LAPACK 3.11.0
LAPACK: Linear Algebra PACKage
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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
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sormr3.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sormr3.f">
13*> [ZIP]</a>
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