Solution to a Linear System in a UDU-Factored Symmetric Matrix in Packed Storage

Calling Sequence

CALL DSPSL	(DA, N, IPIVOT, DB)
CALL SSPSL	(SA, N, IPIVOT, SB)
CALL ZSPSL	(ZA, N, IPIVOT, ZB)
CALL CSPSL	(CA, N, IPIVOT, CB)
void dspsl	(double *da, int n, int *ipivot, double *db)
void sspsl	(float *sa, int n, int *ipivot, float *sb)
void zspsl	(doublecomplex *za, int n, int *ipivot, doublecomplex *zb)
void cspsl	(complex *ca, int n, int *ipivot, complex *cb)

Arguments

xA	UDU factorization of the matrix A, as computed by xSPCO or xSPFA.
N	Order of the matrix A. N 0.
IPIVOT	Pivot vector as computed by xSPCO or xSPFA.
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 = 3)

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

C

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

INTEGER IPIVOT(N)

C

EXTERNAL DSPCO, DSPSL

C

C Initialize the array A to store in packed symmetric format

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

C the vector b shown below.

C

C 1 0 4 15

C A = 0 2 0 b = 12

C 4 0 1 15

C

DATA A / 1.0D0, 0.0D0, 2.0D0, 4.0D0, 0.0D0, 1.0D0 /

DATA B / 1.5D1, 1.2D1, 1.5D1 /

C

PRINT 1000

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

PRINT 1010, A(2), A(3), A(5)

PRINT 1010, A(4), A(5), A(6)

PRINT 1020

PRINT 1030, B

CALL DSPCO (A, N, IPIVOT, RCOND, WORK)

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

PRINT 1040

END IF

CALL DSPSL (A, N, IPIVOT, B)

PRINT 1050

PRINT 1030, B

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (3(3X, F4.1))

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

1030 FORMAT (3X, F4.1)

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

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

C

END

Sample Output

A:
1.0 0.0 4.0
0.0 2.0 0.0
4.0 0.0 1.0
b:
15.0
12.0
15.0
A**(-1) * b:
3.0
6.0
3.0