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
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
|
SUBROUTINE ZHEMVF ( UPLO, N, ALPHA, A, LDA, X, INCX,
$ BETA, Y, INCY )
* .. Scalar Arguments ..
COMPLEX*16 ALPHA, BETA
INTEGER INCX, INCY, LDA, N
CHARACTER*1 UPLO
* .. Array Arguments ..
COMPLEX*16 A( LDA, * ), X( * ), Y( * )
* ..
*
* Purpose
* =======
*
* ZHEMV performs the matrix-vector operation
*
* y := alpha*A*x + beta*y,
*
* where alpha and beta are scalars, x and y are n element vectors and
* A is an n by n hermitian matrix.
*
* Parameters
* ==========
*
* UPLO - CHARACTER*1.
* On entry, UPLO specifies whether the upper or lower
* triangular part of the array A is to be referenced as
* follows:
*
* UPLO = 'U' or 'u' Only the upper triangular part of A
* is to be referenced.
*
* UPLO = 'L' or 'l' Only the lower triangular part of A
* is to be referenced.
*
* Unchanged on exit.
*
* N - INTEGER.
* On entry, N specifies the order of the matrix A.
* N must be at least zero.
* Unchanged on exit.
*
* ALPHA - COMPLEX*16 .
* On entry, ALPHA specifies the scalar alpha.
* Unchanged on exit.
*
* A - COMPLEX*16 array of DIMENSION ( LDA, n ).
* Before entry with UPLO = 'U' or 'u', the leading n by n
* upper triangular part of the array A must contain the upper
* triangular part of the hermitian matrix and the strictly
* lower triangular part of A is not referenced.
* Before entry with UPLO = 'L' or 'l', the leading n by n
* lower triangular part of the array A must contain the lower
* triangular part of the hermitian matrix and the strictly
* upper triangular part of A is not referenced.
* Note that the imaginary parts of the diagonal elements need
* not be set and are assumed to be zero.
* Unchanged on exit.
*
* LDA - INTEGER.
* On entry, LDA specifies the first dimension of A as declared
* in the calling (sub) program. LDA must be at least
* max( 1, n ).
* Unchanged on exit.
*
* X - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCX ) ).
* Before entry, the incremented array X must contain the n
* element vector x.
* Unchanged on exit.
*
* INCX - INTEGER.
* On entry, INCX specifies the increment for the elements of
* X. INCX must not be zero.
* Unchanged on exit.
*
* BETA - COMPLEX*16 .
* On entry, BETA specifies the scalar beta. When BETA is
* supplied as zero then Y need not be set on input.
* Unchanged on exit.
*
* Y - COMPLEX*16 array of dimension at least
* ( 1 + ( n - 1 )*abs( INCY ) ).
* Before entry, the incremented array Y must contain the n
* element vector y. On exit, Y is overwritten by the updated
* vector y.
*
* INCY - INTEGER.
* On entry, INCY specifies the increment for the elements of
* Y. INCY must not be zero.
* Unchanged on exit.
*
*
* Level 2 Blas routine.
*
* -- Written on 22-October-1986.
* Jack Dongarra, Argonne National Lab.
* Jeremy Du Croz, Nag Central Office.
* Sven Hammarling, Nag Central Office.
* Richard Hanson, Sandia National Labs.
*
*
* .. Parameters ..
COMPLEX*16 ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
COMPLEX*16 ZERO
PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
* .. Local Scalars ..
COMPLEX*16 TEMP1, TEMP2
INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* .. External Subroutines ..
EXTERNAL XERBLA
* .. Intrinsic Functions ..
INTRINSIC DCONJG, MAX, DBLE
* ..
* .. Executable Statements ..
*
* Test the input parameters.
*
INFO = 0
IF ( .NOT.LSAME( UPLO, 'U' ).AND.
$ .NOT.LSAME( UPLO, 'L' ).AND.
$ .NOT.LSAME( UPLO, 'V' ).AND.
$ .NOT.LSAME( UPLO, 'M' ))THEN
INFO = 1
ELSE IF( N.LT.0 )THEN
INFO = 2
ELSE IF( LDA.LT.MAX( 1, N ) )THEN
INFO = 5
ELSE IF( INCX.EQ.0 )THEN
INFO = 7
ELSE IF( INCY.EQ.0 )THEN
INFO = 10
END IF
IF( INFO.NE.0 )THEN
CALL XERBLA( 'ZHEMV ', INFO )
RETURN
END IF
*
* Quick return if possible.
*
IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
$ RETURN
*
* Set up the start points in X and Y.
*
IF( INCX.GT.0 )THEN
KX = 1
ELSE
KX = 1 - ( N - 1 )*INCX
END IF
IF( INCY.GT.0 )THEN
KY = 1
ELSE
KY = 1 - ( N - 1 )*INCY
END IF
*
* Start the operations. In this version the elements of A are
* accessed sequentially with one pass through the triangular part
* of A.
*
* First form y := beta*y.
*
IF( BETA.NE.ONE )THEN
IF( INCY.EQ.1 )THEN
IF( BETA.EQ.ZERO )THEN
DO 10, I = 1, N
Y( I ) = ZERO
10 CONTINUE
ELSE
DO 20, I = 1, N
Y( I ) = BETA*Y( I )
20 CONTINUE
END IF
ELSE
IY = KY
IF( BETA.EQ.ZERO )THEN
DO 30, I = 1, N
Y( IY ) = ZERO
IY = IY + INCY
30 CONTINUE
ELSE
DO 40, I = 1, N
Y( IY ) = BETA*Y( IY )
IY = IY + INCY
40 CONTINUE
END IF
END IF
END IF
IF( ALPHA.EQ.ZERO )
$ RETURN
IF( LSAME( UPLO, 'U' ) )THEN
*
* Form y when A is stored in upper triangle.
*
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 60, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
DO 50, I = 1, J - 1
Y( I ) = Y( I ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( I )
50 CONTINUE
Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2
60 CONTINUE
ELSE
JX = KX
JY = KY
DO 80, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
IX = KX
IY = KY
DO 70, I = 1, J - 1
Y( IY ) = Y( IY ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( IX )
IX = IX + INCX
IY = IY + INCY
70 CONTINUE
Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
80 CONTINUE
END IF
RETURN
ENDIF
IF( LSAME( UPLO, 'L' ) )THEN
*
* Form y when A is stored in lower triangle.
*
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 100, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) )
DO 90, I = J + 1, N
Y( I ) = Y( I ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( I )
90 CONTINUE
Y( J ) = Y( J ) + ALPHA*TEMP2
100 CONTINUE
ELSE
JX = KX
JY = KY
DO 120, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) )
IX = JX
IY = JY
DO 110, I = J + 1, N
IX = IX + INCX
IY = IY + INCY
Y( IY ) = Y( IY ) + TEMP1*A( I, J )
TEMP2 = TEMP2 + DCONJG( A( I, J ) )*X( IX )
110 CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
120 CONTINUE
END IF
RETURN
END IF
IF( LSAME( UPLO, 'V' ) )THEN
*
* Form y when A is stored in upper triangle.
*
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 160, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
DO 150, I = 1, J - 1
Y( I ) = Y( I ) + TEMP1* DCONJG(A( I, J ))
TEMP2 = TEMP2 + A( I, J )*X( I )
150 CONTINUE
Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2
160 CONTINUE
ELSE
JX = KX
JY = KY
DO 180, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
IX = KX
IY = KY
DO 170, I = 1, J - 1
Y( IY ) = Y( IY ) + TEMP1* DCONJG(A( I, J ))
TEMP2 = TEMP2 + A( I, J )*X( IX )
IX = IX + INCX
IY = IY + INCY
170 CONTINUE
Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
180 CONTINUE
END IF
RETURN
ENDIF
IF( LSAME( UPLO, 'M' ) )THEN
*
* Form y when A is stored in lower triangle.
*
IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
DO 200, J = 1, N
TEMP1 = ALPHA*X( J )
TEMP2 = ZERO
Y( J ) = Y( J ) + TEMP1*DBLE( A( J, J ) )
DO 190, I = J + 1, N
Y( I ) = Y( I ) + TEMP1*DCONJG(A( I, J ))
TEMP2 = TEMP2 + A( I, J )*X( I )
190 CONTINUE
Y( J ) = Y( J ) + ALPHA*TEMP2
200 CONTINUE
ELSE
JX = KX
JY = KY
DO 220, J = 1, N
TEMP1 = ALPHA*X( JX )
TEMP2 = ZERO
Y( JY ) = Y( JY ) + TEMP1*DBLE( A( J, J ) )
IX = JX
IY = JY
DO 210, I = J + 1, N
IX = IX + INCX
IY = IY + INCY
Y( IY ) = Y( IY ) + TEMP1*DCONJG(A( I, J ))
TEMP2 = TEMP2 + A( I, J )*X( IX )
210 CONTINUE
Y( JY ) = Y( JY ) + ALPHA*TEMP2
JX = JX + INCX
JY = JY + INCY
220 CONTINUE
END IF
RETURN
END IF
*
RETURN
*
* End of ZHEMV .
*
END
|
