UDU or LDL Factorization of a Hermitian Matrix in Packed Storage

Calling Sequence

CALL ZHPTRF	(UPLO, N, ZA, IPIVOT, INFO)
CALL CHPTRF	(UPLO, N, CA, IPIVOT, INFO)
void zhptrf	(char uplo, int n, doublecomplex *za, int *ipivot, int *info)
void chptrf	(char uplo, int n, complex *ca, int *ipivot, 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.
xA	On entry, the upper or lower triangle of the matrix A. The dimension of xA is (N × N + N) / 2. On exit, a UDU or LDL factorization of A.
IPIVOT	On exit, an N-element array containing details of the row interchanges and block structure of D.
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 factorization has been completed, but division by zero will occur if this factorization is used to solve a linear system.

Sample Program

PROGRAM TEST

IMPLICIT NONE

C

INTEGER LENGTA, LDB, LDWORK, N, NRHS

PARAMETER (N = 3)

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

PARAMETER (LDB = N)

PARAMETER (LDWORK = 2 * N)

PARAMETER (NRHS = 1)

C

DOUBLE PRECISION ANORM, RCOND

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

INTEGER ICOL, INFO, IPIVOT(N), IROW

C

EXTERNAL ZHPCON, ZHPTRF, ZHPTRS

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 Factor the matrix.

C

CALL ZHPTRF ('UPPER TRIANGLE OF A STORED', N, A, IPIVOT,

$ INFO)

IF (INFO .LT. 0) THEN

PRINT 1030, ABS(INFO)

STOP 1

ELSE IF (INFO .GT. 0) THEN

PRINT 1040

STOP 2

END IF

C

C Estimate the condition number. Print a warning if it is

C unreasonably high.

C

ANORM = 1.0D1

CALL ZHPCON ('UPPER TRIANGULAR FACTOR OF A', N, A, IPIVOT,

$ ANORM, RCOND, WORK, INFO)

IF (INFO .LT. 0) THEN

PRINT 1050, ABS(INFO)

STOP 3

END IF

PRINT 1060, RCOND

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

PRINT 1070

END IF

C

C Compute and print the solution.

C

CALL ZHPTRS ('UPPER TRIANGULAR FACTOR OF A', N, NRHS, A,

$ IPIVOT, B, LDB, INFO)

IF (INFO .LT. 0) THEN

PRINT 1080, ABS(INFO)

STOP 4

END IF

PRINT 1090

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 ZHPTRF, argument #', I2)

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

1050 FORMAT (1X, 'Illegal argument to ZHPCON, argument #', I2)

1060 FORMAT (/1X,

$ 'Estimated reciprocal condition number of A: ',

$ F5.3)

1070 FORMAT (1X, 'A may be singular to working precision.')

1080 FORMAT (1X, 'Illegal argument to ZHPTRS, argument #', I2)

1090 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)
Estimated reciprocal condition number of A: 0.010
x:
( 1.0, 0.0)
( 0.0, 2.0)
( 1.0, 0.0)