1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
|
SUBROUTINE DLASR( SIDE, PIVOT, DIRECT, M, N, C, S, A, LDA )
*
* -- LAPACK auxiliary routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* October 31, 1992
*
* .. Scalar Arguments ..
CHARACTER DIRECT, PIVOT, SIDE
INTEGER LDA, M, N
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), C( * ), S( * )
* ..
*
* Purpose
* =======
*
* DLASR performs the transformation
*
* A := P*A, when SIDE = 'L' or 'l' ( Left-hand side )
*
* A := A*P', when SIDE = 'R' or 'r' ( Right-hand side )
*
* where A is an m by n real matrix and P is an orthogonal matrix,
* consisting of a sequence of plane rotations determined by the
* parameters PIVOT and DIRECT as follows ( z = m when SIDE = 'L' or 'l'
* and z = n when SIDE = 'R' or 'r' ):
*
* When DIRECT = 'F' or 'f' ( Forward sequence ) then
*
* P = P( z - 1 )*...*P( 2 )*P( 1 ),
*
* and when DIRECT = 'B' or 'b' ( Backward sequence ) then
*
* P = P( 1 )*P( 2 )*...*P( z - 1 ),
*
* where P( k ) is a plane rotation matrix for the following planes:
*
* when PIVOT = 'V' or 'v' ( Variable pivot ),
* the plane ( k, k + 1 )
*
* when PIVOT = 'T' or 't' ( Top pivot ),
* the plane ( 1, k + 1 )
*
* when PIVOT = 'B' or 'b' ( Bottom pivot ),
* the plane ( k, z )
*
* c( k ) and s( k ) must contain the cosine and sine that define the
* matrix P( k ). The two by two plane rotation part of the matrix
* P( k ), R( k ), is assumed to be of the form
*
* R( k ) = ( c( k ) s( k ) ).
* ( -s( k ) c( k ) )
*
* This version vectorises across rows of the array A when SIDE = 'L'.
*
* Arguments
* =========
*
* SIDE (input) 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'
*
* DIRECT (input) 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 )
*
* PIVOT (input) 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)
*
* M (input) INTEGER
* The number of rows of the matrix A. If m <= 1, an immediate
* return is effected.
*
* N (input) INTEGER
* The number of columns of the matrix A. If n <= 1, an
* immediate return is effected.
*
* C, S (input) DOUBLE PRECISION arrays, dimension
* (M-1) if SIDE = 'L'
* (N-1) if SIDE = 'R'
* c(k) and s(k) contain the cosine and sine that define the
* matrix P(k). The two by two plane rotation part of the
* matrix P(k), R(k), is assumed to be of the form
* R( k ) = ( c( k ) s( k ) ).
* ( -s( k ) c( k ) )
*
* A (input/output) 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' if SIDE = 'L'.
*
* LDA (input) INTEGER
* The leading dimension of the array A. LDA >= max(1,M).
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
INTEGER I, INFO, J
DOUBLE PRECISION CTEMP, STEMP, TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Test the input parameters
*
INFO = 0
IF( .NOT.( LSAME( SIDE, 'L' ) .OR. LSAME( SIDE, 'R' ) ) ) THEN
INFO = 1
ELSE IF( .NOT.( LSAME( PIVOT, 'V' ) .OR. LSAME( PIVOT,
$ 'T' ) .OR. LSAME( PIVOT, 'B' ) ) ) THEN
INFO = 2
ELSE IF( .NOT.( LSAME( DIRECT, 'F' ) .OR. LSAME( DIRECT, 'B' ) ) )
$ THEN
INFO = 3
ELSE IF( M.LT.0 ) THEN
INFO = 4
ELSE IF( N.LT.0 ) THEN
INFO = 5
ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
INFO = 9
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'DLASR ', INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( ( M.EQ.0 ) .OR. ( N.EQ.0 ) )
$ RETURN
IF( LSAME( SIDE, 'L' ) ) THEN
*
* Form P * A
*
IF( LSAME( PIVOT, 'V' ) ) THEN
IF( LSAME( DIRECT, 'F' ) ) THEN
DO 20 J = 1, M - 1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 10 I = 1, N
TEMP = A( J+1, I )
A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
10 CONTINUE
END IF
20 CONTINUE
ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
DO 40 J = M - 1, 1, -1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 30 I = 1, N
TEMP = A( J+1, I )
A( J+1, I ) = CTEMP*TEMP - STEMP*A( J, I )
A( J, I ) = STEMP*TEMP + CTEMP*A( J, I )
30 CONTINUE
END IF
40 CONTINUE
END IF
ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
IF( LSAME( DIRECT, 'F' ) ) THEN
DO 60 J = 2, M
CTEMP = C( J-1 )
STEMP = S( J-1 )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 50 I = 1, N
TEMP = A( J, I )
A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
50 CONTINUE
END IF
60 CONTINUE
ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
DO 80 J = M, 2, -1
CTEMP = C( J-1 )
STEMP = S( J-1 )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 70 I = 1, N
TEMP = A( J, I )
A( J, I ) = CTEMP*TEMP - STEMP*A( 1, I )
A( 1, I ) = STEMP*TEMP + CTEMP*A( 1, I )
70 CONTINUE
END IF
80 CONTINUE
END IF
ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
IF( LSAME( DIRECT, 'F' ) ) THEN
DO 100 J = 1, M - 1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 90 I = 1, N
TEMP = A( J, I )
A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
90 CONTINUE
END IF
100 CONTINUE
ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
DO 120 J = M - 1, 1, -1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 110 I = 1, N
TEMP = A( J, I )
A( J, I ) = STEMP*A( M, I ) + CTEMP*TEMP
A( M, I ) = CTEMP*A( M, I ) - STEMP*TEMP
110 CONTINUE
END IF
120 CONTINUE
END IF
END IF
ELSE IF( LSAME( SIDE, 'R' ) ) THEN
*
* Form A * P'
*
IF( LSAME( PIVOT, 'V' ) ) THEN
IF( LSAME( DIRECT, 'F' ) ) THEN
DO 140 J = 1, N - 1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 130 I = 1, M
TEMP = A( I, J+1 )
A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
130 CONTINUE
END IF
140 CONTINUE
ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
DO 160 J = N - 1, 1, -1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 150 I = 1, M
TEMP = A( I, J+1 )
A( I, J+1 ) = CTEMP*TEMP - STEMP*A( I, J )
A( I, J ) = STEMP*TEMP + CTEMP*A( I, J )
150 CONTINUE
END IF
160 CONTINUE
END IF
ELSE IF( LSAME( PIVOT, 'T' ) ) THEN
IF( LSAME( DIRECT, 'F' ) ) THEN
DO 180 J = 2, N
CTEMP = C( J-1 )
STEMP = S( J-1 )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 170 I = 1, M
TEMP = A( I, J )
A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
170 CONTINUE
END IF
180 CONTINUE
ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
DO 200 J = N, 2, -1
CTEMP = C( J-1 )
STEMP = S( J-1 )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 190 I = 1, M
TEMP = A( I, J )
A( I, J ) = CTEMP*TEMP - STEMP*A( I, 1 )
A( I, 1 ) = STEMP*TEMP + CTEMP*A( I, 1 )
190 CONTINUE
END IF
200 CONTINUE
END IF
ELSE IF( LSAME( PIVOT, 'B' ) ) THEN
IF( LSAME( DIRECT, 'F' ) ) THEN
DO 220 J = 1, N - 1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 210 I = 1, M
TEMP = A( I, J )
A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
210 CONTINUE
END IF
220 CONTINUE
ELSE IF( LSAME( DIRECT, 'B' ) ) THEN
DO 240 J = N - 1, 1, -1
CTEMP = C( J )
STEMP = S( J )
IF( ( CTEMP.NE.ONE ) .OR. ( STEMP.NE.ZERO ) ) THEN
DO 230 I = 1, M
TEMP = A( I, J )
A( I, J ) = STEMP*A( I, N ) + CTEMP*TEMP
A( I, N ) = CTEMP*A( I, N ) - STEMP*TEMP
230 CONTINUE
END IF
240 CONTINUE
END IF
END IF
END IF
*
RETURN
*
* End of DLASR
*
END
|
