Sun Performance Library Reference Manual: 1

Generation of Q Defined in LQ Factorization

The subroutines described in this section generate a matrix Q with orthnormal rows that was defined in an LQ factorization computed by xGELQF.

Calling Sequence


CALL DORGLQ	(M, N, K, DA, LDA, DTAU, DWORK, LDWORK, INFO)
CALL SORGLQ	(M, N, K, SA, LDA, STAU, SWORK, LDWORK, INFO)

void dorglq	(int m, int n, int k, double da, int lda, double dtau, int *info)
void sorglq	(int m, int n, int k, float sa, int lda, float stau, int *info)

M	Number of rows of the matrix Q. M 0.
N	Number of columns of the matrix Q. N M.
K	Number of elementary reflectors whose product defines the matrix Q. 0 K M.
xA	On entry, A and TAU contain the LQ factorization of the matrix A as computed by xGELQF. On exit, the M×N matrix Q.
LDA	Leading dimension of the array A as specified in a dimension or type statement. LDA max(1, M).
xTAU	TAU(i) contains the scalar factor of the elementary reflector H(i) for 1 i K as computed by xGELQF.
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 DCOPY, 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 Print the initial value of A.
C
PRINT 1000
PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, M)
C
C Compute the LQ factorization of A.
C
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