1: *> \brief \b DGERQ2 computes the RQ factorization of a general rectangular matrix using an unblocked algorithm.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DGERQ2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dgerq2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dgerq2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dgerq2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, LDA, M, N
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
28: * ..
29: *
30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DGERQ2 computes an RQ factorization of a real m by n matrix A:
37: *> A = R * Q.
38: *> \endverbatim
39: *
40: * Arguments:
41: * ==========
42: *
43: *> \param[in] M
44: *> \verbatim
45: *> M is INTEGER
46: *> The number of rows of the matrix A. M >= 0.
47: *> \endverbatim
48: *>
49: *> \param[in] N
50: *> \verbatim
51: *> N is INTEGER
52: *> The number of columns of the matrix A. N >= 0.
53: *> \endverbatim
54: *>
55: *> \param[in,out] A
56: *> \verbatim
57: *> A is DOUBLE PRECISION 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 orthogonal matrix
64: *> Q as a product of elementary reflectors (see Further
65: *> Details).
66: *> \endverbatim
67: *>
68: *> \param[in] LDA
69: *> \verbatim
70: *> LDA is INTEGER
71: *> The leading dimension of the array A. LDA >= max(1,M).
72: *> \endverbatim
73: *>
74: *> \param[out] TAU
75: *> \verbatim
76: *> TAU is DOUBLE PRECISION array, dimension (min(M,N))
77: *> The scalar factors of the elementary reflectors (see Further
78: *> Details).
79: *> \endverbatim
80: *>
81: *> \param[out] WORK
82: *> \verbatim
83: *> WORK is DOUBLE PRECISION array, dimension (M)
84: *> \endverbatim
85: *>
86: *> \param[out] INFO
87: *> \verbatim
88: *> INFO is INTEGER
89: *> = 0: successful exit
90: *> < 0: if INFO = -i, the i-th argument had an illegal value
91: *> \endverbatim
92: *
93: * Authors:
94: * ========
95: *
96: *> \author Univ. of Tennessee
97: *> \author Univ. of California Berkeley
98: *> \author Univ. of Colorado Denver
99: *> \author NAG Ltd.
100: *
101: *> \date September 2012
102: *
103: *> \ingroup doubleGEcomputational
104: *
105: *> \par Further Details:
106: * =====================
107: *>
108: *> \verbatim
109: *>
110: *> The matrix Q is represented as a product of elementary reflectors
111: *>
112: *> Q = H(1) H(2) . . . H(k), where k = min(m,n).
113: *>
114: *> Each H(i) has the form
115: *>
116: *> H(i) = I - tau * v * v**T
117: *>
118: *> where tau is a real scalar, and v is a real vector with
119: *> v(n-k+i+1:n) = 0 and v(n-k+i) = 1; v(1:n-k+i-1) is stored on exit in
120: *> A(m-k+i,1:n-k+i-1), and tau in TAU(i).
121: *> \endverbatim
122: *>
123: * =====================================================================
124: SUBROUTINE DGERQ2( M, N, A, LDA, TAU, WORK, INFO )
125: *
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..--
129: * September 2012
130: *
131: * .. Scalar Arguments ..
132: INTEGER INFO, LDA, M, N
133: * ..
134: * .. Array Arguments ..
135: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
136: * ..
137: *
138: * =====================================================================
139: *
140: * .. Parameters ..
141: DOUBLE PRECISION ONE
142: PARAMETER ( ONE = 1.0D+0 )
143: * ..
144: * .. Local Scalars ..
145: INTEGER I, K
146: DOUBLE PRECISION AII
147: * ..
148: * .. External Subroutines ..
149: EXTERNAL DLARF, DLARFG, XERBLA
150: * ..
151: * .. Intrinsic Functions ..
152: INTRINSIC MAX, MIN
153: * ..
154: * .. Executable Statements ..
155: *
156: * Test the input arguments
157: *
158: INFO = 0
159: IF( M.LT.0 ) THEN
160: INFO = -1
161: ELSE IF( N.LT.0 ) THEN
162: INFO = -2
163: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
164: INFO = -4
165: END IF
166: IF( INFO.NE.0 ) THEN
167: CALL XERBLA( 'DGERQ2', -INFO )
168: RETURN
169: END IF
170: *
171: K = MIN( M, N )
172: *
173: DO 10 I = K, 1, -1
174: *
175: * Generate elementary reflector H(i) to annihilate
176: * A(m-k+i,1:n-k+i-1)
177: *
178: CALL DLARFG( N-K+I, A( M-K+I, N-K+I ), A( M-K+I, 1 ), LDA,
179: $ TAU( I ) )
180: *
181: * Apply H(i) to A(1:m-k+i-1,1:n-k+i) from the right
182: *
183: AII = A( M-K+I, N-K+I )
184: A( M-K+I, N-K+I ) = ONE
185: CALL DLARF( 'Right', M-K+I-1, N-K+I, A( M-K+I, 1 ), LDA,
186: $ TAU( I ), A, LDA, WORK )
187: A( M-K+I, N-K+I ) = AII
188: 10 CONTINUE
189: RETURN
190: *
191: * End of DGERQ2
192: *
193: END
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