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

Calling Sequence

CALL ZHESV	(UPLO, N, NRHS, ZA, LDA, IPIVOT, ZB, LDB, DWORK, LDWORK, INFO)
CALL CHESV	(UPLO, N, NRHS, CA, LDA, IPIVOT, CB, LDB, SWORK, LDWORK, INFO)
void zhesv	(char uplo, int n, int nrhs, doublecomplex *za, int lda, int *ipivot, doublecomplex *zb, int ldb, int *info)
void chesv	(char uplo, int n, int nrhs, complex *ca, int lda, 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. On exit, the UDU or LDL factorization of A as computed by xHETRF.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, N).
IPIVOT	On exit, pivot indices as computed by xHETRF.
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).
xWORK	Scratch array with a dimension of LDWORK.
LDWORK	Leading dimension of the array WORK as specified in a dimension or type statement. LDWORK 1.
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

DOUBLE PRECISION ZERO

INTEGER LDA, LDB, LDWORK, N, NRHS

PARAMETER (N = 3)

PARAMETER (LDA = N)

PARAMETER (LDB = N)

PARAMETER (LDWORK = 1)

PARAMETER (NRHS = 1)

PARAMETER (ZERO = 0.0D0)

C

COMPLEX*16 A(LDA,N), B(LDB,NRHS), WORK(LDWORK)

INTEGER ICOL, INFO, IPIVOT(N), IROW

C

EXTERNAL ZHESV

INTRINSIC ABS, CMPLX, CONJG, DBLE

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 / (1.0D0,8D8), (8D8,8D8), (8D8,8D8),

$ (1.0D0,-1.0D0), (3.0D0,8D8), (8D8,8D8),

$ (1.0D0,-1.0D0), (3.0D0,-1.0D0), (5.0D0,8D8) /

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

DO 100, IROW = 1, N

PRINT 1010, (CONJG(A(ICOL,IROW)), ICOL = 1, IROW - 1),

$ CMPLX(DBLE(A(IROW,IROW)), ZERO),

$ (A(IROW,ICOL), ICOL = IROW + 1, N)

100 CONTINUE

PRINT 1020

DO 110, IROW = 1, N

PRINT 1010, (A(IROW,ICOL), ICOL = 1, N)

110 CONTINUE

PRINT 1030

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 ZHESV ('UPPER TRIANGLE OF A STORED', N, NRHS, A, LDA,

$ IPIVOT, B, LDB, WORK, LDWORK, INFO)

IF (INFO .LT. 0) THEN

PRINT 1040, ABS(INFO)

STOP 1

ELSE IF (INFO .GT. 0) THEN

PRINT 1050

STOP 2

END IF

PRINT 1060

DO 210, ICOL = 1, NRHS

DO 200, IROW = 1, N

PRINT 1010, B(IROW,ICOL)

200 CONTINUE

210 CONTINUE

C

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

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

1020 FORMAT (/1X, 'A in Hermitian form: (* in unused entries)')

1030 FORMAT (/1X, 'b:')

1040 FORMAT (1X, 'Illegal argument to ZHESV, argument #', I2)

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

1060 FORMAT (/1X, 'x:')

C

END

Sample Output

A in full form:
( 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)
A in Hermitian form: (* in unused entries)
( 1.0,****) ( 1.0,-1.0) ( 1.0,-1.0)
(****,****) ( 3.0,****) ( 3.0,-1.0)
(****,****) (****,****) ( 5.0,****)
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)