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C DGEQR2    SOURCE    BP208322  18/07/10    21:15:01     9872           *> \brief \b DGEQR2 computes the QR factorization of a general rectangular matrix using an unblocked algorithm.**  =========== DOCUMENTATION ===========** Online html documentation available at*            http://www.netlib.org/lapack/explore-html/**> \htmlonly*> Download DGEQR2 + dependencies*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgeqr2.f">*> [TGZ]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgeqr2.f">*> [ZIP]&lt;/a>*> &lt;a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgeqr2.f">*> [TXT]&lt;/a>*> \endhtmlonly**  Definition:*  ===========**       SUBROUTINE DGEQR2( M, N, A, LDA, TAU, WORK, INFO )**       .. Scalar Arguments ..*       INTEGER            INFO, LDA, M, N*       ..*       .. Array Arguments ..*       REAL*8   A( LDA, * ), TAU( * ), WORK( * )*       ..***> \par Purpose:*  =============*>*> \verbatim*>*> DGEQR2 computes a QR factorization of a real m by n matrix A:*> A = Q * R.*> \endverbatim**  Arguments:*  ==========**> \param[in] M*> \verbatim*>          M is INTEGER*>          The number of rows of the matrix A.  M >= 0.*> \endverbatim*>*> \param[in] N*> \verbatim*>          N is INTEGER*>          The number of columns of the matrix A.  N >= 0.*> \endverbatim*>*> \param[in,out] A*> \verbatim*>          A is DOUBLE PRECISION array, dimension (LDA,N)*>          On entry, the m by n matrix A.*>          On exit, the elements on and above the diagonal of the array*>          contain the min(m,n) by n upper trapezoidal matrix R (R is*>          upper triangular if m >= n); the elements below the diagonal,*>          with the array TAU, represent the orthogonal matrix Q as a*>          product of elementary reflectors (see Further Details).*> \endverbatim*>*> \param[in] LDA*> \verbatim*>          LDA is INTEGER*>          The leading dimension of the array A.  LDA >= max(1,M).*> \endverbatim*>*> \param[out] TAU*> \verbatim*>          TAU is DOUBLE PRECISION array, dimension (min(M,N))*>          The scalar factors of the elementary reflectors (see Further*>          Details).*> \endverbatim*>*> \param[out] WORK*> \verbatim*>          WORK is DOUBLE PRECISION array, dimension (N)*> \endverbatim*>*> \param[out] INFO*> \verbatim*>          INFO is INTEGER*>          = 0: successful exit*>          &lt; 0: if INFO = -i, the i-th argument had 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 doubleGEcomputational**> \par Further Details:*  =====================*>*> \verbatim*>*>  The matrix Q is represented as a product of elementary reflectors*>*>     Q = H(1) H(2) . . . H(k), where k = min(m,n).*>*>  Each H(i) has the form*>*>     H(i) = I - tau * v * v**T*>*>  where tau is a real scalar, and v is a real vector with*>  v(1:i-1) = 0 and v(i) = 1; v(i+1:m) is stored on exit in A(i+1:m,i),*>  and tau in TAU(i).*> \endverbatim*>*  =====================================================================      SUBROUTINE DGEQR2( M, N, 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, LDA, M, N*     ..*     .. Array Arguments ..      REAL*8   A( LDA, * ), TAU( * ), WORK( * )*     ..**  =====================================================================**     .. Parameters ..      REAL*8   ONE      PARAMETER          ( ONE = 1.0D+0 )*     ..*     .. Local Scalars ..      INTEGER            I, K      REAL*8   AII*     ..*     .. External Subroutines ..      EXTERNAL           DLARF, DLARFG, XERBLA*     ..**     .. Intrinsic Functions ..*      INTRINSIC          MAX, MIN**     ..**     .. Executable Statements ..**     Test the input arguments*      INFO = 0      IF( M.LT.0 ) THEN         INFO = -1      ELSE IF( N.LT.0 ) THEN         INFO = -2      ELSE IF( LDA.LT.MAX( 1, M ) ) THEN         INFO = -4      END IF      IF( INFO.NE.0 ) THEN         CALL XERBLA( 'DGEQR2', -INFO )         RETURN      END IF*      K = MIN( M, N )*      DO 10 I = 1, K**        Generate elementary reflector H(i) to annihilate A(i+1:m,i)*         CALL DLARFG( M-I+1, A( I, I ), A( MIN( I+1, M ), I ), 1,     $TAU( I ) ) IF( I.LT.N ) THEN** Apply H(i) to A(i:m,i+1:n) from the left* AII = A( I, I ) A( I, I ) = ONE CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),$                  A( I, I+1 ), LDA, WORK )            A( I, I ) = AII         END IF   10 CONTINUE      RETURN**     End of DGEQR2*      END

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