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1.1 bertrand 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.MAX( 1, 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 - 1, 1, -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 - 1, 1, -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'
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 - 1, 1, -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 - 1, 1, -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