1 *> \brief \b CGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
3 * =========== DOCUMENTATION ===========
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
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21 * SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )
23 * .. Scalar Arguments ..
24 * INTEGER INFO, LDA, M, N
26 * .. Array Arguments ..
27 * COMPLEX A( LDA, * ), TAU( * ), WORK( * )
36 *> CGERQ2 computes an RQ factorization of a complex m by n matrix A:
46 *> The number of rows of the matrix A. M >= 0.
52 *> The number of columns of the matrix A. N >= 0.
57 *> A is COMPLEX array, dimension (LDA,N)
58 *> On entry, the m by n matrix A.
59 *> On exit, if m <= n, the upper triangle of the subarray
60 *> A(1:m,n-m+1:n) contains the m by m upper triangular matrix R;
61 *> if m >= n, the elements on and above the (m-n)-th subdiagonal
62 *> contain the m by n upper trapezoidal matrix R; the remaining
63 *> elements, with the array TAU, represent the unitary matrix
64 *> Q as a product of elementary reflectors (see Further
71 *> The leading dimension of the array A. LDA >= max(1,M).
76 *> TAU is COMPLEX array, dimension (min(M,N))
77 *> The scalar factors of the elementary reflectors (see Further
83 *> WORK is COMPLEX array, dimension (M)
89 *> = 0: successful exit
90 *> < 0: if INFO = -i, the i-th argument had an illegal value
96 *> \author Univ. of Tennessee
97 *> \author Univ. of California Berkeley
98 *> \author Univ. of Colorado Denver
101 *> \date September 2012
103 *> \ingroup complexGEcomputational
105 *> \par Further Details:
106 * =====================
110 *> The matrix Q is represented as a product of elementary reflectors
112 *> Q = H(1)**H H(2)**H . . . H(k)**H, where k = min(m,n).
114 *> Each H(i) has the form
116 *> H(i) = I - tau * v * v**H
118 *> where tau is a complex scalar, and v is a complex vector with
119 *> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; conjg(v(1:n-k+i-1)) is stored on
120 *> exit in A(m-k+i,1:n-k+i-1), and tau in TAU(i).
123 * =====================================================================
124 SUBROUTINE CGERQ2( M, N, A, LDA, TAU, WORK, INFO )
126 * -- LAPACK computational routine (version 3.4.2) --
127 * -- LAPACK is a software package provided by Univ. of Tennessee, --
128 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
131 * .. Scalar Arguments ..
132 INTEGER INFO, LDA, M, N
134 * .. Array Arguments ..
135 COMPLEX A( LDA, * ), TAU( * ), WORK( * )
138 * =====================================================================
142 PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ) )
144 * .. Local Scalars ..
148 * .. External Subroutines ..
149 EXTERNAL CLACGV, CLARF, CLARFG, XERBLA
151 * .. Intrinsic Functions ..
154 * .. Executable Statements ..
156 * Test the input arguments
161 ELSE IF( N.LT.0 ) THEN
163 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
167 CALL XERBLA( 'CGERQ2', -INFO )
175 * Generate elementary reflector H(i) to annihilate
178 CALL CLACGV( N-K+I, A( M-K+I, 1 ), LDA )
179 ALPHA = A( M-K+I, N-K+I )
180 CALL CLARFG( N-K+I, ALPHA, A( M-K+I, 1 ), LDA,
183 * Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
185 A( M-K+I, N-K+I ) = ONE
186 CALL CLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
187 $ TAU( I ), A, LDA, WORK )
188 A( M-K+I, N-K+I ) = ALPHA
189 CALL CLACGV( N-K+I-1, A( M-K+I, 1 ), LDA )