1       SUBROUTINE ZLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
  2 *
  3 *  -- LAPACK auxiliary routine (version 3.2) --
  4 *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
  5 *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
  6 *     November 2006
  7 *
  8 *     .. Scalar Arguments ..
  9       CHARACTER          DIRECT, PIVOT, SIDE
 10       INTEGER            LDA, M, N
 11 *     ..
 12 *     .. Array Arguments ..
 13       DOUBLE PRECISION   C( * ), S( * )
 14       COMPLEX*16         A( LDA, * )
 15 *     ..
 16 *
 17 *  Purpose
 18 *  =======
 19 *
 20 *  ZLASR applies a sequence of real plane rotations to a complex matrix
 21 *  A, from either the left or the right.
 22 *
 23 *  When SIDE = 'L', the transformation takes the form
 24 *
 25 *     A := P*A
 26 *
 27 *  and when SIDE = 'R', the transformation takes the form
 28 *
 29 *     A := A*P**T
 30 *
 31 *  where P is an orthogonal matrix consisting of a sequence of z plane
 32 *  rotations, with z = M when SIDE = 'L' and z = N when SIDE = 'R',
 33 *  and P**T is the transpose of P.
 34 *  
 35 *  When DIRECT = 'F' (Forward sequence), then
 36 *  
 37 *     P = P(z-1) * ... * P(2) * P(1)
 38 *  
 39 *  and when DIRECT = 'B' (Backward sequence), then
 40 *  
 41 *     P = P(1) * P(2) * ... * P(z-1)
 42 *  
 43 *  where P(k) is a plane rotation matrix defined by the 2-by-2 rotation
 44 *  
 45 *     R(k) = (  c(k)  s(k) )
 46 *          = ( -s(k)  c(k) ).
 47 *  
 48 *  When PIVOT = 'V' (Variable pivot), the rotation is performed
 49 *  for the plane (k,k+1), i.e., P(k) has the form
 50 *  
 51 *     P(k) = (  1                                            )
 52 *            (       ...                                     )
 53 *            (              1                                )
 54 *            (                   c(k)  s(k)                  )
 55 *            (                  -s(k)  c(k)                  )
 56 *            (                                1              )
 57 *            (                                     ...       )
 58 *            (                                            1  )
 59 *  
 60 *  where R(k) appears as a rank-2 modification to the identity matrix in
 61 *  rows and columns k and k+1.
 62 *  
 63 *  When PIVOT = 'T' (Top pivot), the rotation is performed for the
 64 *  plane (1,k+1), so P(k) has the form
 65 *  
 66 *     P(k) = (  c(k)                    s(k)                 )
 67 *            (         1                                     )
 68 *            (              ...                              )
 69 *            (                     1                         )
 70 *            ( -s(k)                    c(k)                 )
 71 *            (                                 1             )
 72 *            (                                      ...      )
 73 *            (                                             1 )
 74 *  
 75 *  where R(k) appears in rows and columns 1 and k+1.
 76 *  
 77 *  Similarly, when PIVOT = 'B' (Bottom pivot), the rotation is
 78 *  performed for the plane (k,z), giving P(k) the form
 79 *  
 80 *     P(k) = ( 1                                             )
 81 *            (      ...                                      )
 82 *            (             1                                 )
 83 *            (                  c(k)                    s(k) )
 84 *            (                         1                     )
 85 *            (                              ...              )
 86 *            (                                     1         )
 87 *            (                 -s(k)                    c(k) )
 88 *  
 89 *  where R(k) appears in rows and columns k and z.  The rotations are
 90 *  performed without ever forming P(k) explicitly.
 91 *
 92 *  Arguments
 93 *  =========
 94 *
 95 *  SIDE    (input) CHARACTER*1
 96 *          Specifies whether the plane rotation matrix P is applied to
 97 *          A on the left or the right.
 98 *          = 'L':  Left, compute A := P*A
 99 *          = 'R':  Right, compute A:= A*P**T
100 *
101 *  PIVOT   (input) CHARACTER*1
102 *          Specifies the plane for which P(k) is a plane rotation
103 *          matrix.
104 *          = 'V':  Variable pivot, the plane (k,k+1)
105 *          = 'T':  Top pivot, the plane (1,k+1)
106 *          = 'B':  Bottom pivot, the plane (k,z)
107 *
108 *  DIRECT  (input) CHARACTER*1
109 *          Specifies whether P is a forward or backward sequence of
110 *          plane rotations.
111 *          = 'F':  Forward, P = P(z-1)*...*P(2)*P(1)
112 *          = 'B':  Backward, P = P(1)*P(2)*...*P(z-1)
113 *
114 *  M       (input) INTEGER
115 *          The number of rows of the matrix A.  If m <= 1, an immediate
116 *          return is effected.
117 *
118 *  N       (input) INTEGER
119 *          The number of columns of the matrix A.  If n <= 1, an
120 *          immediate return is effected.
121 *
122 *  C       (input) DOUBLE PRECISION array, dimension
123 *                  (M-1) if SIDE = 'L'
124 *                  (N-1) if SIDE = 'R'
125 *          The cosines c(k) of the plane rotations.
126 *
127 *  S       (input) DOUBLE PRECISION array, dimension
128 *                  (M-1) if SIDE = 'L'
129 *                  (N-1) if SIDE = 'R'
130 *          The sines s(k) of the plane rotations.  The 2-by-2 plane
131 *          rotation part of the matrix P(k), R(k), has the form
132 *          R(k) = (  c(k)  s(k) )
133 *                 ( -s(k)  c(k) ).
134 *
135 *  A       (input/output) COMPLEX*16 array, dimension (LDA,N)
136 *          The M-by-N matrix A.  On exit, A is overwritten by P*A if
137 *          SIDE = 'R' or by A*P**T if SIDE = 'L'.
138 *
139 *  LDA     (input) INTEGER
140 *          The leading dimension of the array A.  LDA >= max(1,M).
141 *
142 *  =====================================================================
143 *
144 *     .. Parameters ..
145       DOUBLE PRECISION   ONE, ZERO
146       PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
147 *     ..
148 *     .. Local Scalars ..
149       INTEGER            I, INFO, J
150       DOUBLE PRECISION   CTEMP, STEMP
151       COMPLEX*16         TEMP
152 *     ..
153 *     .. Intrinsic Functions ..
154       INTRINSIC          MAX
155 *     ..
156 *     .. External Functions ..
157       LOGICAL            LSAME
158       EXTERNAL           LSAME
159 *     ..
160 *     .. External Subroutines ..
161       EXTERNAL           XERBLA
162 *     ..
163 *     .. Executable Statements ..
164 *
165 *     Test the input parameters
166 *
167       INFO = 0
168       IF.NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
169          INFO = 1
170       ELSE IF.NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
171      $         'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
172          INFO = 2
173       ELSE IF.NOT.( LSAME( DIRECT'F' ) .OR. LSAME( DIRECT'B' ) ) )
174      $          THEN
175          INFO = 3
176       ELSE IF( M.LT.0 ) THEN
177          INFO = 4
178       ELSE IF( N.LT.0 ) THEN
179          INFO = 5
180       ELSE IF( LDA.LT.MAX1, M ) ) THEN
181          INFO = 9
182       END IF
183       IF( INFO.NE.0 ) THEN
184          CALL XERBLA( 'ZLASR ', INFO )
185          RETURN
186       END IF
187 *
188 *     Quick return if possible
189 *
190       IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
191      $   RETURN
192       IF( LSAME( SIDE, 'L' ) ) THEN
193 *
194 *        Form  P * A
195 *
196          IF( LSAME( PIVOT, 'V' ) ) THEN
197             IF( LSAME( DIRECT'F' ) ) THEN
198                DO 20 J = 1, M - 1
199                   CTEMP = C( J )
200                   STEMP = S( J )
201                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
202                      DO 10 I = 1, N
203                         TEMP = A( J+1, I )
204                         A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
205                         A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
206    10                CONTINUE
207                   END IF
208    20          CONTINUE
209             ELSE IF( LSAME( DIRECT'B' ) ) THEN
210                DO 40 J = M - 11-1
211                   CTEMP = C( J )
212                   STEMP = S( J )
213                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
214                      DO 30 I = 1, N
215                         TEMP = A( J+1, I )
216                         A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
217                         A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
218    30                CONTINUE
219                   END IF
220    40          CONTINUE
221             END IF
222          ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
223             IF( LSAME( DIRECT'F' ) ) THEN
224                DO 60 J = 2, M
225                   CTEMP = C( J-1 )
226                   STEMP = S( J-1 )
227                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
228                      DO 50 I = 1, N
229                         TEMP = A( J, I )
230                         A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
231                         A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
232    50                CONTINUE
233                   END IF
234    60          CONTINUE
235             ELSE IF( LSAME( DIRECT'B' ) ) THEN
236                DO 80 J = M, 2-1
237                   CTEMP = C( J-1 )
238                   STEMP = S( J-1 )
239                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
240                      DO 70 I = 1, N
241                         TEMP = A( J, I )
242                         A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
243                         A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
244    70                CONTINUE
245                   END IF
246    80          CONTINUE
247             END IF
248          ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
249             IF( LSAME( DIRECT'F' ) ) THEN
250                DO 100 J = 1, M - 1
251                   CTEMP = C( J )
252                   STEMP = S( J )
253                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
254                      DO 90 I = 1, N
255                         TEMP = A( J, I )
256                         A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
257                         A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
258    90                CONTINUE
259                   END IF
260   100          CONTINUE
261             ELSE IF( LSAME( DIRECT'B' ) ) THEN
262                DO 120 J = M - 11-1
263                   CTEMP = C( J )
264                   STEMP = S( J )
265                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
266                      DO 110 I = 1, N
267                         TEMP = A( J, I )
268                         A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
269                         A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
270   110                CONTINUE
271                   END IF
272   120          CONTINUE
273             END IF
274          END IF
275       ELSE IF( LSAME( SIDE, 'R' ) ) THEN
276 *
277 *        Form A * P**T
278 *
279          IF( LSAME( PIVOT, 'V' ) ) THEN
280             IF( LSAME( DIRECT'F' ) ) THEN
281                DO 140 J = 1, N - 1
282                   CTEMP = C( J )
283                   STEMP = S( J )
284                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
285                      DO 130 I = 1, M
286                         TEMP = A( I, J+1 )
287                         A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
288                         A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
289   130                CONTINUE
290                   END IF
291   140          CONTINUE
292             ELSE IF( LSAME( DIRECT'B' ) ) THEN
293                DO 160 J = N - 11-1
294                   CTEMP = C( J )
295                   STEMP = S( J )
296                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
297                      DO 150 I = 1, M
298                         TEMP = A( I, J+1 )
299                         A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
300                         A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
301   150                CONTINUE
302                   END IF
303   160          CONTINUE
304             END IF
305          ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
306             IF( LSAME( DIRECT'F' ) ) THEN
307                DO 180 J = 2, N
308                   CTEMP = C( J-1 )
309                   STEMP = S( J-1 )
310                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
311                      DO 170 I = 1, M
312                         TEMP = A( I, J )
313                         A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
314                         A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
315   170                CONTINUE
316                   END IF
317   180          CONTINUE
318             ELSE IF( LSAME( DIRECT'B' ) ) THEN
319                DO 200 J = N, 2-1
320                   CTEMP = C( J-1 )
321                   STEMP = S( J-1 )
322                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
323                      DO 190 I = 1, M
324                         TEMP = A( I, J )
325                         A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
326                         A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
327   190                CONTINUE
328                   END IF
329   200          CONTINUE
330             END IF
331          ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
332             IF( LSAME( DIRECT'F' ) ) THEN
333                DO 220 J = 1, N - 1
334                   CTEMP = C( J )
335                   STEMP = S( J )
336                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
337                      DO 210 I = 1, M
338                         TEMP = A( I, J )
339                         A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
340                         A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
341   210                CONTINUE
342                   END IF
343   220          CONTINUE
344             ELSE IF( LSAME( DIRECT'B' ) ) THEN
345                DO 240 J = N - 11-1
346                   CTEMP = C( J )
347                   STEMP = S( J )
348                   IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
349                      DO 230 I = 1, M
350                         TEMP = A( I, J )
351                         A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
352                         A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
353   230                CONTINUE
354                   END IF
355   240          CONTINUE
356             END IF
357          END IF
358       END IF
359 *
360       RETURN
361 *
362 *     End of ZLASR
363 *
364       END