Annotation of rpl/lapack/lapack/dorg2l.f, revision 1.18
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: *
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 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">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE DORG2L( 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: *> 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: *
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: *
110: *> \ingroup doubleOTHERcomputational
111: *
112: * =====================================================================
1.1 bertrand 113: SUBROUTINE DORG2L( M, N, K, A, LDA, TAU, WORK, INFO )
114: *
1.18 ! bertrand 115: * -- LAPACK computational routine --
1.1 bertrand 116: * -- LAPACK is a software package provided by Univ. of Tennessee, --
117: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
118: *
119: * .. Scalar Arguments ..
120: INTEGER INFO, K, LDA, M, N
121: * ..
122: * .. Array Arguments ..
123: DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
124: * ..
125: *
126: * =====================================================================
127: *
128: * .. Parameters ..
129: DOUBLE PRECISION ONE, ZERO
130: PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
131: * ..
132: * .. Local Scalars ..
133: INTEGER I, II, J, L
134: * ..
135: * .. External Subroutines ..
136: EXTERNAL DLARF, DSCAL, XERBLA
137: * ..
138: * .. Intrinsic Functions ..
139: INTRINSIC MAX
140: * ..
141: * .. Executable Statements ..
142: *
143: * Test the input arguments
144: *
145: INFO = 0
146: IF( M.LT.0 ) THEN
147: INFO = -1
148: ELSE IF( N.LT.0 .OR. N.GT.M ) THEN
149: INFO = -2
150: ELSE IF( K.LT.0 .OR. K.GT.N ) THEN
151: INFO = -3
152: ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
153: INFO = -5
154: END IF
155: IF( INFO.NE.0 ) THEN
156: CALL XERBLA( 'DORG2L', -INFO )
157: RETURN
158: END IF
159: *
160: * Quick return if possible
161: *
162: IF( N.LE.0 )
163: $ RETURN
164: *
165: * Initialise columns 1:n-k to columns of the unit matrix
166: *
167: DO 20 J = 1, N - K
168: DO 10 L = 1, M
169: A( L, J ) = ZERO
170: 10 CONTINUE
171: A( M-N+J, J ) = ONE
172: 20 CONTINUE
173: *
174: DO 40 I = 1, K
175: II = N - K + I
176: *
177: * Apply H(i) to A(1:m-k+i,1:n-k+i) from the left
178: *
179: A( M-N+II, II ) = ONE
180: CALL DLARF( 'Left', M-N+II, II-1, A( 1, II ), 1, TAU( I ), A,
181: $ LDA, WORK )
182: CALL DSCAL( M-N+II-1, -TAU( I ), A( 1, II ), 1 )
183: A( M-N+II, II ) = ONE - TAU( I )
184: *
185: * Set A(m-k+i+1:m,n-k+i) to zero
186: *
187: DO 30 L = M - N + II + 1, M
188: A( L, II ) = ZERO
189: 30 CONTINUE
190: 40 CONTINUE
191: RETURN
192: *
193: * End of DORG2L
194: *
195: END
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