Cholesky Decomposition of a Symmetric Positive Definite Matrix

Calling Sequence

CALL DCHDC	(DA, LDA, N, DWORK, IPIVOT, JOB, INFO)
CALL SCHDC	(SA, LDA, N, SWORK, IPIVOT, JOB, INFO)
CALL ZCHDC	(ZA, LDA, N, ZWORK, IPIVOT, JOB, INFO)
CALL CCHDC	(CA, LDA, N, CWORK, IPIVOT, JOB, INFO)
void dchdc	(double *da, int lda, int n, int *ipivot, int job, int *info)
void schdc	(float *sa, int lda, int n, int *ipivot, int job, int *info)
void zchdc	(doublecomplex *za, int lda, int n, int *ipivot, int job, int *info)
void cchdc	(complex *ca, int lda, int n, int *ipivot, int job, int *info)

Arguments

xA	On entry, the upper triangle of A. On exit, the upper triangle of the Cholesky factor, as permuted by pivoting if pivoting was selected. 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 matrix A. N 0.
xWORK	Scratch array with a dimension of N.
IPIVOT	If JOB selected no pivoting then IPIVOT is not referenced. On entry, if JOB selected pivoting, IPIVOT contains integers representing array indices that control the selection of pivot elements from the diagonal of A according to the system below:
	IPIVOT(k) > 0	A(k,k) is an initial element.
	IPIVOT(k) = 0	A(k,k) is a free element.
	IPIVOT(k) < 0	A(k,k) is a final element.
	Before the decomposition is computed, symmetric row and column interchanges are used to move initial elements to the beginning of A and final elements to the end of A. During the computation, symmetric row and column interchanges are used to move the largest remaining free diagonal element into the pivot position.
	On exit, IPIVOT(k) contains the index of the diagonal element of A that was moved into the kth position.
JOB	Determines how decomposition is done:
	0	without pivoting
	not 0	with pivoting
INFO	On exit:
	Returns the index of the last positive diagonal element of the Cholesky factor.
	The subroutine was successful if INFO = N.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N, NOPIV

PARAMETER (N = 4)

PARAMETER (LDA = N)

PARAMETER (NOPIV = 0)

C

DOUBLE PRECISION A(LDA,N), WORK(N)

INTEGER I, INFO, IPIVOT(N), J, JOB

C

EXTERNAL DCHDC

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, I = 1, N

PRINT 1010, (A(J,I), J = 1, I), (A(I,J), J = I + 1, N)

100 CONTINUE

PRINT 1020

PRINT 1010, ((A(I,J), J = 1, N), I = 1, N)

JOB = NOPIV

CALL DCHDC (A, LDA, N, WORK, IPIVOT, JOB, INFO)

IF (INFO .EQ. N) THEN

PRINT 1030

PRINT 1010, A(1,1), A(1,2), A(1,3), A(1,4)

PRINT 1040, A(2,2), A(2,3), A(2,4)

PRINT 1050, A(3,3), A(3,4)

PRINT 1060, A(4,4)

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, 'Upper Cholesky factor:')

1040 FORMAT (10X, 3(3X, F7.3))

1050 FORMAT (20X, 2(3X, F7.3))

1060 FORMAT (30X, 1(3X, F7.3))

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
Upper Cholesky factor:
2.000 1.500 1.000 0.500
1.323 1.134 0.945
1.309 1.091
1.291