LAPACK  3.8.0
LAPACK: Linear Algebra PACKage

◆ 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 = '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.
Date
December 2016

Definition at line 201 of file dlasr.f.

201 *
202 * -- LAPACK auxiliary routine (version 3.7.0) --
203 * -- LAPACK is a software package provided by Univ. of Tennessee, --
204 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
205 * December 2016
206 *
207 * .. Scalar Arguments ..
208  CHARACTER direct, pivot, side
209  INTEGER lda, m, n
210 * ..
211 * .. Array Arguments ..
212  DOUBLE PRECISION a( lda, * ), c( * ), s( * )
213 * ..
214 *
215 * =====================================================================
216 *
217 * .. Parameters ..
218  DOUBLE PRECISION one, zero
219  parameter( one = 1.0d+0, zero = 0.0d+0 )
220 * ..
221 * .. Local Scalars ..
222  INTEGER i, info, j
223  DOUBLE PRECISION ctemp, stemp, temp
224 * ..
225 * .. External Functions ..
226  LOGICAL lsame
227  EXTERNAL lsame
228 * ..
229 * .. External Subroutines ..
230  EXTERNAL xerbla
231 * ..
232 * .. Intrinsic Functions ..
233  INTRINSIC max
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( 'DLASR ', 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 DLASR
435 *
subroutine xerbla(SRNAME, INFO)
XERBLA
Definition: xerbla.f:62
logical function lsame(CA, CB)
LSAME
Definition: lsame.f:55
Here is the call graph for this function:
Here is the caller graph for this function: