Sun Performance Library Reference Manual: 1

Generation of Q Defined in QR Factorization

The subroutines described in this section generate a matrix Q with orthonormal columns that was defined in a QR factorization computed by xGEQRF.

Calling Sequence


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

void dorgqr	(int m, int n, int k, double da, int lda, double dtau, int *info)
void sorgqr	(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. M N 0.
K	Number of elementary reflectors whose product defines the matrix Q. N K 0.
xA	On entry, A and TAU contain the QR factorization of the matrix A as computed by xGEQRF. 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 xGEQRF.
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, N).
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, LDR, LDWORK, M, N
PARAMETER (M = 4)
PARAMETER (N = 3)
PARAMETER (LDA = M)
PARAMETER (LDR = N)
PARAMETER (LDWORK = N)
C
DOUBLE PRECISION A(LDA,N), R(LDR,N), TAU(N), WORK(LDWORK)
INTEGER ICOL, INFO, IROW
C
EXTERNAL DCOPY, DGEQRF, DORGQR
INTRINSIC ABS
C
C Initialize the array A to store the matrix A shown below.
C
C 1 6 2
C A = 1 -2 -8
C 1 -2 4
C 1 6 14
C
DATA A / 4*1.0D0, 6.0D0, -2.0D0, -2.0D0, 6.0D0,
$ 2.0D0, -8.0D0, 4.0D0, 1.4D1 /
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 QR factorization of A.
C
CALL DGEQRF (M, N, A, LDA, TAU, WORK, LDWORK, INFO)
IF (INFO .NE. 0) THEN
PRINT 1020, ABS(INFO)
STOP 1
END IF
DO 100, ICOL = 1, N
CALL DCOPY (N, A(1,ICOL), 1, R(1,ICOL), 1)
100 CONTINUE
C
C Compute and print the matrix Q used in the QR factorization
C of A.
C
CALL DORGQR (M, N, N, A, LDA, TAU, WORK, LDWORK, INFO)
IF (INFO .NE. 0) THEN
PRINT 1030, ABS(INFO)
STOP 2
END IF
PRINT 1040
PRINT 1010, ((A(IROW,ICOL), ICOL = 1, N), IROW = 1, M)
PRINT 1050
DO 110, IROW = 1, N
PRINT 1010, (0.0D0, ICOL = 1, IROW - 1),
$ (R(IROW,ICOL), ICOL = IROW, N)
110 CONTINUE
C
1000 FORMAT (1X, 'A:')
1010 FORMAT (3(3X, F8.4))
1020 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DGEQRF.')
1030 FORMAT (1X, 'Illegal value for argument #', I1,
$ ' in DORGQR.')
1040 FORMAT (/1X, 'Q:')
1050 FORMAT (/1X, 'R:')
C
END

Sample Output