LAPACK 3.12.1
LAPACK: Linear Algebra PACKage
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◆ dlasr()

subroutine dlasr ( character side,
character pivot,
character direct,
integer m,
integer n,
double precision, dimension( * ) c,
double precision, dimension( * ) s,
double precision, dimension( lda, * ) a,
integer lda )

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

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

Purpose:
!>
!> DLASR applies a sequence of plane rotations to a real 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 DOUBLE PRECISION array, dimension
!>                  (M-1) if SIDE = 'L'
!>                  (N-1) if SIDE = 'R'
!>          The cosines c(k) of the plane rotations.
!>
[in]S
!>          S is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDA,N)
!>          The M-by-N matrix A.  On exit, A is overwritten by P*A if
!>          SIDE = 'L' or by A*P**T if SIDE = 'R'.
!>
[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 196 of file dlasr.f.

197*
198* -- LAPACK auxiliary routine --
199* -- LAPACK is a software package provided by Univ. of Tennessee, --
200* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
201*
202* .. Scalar Arguments ..
203 CHARACTER DIRECT, PIVOT, SIDE
204 INTEGER LDA, M, N
205* ..
206* .. Array Arguments ..
207 DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
208* ..
209*
210* =====================================================================
211*
212* .. Parameters ..
213 DOUBLE PRECISION ONE, ZERO
214 parameter( one = 1.0d+0, zero = 0.0d+0 )
215* ..
216* .. Local Scalars ..
217 INTEGER I, INFO, J
218 DOUBLE PRECISION CTEMP, STEMP, TEMP
219* ..
220* .. External Functions ..
221 LOGICAL LSAME
222 EXTERNAL lsame
223* ..
224* .. External Subroutines ..
225 EXTERNAL xerbla
226* ..
227* .. Intrinsic Functions ..
228 INTRINSIC max
229* ..
230* .. Executable Statements ..
231*
232* Test the input parameters
233*
234 info = 0
235 IF( .NOT.( lsame( side, 'L' ) .OR.
236 $ lsame( side, 'R' ) ) ) THEN
237 info = 1
238 ELSE IF( .NOT.( lsame( pivot, 'V' ) .OR. lsame( pivot,
239 $ 'T' ) .OR. lsame( pivot, 'B' ) ) ) THEN
240 info = 2
241 ELSE IF( .NOT.( lsame( direct, 'F' ) .OR.
242 $ 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*
xerbla
subroutine xerbla(srname, info)
Definition cblat2.f:3285
lsame
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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