LAPACK  3.10.1
LAPACK: Linear Algebra PACKage
sormr3.f
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1 *> \brief \b SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stzrzf (unblocked algorithm).
2 *
3 * =========== DOCUMENTATION ===========
4 *
5 * Online html documentation available at
6 * http://www.netlib.org/lapack/explore-html/
7 *
8 *> \htmlonly
9 *> Download SORMR3 + dependencies
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14 *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sormr3.f">
15 *> [TXT]</a>
16 *> \endhtmlonly
17 *
18 * Definition:
19 * ===========
20 *
21 * SUBROUTINE SORMR3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
22 * WORK, INFO )
23 *
24 * .. Scalar Arguments ..
25 * CHARACTER SIDE, TRANS
26 * INTEGER INFO, K, L, 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 *> SORMR3 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 = 'C', or
43 *>
44 *> C * Q if SIDE = 'R' and TRANS = 'N', or
45 *>
46 *> C * Q**T if SIDE = 'R' and TRANS = 'C',
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 STZRZF. 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] L
96 *> \verbatim
97 *> L is INTEGER
98 *> The number of columns of the matrix A containing
99 *> the meaningful part of the Householder reflectors.
100 *> If SIDE = 'L', M >= L >= 0, if SIDE = 'R', N >= L >= 0.
101 *> \endverbatim
102 *>
103 *> \param[in] A
104 *> \verbatim
105 *> A is REAL array, dimension
106 *> (LDA,M) if SIDE = 'L',
107 *> (LDA,N) if SIDE = 'R'
108 *> The i-th row must contain the vector which defines the
109 *> elementary reflector H(i), for i = 1,2,...,k, as returned by
110 *> STZRZF in the last k rows of its array argument A.
111 *> A is modified by the routine but restored on exit.
112 *> \endverbatim
113 *>
114 *> \param[in] LDA
115 *> \verbatim
116 *> LDA is INTEGER
117 *> The leading dimension of the array A. LDA >= max(1,K).
118 *> \endverbatim
119 *>
120 *> \param[in] TAU
121 *> \verbatim
122 *> TAU is REAL array, dimension (K)
123 *> TAU(i) must contain the scalar factor of the elementary
124 *> reflector H(i), as returned by STZRZF.
125 *> \endverbatim
126 *>
127 *> \param[in,out] C
128 *> \verbatim
129 *> C is REAL array, dimension (LDC,N)
130 *> On entry, the m-by-n matrix C.
131 *> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q.
132 *> \endverbatim
133 *>
134 *> \param[in] LDC
135 *> \verbatim
136 *> LDC is INTEGER
137 *> The leading dimension of the array C. LDC >= max(1,M).
138 *> \endverbatim
139 *>
140 *> \param[out] WORK
141 *> \verbatim
142 *> WORK is REAL array, dimension
143 *> (N) if SIDE = 'L',
144 *> (M) if SIDE = 'R'
145 *> \endverbatim
146 *>
147 *> \param[out] INFO
148 *> \verbatim
149 *> INFO is INTEGER
150 *> = 0: successful exit
151 *> < 0: if INFO = -i, the i-th argument had an illegal value
152 *> \endverbatim
153 *
154 * Authors:
155 * ========
156 *
157 *> \author Univ. of Tennessee
158 *> \author Univ. of California Berkeley
159 *> \author Univ. of Colorado Denver
160 *> \author NAG Ltd.
161 *
162 *> \ingroup realOTHERcomputational
163 *
164 *> \par Contributors:
165 * ==================
166 *>
167 *> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
168 *
169 *> \par Further Details:
170 * =====================
171 *>
172 *> \verbatim
173 *> \endverbatim
174 *>
175 * =====================================================================
176  SUBROUTINE sormr3( SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC,
177  $ WORK, INFO )
178 *
179 * -- LAPACK computational routine --
180 * -- LAPACK is a software package provided by Univ. of Tennessee, --
181 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
182 *
183 * .. Scalar Arguments ..
184  CHARACTER SIDE, TRANS
185  INTEGER INFO, K, L, LDA, LDC, M, N
186 * ..
187 * .. Array Arguments ..
188  REAL A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * )
189 * ..
190 *
191 * =====================================================================
192 *
193 * .. Local Scalars ..
194  LOGICAL LEFT, NOTRAN
195  INTEGER I, I1, I2, I3, IC, JA, JC, MI, NI, NQ
196 * ..
197 * .. External Functions ..
198  LOGICAL LSAME
199  EXTERNAL lsame
200 * ..
201 * .. External Subroutines ..
202  EXTERNAL slarz, xerbla
203 * ..
204 * .. Intrinsic Functions ..
205  INTRINSIC max
206 * ..
207 * .. Executable Statements ..
208 *
209 * Test the input arguments
210 *
211  info = 0
212  left = lsame( side, 'L' )
213  notran = lsame( trans, 'N' )
214 *
215 * NQ is the order of Q
216 *
217  IF( left ) THEN
218  nq = m
219  ELSE
220  nq = n
221  END IF
222  IF( .NOT.left .AND. .NOT.lsame( side, 'R' ) ) THEN
223  info = -1
224  ELSE IF( .NOT.notran .AND. .NOT.lsame( trans, 'T' ) ) THEN
225  info = -2
226  ELSE IF( m.LT.0 ) THEN
227  info = -3
228  ELSE IF( n.LT.0 ) THEN
229  info = -4
230  ELSE IF( k.LT.0 .OR. k.GT.nq ) THEN
231  info = -5
232  ELSE IF( l.LT.0 .OR. ( left .AND. ( l.GT.m ) ) .OR.
233  $ ( .NOT.left .AND. ( l.GT.n ) ) ) THEN
234  info = -6
235  ELSE IF( lda.LT.max( 1, k ) ) THEN
236  info = -8
237  ELSE IF( ldc.LT.max( 1, m ) ) THEN
238  info = -11
239  END IF
240  IF( info.NE.0 ) THEN
241  CALL xerbla( 'SORMR3', -info )
242  RETURN
243  END IF
244 *
245 * Quick return if possible
246 *
247  IF( m.EQ.0 .OR. n.EQ.0 .OR. k.EQ.0 )
248  $ RETURN
249 *
250  IF( ( left .AND. .NOT.notran .OR. .NOT.left .AND. notran ) ) THEN
251  i1 = 1
252  i2 = k
253  i3 = 1
254  ELSE
255  i1 = k
256  i2 = 1
257  i3 = -1
258  END IF
259 *
260  IF( left ) THEN
261  ni = n
262  ja = m - l + 1
263  jc = 1
264  ELSE
265  mi = m
266  ja = n - l + 1
267  ic = 1
268  END IF
269 *
270  DO 10 i = i1, i2, i3
271  IF( left ) THEN
272 *
273 * H(i) or H(i)**T is applied to C(i:m,1:n)
274 *
275  mi = m - i + 1
276  ic = i
277  ELSE
278 *
279 * H(i) or H(i)**T is applied to C(1:m,i:n)
280 *
281  ni = n - i + 1
282  jc = i
283  END IF
284 *
285 * Apply H(i) or H(i)**T
286 *
287  CALL slarz( side, mi, ni, l, a( i, ja ), lda, tau( i ),
288  $ c( ic, jc ), ldc, work )
289 *
290  10 CONTINUE
291 *
292  RETURN
293 *
294 * End of SORMR3
295 *
296  END
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:60
subroutine slarz(SIDE, M, N, L, V, INCV, TAU, C, LDC, WORK)
SLARZ applies an elementary reflector (as returned by stzrzf) to a general matrix.
Definition: slarz.f:145
subroutine sormr3(SIDE, TRANS, M, N, K, L, A, LDA, TAU, C, LDC, WORK, INFO)
SORMR3 multiplies a general matrix by the orthogonal matrix from a RZ factorization determined by stz...
Definition: sormr3.f:178