LAPACK  3.6.1 LAPACK: Linear Algebra PACKage
sorm2l.f
Go to the documentation of this file.
1 *> \brief \b SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sgeqlf (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
10 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sorm2l.f">
11 *> [TGZ]</a>
12 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sorm2l.f">
13 *> [ZIP]</a>
14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sorm2l.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SORM2L( 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 * REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
30 * ..
31 *
32 *
33 *> \par Purpose:
34 * =============
35 *>
36 *> \verbatim
37 *>
38 *> SORM2L 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(k) . . . H(2) H(1)
52 *>
53 *> as returned by SGEQLF. 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 REAL 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 *> SGEQLF in the last 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 REAL array, dimension (K)
115 *> TAU(i) must contain the scalar factor of the elementary
116 *> reflector H(i), as returned by SGEQLF.
117 *> \endverbatim
118 *>
119 *> \param[in,out] C
120 *> \verbatim
121 *> C is REAL 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 REAL 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 *> \date September 2012
155 *
156 *> \ingroup realOTHERcomputational
157 *
158 * =====================================================================
159  SUBROUTINE sorm2l( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC,
160  \$ work, info )
161 *
162 * -- LAPACK computational routine (version 3.4.2) --
163 * -- LAPACK is a software package provided by Univ. of Tennessee, --
164 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
165 * September 2012
166 *
167 * .. Scalar Arguments ..
168  CHARACTER SIDE, TRANS
169  INTEGER INFO, K, LDA, LDC, M, N
170 * ..
171 * .. Array Arguments ..
172  REAL A( lda, * ), C( ldc, * ), TAU( * ), WORK( * )
173 * ..
174 *
175 * =====================================================================
176 *
177 * .. Parameters ..
178  REAL ONE
179  parameter ( one = 1.0e+0 )
180 * ..
181 * .. Local Scalars ..
182  LOGICAL LEFT, NOTRAN
183  INTEGER I, I1, I2, I3, MI, NI, NQ
184  REAL AII
185 * ..
186 * .. External Functions ..
187  LOGICAL LSAME
188  EXTERNAL lsame
189 * ..
190 * .. External Subroutines ..
191  EXTERNAL slarf, xerbla
192 * ..
193 * .. Intrinsic Functions ..
194  INTRINSIC max
195 * ..
196 * .. Executable Statements ..
197 *
198 * Test the input arguments
199 *
200  info = 0
201  left = lsame( side, 'L' )
202  notran = lsame( trans, 'N' )
203 *
204 * NQ is the order of Q
205 *
206  IF( left ) THEN
207  nq = m
208  ELSE
209  nq = n
210  END IF
211  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
212  info = -1
213  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
214  info = -2
215  ELSE IF( m.LT.0 ) THEN
216  info = -3
217  ELSE IF( n.LT.0 ) THEN
218  info = -4
219  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
220  info = -5
221  ELSE IF( lda.LT.max( 1, nq ) ) THEN
222  info = -7
223  ELSE IF( ldc.LT.max( 1, m ) ) THEN
224  info = -10
225  END IF
226  IF( info.NE.0 ) THEN
227  CALL xerbla( 'SORM2L', -info )
228  RETURN
229  END IF
230 *
231 * Quick return if possible
232 *
233  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
234  \$ RETURN
235 *
236  IF( ( left .AND. notran ) .OR. ( .NOT.left .AND. .NOT.notran ) )
237  \$ THEN
238  i1 = 1
239  i2 = k
240  i3 = 1
241  ELSE
242  i1 = k
243  i2 = 1
244  i3 = -1
245  END IF
246 *
247  IF( left ) THEN
248  ni = n
249  ELSE
250  mi = m
251  END IF
252 *
253  DO 10 i = i1, i2, i3
254  IF( left ) THEN
255 *
256 * H(i) is applied to C(1:m-k+i,1:n)
257 *
258  mi = m - k + i
259  ELSE
260 *
261 * H(i) is applied to C(1:m,1:n-k+i)
262 *
263  ni = n - k + i
264  END IF
265 *
266 * Apply H(i)
267 *
268  aii = a( nq-k+i, i )
269  a( nq-k+i, i ) = one
270  CALL slarf( side, mi, ni, a( 1, i ), 1, tau( i ), c, ldc,
271  \$ work )
272  a( nq-k+i, i ) = aii
273  10 CONTINUE
274  RETURN
275 *
276 * End of SORM2L
277 *
278  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
subroutine sorm2l(SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, WORK, INFO)
SORM2L multiplies a general matrix by the orthogonal matrix from a QL factorization determined by sge...
Definition: sorm2l.f:161
subroutine slarf(SIDE, M, N, V, INCV, TAU, C, LDC, WORK)
SLARF applies an elementary reflector to a general rectangular matrix.
Definition: slarf.f:126