(3P)

NAME

cspdi - compute the determinant, inertia, and inverse of a symmetric matrix A in packed storage, which has been UDU-factored by xSPCO or xSPFA.

SYNOPSIS

CALL DSPDI (DA, N, IPIVOT, DDET, INERT, DWORK, JOB)

CALL SSPDI (SA, N, IPIVOT, SDET, INERT, SWORK, JOB)

CALL ZSPDI (ZA, N, IPIVOT, ZDET, ZWORK, JOB)

CALL CSPDI (CA, N, IPIVOT, CDET, CWORK, JOB)

void dspdi(double ∗dap, long int n, long int ∗kpvt, double ∗det,
long int ∗inert, long int job)

void sspdi(float ∗sap, long int n, long int ∗kpvt, float ∗det, long
int ∗inert, long int job)

void zspdi(doublecomplex ∗zap, long int n, long int ∗kpvt,
doublecomplex ∗det, long int job)

void cspdi(complex ∗cap, long int n, long int ∗kpvt,
complex ∗det, long int job)

ARGUMENTS

xAOn entry, the UDU factorization of the matrix A, as computed
by xSPCO or SPFA. 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 xSPCO or xSPFA.

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 xSPCO has set RCOND = 0 or if xSPFA has set INFO <> 0.

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
      DOUBLE PRECISION A(LENGTA), DET(2), RCOND, WORK(N)
      INTEGER           INERT(3), IPIVOT(N), JOB
C
      EXTERNAL          DSPCO, DSPDI
C
C     Initialize the array A to store in packed symmetric format
C     the matrix A shown below.
C
C         1 0 4
C     A = 0 2 0
C         4 0 3
C
      DATA A / 3.0D0, 2.0D0, 2.0D0, 1.0D0, 1.0D0, 1.0D0 /
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)
      CALL DSPCO (A, N, IPIVOT, RCOND, WORK)
      IF ((RCOND + 1.0D0) .EQ. RCOND) THEN
        PRINT 1020
      END IF
      JOB = IDODET + IDOINV + IDOINR
      CALL DSPDI (A, N, IPIVOT, DET, INERT, WORK, JOB)
      PRINT 1030, DET(1) ∗ (10.0D0 ∗∗ DET(2))
      PRINT 1040, INERT
      PRINT 1050
      PRINT 1010, A(1), A(2), A(4)
      PRINT 1010, A(2), A(3), A(5)
      PRINT 1010, A(4), A(5), A(6)
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (3(3X, F5.2))
1020 FORMAT (1X, ’A may be singular to working precision.’)
1030 FORMAT (/1X, ’Determinant of A: ’, F7.3)
1040 FORMAT (1X, ’Inertia of A: <’, I1, ’,’, I1, ’,’, I1, ’>’)
1050 FORMAT (/1X, ’A∗∗(-1):’)
C
      END

SAMPLE OUTPUT

A:
    3.00    2.00    1.00
    2.00    2.00    1.00
    1.00    1.00    1.00

Determinant of A:   1.000
Inertia of A: <3,0,0>

A∗∗(-1):
    1.00   -1.00    0.00
   -1.00    2.00   -1.00
    0.00   -1.00    2.00