1*> \brief \b DLASR applies a sequence of plane rotations to a general rectangular matrix.
2*
3*  =========== DOCUMENTATION ===========
4*
5* Online html documentation available at
6*            http://www.netlib.org/lapack/explore-html/
7*
8*> \htmlonly
9*> Download DLASR + dependencies
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11*> [TGZ]</a>
12*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasr.f">
13*> [ZIP]</a>
14*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasr.f">
15*> [TXT]</a>
16*> \endhtmlonly
17*
18*  Definition:
19*  ===========
20*
21*       SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
22*
23*       .. Scalar Arguments ..
24*       CHARACTER          DIRECT, PIVOT, SIDE
25*       INTEGER            LDA, M, N
26*       ..
27*       .. Array Arguments ..
28*       DOUBLE PRECISION   A( LDA, * ), C( * ), S( * )
29*       ..
30*
31*
32*> \par Purpose:
33*  =============
34*>
35*> \verbatim
36*>
37*> DLASR applies a sequence of plane rotations to a real matrix A,
38*> from either the left or the right.
39*>
40*> When SIDE = 'L', the transformation takes the form
41*>
42*>    A := P*A
43*>
44*> and when SIDE = 'R', the transformation takes the form
45*>
46*>    A := A*P**T
47*>
48*> where P is an orthogonal matrix consisting of a sequence of z plane
49*> rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
50*> and P**T is the transpose of P.
51*>
52*> When DIRECT = 'F' (Forward sequence), then
53*>
54*>    P = P(z-1) * ... * P(2) * P(1)
55*>
56*> and when DIRECT = 'B' (Backward sequence), then
57*>
58*>    P = P(1) * P(2) * ... * P(z-1)
59*>
60*> where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
61*>
62*>    R(k) = (  c(k)  s(k) )
63*>         = ( -s(k)  c(k) ).
64*>
65*> When PIVOT = 'V' (Variable pivot), the rotation is performed
66*> for the plane (k,k+1), i.e., P(k) has the form
67*>
68*>    P(k) = (  1                                            )
69*>           (       ...                                     )
70*>           (              1                                )
71*>           (                   c(k)  s(k)                  )
72*>           (                  -s(k)  c(k)                  )
73*>           (                                1              )
74*>           (                                     ...       )
75*>           (                                            1  )
76*>
77*> where R(k) appears as a rank-2 modification to the identity matrix in
78*> rows and columns k and k+1.
79*>
80*> When PIVOT = 'T' (Top pivot), the rotation is performed for the
81*> plane (1,k+1), so P(k) has the form
82*>
83*>    P(k) = (  c(k)                    s(k)                 )
84*>           (         1                                     )
85*>           (              ...                              )
86*>           (                     1                         )
87*>           ( -s(k)                    c(k)                 )
88*>           (                                 1             )
89*>           (                                      ...      )
90*>           (                                             1 )
91*>
92*> where R(k) appears in rows and columns 1 and k+1.
93*>
94*> Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
95*> performed for the plane (k,z), giving P(k) the form
96*>
97*>    P(k) = ( 1                                             )
98*>           (      ...                                      )
99*>           (             1                                 )
100*>           (                  c(k)                    s(k) )
101*>           (                         1                     )
102*>           (                              ...              )
103*>           (                                     1         )
104*>           (                 -s(k)                    c(k) )
105*>
106*> where R(k) appears in rows and columns k and z.  The rotations are
107*> performed without ever forming P(k) explicitly.
108*> \endverbatim
109*
110*  Arguments:
111*  ==========
112*
113*> \param[in] SIDE
114*> \verbatim
115*>          SIDE is CHARACTER*1
116*>          Specifies whether the plane rotation matrix P is applied to
117*>          A on the left or the right.
118*>          = 'L':  Left, compute A := P*A
119*>          = 'R':  Right, compute A:= A*P**T
120*> \endverbatim
121*>
122*> \param[in] PIVOT
123*> \verbatim
124*>          PIVOT is CHARACTER*1
125*>          Specifies the plane for which P(k) is a plane rotation
126*>          matrix.
127*>          = 'V':  Variable pivot, the plane (k,k+1)
128*>          = 'T':  Top pivot, the plane (1,k+1)
129*>          = 'B':  Bottom pivot, the plane (k,z)
130*> \endverbatim
131*>
132*> \param[in] DIRECT
133*> \verbatim
134*>          DIRECT is CHARACTER*1
135*>          Specifies whether P is a forward or backward sequence of
136*>          plane rotations.
137*>          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
138*>          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
139*> \endverbatim
140*>
141*> \param[in] M
142*> \verbatim
143*>          M is INTEGER
144*>          The number of rows of the matrix A.  If m <= 1, an immediate
145*>          return is effected.
146*> \endverbatim
147*>
148*> \param[in] N
149*> \verbatim
150*>          N is INTEGER
151*>          The number of columns of the matrix A.  If n <= 1, an
152*>          immediate return is effected.
153*> \endverbatim
154*>
155*> \param[in] C
156*> \verbatim
157*>          C is DOUBLE PRECISION array, dimension
158*>                  (M-1) if SIDE = 'L'
159*>                  (N-1) if SIDE = 'R'
160*>          The cosines c(k) of the plane rotations.
161*> \endverbatim
162*>
163*> \param[in] S
164*> \verbatim
165*>          S is DOUBLE PRECISION array, dimension
166*>                  (M-1) if SIDE = 'L'
167*>                  (N-1) if SIDE = 'R'
168*>          The sines s(k) of the plane rotations.  The 2-by-2 plane
169*>          rotation part of the matrix P(k), R(k), has the form
170*>          R(k) = (  c(k)  s(k) )
171*>                 ( -s(k)  c(k) ).
172*> \endverbatim
173*>
174*> \param[in,out] A
175*> \verbatim
176*>          A is DOUBLE PRECISION array, dimension (LDA,N)
177*>          The M-by-N matrix A.  On exit, A is overwritten by P*A if
178*>          SIDE = 'L' or by A*P**T if SIDE = 'R'.
179*> \endverbatim
180*>
181*> \param[in] LDA
182*> \verbatim
183*>          LDA is INTEGER
184*>          The leading dimension of the array A.  LDA >= max(1,M).
185*> \endverbatim
186*
187*  Authors:
188*  ========
189*
190*> \author Univ. of Tennessee
191*> \author Univ. of California Berkeley
192*> \author Univ. of Colorado Denver
193*> \author NAG Ltd.
194*
195*> \ingroup OTHERauxiliary
196*
197*  =====================================================================
198      SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
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      DOUBLE PRECISION   A( LDA, * ), C( * ), S( * )
210*     ..
211*
212*  =====================================================================
213*
214*     .. Parameters ..
215      DOUBLE PRECISION   ONE, ZERO
216      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
217*     ..
218*     .. Local Scalars ..
219      INTEGER            I, INFO, J
220      DOUBLE PRECISION   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( '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*
433      END
434