LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
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dlasr.f
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1*> \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix.
2*
3* =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6* http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLASR + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
22*
23* .. Scalar Arguments ..
24* CHARACTER DIRECT, PIVOT, SIDE
25* INTEGER LDA, M, N
26* ..
27* .. Array Arguments ..
28* DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
29* ..
30*
31*
32*> \par Purpose:
33* =============
34*>
35*> \verbatim
36*>
37*> DLASR applies a sequence of plane rotations to a real matrix A,
38*> from either the left or the right.
39*>
40*> When SIDE = 'L', the transformation takes the form
41*>
42*> A := P*A
43*>
44*> and when SIDE = 'R', the transformation takes the form
45*>
46*> A := A*P**T
47*>
48*> where P is an orthogonal matrix consisting of a sequence of z plane
49*> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
50*> and P**T is the transpose of P.
51*>
52*> When DIRECT = 'F' (Forward sequence), then
53*>
54*> P = P(z-1) * ... * P(2) * P(1)
55*>
56*> and when DIRECT = 'B' (Backward sequence), then
57*>
58*> P = P(1) * P(2) * ... * P(z-1)
59*>
60*> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
61*>
62*> R(k) = ( c(k) s(k) )
63*> = ( -s(k) c(k) ).
64*>
65*> When PIVOT = 'V' (Variable pivot), the rotation is performed
66*> for the plane (k,k+1), i.e., P(k) has the form
67*>
68*> P(k) = ( 1 )
69*> ( ... )
70*> ( 1 )
71*> ( c(k) s(k) )
72*> ( -s(k) c(k) )
73*> ( 1 )
74*> ( ... )
75*> ( 1 )
76*>
77*> where R(k) appears as a rank-2 modification to the identity matrix in
78*> rows and columns k and k+1.
79*>
80*> When PIVOT = 'T' (Top pivot), the rotation is performed for the
81*> plane (1,k+1), so P(k) has the form
82*>
83*> P(k) = ( c(k) s(k) )
84*> ( 1 )
85*> ( ... )
86*> ( 1 )
87*> ( -s(k) c(k) )
88*> ( 1 )
89*> ( ... )
90*> ( 1 )
91*>
92*> where R(k) appears in rows and columns 1 and k+1.
93*>
94*> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
95*> performed for the plane (k,z), giving P(k) the form
96*>
97*> P(k) = ( 1 )
98*> ( ... )
99*> ( 1 )
100*> ( c(k) s(k) )
101*> ( 1 )
102*> ( ... )
103*> ( 1 )
104*> ( -s(k) c(k) )
105*>
106*> where R(k) appears in rows and columns k and z. The rotations are
107*> performed without ever forming P(k) explicitly.
108*> \endverbatim
109*
110* Arguments:
111* ==========
112*
113*> \param[in] SIDE
114*> \verbatim
115*> SIDE is CHARACTER*1
116*> Specifies whether the plane rotation matrix P is applied to
117*> A on the left or the right.
118*> = 'L': Left, compute A := P*A
119*> = 'R': Right, compute A:= A*P**T
120*> \endverbatim
121*>
122*> \param[in] PIVOT
123*> \verbatim
124*> PIVOT is CHARACTER*1
125*> Specifies the plane for which P(k) is a plane rotation
126*> matrix.
127*> = 'V': Variable pivot, the plane (k,k+1)
128*> = 'T': Top pivot, the plane (1,k+1)
129*> = 'B': Bottom pivot, the plane (k,z)
130*> \endverbatim
131*>
132*> \param[in] DIRECT
133*> \verbatim
134*> DIRECT is CHARACTER*1
135*> Specifies whether P is a forward or backward sequence of
136*> plane rotations.
137*> = 'F': Forward, P = P(z-1)*...*P(2)*P(1)
138*> = 'B': Backward, P = P(1)*P(2)*...*P(z-1)
139*> \endverbatim
140*>
141*> \param[in] M
142*> \verbatim
143*> M is INTEGER
144*> The number of rows of the matrix A. If m <= 1, an immediate
145*> return is effected.
146*> \endverbatim
147*>
148*> \param[in] N
149*> \verbatim
150*> N is INTEGER
151*> The number of columns of the matrix A. If n <= 1, an
152*> immediate return is effected.
153*> \endverbatim
154*>
155*> \param[in] C
156*> \verbatim
157*> C is DOUBLE PRECISION array, dimension
158*> (M-1) if SIDE = 'L'
159*> (N-1) if SIDE = 'R'
160*> The cosines c(k) of the plane rotations.
161*> \endverbatim
162*>
163*> \param[in] S
164*> \verbatim
165*> S is DOUBLE PRECISION array, dimension
166*> (M-1) if SIDE = 'L'
167*> (N-1) if SIDE = 'R'
168*> The sines s(k) of the plane rotations. The 2-by-2 plane
169*> rotation part of the matrix P(k), R(k), has the form
170*> R(k) = ( c(k) s(k) )
171*> ( -s(k) c(k) ).
172*> \endverbatim
173*>
174*> \param[in,out] A
175*> \verbatim
176*> A is DOUBLE PRECISION array, dimension (LDA,N)
177*> The M-by-N matrix A. On exit, A is overwritten by P*A if
178*> SIDE = 'L' or by A*P**T if SIDE = 'R'.
179*> \endverbatim
180*>
181*> \param[in] LDA
182*> \verbatim
183*> LDA is INTEGER
184*> The leading dimension of the array A. LDA >= max(1,M).
185*> \endverbatim
186*
187* Authors:
188* ========
189*
190*> \author Univ. of Tennessee
191*> \author Univ. of California Berkeley
192*> \author Univ. of Colorado Denver
193*> \author NAG Ltd.
194*
195*> \ingroup lasr
196*
197* =====================================================================
198 SUBROUTINE dlasr( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
199*
200* -- LAPACK auxiliary routine --
201* -- LAPACK is a software package provided by Univ. of Tennessee, --
202* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
203*
204* .. Scalar Arguments ..
205 CHARACTER DIRECT, PIVOT, SIDE
206 INTEGER LDA, M, N
207* ..
208* .. Array Arguments ..
209 DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
210* ..
211*
212* =====================================================================
213*
214* .. Parameters ..
215 DOUBLE PRECISION ONE, ZERO
216 parameter( one = 1.0d+0, zero = 0.0d+0 )
217* ..
218* .. Local Scalars ..
219 INTEGER I, INFO, J
220 DOUBLE PRECISION CTEMP, STEMP, TEMP
221* ..
222* .. External Functions ..
223 LOGICAL LSAME
224 EXTERNAL lsame
225* ..
226* .. External Subroutines ..
227 EXTERNAL xerbla
228* ..
229* .. Intrinsic Functions ..
230 INTRINSIC max
231* ..
232* .. Executable Statements ..
233*
234* Test the input parameters
235*
236 info = 0
237 IF( .NOT.( lsame( side, 'L' ) .OR. lsame( side, 'R' ) ) ) THEN
238 info = 1
239 ELSE IF( .NOT.( lsame( pivot, 'V' ) .OR. lsame( pivot,
240 $ 'T' ) .OR. lsame( pivot, 'B' ) ) ) THEN
241 info = 2
242 ELSE IF( .NOT.( lsame( direct, 'F' ) .OR. lsame( direct, 'B' ) ) )
243 $ THEN
244 info = 3
245 ELSE IF( m.LT.0 ) THEN
246 info = 4
247 ELSE IF( n.LT.0 ) THEN
248 info = 5
249 ELSE IF( lda.LT.max( 1, m ) ) THEN
250 info = 9
251 END IF
252 IF( info.NE.0 ) THEN
253 CALL xerbla( 'DLASR ', info )
254 RETURN
255 END IF
256*
257* Quick return if possible
258*
259 IF( ( m.EQ.0 ) .OR. ( n.EQ.0 ) )
260 $ RETURN
261 IF( lsame( side, 'L' ) ) THEN
262*
263* Form P * A
264*
265 IF( lsame( pivot, 'V' ) ) THEN
266 IF( lsame( direct, 'F' ) ) THEN
267 DO 20 j = 1, m - 1
268 ctemp = c( j )
269 stemp = s( j )
270 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
271 DO 10 i = 1, n
272 temp = a( j+1, i )
273 a( j+1, i ) = ctemp*temp - stemp*a( j, i )
274 a( j, i ) = stemp*temp + ctemp*a( j, i )
275 10 CONTINUE
276 END IF
277 20 CONTINUE
278 ELSE IF( lsame( direct, 'B' ) ) THEN
279 DO 40 j = m - 1, 1, -1
280 ctemp = c( j )
281 stemp = s( j )
282 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
283 DO 30 i = 1, n
284 temp = a( j+1, i )
285 a( j+1, i ) = ctemp*temp - stemp*a( j, i )
286 a( j, i ) = stemp*temp + ctemp*a( j, i )
287 30 CONTINUE
288 END IF
289 40 CONTINUE
290 END IF
291 ELSE IF( lsame( pivot, 'T' ) ) THEN
292 IF( lsame( direct, 'F' ) ) THEN
293 DO 60 j = 2, m
294 ctemp = c( j-1 )
295 stemp = s( j-1 )
296 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
297 DO 50 i = 1, n
298 temp = a( j, i )
299 a( j, i ) = ctemp*temp - stemp*a( 1, i )
300 a( 1, i ) = stemp*temp + ctemp*a( 1, i )
301 50 CONTINUE
302 END IF
303 60 CONTINUE
304 ELSE IF( lsame( direct, 'B' ) ) THEN
305 DO 80 j = m, 2, -1
306 ctemp = c( j-1 )
307 stemp = s( j-1 )
308 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
309 DO 70 i = 1, n
310 temp = a( j, i )
311 a( j, i ) = ctemp*temp - stemp*a( 1, i )
312 a( 1, i ) = stemp*temp + ctemp*a( 1, i )
313 70 CONTINUE
314 END IF
315 80 CONTINUE
316 END IF
317 ELSE IF( lsame( pivot, 'B' ) ) THEN
318 IF( lsame( direct, 'F' ) ) THEN
319 DO 100 j = 1, m - 1
320 ctemp = c( j )
321 stemp = s( j )
322 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
323 DO 90 i = 1, n
324 temp = a( j, i )
325 a( j, i ) = stemp*a( m, i ) + ctemp*temp
326 a( m, i ) = ctemp*a( m, i ) - stemp*temp
327 90 CONTINUE
328 END IF
329 100 CONTINUE
330 ELSE IF( lsame( direct, 'B' ) ) THEN
331 DO 120 j = m - 1, 1, -1
332 ctemp = c( j )
333 stemp = s( j )
334 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
335 DO 110 i = 1, n
336 temp = a( j, i )
337 a( j, i ) = stemp*a( m, i ) + ctemp*temp
338 a( m, i ) = ctemp*a( m, i ) - stemp*temp
339 110 CONTINUE
340 END IF
341 120 CONTINUE
342 END IF
343 END IF
344 ELSE IF( lsame( side, 'R' ) ) THEN
345*
346* Form A * P**T
347*
348 IF( lsame( pivot, 'V' ) ) THEN
349 IF( lsame( direct, 'F' ) ) THEN
350 DO 140 j = 1, n - 1
351 ctemp = c( j )
352 stemp = s( j )
353 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
354 DO 130 i = 1, m
355 temp = a( i, j+1 )
356 a( i, j+1 ) = ctemp*temp - stemp*a( i, j )
357 a( i, j ) = stemp*temp + ctemp*a( i, j )
358 130 CONTINUE
359 END IF
360 140 CONTINUE
361 ELSE IF( lsame( direct, 'B' ) ) THEN
362 DO 160 j = n - 1, 1, -1
363 ctemp = c( j )
364 stemp = s( j )
365 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
366 DO 150 i = 1, m
367 temp = a( i, j+1 )
368 a( i, j+1 ) = ctemp*temp - stemp*a( i, j )
369 a( i, j ) = stemp*temp + ctemp*a( i, j )
370 150 CONTINUE
371 END IF
372 160 CONTINUE
373 END IF
374 ELSE IF( lsame( pivot, 'T' ) ) THEN
375 IF( lsame( direct, 'F' ) ) THEN
376 DO 180 j = 2, n
377 ctemp = c( j-1 )
378 stemp = s( j-1 )
379 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
380 DO 170 i = 1, m
381 temp = a( i, j )
382 a( i, j ) = ctemp*temp - stemp*a( i, 1 )
383 a( i, 1 ) = stemp*temp + ctemp*a( i, 1 )
384 170 CONTINUE
385 END IF
386 180 CONTINUE
387 ELSE IF( lsame( direct, 'B' ) ) THEN
388 DO 200 j = n, 2, -1
389 ctemp = c( j-1 )
390 stemp = s( j-1 )
391 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
392 DO 190 i = 1, m
393 temp = a( i, j )
394 a( i, j ) = ctemp*temp - stemp*a( i, 1 )
395 a( i, 1 ) = stemp*temp + ctemp*a( i, 1 )
396 190 CONTINUE
397 END IF
398 200 CONTINUE
399 END IF
400 ELSE IF( lsame( pivot, 'B' ) ) THEN
401 IF( lsame( direct, 'F' ) ) THEN
402 DO 220 j = 1, n - 1
403 ctemp = c( j )
404 stemp = s( j )
405 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
406 DO 210 i = 1, m
407 temp = a( i, j )
408 a( i, j ) = stemp*a( i, n ) + ctemp*temp
409 a( i, n ) = ctemp*a( i, n ) - stemp*temp
410 210 CONTINUE
411 END IF
412 220 CONTINUE
413 ELSE IF( lsame( direct, 'B' ) ) THEN
414 DO 240 j = n - 1, 1, -1
415 ctemp = c( j )
416 stemp = s( j )
417 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
418 DO 230 i = 1, m
419 temp = a( i, j )
420 a( i, j ) = stemp*a( i, n ) + ctemp*temp
421 a( i, n ) = ctemp*a( i, n ) - stemp*temp
422 230 CONTINUE
423 END IF
424 240 CONTINUE
425 END IF
426 END IF
427 END IF
428*
429 RETURN
430*
431* End of DLASR
432*
433 END
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
dlasr
subroutine dlasr(side, pivot, direct, m, n, c, s, a, lda)
DLASR applies a sequence of plane rotations to a general rectangular matrix.
Definition dlasr.f:199