*> \brief \b DORGR2 generates all or part of the orthogonal matrix Q from an RQ factorization determined by sgerqf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download DORGR2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DORGR2 generates an m by n real matrix Q with orthonormal rows, *> which is defined as the last m rows of a product of k elementary *> reflectors of order n *> *> Q = H(1) H(2) . . . H(k) *> *> as returned by DGERQF. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix Q. N >= M. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> matrix Q. M >= K >= 0. *> \endverbatim *> *> \param[in,out] A *> \verbatim *> A is DOUBLE PRECISION array, dimension (LDA,N) *> On entry, the (m-k+i)-th row must contain the vector which *> defines the elementary reflector H(i), for i = 1,2,...,k, as *> returned by DGERQF in the last k rows of its array argument *> A. *> On exit, the m by n matrix Q. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The first dimension of the array A. LDA >= max(1,M). *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is DOUBLE PRECISION array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by DGERQF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION array, dimension (M) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument has an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date December 2016 * *> \ingroup doubleOTHERcomputational * * ===================================================================== SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO ) * * -- LAPACK computational routine (version 3.7.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * December 2016 * * .. Scalar Arguments .. INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, II, J, L * .. * .. External Subroutines .. EXTERNAL DLARF, DSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC MAX * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.M ) THEN INFO = -2 ELSE IF( K.LT.0 .OR. K.GT.M ) THEN INFO = -3 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -5 END IF IF( INFO.NE.0 ) THEN CALL XERBLA( 'DORGR2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.LE.0 ) \$ RETURN * IF( K.LT.M ) THEN * * Initialise rows 1:m-k to rows of the unit matrix * DO 20 J = 1, N DO 10 L = 1, M - K A( L, J ) = ZERO 10 CONTINUE IF( J.GT.N-M .AND. J.LE.N-K ) \$ A( M-N+J, J ) = ONE 20 CONTINUE END IF * DO 40 I = 1, K II = M - K + I * * Apply H(i) to A(1:m-k+i,1:n-k+i) from the right * A( II, N-M+II ) = ONE CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ), \$ A, LDA, WORK ) CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA ) A( II, N-M+II ) = ONE - TAU( I ) * * Set A(m-k+i,n-k+i+1:n) to zero * DO 30 L = N - M + II + 1, N A( II, L ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of DORGR2 * END