Annotation of rpl/lapack/lapack/dorg2r.f, revision 1.17
1.11 bertrand 1: *> \brief \b DORG2R generates all or part of the orthogonal matrix Q from a QR factorization determined by sgeqrf (unblocked algorithm).
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download DORG2R + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorg2r.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorg2r.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorg2r.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
1.15 bertrand 22: *
1.8 bertrand 23: * .. Scalar Arguments ..
24: * INTEGER INFO, K, LDA, M, N
25: * ..
26: * .. Array Arguments ..
27: * DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
28: * ..
1.15 bertrand 29: *
1.8 bertrand 30: *
31: *> \par Purpose:
32: * =============
33: *>
34: *> \verbatim
35: *>
36: *> DORG2R generates an m by n real matrix Q with orthonormal columns,
37: *> which is defined as the first n columns of a product of k elementary
38: *> reflectors of order m
39: *>
40: *> Q = H(1) H(2) . . . H(k)
41: *>
42: *> as returned by DGEQRF.
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. M >= N >= 0.
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. N >= 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 i-th column must contain the vector which
71: *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72: *> returned by DGEQRF in the first k columns of its array
73: *> argument 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 DGEQRF.
88: *> \endverbatim
89: *>
90: *> \param[out] WORK
91: *> \verbatim
92: *> WORK is DOUBLE PRECISION array, dimension (N)
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: *
1.15 bertrand 105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
1.8 bertrand 109: *
1.15 bertrand 110: *> \date December 2016
1.8 bertrand 111: *
112: *> \ingroup doubleOTHERcomputational
113: *
114: * =====================================================================
1.1 bertrand 115: SUBROUTINE DORG2R( M, N, K, A, LDA, TAU, WORK, INFO )
116: *
1.15 bertrand 117: * -- LAPACK computational routine (version 3.7.0) --
1.1 bertrand 118: * -- LAPACK is a software package provided by Univ. of Tennessee, --
119: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
1.15 bertrand 120: * December 2016
1.1 bertrand 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, 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.0 .OR. N.GT.M ) THEN
152: INFO = -2
153: ELSE IF( K.LT.0 .OR. K.GT.N ) 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( 'DORG2R', -INFO )
160: RETURN
161: END IF
162: *
163: * Quick return if possible
164: *
165: IF( N.LE.0 )
166: $ RETURN
167: *
168: * Initialise columns k+1:n to columns of the unit matrix
169: *
170: DO 20 J = K + 1, N
171: DO 10 L = 1, M
172: A( L, J ) = ZERO
173: 10 CONTINUE
174: A( J, J ) = ONE
175: 20 CONTINUE
176: *
177: DO 40 I = K, 1, -1
178: *
179: * Apply H(i) to A(i:m,i:n) from the left
180: *
181: IF( I.LT.N ) THEN
182: A( I, I ) = ONE
183: CALL DLARF( 'Left', M-I+1, N-I, A( I, I ), 1, TAU( I ),
184: $ A( I, I+1 ), LDA, WORK )
185: END IF
186: IF( I.LT.M )
187: $ CALL DSCAL( M-I, -TAU( I ), A( I+1, I ), 1 )
188: A( I, I ) = ONE - TAU( I )
189: *
190: * Set A(1:i-1,i) to zero
191: *
192: DO 30 L = 1, I - 1
193: A( L, I ) = ZERO
194: 30 CONTINUE
195: 40 CONTINUE
196: RETURN
197: *
198: * End of DORG2R
199: *
200: END
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