LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ clasr()

subroutine clasr ( character side,
character pivot,
character direct,
integer m,
integer n,
real, dimension( * ) c,
real, dimension( * ) s,
complex, dimension( lda, * ) a,
integer lda )

CLASR applies a sequence of plane rotations to a general rectangular matrix.

Download CLASR + dependencies [TGZ] [ZIP] [TXT]

Purpose:
!>
!> CLASR applies a sequence of real plane rotations to a complex matrix
!> A, from either the left or the right.
!>
!> When SIDE = 'L', the transformation takes the form
!>
!>    A := P*A
!>
!> and when SIDE = 'R', the transformation takes the form
!>
!>    A := A*P**T
!>
!> where P is an orthogonal matrix consisting of a sequence of z plane
!> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
!> and P**T is the transpose of P.
!>
!> When DIRECT = 'F' (Forward sequence), then
!>
!>    P = P(z-1) * ... * P(2) * P(1)
!>
!> and when DIRECT = 'B' (Backward sequence), then
!>
!>    P = P(1) * P(2) * ... * P(z-1)
!>
!> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
!>
!>    R(k) = (  c(k)  s(k) )
!>         = ( -s(k)  c(k) ).
!>
!> When PIVOT = 'V' (Variable pivot), the rotation is performed
!> for the plane (k,k+1), i.e., P(k) has the form
!>
!>    P(k) = (  1                                            )
!>           (       ...                                     )
!>           (              1                                )
!>           (                   c(k)  s(k)                  )
!>           (                  -s(k)  c(k)                  )
!>           (                                1              )
!>           (                                     ...       )
!>           (                                            1  )
!>
!> where R(k) appears as a rank-2 modification to the identity matrix in
!> rows and columns k and k+1.
!>
!> When PIVOT = 'T' (Top pivot), the rotation is performed for the
!> plane (1,k+1), so P(k) has the form
!>
!>    P(k) = (  c(k)                    s(k)                 )
!>           (         1                                     )
!>           (              ...                              )
!>           (                     1                         )
!>           ( -s(k)                    c(k)                 )
!>           (                                 1             )
!>           (                                      ...      )
!>           (                                             1 )
!>
!> where R(k) appears in rows and columns 1 and k+1.
!>
!> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
!> performed for the plane (k,z), giving P(k) the form
!>
!>    P(k) = ( 1                                             )
!>           (      ...                                      )
!>           (             1                                 )
!>           (                  c(k)                    s(k) )
!>           (                         1                     )
!>           (                              ...              )
!>           (                                     1         )
!>           (                 -s(k)                    c(k) )
!>
!> where R(k) appears in rows and columns k and z.  The rotations are
!> performed without ever forming P(k) explicitly.
!>
Parameters
[in]SIDE
!>          SIDE is CHARACTER*1
!>          Specifies whether the plane rotation matrix P is applied to
!>          A on the left or the right.
!>          = 'L':  Left, compute A := P*A
!>          = 'R':  Right, compute A:= A*P**T
!>
[in]PIVOT
!>          PIVOT is CHARACTER*1
!>          Specifies the plane for which P(k) is a plane rotation
!>          matrix.
!>          = 'V':  Variable pivot, the plane (k,k+1)
!>          = 'T':  Top pivot, the plane (1,k+1)
!>          = 'B':  Bottom pivot, the plane (k,z)
!>
[in]DIRECT
!>          DIRECT is CHARACTER*1
!>          Specifies whether P is a forward or backward sequence of
!>          plane rotations.
!>          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
!>          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
!>
[in]M
!>          M is INTEGER
!>          The number of rows of the matrix A.  If m <= 1, an immediate
!>          return is effected.
!>
[in]N
!>          N is INTEGER
!>          The number of columns of the matrix A.  If n <= 1, an
!>          immediate return is effected.
!>
[in]C
!>          C is REAL array, dimension
!>                  (M-1) if SIDE = 'L'
!>                  (N-1) if SIDE = 'R'
!>          The cosines c(k) of the plane rotations.
!>
[in]S
!>          S is REAL array, dimension
!>                  (M-1) if SIDE = 'L'
!>                  (N-1) if SIDE = 'R'
!>          The sines s(k) of the plane rotations.  The 2-by-2 plane
!>          rotation part of the matrix P(k), R(k), has the form
!>          R(k) = (  c(k)  s(k) )
!>                 ( -s(k)  c(k) ).
!>
[in,out]A
!>          A is COMPLEX array, dimension (LDA,N)
!>          The M-by-N matrix A.  On exit, A is overwritten by P*A if
!>          SIDE = 'R' or by A*P**T if SIDE = 'L'.
!>
[in]LDA
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,M).
!>
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 197 of file clasr.f.

198*
199* -- LAPACK auxiliary routine --
200* -- LAPACK is a software package provided by Univ. of Tennessee, --
201* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
202*
203* .. Scalar Arguments ..
204 CHARACTER DIRECT, PIVOT, SIDE
205 INTEGER LDA, M, N
206* ..
207* .. Array Arguments ..
208 REAL C( * ), S( * )
209 COMPLEX A( LDA, * )
210* ..
211*
212* =====================================================================
213*
214* .. Parameters ..
215 REAL ONE, ZERO
216 parameter( one = 1.0e+0, zero = 0.0e+0 )
217* ..
218* .. Local Scalars ..
219 INTEGER I, INFO, J
220 REAL CTEMP, STEMP
221 COMPLEX TEMP
222* ..
223* .. Intrinsic Functions ..
224 INTRINSIC max
225* ..
226* .. External Functions ..
227 LOGICAL LSAME
228 EXTERNAL lsame
229* ..
230* .. External Subroutines ..
231 EXTERNAL xerbla
232* ..
233* .. Executable Statements ..
234*
235* Test the input parameters
236*
237 info = 0
238 IF( .NOT.( lsame( side, 'L' ) .OR.
239 $ lsame( side, 'R' ) ) ) THEN
240 info = 1
241 ELSE IF( .NOT.( lsame( pivot, 'V' ) .OR. lsame( pivot,
242 $ 'T' ) .OR. lsame( pivot, 'B' ) ) ) THEN
243 info = 2
244 ELSE IF( .NOT.( lsame( direct, 'F' ) .OR.
245 $ 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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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