LAPACK 3.12.0 LAPACK: Linear Algebra PACKage
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## ◆ slasr()

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

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

Purpose:
``` SLASR 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 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 REAL 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).```

Definition at line 198 of file slasr.f.

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 REAL A( LDA, * ), C( * ), S( * )
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, 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( 'SLASR ', 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 SLASR
432*
subroutine xerbla(srname, info)
Definition cblat2.f:3285
logical function lsame(ca, cb)
LSAME
Definition lsame.f:48
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