Sun Performance Library Reference Manual: 1

LQ Factorization of a General Matrix

The subroutines described in this section compute an LQ factorization of a general matrix A.

Calling Sequence


CALL DGELQF	(M, N, DA, LDA, DTAU, DWORK, LDWORK, INFO)
CALL SGELQF	(M, N, SA, LDA, STAU, SWORK, LDWORK, INFO)
CALL ZGELQF	(M, N, ZA, LDA, ZTAU, ZWORK, LDWORK, INFO)
CALL CGELQF	(M, N, CA, LDA, CTAU, CWORK, LDWORK, INFO)

void dgelqf	(int m, int n, double da, int lda, double dtau, int *info)
void sgelqf	(int m, int n, float sa, int lda, float stau, int *info)
void zgelqf	(int m, int n, doublecomplex za, int lda, doublecomplex ztau, int *info)
void cgelqf	(int m, int n, complex ca, int lda, complex ctau, int *info)

M	Number of rows of the matrix A. M 0.
N	Number of columns of the matrix A. N 0.
xA	On entry, the matrix A. On exit, A and TAU contain an LQ factorization of the matrix A.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, M).
xTAU	On exit, the min(M, N) scalar factors of the elementary reflectors. The elementary reflectors in xTAU together with xA contain an LQ factorization of the matrix A that can be used by other LAPACK subroutines that operate on the matrix A.
xWORK	Scratch array with a dimension of LDWORK.
LDWORK	Leading dimension of the array WORK as specified in a dimension or type statement. LDWORK max(1, M).
INFO	On exit:
	INFO = 0	Subroutine completed normally.
	INFO < 0	The ith argument, where i = \|INFO\|, had an illegal value.

Sample Program



PROGRAM TEST
IMPLICIT NONE
C
INTEGER LDA, LDWORK, M, N
PARAMETER (M = 4)
PARAMETER (N = 4)
PARAMETER (LDA = M)
PARAMETER (LDWORK = M)
C
DOUBLE PRECISION A(LDA,N), TAU(N), WORK(LDWORK)
INTEGER ICOL, INFO, IROW
C
EXTERNAL DGELQF, DORGLQ
INTRINSIC ABS, MIN
C
C Initialize the array A to store the matrix A shown below.
C
C 1 1 1 1
C A = 1 -1 1 -1
C 5 -5 -1 1
C 9 -1 -5 -3
C
DATA A / 1.0D0, 1.0D0, 5.0D0, 9.0D0,
$ 1.0D0, -1.0D0, -5.0D0, -1.0D0,
$ 1.0D0, 1.0D0, -1.0D0, -5.0D0,
$ 1.0D0, -1.0D0, 1.0D0, -3.0D0 /
C
C Compute the LQ factorization of A and print L.
C
PRINT 1000
PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, M)
CALL DGELQF (M, N, A, LDA, TAU, WORK, LDWORK, INFO)
IF (INFO .NE. 0) THEN
PRINT 1020, ABS(INFO)
STOP 1
END IF
PRINT 1030
DO 100, IROW = 1, M
PRINT 1010, (A(IROW,ICOL), ICOL = 1, MIN(N,IROW)),
$ (0.0D0, ICOL = IROW + 1, N)
100 CONTINUE
C
C Compute and print the matrix Q used in the LQ factorization
C of A.
C
CALL DORGLQ (N, N, N, A, LDA, TAU, WORK, LDWORK, INFO)
IF (INFO .NE. 0) THEN
PRINT 1040, ABS(INFO)
STOP 2
END IF
PRINT 1050
PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, N)
C
1000 FORMAT (1X, 'A:')
1010 FORMAT (4(3X, F8.4))
1020 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DGELQF.')
1030 FORMAT (/1X, 'L:')
1040 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DORGLQ.')
1050 FORMAT (/1X, 'Q:')
C
END

Sample Output