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dorg2l
C DORG2L    SOURCE    BP208322  22/09/16    21:15:04     11454          *> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).**  =========== DOCUMENTATION ===========** Online html documentation available at*            http://www.netlib.org/lapack/explore-html/**> \htmlonly*> Download DORG2L + dependencies*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorg2l.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorg2l.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorg2l.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )**       .. Scalar Arguments ..*       INTEGER            INFO, K, LDA, M, N*       ..*       .. Array Arguments ..*       REAL*8   A( LDA, * ), TAU( * ), WORK( * )*       ..***> \par Purpose:*  =============*>*> \verbatim*>*> DORG2L generates an m by n real matrix Q with orthonormal columns,*> which is defined as the last n columns of a product of k elementary*> reflectors of order m*>*>       Q  =  H(k) . . . H(2) H(1)*>*> as returned by DGEQLF.*> \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. M >= N >= 0.*> \endverbatim*>*> \param[in] K*> \verbatim*>          K is INTEGER*>          The number of elementary reflectors whose product defines the*>          matrix Q. N >= K >= 0.*> \endverbatim*>*> \param[in,out] A*> \verbatim*>          A is REAL*8 array, dimension (LDA,N)*>          On entry, the (n-k+i)-th column must contain the vector which*>          defines the elementary reflector H(i), for i = 1,2,...,k, as*>          returned by DGEQLF in the last k columns 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 REAL*8 array, dimension (K)*>          TAU(i) must contain the scalar factor of the elementary*>          reflector H(i), as returned by DGEQLF.*> \endverbatim*>*> \param[out] WORK*> \verbatim*>          WORK is REAL*8 array, dimension (N)*> \endverbatim*>*> \param[out] INFO*> \verbatim*>          INFO is INTEGER*>          = 0: successful exit*>          &lt; 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.**> \ingroup doubleOTHERcomputational**  =====================================================================      SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )**  -- LAPACK computational routine --*  -- LAPACK is a software package provided by Univ. of Tennessee,    --*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--**     .. Scalar Arguments ..      INTEGER            INFO, K, LDA, M, N*     ..*     .. Array Arguments ..      REAL*8   A( LDA, * ), TAU( * ), WORK( * )*     ..**  =====================================================================**     .. Parameters ..      REAL*8   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.0 .OR. N.GT.M ) THEN         INFO = -2      ELSE IF( K.LT.0 .OR. K.GT.N ) THEN         INFO = -3      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN         INFO = -5      END IF      IF( INFO.NE.0 ) THEN         CALL XERBLA( 'DORG2L', -INFO )         RETURN      END IF**     Quick return if possible*      IF( N.LE.0 )     $RETURN** Initialise columns 1:n-k to columns of the unit matrix* DO 20 J = 1, N - K DO 10 L = 1, M A( L, J ) = ZERO 10 CONTINUE A( M-N+J, J ) = ONE 20 CONTINUE* DO 40 I = 1, K II = N - K + I** Apply H(i) to A(1:m-k+i,1:n-k+i) from the left* A( M-N+II, II ) = ONE CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,$               LDA, WORK )         CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )         A( M-N+II, II ) = ONE - TAU( I )**        Set A(m-k+i+1:m,n-k+i) to zero*         DO 30 L = M - N + II + 1, M            A( L, II ) = ZERO   30    CONTINUE   40 CONTINUE      RETURN**     End of DORG2L*      END  

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