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

Calling Sequence

CALL ZHPSL	(ZA, N, IPIVOT, ZB)
CALL CHPSL	(CA, N, IPIVOT, CB)
void zhpsl	(doublecomplex *za, int n, int *ipivot, doublecomplex *zb)
void chpsl	(complex *ca, int n, int *ipivot, complex *cb)

Arguments

xA	On entry, the UDU factorization of the matrix A, as computed xHPCO or xHPFA.
N	Order of the matrix A. N 0.
IPIVOT	Pivot vector as computed by xHPCO or xHPFA.
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

REAL RCOND

COMPLEX A(LENGTA), B(N), WORK(N)

INTEGER IPIVOT(N)

C

EXTERNAL CHPCO, CHPSL

INTRINSIC CONJG

C

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

C Initialize the array B to store the vector b shown below.

C

C 1 1+2i 1+2i 95-180i

C A = 1+2i 6 -2+6i b = 545-118i

C 1+2i -2+6i 11 865+ 62i

C

C

DATA A / (1.0,0.0), (1.0,-2.0), (6.0,0.0),

$ (1.0,-2.0), (6.0,-2.0), (11.0,0.0) /

DATA B / (95.0,-180.0), (545.0,-118.0), (865.0,62.0) /

C

PRINT 1000

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

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

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

PRINT 1020

PRINT 1030, B

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

PRINT 1040, RCOND

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

PRINT 1050

END IF

CALL CHPSL (A, N, IPIVOT, B)

PRINT 1060

PRINT 1030, B

C

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

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

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

1030 FORMAT (3X, '(', F6.1, ',', F6.1, ')')

1040 FORMAT (/1X, 'Reciprocal condition number of A:', F6.3)

1050 FORMAT (1X, 'A may be singular to working precision.')

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

C

END

Sample Output

A in full form:
( 1.0, 0.0) ( 1.0,-2.0) ( 1.0,-2.0)
( 1.0, 2.0) ( 6.0, 0.0) ( 6.0,-2.0)
( 1.0, 2.0) ( 6.0, 2.0) (11.0, 0.0)
b:
( 95.0,-180.0)
( 545.0,-118.0)
( 865.0, 62.0)
Reciprocal condition number of A: 0.001
A**(-1) * b:
( 5.0, 0.0)
( 26.0, 0.0)
( 64.0, 0.0)