*> \brief \b CUNGL2 generates all or part of the unitary matrix Q from an LQ factorization determined by cgelqf (unblocked algorithm). * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CUNGL2 + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \endhtmlonly * * Definition: * =========== * * SUBROUTINE CUNGL2( M, N, K, A, LDA, TAU, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, K, LDA, M, N * .. * .. Array Arguments .. * COMPLEX A( LDA, * ), TAU( * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CUNGL2 generates an m-by-n complex matrix Q with orthonormal rows, *> which is defined as the first m rows of a product of k elementary *> reflectors of order n *> *> Q = H(k)**H . . . H(2)**H H(1)**H *> *> as returned by CGELQF. *> \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 COMPLEX array, dimension (LDA,N) *> On entry, the i-th row must contain the vector which defines *> the elementary reflector H(i), for i = 1,2,...,k, as returned *> by CGELQF in the first 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 COMPLEX array, dimension (K) *> TAU(i) must contain the scalar factor of the elementary *> reflector H(i), as returned by CGELQF. *> \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 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 complexOTHERcomputational * * ===================================================================== SUBROUTINE CUNGL2( 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 .. COMPLEX A( LDA, * ), TAU( * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX ONE, ZERO PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), \$ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. INTEGER I, J, L * .. * .. External Subroutines .. EXTERNAL CLACGV, CLARF, CSCAL, XERBLA * .. * .. Intrinsic Functions .. INTRINSIC CONJG, 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( 'CUNGL2', -INFO ) RETURN END IF * * Quick return if possible * IF( M.LE.0 ) \$ RETURN * IF( K.LT.M ) THEN * * Initialise rows k+1:m to rows of the unit matrix * DO 20 J = 1, N DO 10 L = K + 1, M A( L, J ) = ZERO 10 CONTINUE IF( J.GT.K .AND. J.LE.M ) \$ A( J, J ) = ONE 20 CONTINUE END IF * DO 40 I = K, 1, -1 * * Apply H(i)**H to A(i:m,i:n) from the right * IF( I.LT.N ) THEN CALL CLACGV( N-I, A( I, I+1 ), LDA ) IF( I.LT.M ) THEN A( I, I ) = ONE CALL CLARF( 'Right', M-I, N-I+1, A( I, I ), LDA, \$ CONJG( TAU( I ) ), A( I+1, I ), LDA, WORK ) END IF CALL CSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA ) CALL CLACGV( N-I, A( I, I+1 ), LDA ) END IF A( I, I ) = ONE - CONJG( TAU( I ) ) * * Set A(i,1:i-1,i) to zero * DO 30 L = 1, I - 1 A( I, L ) = ZERO 30 CONTINUE 40 CONTINUE RETURN * * End of CUNGL2 * END