Determinant and Inverse of a Cholesky-Factored Symmetric Positive Definite Matrix in Packed Storage

Calling Sequence

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 *da, int n, double *ddet, int job)
void sppdi	(float *sa, int n, float *sdet, int job)
void zppdi	(doublecomplex *za, int n, double *ddet, int job)
void cppdi	(complex *ca, int n, float *sdet, int job)

Arguments

xA	On 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.
N	Order of the original matrix A. N 0.
xDET	On exit, the determinant of the matrix A. The determinant is stored as b × 10expon 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.
JOB	Determines 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

C store 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