Solution to a Linear System in a Hermitian Matrix in Packed Storage (Simple Driver)

Calling Sequence

CALL ZHPSV	(UPLO, N, NRHS, ZA, IPIVOT, ZB, LDB, INFO)
CALL CHPSV	(UPLO, N, NRHS, CA, IPIVOT, CB, LDB, INFO)
void zhpsv	(char uplo, int n, int nrhs, doublecomplex *za, int *ipivot, doublecomplex *zb, int ldb, int *info)
void chpsv	(char uplo, int n, int nrhs, complex *ca, int *ipivot, complex *cb, int ldb, int *info)

Arguments

UPLO	Indicates whether xA contains the upper or lower triangle of the matrix. The legal values for UPLO are listed below. Any values not listed below are illegal.
	'U' or 'u'	xA contains the upper triangle.
	'L' or 'l'	xA contains the lower triangle.
N	Order of the matrix A. N 0.
NRHS	Number of right-hand sides, equal to the number of columns of the matrix B. NRHS 0.
xA	On entry, the upper or lower triangle of the matrix A. The dimension of xA is (N × N + N) / 2. On exit, the UDU or LDL factorization of A as computed by xHPTRF.
IPIVOT	On exit, pivot indices as computed by xHPTRF.
xB	On entry, the N×NRHS right-hand side matrix B. On exit, the N×NRHS solution matrix X.
LDB	Leading dimension of the array B as specified in a dimension or type statement. LDB max(1, N).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = |INFO|, had an illegal value.
	INFO > 0	D(i,i), where i = INFO, is exactly zero, and D is therefore singular. The UDU or LDL factorization has been completed, but the solution could not be computed.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LDB, LDWORK, LENGTA, N, NRHS

PARAMETER (N = 3)

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

PARAMETER (LDB = N)

PARAMETER (LDWORK = 1)

PARAMETER (NRHS = 1)

C

COMPLEX*16 A(LENGTA), B(LDB,NRHS)

INTEGER ICOL, INFO, IPIVOT(N), IROW

C

EXTERNAL ZHPSV

INTRINSIC ABS, CONJG

C

C Initialize the array A to store the coefficient array A

C shown below. Initialize the array B to store the right

C hand side vector b shown below.

C

C 1 1-i 1-i 4+i

C A = 1+i 3 3-i b = 4+6i

C 1+i 3+i 5 4+7i

C

DATA A / (1.0D0,0.0D0), (1.0D0,-1.0D0), (3.0D0,0.0D0),

$ (1.0D0,-1.0D0), (3.0D0,-1.0D0), (5.0D0,0.0D0) /

DATA B / (4.0D0,1.0D0), (4.0D0,6.0D0), (4.0D0,7.0D0) /

C

C Print the initial value of the arrays.

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

DO 130, ICOL = 1, NRHS

DO 120, IROW = 1, N

PRINT 1010, B(IROW,ICOL)

120 CONTINUE

130 CONTINUE

C

C Compute and print the solution.

C

CALL ZHPSV ('UPPER TRIANGLE OF A STORED', N, NRHS, A,

$ IPIVOT, B, LDB, INFO)

IF (INFO .LT. 0) THEN

PRINT 1030, ABS(INFO)

STOP 1

ELSE IF (INFO .GT. 0) THEN

PRINT 1040

STOP 2

END IF

PRINT 1050

DO 210, ICOL = 1, NRHS

DO 200, IROW = 1, N

PRINT 1010, B(IROW,ICOL)

200 CONTINUE

210 CONTINUE

C

1000 FORMAT (1X, 'A:')

1010 FORMAT (1X, 10(: 2X, '(', F4.1, ',', F4.1, ')'))

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

1030 FORMAT (1X, 'Illegal argument to ZHPSV, argument #', I2)

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

1050 FORMAT (/1X, 'x:')

C

END

Sample Output

A:
( 1.0, 0.0) ( 1.0,-1.0) ( 1.0,-1.0)
( 1.0, 1.0) ( 3.0, 0.0) ( 3.0,-1.0)
( 1.0, 1.0) ( 3.0, 1.0) ( 5.0, 0.0)
b:
( 4.0, 1.0)
( 4.0, 6.0)
( 4.0, 7.0)
x:
( 1.0, 0.0)
( 0.0, 2.0)
( 1.0, 0.0)