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

Calling Sequence

CALL DPODI	(DA, LDA, N, DDET, JOB)
CALL SPODI	(SA, LDA, N, SDET, JOB)
CALL ZPODI	(ZA, LDA, N, DDET, JOB)
CALL CPODI	(CA, LDA, N, SDET, JOB)
void dpodi	(double *da, int lda, int n, double *ddet, int job)
void spodi	(float *sa, int lda, int n, float *sdet, int job)
void zpodi	(doublecomplex *za, int lda, int n, double *ddet, int job)
void cpodi	(complex *ca, int lda, int n, float *sdet, int job)

Arguments

xA	On entry, the Cholesky factorization of the matrix A, as computed by xPOCO, xPOFA, or xQRDC. 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.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1,N).
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, LDA, N

PARAMETER (INVDET = 11)

PARAMETER (N = 4)

PARAMETER (LDA = N)

C

DOUBLE PRECISION A(LDA,N), DET(2)

INTEGER ICOL, INFO, IROW, JOB

C

EXTERNAL DPODI, DPOFA

C

C Initialize the array A to store in symmetric storage mode

C the matrix A 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*8D8, 3.0D0, 4.0D0, 2*8D8, 2.0D0, 3.0D0,

$ 4.0D0, 8D8, 1.0D0, 2.0D0, 3.0D0, 4.0D0 /

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 DPOFA (A, LDA, N, INFO)

IF (INFO .EQ. 0) THEN

JOB = INVDET

CALL DPODI (A, LDA, N, DET, JOB)

PRINT 1050

DO 110, IROW = 1, N

PRINT 1010, (A(ICOL,IROW), ICOL = 1, IROW),

$ (A(IROW,ICOL), ICOL = IROW + 1, N)

110 CONTINUE

PRINT 1060, DET(1) * (10.0D0 ** DET(2))

ELSE

PRINT 1070

END IF

C

1000 FORMAT (1X, 'A in full form:')

1010 FORMAT (4(3X, F7.3))

1020 FORMAT (/1X, 'A in symmetric form: (* in unused entries)')

1030 FORMAT (/1X, 'b:')

1040 FORMAT (3X, F7.3)

1050 FORMAT (/1X, 'A**(-1):')

1060 FORMAT (/1X, 'The determinant of A is ', F5.1)

1070 FORMAT (/1X, 'A is not positive definite.')

C

END

Sample Output

A in full form:
4.000 3.000 2.000 1.000
3.000 4.000 3.000 2.000
2.000 3.000 4.000 3.000
1.000 2.000 3.000 4.000
A in symmetric form: (* in unused entries)
4.000 3.000 2.000 1.000
******* 4.000 3.000 2.000
******* ******* 4.000 3.000
******* ******* ******* 4.000
A**(-1):
0.600 -0.500 0.000 0.100
-0.500 1.000 -0.500 0.000
0.000 -0.500 1.000 -0.500
0.100 0.000 -0.500 0.600
The determinant of A is 20.0