zspfa(3P)

NAME

zspfa - compute the UDU factorization of a symmetric matrix A in packed storage. It is typical to follow a call to xSPFA with a call to xSPSL to solve Ax = b or to xSPDI to compute the determinant, inverse, and inertia of A.

SYNOPSIS

CALL DSPFA (DA, N, IPIVOT, INFO)

CALL SSPFA (SA, N, IPIVOT, INFO)

CALL ZSPFA (ZA, N, IPIVOT, INFO)

CALL CSPFA (CA, N, IPIVOT, INFO)

void dspfa(double ∗dap, long int n, long int ∗kpvt, long int ∗info)

void sspfa(float ∗sap, long int n, long int ∗kpvt, long int ∗info)

void zspfa(doublecomplex ∗zap, long int n, long int ∗kpvt,
long int ∗info)

void cspfa(complex ∗cap, long int n, long int ∗kpvt,
long int ∗info)

ARGUMENTS

xAOn entry, the upper triangle of the matrix A.
On exit, a UDU factorization of the matrix A.

NOrder of the matrix A. N >= 0.

IPIVOTOn exit, a vector of pivot indices.

INFOOn exit:
INFO = 0Subroutine completed normally.
INFO > 0Returns a value k if the kth pivot block is singular to indicate that xSPSL or xSPDI will divide by zero if called.

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           IDODET, IDOINR, IDOINV, JOB, LENGTA, N
      PARAMETER        (IDODET = 10)
      PARAMETER        (IDOINR = 100)
      PARAMETER        (IDOINV = 1)
      PARAMETER        (JOB = 111)
      PARAMETER        (N = 3)
      PARAMETER        (LENGTA = (N ∗ N + N) / 2)
C
      DOUBLE PRECISION A(LENGTA), DET(2), WORK(N)
      INTEGER           INERT(3), INFO, IPIVOT(N)
C
      EXTERNAL          DSPDI, DSPFA
C
C     Initialize the array A to store in packed symmetric format
C     the matrix A shown below.
C
C         3 2 1
C     A = 2 2 1
C         1 1 1
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 DSPFA (A, N, IPIVOT, INFO)
      IF (INFO .EQ. 0) THEN
        CALL DSPDI (A, N, IPIVOT, DET, INERT, WORK, JOB)
        PRINT 1020, DET(1) ∗ (10.0D0 ∗∗ DET(2))
        PRINT 1030, INERT
        PRINT 1040
        PRINT 1010, A(1), A(2), A(4)
        PRINT 1010, A(2), A(3), A(5)
        PRINT 1010, A(4), A(5), A(6)
      ELSE
        PRINT 1050
      END IF
C
1000 FORMAT (1X, ’A:’)
1010 FORMAT (3(3X, F5.2))
1020 FORMAT (/1X, ’Determinant of A: ’, F7.3)
1030 FORMAT (1X, ’Inertia of A: <’, I1, ’,’, I1, ’,’, I1, ’>’)
1040 FORMAT (/1X, ’A∗∗(-1):’)
1050 FORMAT (1X, ’A is too ill-conditioned.’)
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