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

Calling Sequence

CALL DPPSL	(DA, N, DB)
CALL SPPSL	(SA, N, SB)
CALL ZPPSL	(ZA, N, ZB)
CALL CPPSL	(CA, N, CB)
void dppsl	(double *da, int n, double *db)
void sppsl	(float *sa, int n, float *sb)
void zppsl	(doublecomplex *za, int n, doublecomplex *zb)
void cppsl	(complex *ca, int n, complex *cb)

Arguments

xA	Cholesky factorization of the matrix A, as computed by xPPCO or xPPFA.
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 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 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, 3.0D0, 4.0D0, 2.0D0, 3.0D0, 4.0D0,

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

DATA B / 4*2.0D1 /

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

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