1: *> \brief \b DORGR2
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORGR2 + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgr2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
22: *
23: * .. Scalar Arguments ..
24: * INTEGER INFO, K, 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: *> DORGR2 generates an m by n real matrix Q with orthonormal rows,
37: *> which is defined as the last m rows of a product of k elementary
38: *> reflectors of order n
39: *>
40: *> Q = H(1) H(2) . . . H(k)
41: *>
42: *> as returned by DGERQF.
43: *> \endverbatim
44: *
45: * Arguments:
46: * ==========
47: *
48: *> \param[in] M
49: *> \verbatim
50: *> M is INTEGER
51: *> The number of rows of the matrix Q. M >= 0.
52: *> \endverbatim
53: *>
54: *> \param[in] N
55: *> \verbatim
56: *> N is INTEGER
57: *> The number of columns of the matrix Q. N >= M.
58: *> \endverbatim
59: *>
60: *> \param[in] K
61: *> \verbatim
62: *> K is INTEGER
63: *> The number of elementary reflectors whose product defines the
64: *> matrix Q. M >= K >= 0.
65: *> \endverbatim
66: *>
67: *> \param[in,out] A
68: *> \verbatim
69: *> A is DOUBLE PRECISION array, dimension (LDA,N)
70: *> On entry, the (m-k+i)-th row must contain the vector which
71: *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72: *> returned by DGERQF in the last k rows of its array argument
73: *> A.
74: *> On exit, the m by n matrix Q.
75: *> \endverbatim
76: *>
77: *> \param[in] LDA
78: *> \verbatim
79: *> LDA is INTEGER
80: *> The first dimension of the array A. LDA >= max(1,M).
81: *> \endverbatim
82: *>
83: *> \param[in] TAU
84: *> \verbatim
85: *> TAU is DOUBLE PRECISION array, dimension (K)
86: *> TAU(i) must contain the scalar factor of the elementary
87: *> reflector H(i), as returned by DGERQF.
88: *> \endverbatim
89: *>
90: *> \param[out] WORK
91: *> \verbatim
92: *> WORK is DOUBLE PRECISION array, dimension (M)
93: *> \endverbatim
94: *>
95: *> \param[out] INFO
96: *> \verbatim
97: *> INFO is INTEGER
98: *> = 0: successful exit
99: *> < 0: if INFO = -i, the i-th argument has an illegal value
100: *> \endverbatim
101: *
102: * Authors:
103: * ========
104: *
105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
109: *
110: *> \date November 2011
111: *
112: *> \ingroup doubleOTHERcomputational
113: *
114: * =====================================================================
115: SUBROUTINE DORGR2( M, N, K, A, LDA, TAU, WORK, INFO )
116: *
117: * -- LAPACK computational routine (version 3.4.0) --
118: * -- LAPACK is a software package provided by Univ. of Tennessee, --
119: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
120: * November 2011
121: *
122: * .. Scalar Arguments ..
123: INTEGER INFO, K, LDA, M, N
124: * ..
125: * .. Array Arguments ..
126: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
127: * ..
128: *
129: * =====================================================================
130: *
131: * .. Parameters ..
132: DOUBLE PRECISION ONE, ZERO
133: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
134: * ..
135: * .. Local Scalars ..
136: INTEGER I, II, J, L
137: * ..
138: * .. External Subroutines ..
139: EXTERNAL DLARF, DSCAL, XERBLA
140: * ..
141: * .. Intrinsic Functions ..
142: INTRINSIC MAX
143: * ..
144: * .. Executable Statements ..
145: *
146: * Test the input arguments
147: *
148: INFO = 0
149: IF( M.LT.0 ) THEN
150: INFO = -1
151: ELSE IF( N.LT.M ) THEN
152: INFO = -2
153: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
154: INFO = -3
155: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
156: INFO = -5
157: END IF
158: IF( INFO.NE.0 ) THEN
159: CALL XERBLA( 'DORGR2', -INFO )
160: RETURN
161: END IF
162: *
163: * Quick return if possible
164: *
165: IF( M.LE.0 )
166: $ RETURN
167: *
168: IF( K.LT.M ) THEN
169: *
170: * Initialise rows 1:m-k to rows of the unit matrix
171: *
172: DO 20 J = 1, N
173: DO 10 L = 1, M - K
174: A( L, J ) = ZERO
175: 10 CONTINUE
176: IF( J.GT.N-M .AND. J.LE.N-K )
177: $ A( M-N+J, J ) = ONE
178: 20 CONTINUE
179: END IF
180: *
181: DO 40 I = 1, K
182: II = M - K + I
183: *
184: * Apply H(i) to A(1:m-k+i,1:n-k+i) from the right
185: *
186: A( II, N-M+II ) = ONE
187: CALL DLARF( 'Right', II-1, N-M+II, A( II, 1 ), LDA, TAU( I ),
188: $ A, LDA, WORK )
189: CALL DSCAL( N-M+II-1, -TAU( I ), A( II, 1 ), LDA )
190: A( II, N-M+II ) = ONE - TAU( I )
191: *
192: * Set A(m-k+i,n-k+i+1:n) to zero
193: *
194: DO 30 L = N - M + II + 1, N
195: A( II, L ) = ZERO
196: 30 CONTINUE
197: 40 CONTINUE
198: RETURN
199: *
200: * End of DORGR2
201: *
202: END
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