Annotation of rpl/lapack/lapack/dorg2l.f, revision 1.14
1.11 bertrand 1: *> \brief \b DORG2L generates all or part of the orthogonal matrix Q from a QL factorization determined by sgeqlf (unblocked algorithm).
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORG2L + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorg2l.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorg2l.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorg2l.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORG2L( 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: *> DORG2L generates an m by n real matrix Q with orthonormal columns,
37: *> which is defined as the last n columns of a product of k elementary
38: *> reflectors of order m
39: *>
40: *> Q = H(k) . . . H(2) H(1)
41: *>
42: *> as returned by DGEQLF.
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 (n-k+i)-th column must contain the vector which
71: *> defines the elementary reflector H(i), for i = 1,2,...,k, as
72: *> returned by DGEQLF in the last 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 DGEQLF.
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: *
105: *> \author Univ. of Tennessee
106: *> \author Univ. of California Berkeley
107: *> \author Univ. of Colorado Denver
108: *> \author NAG Ltd.
109: *
1.11 bertrand 110: *> \date September 2012
1.8 bertrand 111: *
112: *> \ingroup doubleOTHERcomputational
113: *
114: * =====================================================================
1.1 bertrand 115: SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
116: *
1.11 bertrand 117: * -- LAPACK computational routine (version 3.4.2) --
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..--
1.11 bertrand 120: * September 2012
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, 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.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( 'DORG2L', -INFO )
160: RETURN
161: END IF
162: *
163: * Quick return if possible
164: *
165: IF( N.LE.0 )
166: $ RETURN
167: *
168: * Initialise columns 1:n-k to columns of the unit matrix
169: *
170: DO 20 J = 1, N - K
171: DO 10 L = 1, M
172: A( L, J ) = ZERO
173: 10 CONTINUE
174: A( M-N+J, J ) = ONE
175: 20 CONTINUE
176: *
177: DO 40 I = 1, K
178: II = N - K + I
179: *
180: * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
181: *
182: A( M-N+II, II ) = ONE
183: CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
184: $ LDA, WORK )
185: CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
186: A( M-N+II, II ) = ONE - TAU( I )
187: *
188: * Set A(m-k+i+1:m,n-k+i) to zero
189: *
190: DO 30 L = M - N + II + 1, M
191: A( L, II ) = ZERO
192: 30 CONTINUE
193: 40 CONTINUE
194: RETURN
195: *
196: * End of DORG2L
197: *
198: END
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