*> \brief \b CGELQ2 computes the LQ 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 CGELQ2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * COMPLEX A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CGELQ2 computes an LQ factorization of a complex m by n matrix A: *> A = L * Q. *> \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 COMPLEX array, dimension (LDA,N) *> On entry, the m by n matrix A. *> On exit, the elements on and below the diagonal of the array *> contain the m by min(m,n) lower trapezoidal matrix L (L is *> lower triangular if m <= n); the elements above the diagonal, *> with the array TAU, represent the unitary 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 COMPLEX array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX array, dimension (M) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 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 complexGEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of elementary reflectors *> *> Q = H(k)**H . . . H(2)**H H(1)**H, where k = min(m,n). *> *> Each H(i) has the form *> *> H(i) = I - tau * v * v**H *> *> where tau is a complex scalar, and v is a complex vector with *> v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in *> A(i,i+1:n), and tau in TAU(i). *> \endverbatim *> * ===================================================================== SUBROUTINE CGELQ2( 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 .. COMPLEX A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ONE PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, K COMPLEX ALPHA * .. * .. External Subroutines .. EXTERNAL CLACGV, CLARF, CLARFG, 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( 'CGELQ2', -INFO ) RETURN END IF * K = MIN( M, N ) * DO 10 I = 1, K * * Generate elementary reflector H(i) to annihilate A(i,i+1:n) * CALL CLACGV( N-I+1, A( I, I ), LDA ) ALPHA = A( I, I ) CALL CLARFG( N-I+1, ALPHA, A( I, MIN( I+1, N ) ), LDA, \$ TAU( I ) ) IF( I.LT.M ) THEN * * Apply H(i) to A(i+1:m,i:n) from the right * A( I, I ) = ONE CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, TAU( I ), \$ A( I+1, I ), LDA, WORK ) END IF A( I, I ) = ALPHA CALL CLACGV( N-I+1, A( I, I ), LDA ) 10 CONTINUE RETURN * * End of CGELQ2 * END