1: *> \brief \b DORGL2
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download DORGL2 + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dorgl2.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dorgl2.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dorgl2.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORGL2( 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: *> DORGL2 generates an m by n real matrix Q with orthonormal rows,
37: *> which is defined as the first m rows of a product of k elementary
38: *> reflectors of order n
39: *>
40: *> Q = H(k) . . . H(2) H(1)
41: *>
42: *> as returned by DGELQF.
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 i-th row must contain the vector which defines
71: *> the elementary reflector H(i), for i = 1,2,...,k, as returned
72: *> by DGELQF in the first k rows of its array argument A.
73: *> On exit, the m-by-n matrix Q.
74: *> \endverbatim
75: *>
76: *> \param[in] LDA
77: *> \verbatim
78: *> LDA is INTEGER
79: *> The first dimension of the array A. LDA >= max(1,M).
80: *> \endverbatim
81: *>
82: *> \param[in] TAU
83: *> \verbatim
84: *> TAU is DOUBLE PRECISION array, dimension (K)
85: *> TAU(i) must contain the scalar factor of the elementary
86: *> reflector H(i), as returned by DGELQF.
87: *> \endverbatim
88: *>
89: *> \param[out] WORK
90: *> \verbatim
91: *> WORK is DOUBLE PRECISION array, dimension (M)
92: *> \endverbatim
93: *>
94: *> \param[out] INFO
95: *> \verbatim
96: *> INFO is INTEGER
97: *> = 0: successful exit
98: *> < 0: if INFO = -i, the i-th argument has an illegal value
99: *> \endverbatim
100: *
101: * Authors:
102: * ========
103: *
104: *> \author Univ. of Tennessee
105: *> \author Univ. of California Berkeley
106: *> \author Univ. of Colorado Denver
107: *> \author NAG Ltd.
108: *
109: *> \date November 2011
110: *
111: *> \ingroup doubleOTHERcomputational
112: *
113: * =====================================================================
114: SUBROUTINE DORGL2( M, N, K, A, LDA, TAU, WORK, INFO )
115: *
116: * -- LAPACK computational routine (version 3.4.0) --
117: * -- LAPACK is a software package provided by Univ. of Tennessee, --
118: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
119: * November 2011
120: *
121: * .. Scalar Arguments ..
122: INTEGER INFO, K, LDA, M, N
123: * ..
124: * .. Array Arguments ..
125: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
126: * ..
127: *
128: * =====================================================================
129: *
130: * .. Parameters ..
131: DOUBLE PRECISION ONE, ZERO
132: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
133: * ..
134: * .. Local Scalars ..
135: INTEGER I, J, L
136: * ..
137: * .. External Subroutines ..
138: EXTERNAL DLARF, DSCAL, XERBLA
139: * ..
140: * .. Intrinsic Functions ..
141: INTRINSIC MAX
142: * ..
143: * .. Executable Statements ..
144: *
145: * Test the input arguments
146: *
147: INFO = 0
148: IF( M.LT.0 ) THEN
149: INFO = -1
150: ELSE IF( N.LT.M ) THEN
151: INFO = -2
152: ELSE IF( K.LT.0 .OR. K.GT.M ) THEN
153: INFO = -3
154: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
155: INFO = -5
156: END IF
157: IF( INFO.NE.0 ) THEN
158: CALL XERBLA( 'DORGL2', -INFO )
159: RETURN
160: END IF
161: *
162: * Quick return if possible
163: *
164: IF( M.LE.0 )
165: $ RETURN
166: *
167: IF( K.LT.M ) THEN
168: *
169: * Initialise rows k+1:m to rows of the unit matrix
170: *
171: DO 20 J = 1, N
172: DO 10 L = K + 1, M
173: A( L, J ) = ZERO
174: 10 CONTINUE
175: IF( J.GT.K .AND. J.LE.M )
176: $ A( J, J ) = ONE
177: 20 CONTINUE
178: END IF
179: *
180: DO 40 I = K, 1, -1
181: *
182: * Apply H(i) to A(i:m,i:n) from the right
183: *
184: IF( I.LT.N ) THEN
185: IF( I.LT.M ) THEN
186: A( I, I ) = ONE
187: CALL DLARF( 'Right', M-I, N-I+1, A( I, I ), LDA,
188: $ TAU( I ), A( I+1, I ), LDA, WORK )
189: END IF
190: CALL DSCAL( N-I, -TAU( I ), A( I, I+1 ), LDA )
191: END IF
192: A( I, I ) = ONE - TAU( I )
193: *
194: * Set A(i,1:i-1) to zero
195: *
196: DO 30 L = 1, I - 1
197: A( I, L ) = ZERO
198: 30 CONTINUE
199: 40 CONTINUE
200: RETURN
201: *
202: * End of DORGL2
203: *
204: END
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