LAPACK  3.10.0
LAPACK: Linear Algebra PACKage
dorm2r.f
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1 *> \brief \b DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sgeqrf (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
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15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE DORM2R( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
22 * WORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS
26 * INTEGER INFO, K, LDA, LDC, M, N
27 * ..
28 * .. Array Arguments ..
29 * DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> DORM2R overwrites the general real m by n matrix C with
39 *>
40 *> Q * C if SIDE = 'L' and TRANS = 'N', or
41 *>
42 *> Q**T* C if SIDE = 'L' and TRANS = 'T', or
43 *>
44 *> C * Q if SIDE = 'R' and TRANS = 'N', or
45 *>
46 *> C * Q**T if SIDE = 'R' and TRANS = 'T',
47 *>
48 *> where Q is a real orthogonal matrix defined as the product of k
49 *> elementary reflectors
50 *>
51 *> Q = H(1) H(2) . . . H(k)
52 *>
53 *> as returned by DGEQRF. Q is of order m if SIDE = 'L' and of order n
54 *> if SIDE = 'R'.
55 *> \endverbatim
56 *
57 * Arguments:
58 * ==========
59 *
60 *> \param[in] SIDE
61 *> \verbatim
62 *> SIDE is CHARACTER*1
63 *> = 'L': apply Q or Q**T from the Left
64 *> = 'R': apply Q or Q**T from the Right
65 *> \endverbatim
66 *>
67 *> \param[in] TRANS
68 *> \verbatim
69 *> TRANS is CHARACTER*1
70 *> = 'N': apply Q (No transpose)
71 *> = 'T': apply Q**T (Transpose)
72 *> \endverbatim
73 *>
74 *> \param[in] M
75 *> \verbatim
76 *> M is INTEGER
77 *> The number of rows of the matrix C. M >= 0.
78 *> \endverbatim
79 *>
80 *> \param[in] N
81 *> \verbatim
82 *> N is INTEGER
83 *> The number of columns of the matrix C. N >= 0.
84 *> \endverbatim
85 *>
86 *> \param[in] K
87 *> \verbatim
88 *> K is INTEGER
89 *> The number of elementary reflectors whose product defines
90 *> the matrix Q.
91 *> If SIDE = 'L', M >= K >= 0;
92 *> if SIDE = 'R', N >= K >= 0.
93 *> \endverbatim
94 *>
95 *> \param[in] A
96 *> \verbatim
97 *> A is DOUBLE PRECISION array, dimension (LDA,K)
98 *> The i-th column must contain the vector which defines the
99 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
100 *> DGEQRF in the first k columns of its array argument A.
101 *> A is modified by the routine but restored on exit.
102 *> \endverbatim
103 *>
104 *> \param[in] LDA
105 *> \verbatim
106 *> LDA is INTEGER
107 *> The leading dimension of the array A.
108 *> If SIDE = 'L', LDA >= max(1,M);
109 *> if SIDE = 'R', LDA >= max(1,N).
110 *> \endverbatim
111 *>
112 *> \param[in] TAU
113 *> \verbatim
114 *> TAU is DOUBLE PRECISION array, dimension (K)
115 *> TAU(i) must contain the scalar factor of the elementary
116 *> reflector H(i), as returned by DGEQRF.
117 *> \endverbatim
118 *>
119 *> \param[in,out] C
120 *> \verbatim
121 *> C is DOUBLE PRECISION array, dimension (LDC,N)
122 *> On entry, the m by n matrix C.
123 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
124 *> \endverbatim
125 *>
126 *> \param[in] LDC
127 *> \verbatim
128 *> LDC is INTEGER
129 *> The leading dimension of the array C. LDC >= max(1,M).
130 *> \endverbatim
131 *>
132 *> \param[out] WORK
133 *> \verbatim
134 *> WORK is DOUBLE PRECISION array, dimension
135 *> (N) if SIDE = 'L',
136 *> (M) if SIDE = 'R'
137 *> \endverbatim
138 *>
139 *> \param[out] INFO
140 *> \verbatim
141 *> INFO is INTEGER
142 *> = 0: successful exit
143 *> < 0: if INFO = -i, the i-th argument had an illegal value
144 *> \endverbatim
145 *
146 * Authors:
147 * ========
148 *
149 *> \author Univ. of Tennessee
150 *> \author Univ. of California Berkeley
151 *> \author Univ. of Colorado Denver
152 *> \author NAG Ltd.
153 *
154 *> \ingroup doubleOTHERcomputational
155 *
156 * =====================================================================
157  SUBROUTINE dorm2r( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
158  $ WORK, INFO )
159 *
160 * -- LAPACK computational routine --
161 * -- LAPACK is a software package provided by Univ. of Tennessee, --
162 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163 *
164 * .. Scalar Arguments ..
165  CHARACTER SIDE, TRANS
166  INTEGER INFO, K, LDA, LDC, M, N
167 * ..
168 * .. Array Arguments ..
169  DOUBLE PRECISION A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
170 * ..
171 *
172 * =====================================================================
173 *
174 * .. Parameters ..
175  DOUBLE PRECISION ONE
176  parameter( one = 1.0d+0 )
177 * ..
178 * .. Local Scalars ..
179  LOGICAL LEFT, NOTRAN
180  INTEGER I, I1, I2, I3, IC, JC, MI, NI, NQ
181  DOUBLE PRECISION AII
182 * ..
183 * .. External Functions ..
184  LOGICAL LSAME
185  EXTERNAL lsame
186 * ..
187 * .. External Subroutines ..
188  EXTERNAL dlarf, xerbla
189 * ..
190 * .. Intrinsic Functions ..
191  INTRINSIC max
192 * ..
193 * .. Executable Statements ..
194 *
195 * Test the input arguments
196 *
197  info = 0
198  left = lsame( side, 'L' )
199  notran = lsame( trans, 'N' )
200 *
201 * NQ is the order of Q
202 *
203  IF( left ) THEN
204  nq = m
205  ELSE
206  nq = n
207  END IF
208  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
209  info = -1
210  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
211  info = -2
212  ELSE IF( m.LT.0 ) THEN
213  info = -3
214  ELSE IF( n.LT.0 ) THEN
215  info = -4
216  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
217  info = -5
218  ELSE IF( lda.LT.max( 1, nq ) ) THEN
219  info = -7
220  ELSE IF( ldc.LT.max( 1, m ) ) THEN
221  info = -10
222  END IF
223  IF( info.NE.0 ) THEN
224  CALL xerbla( 'DORM2R', -info )
225  RETURN
226  END IF
227 *
228 * Quick return if possible
229 *
230  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
231  $ RETURN
232 *
233  IF( ( left .AND. .NOT.notran ) .OR. ( .NOT.left .AND. notran ) )
234  $ THEN
235  i1 = 1
236  i2 = k
237  i3 = 1
238  ELSE
239  i1 = k
240  i2 = 1
241  i3 = -1
242  END IF
243 *
244  IF( left ) THEN
245  ni = n
246  jc = 1
247  ELSE
248  mi = m
249  ic = 1
250  END IF
251 *
252  DO 10 i = i1, i2, i3
253  IF( left ) THEN
254 *
255 * H(i) is applied to C(i:m,1:n)
256 *
257  mi = m - i + 1
258  ic = i
259  ELSE
260 *
261 * H(i) is applied to C(1:m,i:n)
262 *
263  ni = n - i + 1
264  jc = i
265  END IF
266 *
267 * Apply H(i)
268 *
269  aii = a( i, i )
270  a( i, i ) = one
271  CALL dlarf( side, mi, ni, a( i, i ), 1, tau( i ), c( ic, jc ),
272  $ ldc, work )
273  a( i, i ) = aii
274  10 CONTINUE
275  RETURN
276 *
277 * End of DORM2R
278 *
279  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine dlarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
DLARF applies an elementary reflector to a general rectangular matrix.
Definition: dlarf.f:124
subroutine dorm2r(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
DORM2R multiplies a general matrix by the orthogonal matrix from a QR factorization determined by sge...
Definition: dorm2r.f:159