1: *> \brief \b ZGEMV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: * Definition:
9: * ===========
10: *
11: * SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA,BETA
15: * INTEGER INCX,INCY,LDA,M,N
16: * CHARACTER TRANS
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZGEMV performs one of the matrix-vector operations
29: *>
30: *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y, or
31: *>
32: *> y := alpha*A**H*x + beta*y,
33: *>
34: *> where alpha and beta are scalars, x and y are vectors and A is an
35: *> m by n matrix.
36: *> \endverbatim
37: *
38: * Arguments:
39: * ==========
40: *
41: *> \param[in] TRANS
42: *> \verbatim
43: *> TRANS is CHARACTER*1
44: *> On entry, TRANS specifies the operation to be performed as
45: *> follows:
46: *>
47: *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
48: *>
49: *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
50: *>
51: *> TRANS = 'C' or 'c' y := alpha*A**H*x + beta*y.
52: *> \endverbatim
53: *>
54: *> \param[in] M
55: *> \verbatim
56: *> M is INTEGER
57: *> On entry, M specifies the number of rows of the matrix A.
58: *> M must be at least zero.
59: *> \endverbatim
60: *>
61: *> \param[in] N
62: *> \verbatim
63: *> N is INTEGER
64: *> On entry, N specifies the number of columns of the matrix A.
65: *> N must be at least zero.
66: *> \endverbatim
67: *>
68: *> \param[in] ALPHA
69: *> \verbatim
70: *> ALPHA is COMPLEX*16
71: *> On entry, ALPHA specifies the scalar alpha.
72: *> \endverbatim
73: *>
74: *> \param[in] A
75: *> \verbatim
76: *> A is COMPLEX*16 array, dimension ( LDA, N )
77: *> Before entry, the leading m by n part of the array A must
78: *> contain the matrix of coefficients.
79: *> \endverbatim
80: *>
81: *> \param[in] LDA
82: *> \verbatim
83: *> LDA is INTEGER
84: *> On entry, LDA specifies the first dimension of A as declared
85: *> in the calling (sub) program. LDA must be at least
86: *> max( 1, m ).
87: *> \endverbatim
88: *>
89: *> \param[in] X
90: *> \verbatim
91: *> X is COMPLEX*16 array, dimension at least
92: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
93: *> and at least
94: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
95: *> Before entry, the incremented array X must contain the
96: *> vector x.
97: *> \endverbatim
98: *>
99: *> \param[in] INCX
100: *> \verbatim
101: *> INCX is INTEGER
102: *> On entry, INCX specifies the increment for the elements of
103: *> X. INCX must not be zero.
104: *> \endverbatim
105: *>
106: *> \param[in] BETA
107: *> \verbatim
108: *> BETA is COMPLEX*16
109: *> On entry, BETA specifies the scalar beta. When BETA is
110: *> supplied as zero then Y need not be set on input.
111: *> \endverbatim
112: *>
113: *> \param[in,out] Y
114: *> \verbatim
115: *> Y is COMPLEX*16 array, dimension at least
116: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
117: *> and at least
118: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
119: *> Before entry with BETA non-zero, the incremented array Y
120: *> must contain the vector y. On exit, Y is overwritten by the
121: *> updated vector y.
122: *> \endverbatim
123: *>
124: *> \param[in] INCY
125: *> \verbatim
126: *> INCY is INTEGER
127: *> On entry, INCY specifies the increment for the elements of
128: *> Y. INCY must not be zero.
129: *> \endverbatim
130: *
131: * Authors:
132: * ========
133: *
134: *> \author Univ. of Tennessee
135: *> \author Univ. of California Berkeley
136: *> \author Univ. of Colorado Denver
137: *> \author NAG Ltd.
138: *
139: *> \ingroup complex16_blas_level2
140: *
141: *> \par Further Details:
142: * =====================
143: *>
144: *> \verbatim
145: *>
146: *> Level 2 Blas routine.
147: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
148: *>
149: *> -- Written on 22-October-1986.
150: *> Jack Dongarra, Argonne National Lab.
151: *> Jeremy Du Croz, Nag Central Office.
152: *> Sven Hammarling, Nag Central Office.
153: *> Richard Hanson, Sandia National Labs.
154: *> \endverbatim
155: *>
156: * =====================================================================
157: SUBROUTINE ZGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
158: *
159: * -- Reference BLAS level2 routine --
160: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
161: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
162: *
163: * .. Scalar Arguments ..
164: COMPLEX*16 ALPHA,BETA
165: INTEGER INCX,INCY,LDA,M,N
166: CHARACTER TRANS
167: * ..
168: * .. Array Arguments ..
169: COMPLEX*16 A(LDA,*),X(*),Y(*)
170: * ..
171: *
172: * =====================================================================
173: *
174: * .. Parameters ..
175: COMPLEX*16 ONE
176: PARAMETER (ONE= (1.0D+0,0.0D+0))
177: COMPLEX*16 ZERO
178: PARAMETER (ZERO= (0.0D+0,0.0D+0))
179: * ..
180: * .. Local Scalars ..
181: COMPLEX*16 TEMP
182: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
183: LOGICAL NOCONJ
184: * ..
185: * .. External Functions ..
186: LOGICAL LSAME
187: EXTERNAL LSAME
188: * ..
189: * .. External Subroutines ..
190: EXTERNAL XERBLA
191: * ..
192: * .. Intrinsic Functions ..
193: INTRINSIC DCONJG,MAX
194: * ..
195: *
196: * Test the input parameters.
197: *
198: INFO = 0
199: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
200: + .NOT.LSAME(TRANS,'C')) THEN
201: INFO = 1
202: ELSE IF (M.LT.0) THEN
203: INFO = 2
204: ELSE IF (N.LT.0) THEN
205: INFO = 3
206: ELSE IF (LDA.LT.MAX(1,M)) THEN
207: INFO = 6
208: ELSE IF (INCX.EQ.0) THEN
209: INFO = 8
210: ELSE IF (INCY.EQ.0) THEN
211: INFO = 11
212: END IF
213: IF (INFO.NE.0) THEN
214: CALL XERBLA('ZGEMV ',INFO)
215: RETURN
216: END IF
217: *
218: * Quick return if possible.
219: *
220: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
221: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
222: *
223: NOCONJ = LSAME(TRANS,'T')
224: *
225: * Set LENX and LENY, the lengths of the vectors x and y, and set
226: * up the start points in X and Y.
227: *
228: IF (LSAME(TRANS,'N')) THEN
229: LENX = N
230: LENY = M
231: ELSE
232: LENX = M
233: LENY = N
234: END IF
235: IF (INCX.GT.0) THEN
236: KX = 1
237: ELSE
238: KX = 1 - (LENX-1)*INCX
239: END IF
240: IF (INCY.GT.0) THEN
241: KY = 1
242: ELSE
243: KY = 1 - (LENY-1)*INCY
244: END IF
245: *
246: * Start the operations. In this version the elements of A are
247: * accessed sequentially with one pass through A.
248: *
249: * First form y := beta*y.
250: *
251: IF (BETA.NE.ONE) THEN
252: IF (INCY.EQ.1) THEN
253: IF (BETA.EQ.ZERO) THEN
254: DO 10 I = 1,LENY
255: Y(I) = ZERO
256: 10 CONTINUE
257: ELSE
258: DO 20 I = 1,LENY
259: Y(I) = BETA*Y(I)
260: 20 CONTINUE
261: END IF
262: ELSE
263: IY = KY
264: IF (BETA.EQ.ZERO) THEN
265: DO 30 I = 1,LENY
266: Y(IY) = ZERO
267: IY = IY + INCY
268: 30 CONTINUE
269: ELSE
270: DO 40 I = 1,LENY
271: Y(IY) = BETA*Y(IY)
272: IY = IY + INCY
273: 40 CONTINUE
274: END IF
275: END IF
276: END IF
277: IF (ALPHA.EQ.ZERO) RETURN
278: IF (LSAME(TRANS,'N')) THEN
279: *
280: * Form y := alpha*A*x + y.
281: *
282: JX = KX
283: IF (INCY.EQ.1) THEN
284: DO 60 J = 1,N
285: TEMP = ALPHA*X(JX)
286: DO 50 I = 1,M
287: Y(I) = Y(I) + TEMP*A(I,J)
288: 50 CONTINUE
289: JX = JX + INCX
290: 60 CONTINUE
291: ELSE
292: DO 80 J = 1,N
293: TEMP = ALPHA*X(JX)
294: IY = KY
295: DO 70 I = 1,M
296: Y(IY) = Y(IY) + TEMP*A(I,J)
297: IY = IY + INCY
298: 70 CONTINUE
299: JX = JX + INCX
300: 80 CONTINUE
301: END IF
302: ELSE
303: *
304: * Form y := alpha*A**T*x + y or y := alpha*A**H*x + y.
305: *
306: JY = KY
307: IF (INCX.EQ.1) THEN
308: DO 110 J = 1,N
309: TEMP = ZERO
310: IF (NOCONJ) THEN
311: DO 90 I = 1,M
312: TEMP = TEMP + A(I,J)*X(I)
313: 90 CONTINUE
314: ELSE
315: DO 100 I = 1,M
316: TEMP = TEMP + DCONJG(A(I,J))*X(I)
317: 100 CONTINUE
318: END IF
319: Y(JY) = Y(JY) + ALPHA*TEMP
320: JY = JY + INCY
321: 110 CONTINUE
322: ELSE
323: DO 140 J = 1,N
324: TEMP = ZERO
325: IX = KX
326: IF (NOCONJ) THEN
327: DO 120 I = 1,M
328: TEMP = TEMP + A(I,J)*X(IX)
329: IX = IX + INCX
330: 120 CONTINUE
331: ELSE
332: DO 130 I = 1,M
333: TEMP = TEMP + DCONJG(A(I,J))*X(IX)
334: IX = IX + INCX
335: 130 CONTINUE
336: END IF
337: Y(JY) = Y(JY) + ALPHA*TEMP
338: JY = JY + INCY
339: 140 CONTINUE
340: END IF
341: END IF
342: *
343: RETURN
344: *
345: * End of ZGEMV
346: *
347: END
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