LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ 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.

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

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).
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

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)
XERBLA
Definition: xerbla.f:60
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:53
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