dppdi(3P)

NAME

dppdi - compute the determinant and inverse of a symmetric positive definite matrix A in packed storage, which has been Cholesky-factored by xPPCO or xPPFA.

SYNOPSIS

CALL DPPDI (DA, N, DDET, JOB)

CALL SPPDI (SA, N, SDET, JOB)

CALL ZPPDI (ZA, N, DDET, JOB)

CALL CPPDI (CA, N, SDET, JOB)

void dppdi(double ∗dap, long int n, double ∗det, long int job)

void sppdi(float ∗sap, long int n, float ∗det, long int job)

void zppdi(doublecomplex ∗zap, long int n, double ∗det,
long int job)

void cppdi(complex ∗cap, long int n, float ∗det, long int job)

ARGUMENTS

xAOn entry, the Cholesky factorization of the matrix A, as
computed by xPPCO or xPPFA. On exit, the inverse of the original matrix A if the inverse was requested, otherwise A is unchanged. The strict lower triangle of A is not referenced.

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

xDETOn exit, 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.

JOBDetermines which operation the subroutine will perform:
11 both determinant and inverse
01 inverse only
10 determinant only

SAMPLE PROGRAM

      PROGRAM TEST
      IMPLICIT NONE
C
      INTEGER           INVDET, LENGTA, N
      PARAMETER        (INVDET = 11)
      PARAMETER        (N = 4)
      PARAMETER        (LENGTA = (N ∗ N + N) / 2)
C
      DOUBLE PRECISION A(LENGTA), DET(2)
      INTEGER           INFO, JOB
C
      EXTERNAL          DPPFA, DPPDI
C
C     Initialize the array A to store in packed symmetric storage
C     mode the matrix A shown below. Initialize the array B to store
C     the vector B shown below.
C
C         4 3 2 1
C     A = 3 4 3 2
C         2 3 4 3
C         1 2 3 4
C
      DATA A / 4.0D0, 3.0D0, 4.0D0, 2.0D0, 3.0D0, 4.0D0,
     $         1.0D0, 2.0D0, 3.0D0, 4.0D0 /
C
      PRINT 1000
      PRINT 1010, A(1), A(2), A(4), A(7)
      PRINT 1010, A(2), A(3), A(5), A(8)
      PRINT 1010, A(4), A(5), A(6), A(9)
      PRINT 1010, A(7), A(8), A(9), A(10)
      CALL DPPFA (A, N, INFO)
      IF (INFO .EQ. 0) THEN
        JOB = INVDET
        CALL DPPDI (A, N, DET, JOB)
        PRINT 1020, DET(1) ∗ (1.0D1 ∗∗ DET(2))
        PRINT 1030
        PRINT 1010, A(1), A(2), A(4), A(7)
        PRINT 1010, A(2), A(3), A(5), A(8)
        PRINT 1010, A(4), A(5), A(6), A(9)
        PRINT 1010, A(7), A(8), A(9), A(10)
      ELSE
        PRINT 1040
      END IF
C
1000 FORMAT (1X, ’A in full form:’)
1010 FORMAT (4(3X, F5.1))
1020 FORMAT (/1X, ’Determinant of A is ’, F4.1)
1030 FORMAT (/1X, ’A∗∗(-1):’)
1040 FORMAT (/1X, ’A is too ill-conditioned.’)
C
      END

SAMPLE OUTPUT

A in full form:
     4.0     3.0     2.0     1.0
     3.0     4.0     3.0     2.0
     2.0     3.0     4.0     3.0
     1.0     2.0     3.0     4.0

Determinant of A is 20.0

A∗∗(-1):
     0.6    -0.5     0.0     0.1
    -0.5     1.0    -0.5     0.0
     0.0    -0.5     1.0    -0.5
     0.1     0.0    -0.5     0.6