*> \brief \b ZGEQL2 computes the QL 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 ZGEQL2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, LDA, M, N * .. * .. Array Arguments .. * COMPLEX*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZGEQL2 computes a QL factorization of a complex m by n matrix A: *> A = Q * L. *> \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*16 array, dimension (LDA,N) *> On entry, the m by n matrix A. *> On exit, if m >= n, the lower triangle of the subarray *> A(m-n+1:m,1:n) contains the n by n lower triangular matrix L; *> if m <= n, the elements on and below the (n-m)-th *> superdiagonal contain the m by n lower trapezoidal matrix L; *> the remaining elements, 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*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors (see Further *> Details). *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (N) *> \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 complex16GEcomputational * *> \par Further Details: * ===================== *> *> \verbatim *> *> The matrix Q is represented as a product of elementary reflectors *> *> Q = H(k) . . . H(2) H(1), 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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in *> A(1:m-k+i-1,n-k+i), and tau in TAU(i). *> \endverbatim *> * ===================================================================== SUBROUTINE ZGEQL2( 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*16 A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ONE PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, K COMPLEX*16 ALPHA * .. * .. External Subroutines .. EXTERNAL XERBLA, ZLARF, ZLARFG * .. * .. Intrinsic Functions .. INTRINSIC DCONJG, 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( 'ZGEQL2', -INFO ) RETURN END IF * K = MIN( M, N ) * DO 10 I = K, 1, -1 * * Generate elementary reflector H(i) to annihilate * A(1:m-k+i-1,n-k+i) * ALPHA = A( M-K+I, N-K+I ) CALL ZLARFG( M-K+I, ALPHA, A( 1, N-K+I ), 1, TAU( I ) ) * * Apply H(i)**H to A(1:m-k+i,1:n-k+i-1) from the left * A( M-K+I, N-K+I ) = ONE CALL ZLARF( 'Left', M-K+I, N-K+I-1, A( 1, N-K+I ), 1, \$ DCONJG( TAU( I ) ), A, LDA, WORK ) A( M-K+I, N-K+I ) = ALPHA 10 CONTINUE RETURN * * End of ZGEQL2 * END