Cholesky Factorization and Condition Number of a Symmetric Positive Definite Matrix in Packed Storage

Calling Sequence

CALL DPPCO	(DA, N, DRCOND, DWORK, INFO)
CALL SPPCO	(SA, N, SRCOND, SWORK, INFO)
CALL ZPPCO	(ZA, N, DRCOND, ZWORK, INFO)
CALL CPPCO	(CA, N, SRCOND, CWORK, INFO)
void dppco	(double *da, int n, double *drcond, int *info)
void sppco	(float *sa, int n, float *srcond, int *info)
void zppco	(doublecomplex *za, int n, double *drcond, int *info)
void cppco	(complex *ca, int n, float *srcond, int *info)

Arguments

xA	On entry, the upper triangle of the matrix A. On exit, a Cholesky factorization of the matrix A.
N	Order of the matrix A. N 0.
xRCOND	On exit, an estimate of the reciprocal condition number of A. 0.0 RCOND 1.0. As the value of RCOND gets smaller, operations with A such as solving Ax = b may become less stable. If RCOND satisfies RCOND + 1.0 = 1.0 then A may be singular to working precision.
xWORK	Scratch array with a dimension of N.
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO > 0	Returns a value k if the leading minor of order k is not positive definite.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LENGTA, N

PARAMETER (N = 4)

PARAMETER (LENGTA = (N * N + N) / 2)

C

DOUBLE PRECISION A(LENGTA), B(N), RCOND, WORK(N)

INTEGER INFO

C

EXTERNAL DPPCO, DPPSL

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 matrix B shown below.

C

C 4 3 2 1 60

C A = 3 4 3 2 b = 20

C 2 3 4 3 20

C 1 2 3 4 60

C

DATA A / 4.0D0, 3.0D0, 4.0D0, 2.0D0, 3.0D0, 4.0D0,

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

DATA B / 6.0D1, 2.0D1, 2.0D1, 6.0D1 /

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)

PRINT 1020

PRINT 1030, B

CALL DPPCO (A, N, RCOND, WORK, INFO)

IF ((RCOND + 1.0D0) .EQ. RCOND) THEN

PRINT 1040

END IF

CALL DPPSL (A, N, B)

PRINT 1050, RCOND

PRINT 1060

PRINT 1030, B

C

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

1010 FORMAT (5(3X, F7.3))

1020 FORMAT (/1X, 'b:')

1030 FORMAT (3X, F7.3)

1040 FORMAT (1X, 'A may be singular to working precision.')

1050 FORMAT (/1X, 'Reciprocal condition of A:', F5.2)

1060 FORMAT (/1X, 'A**(-1) * b:')

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
b:
60.000
20.000
20.000
60.000
Reciprocal condition of A: 0.04
A**(-1) * b:
32.000
-20.000
-20.000
32.000