LAPACK 3.12.0
LAPACK: Linear Algebra PACKage
Loading...
Searching...
No Matches
clasr.f
Go to the documentation of this file.
1*> \brief \b CLASR 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 CLASR + dependencies
10*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/clasr.f">
11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/clasr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/clasr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18* Definition:
19* ===========
20*
21* SUBROUTINE CLASR( 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* REAL C( * ), S( * )
29* COMPLEX A( LDA, * )
30* ..
31*
32*
33*> \par Purpose:
34* =============
35*>
36*> \verbatim
37*>
38*> CLASR applies a sequence of real plane rotations to a complex matrix
39*> A, from either the left or the right.
40*>
41*> When SIDE = 'L', the transformation takes the form
42*>
43*> A := P*A
44*>
45*> and when SIDE = 'R', the transformation takes the form
46*>
47*> A := A*P**T
48*>
49*> where P is an orthogonal matrix consisting of a sequence of z plane
50*> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
51*> and P**T is the transpose of P.
52*>
53*> When DIRECT = 'F' (Forward sequence), then
54*>
55*> P = P(z-1) * ... * P(2) * P(1)
56*>
57*> and when DIRECT = 'B' (Backward sequence), then
58*>
59*> P = P(1) * P(2) * ... * P(z-1)
60*>
61*> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
62*>
63*> R(k) = ( c(k) s(k) )
64*> = ( -s(k) c(k) ).
65*>
66*> When PIVOT = 'V' (Variable pivot), the rotation is performed
67*> for the plane (k,k+1), i.e., P(k) has the form
68*>
69*> P(k) = ( 1 )
70*> ( ... )
71*> ( 1 )
72*> ( c(k) s(k) )
73*> ( -s(k) c(k) )
74*> ( 1 )
75*> ( ... )
76*> ( 1 )
77*>
78*> where R(k) appears as a rank-2 modification to the identity matrix in
79*> rows and columns k and k+1.
80*>
81*> When PIVOT = 'T' (Top pivot), the rotation is performed for the
82*> plane (1,k+1), so P(k) has the form
83*>
84*> P(k) = ( c(k) s(k) )
85*> ( 1 )
86*> ( ... )
87*> ( 1 )
88*> ( -s(k) c(k) )
89*> ( 1 )
90*> ( ... )
91*> ( 1 )
92*>
93*> where R(k) appears in rows and columns 1 and k+1.
94*>
95*> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
96*> performed for the plane (k,z), giving P(k) the form
97*>
98*> P(k) = ( 1 )
99*> ( ... )
100*> ( 1 )
101*> ( c(k) s(k) )
102*> ( 1 )
103*> ( ... )
104*> ( 1 )
105*> ( -s(k) c(k) )
106*>
107*> where R(k) appears in rows and columns k and z. The rotations are
108*> performed without ever forming P(k) explicitly.
109*> \endverbatim
110*
111* Arguments:
112* ==========
113*
114*> \param[in] SIDE
115*> \verbatim
116*> SIDE is CHARACTER*1
117*> Specifies whether the plane rotation matrix P is applied to
118*> A on the left or the right.
119*> = 'L': Left, compute A := P*A
120*> = 'R': Right, compute A:= A*P**T
121*> \endverbatim
122*>
123*> \param[in] PIVOT
124*> \verbatim
125*> PIVOT is CHARACTER*1
126*> Specifies the plane for which P(k) is a plane rotation
127*> matrix.
128*> = 'V': Variable pivot, the plane (k,k+1)
129*> = 'T': Top pivot, the plane (1,k+1)
130*> = 'B': Bottom pivot, the plane (k,z)
131*> \endverbatim
132*>
133*> \param[in] DIRECT
134*> \verbatim
135*> DIRECT is CHARACTER*1
136*> Specifies whether P is a forward or backward sequence of
137*> plane rotations.
138*> = 'F': Forward, P = P(z-1)*...*P(2)*P(1)
139*> = 'B': Backward, P = P(1)*P(2)*...*P(z-1)
140*> \endverbatim
141*>
142*> \param[in] M
143*> \verbatim
144*> M is INTEGER
145*> The number of rows of the matrix A. If m <= 1, an immediate
146*> return is effected.
147*> \endverbatim
148*>
149*> \param[in] N
150*> \verbatim
151*> N is INTEGER
152*> The number of columns of the matrix A. If n <= 1, an
153*> immediate return is effected.
154*> \endverbatim
155*>
156*> \param[in] C
157*> \verbatim
158*> C is REAL array, dimension
159*> (M-1) if SIDE = 'L'
160*> (N-1) if SIDE = 'R'
161*> The cosines c(k) of the plane rotations.
162*> \endverbatim
163*>
164*> \param[in] S
165*> \verbatim
166*> S is REAL array, dimension
167*> (M-1) if SIDE = 'L'
168*> (N-1) if SIDE = 'R'
169*> The sines s(k) of the plane rotations. The 2-by-2 plane
170*> rotation part of the matrix P(k), R(k), has the form
171*> R(k) = ( c(k) s(k) )
172*> ( -s(k) c(k) ).
173*> \endverbatim
174*>
175*> \param[in,out] A
176*> \verbatim
177*> A is COMPLEX array, dimension (LDA,N)
178*> The M-by-N matrix A. On exit, A is overwritten by P*A if
179*> SIDE = 'R' or by A*P**T if SIDE = 'L'.
180*> \endverbatim
181*>
182*> \param[in] LDA
183*> \verbatim
184*> LDA is INTEGER
185*> The leading dimension of the array A. LDA >= max(1,M).
186*> \endverbatim
187*
188* Authors:
189* ========
190*
191*> \author Univ. of Tennessee
192*> \author Univ. of California Berkeley
193*> \author Univ. of Colorado Denver
194*> \author NAG Ltd.
195*
196*> \ingroup lasr
197*
198* =====================================================================
199 SUBROUTINE clasr( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
200*
201* -- LAPACK auxiliary routine --
202* -- LAPACK is a software package provided by Univ. of Tennessee, --
203* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
204*
205* .. Scalar Arguments ..
206 CHARACTER DIRECT, PIVOT, SIDE
207 INTEGER LDA, M, N
208* ..
209* .. Array Arguments ..
210 REAL C( * ), S( * )
211 COMPLEX A( LDA, * )
212* ..
213*
214* =====================================================================
215*
216* .. Parameters ..
217 REAL ONE, ZERO
218 parameter( one = 1.0e+0, zero = 0.0e+0 )
219* ..
220* .. Local Scalars ..
221 INTEGER I, INFO, J
222 REAL CTEMP, STEMP
223 COMPLEX TEMP
224* ..
225* .. Intrinsic Functions ..
226 INTRINSIC max
227* ..
228* .. External Functions ..
229 LOGICAL LSAME
230 EXTERNAL lsame
231* ..
232* .. External Subroutines ..
233 EXTERNAL xerbla
234* ..
235* .. Executable Statements ..
236*
237* Test the input parameters
238*
239 info = 0
240 IF( .NOT.( lsame( side, 'L' ) .OR. lsame( side, 'R' ) ) ) THEN
241 info = 1
242 ELSE IF( .NOT.( lsame( pivot, 'V' ) .OR. lsame( pivot,
243 $ 'T' ) .OR. lsame( pivot, 'B' ) ) ) THEN
244 info = 2
245 ELSE IF( .NOT.( lsame( direct, 'F' ) .OR. lsame( direct, 'B' ) ) )
246 $ THEN
247 info = 3
248 ELSE IF( m.LT.0 ) THEN
249 info = 4
250 ELSE IF( n.LT.0 ) THEN
251 info = 5
252 ELSE IF( lda.LT.max( 1, m ) ) THEN
253 info = 9
254 END IF
255 IF( info.NE.0 ) THEN
256 CALL xerbla( 'CLASR ', info )
257 RETURN
258 END IF
259*
260* Quick return if possible
261*
262 IF( ( m.EQ.0 ) .OR. ( n.EQ.0 ) )
263 $ RETURN
264 IF( lsame( side, 'L' ) ) THEN
265*
266* Form P * A
267*
268 IF( lsame( pivot, 'V' ) ) THEN
269 IF( lsame( direct, 'F' ) ) THEN
270 DO 20 j = 1, m - 1
271 ctemp = c( j )
272 stemp = s( j )
273 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
274 DO 10 i = 1, n
275 temp = a( j+1, i )
276 a( j+1, i ) = ctemp*temp - stemp*a( j, i )
277 a( j, i ) = stemp*temp + ctemp*a( j, i )
278 10 CONTINUE
279 END IF
280 20 CONTINUE
281 ELSE IF( lsame( direct, 'B' ) ) THEN
282 DO 40 j = m - 1, 1, -1
283 ctemp = c( j )
284 stemp = s( j )
285 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
286 DO 30 i = 1, n
287 temp = a( j+1, i )
288 a( j+1, i ) = ctemp*temp - stemp*a( j, i )
289 a( j, i ) = stemp*temp + ctemp*a( j, i )
290 30 CONTINUE
291 END IF
292 40 CONTINUE
293 END IF
294 ELSE IF( lsame( pivot, 'T' ) ) THEN
295 IF( lsame( direct, 'F' ) ) THEN
296 DO 60 j = 2, m
297 ctemp = c( j-1 )
298 stemp = s( j-1 )
299 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
300 DO 50 i = 1, n
301 temp = a( j, i )
302 a( j, i ) = ctemp*temp - stemp*a( 1, i )
303 a( 1, i ) = stemp*temp + ctemp*a( 1, i )
304 50 CONTINUE
305 END IF
306 60 CONTINUE
307 ELSE IF( lsame( direct, 'B' ) ) THEN
308 DO 80 j = m, 2, -1
309 ctemp = c( j-1 )
310 stemp = s( j-1 )
311 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
312 DO 70 i = 1, n
313 temp = a( j, i )
314 a( j, i ) = ctemp*temp - stemp*a( 1, i )
315 a( 1, i ) = stemp*temp + ctemp*a( 1, i )
316 70 CONTINUE
317 END IF
318 80 CONTINUE
319 END IF
320 ELSE IF( lsame( pivot, 'B' ) ) THEN
321 IF( lsame( direct, 'F' ) ) THEN
322 DO 100 j = 1, m - 1
323 ctemp = c( j )
324 stemp = s( j )
325 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
326 DO 90 i = 1, n
327 temp = a( j, i )
328 a( j, i ) = stemp*a( m, i ) + ctemp*temp
329 a( m, i ) = ctemp*a( m, i ) - stemp*temp
330 90 CONTINUE
331 END IF
332 100 CONTINUE
333 ELSE IF( lsame( direct, 'B' ) ) THEN
334 DO 120 j = m - 1, 1, -1
335 ctemp = c( j )
336 stemp = s( j )
337 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
338 DO 110 i = 1, n
339 temp = a( j, i )
340 a( j, i ) = stemp*a( m, i ) + ctemp*temp
341 a( m, i ) = ctemp*a( m, i ) - stemp*temp
342 110 CONTINUE
343 END IF
344 120 CONTINUE
345 END IF
346 END IF
347 ELSE IF( lsame( side, 'R' ) ) THEN
348*
349* Form A * P**T
350*
351 IF( lsame( pivot, 'V' ) ) THEN
352 IF( lsame( direct, 'F' ) ) THEN
353 DO 140 j = 1, n - 1
354 ctemp = c( j )
355 stemp = s( j )
356 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
357 DO 130 i = 1, m
358 temp = a( i, j+1 )
359 a( i, j+1 ) = ctemp*temp - stemp*a( i, j )
360 a( i, j ) = stemp*temp + ctemp*a( i, j )
361 130 CONTINUE
362 END IF
363 140 CONTINUE
364 ELSE IF( lsame( direct, 'B' ) ) THEN
365 DO 160 j = n - 1, 1, -1
366 ctemp = c( j )
367 stemp = s( j )
368 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
369 DO 150 i = 1, m
370 temp = a( i, j+1 )
371 a( i, j+1 ) = ctemp*temp - stemp*a( i, j )
372 a( i, j ) = stemp*temp + ctemp*a( i, j )
373 150 CONTINUE
374 END IF
375 160 CONTINUE
376 END IF
377 ELSE IF( lsame( pivot, 'T' ) ) THEN
378 IF( lsame( direct, 'F' ) ) THEN
379 DO 180 j = 2, n
380 ctemp = c( j-1 )
381 stemp = s( j-1 )
382 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
383 DO 170 i = 1, m
384 temp = a( i, j )
385 a( i, j ) = ctemp*temp - stemp*a( i, 1 )
386 a( i, 1 ) = stemp*temp + ctemp*a( i, 1 )
387 170 CONTINUE
388 END IF
389 180 CONTINUE
390 ELSE IF( lsame( direct, 'B' ) ) THEN
391 DO 200 j = n, 2, -1
392 ctemp = c( j-1 )
393 stemp = s( j-1 )
394 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
395 DO 190 i = 1, m
396 temp = a( i, j )
397 a( i, j ) = ctemp*temp - stemp*a( i, 1 )
398 a( i, 1 ) = stemp*temp + ctemp*a( i, 1 )
399 190 CONTINUE
400 END IF
401 200 CONTINUE
402 END IF
403 ELSE IF( lsame( pivot, 'B' ) ) THEN
404 IF( lsame( direct, 'F' ) ) THEN
405 DO 220 j = 1, n - 1
406 ctemp = c( j )
407 stemp = s( j )
408 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
409 DO 210 i = 1, m
410 temp = a( i, j )
411 a( i, j ) = stemp*a( i, n ) + ctemp*temp
412 a( i, n ) = ctemp*a( i, n ) - stemp*temp
413 210 CONTINUE
414 END IF
415 220 CONTINUE
416 ELSE IF( lsame( direct, 'B' ) ) THEN
417 DO 240 j = n - 1, 1, -1
418 ctemp = c( j )
419 stemp = s( j )
420 IF( ( ctemp.NE.one ) .OR. ( stemp.NE.zero ) ) THEN
421 DO 230 i = 1, m
422 temp = a( i, j )
423 a( i, j ) = stemp*a( i, n ) + ctemp*temp
424 a( i, n ) = ctemp*a( i, n ) - stemp*temp
425 230 CONTINUE
426 END IF
427 240 CONTINUE
428 END IF
429 END IF
430 END IF
431*
432 RETURN
433*
434* End of CLASR
435*
436 END
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
clasr
subroutine clasr(side, pivot, direct, m, n, c, s, a, lda)
CLASR applies a sequence of plane rotations to a general rectangular matrix.
Definition clasr.f:200