Solution to a Linear System in a Cholesky-Factored Symmetric Positive Definite Matrix

Calling Sequence

CALL DPOSL	(DA, LDA, N, DB)
CALL SPOSL	(SA, LDA, N, SB)
CALL ZPOSL	(ZA, LDA, N, ZB)
CALL CPOSL	(CA, LDA, N, CB)
void dposl	(double *da, int lda, int n, double *db)
void sposl	(float *sa, int lda, int n, float *sb)
void zposl	(doublecomplex *za, int lda, int n, doublecomplex *zb)
void cposl	(complex *ca, int lda, int n, complex *cb)

Arguments

xA	Cholesky factorization of the matrix A, as computed by xPOCO or xPOFA.
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.
xB	On entry, the right-hand side vector b. On exit, the solution vector x.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDA, N

PARAMETER (N = 4)

PARAMETER (LDA = N)

C

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

INTEGER ICOL, INFO, IROW

C

EXTERNAL DPOCO, DPOSL

C

C Initialize the array A to store in symmetric storage mode

C the matrix A shown below. Initialize the array B to store

C the vector B shown below.

C

C 4 3 2 1 20

C A = 3 4 3 2 b = 20

C 2 3 4 3 20

C 1 2 3 4 20

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 /

DATA B / 4*2.0D1 /

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)

PRINT 1030

PRINT 1040, B

CALL DPOCO (A, LDA, N, RCOND, WORK, INFO)

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

PRINT 1050

END IF

CALL DPOSL (A, LDA, N, B)

PRINT 1060

PRINT 1040, B

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 may be singular to working precision.')

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
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
b:
20.000
20.000
20.000
20.000
A**(-1) * b:
4.000
0.000
0.000
4.000