1: *> \brief \b DGEMV
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 DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA,BETA
15: * INTEGER INCX,INCY,LDA,M,N
16: * CHARACTER TRANS
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DGEMV performs one of the matrix-vector operations
29: *>
30: *> y := alpha*A*x + beta*y, or y := alpha*A**T*x + beta*y,
31: *>
32: *> where alpha and beta are scalars, x and y are vectors and A is an
33: *> m by n matrix.
34: *> \endverbatim
35: *
36: * Arguments:
37: * ==========
38: *
39: *> \param[in] TRANS
40: *> \verbatim
41: *> TRANS is CHARACTER*1
42: *> On entry, TRANS specifies the operation to be performed as
43: *> follows:
44: *>
45: *> TRANS = 'N' or 'n' y := alpha*A*x + beta*y.
46: *>
47: *> TRANS = 'T' or 't' y := alpha*A**T*x + beta*y.
48: *>
49: *> TRANS = 'C' or 'c' y := alpha*A**T*x + beta*y.
50: *> \endverbatim
51: *>
52: *> \param[in] M
53: *> \verbatim
54: *> M is INTEGER
55: *> On entry, M specifies the number of rows of the matrix A.
56: *> M must be at least zero.
57: *> \endverbatim
58: *>
59: *> \param[in] N
60: *> \verbatim
61: *> N is INTEGER
62: *> On entry, N specifies the number of columns of the matrix A.
63: *> N must be at least zero.
64: *> \endverbatim
65: *>
66: *> \param[in] ALPHA
67: *> \verbatim
68: *> ALPHA is DOUBLE PRECISION.
69: *> On entry, ALPHA specifies the scalar alpha.
70: *> \endverbatim
71: *>
72: *> \param[in] A
73: *> \verbatim
74: *> A is DOUBLE PRECISION array, dimension ( LDA, N )
75: *> Before entry, the leading m by n part of the array A must
76: *> contain the matrix of coefficients.
77: *> \endverbatim
78: *>
79: *> \param[in] LDA
80: *> \verbatim
81: *> LDA is INTEGER
82: *> On entry, LDA specifies the first dimension of A as declared
83: *> in the calling (sub) program. LDA must be at least
84: *> max( 1, m ).
85: *> \endverbatim
86: *>
87: *> \param[in] X
88: *> \verbatim
89: *> X is DOUBLE PRECISION array, dimension at least
90: *> ( 1 + ( n - 1 )*abs( INCX ) ) when TRANS = 'N' or 'n'
91: *> and at least
92: *> ( 1 + ( m - 1 )*abs( INCX ) ) otherwise.
93: *> Before entry, the incremented array X must contain the
94: *> vector x.
95: *> \endverbatim
96: *>
97: *> \param[in] INCX
98: *> \verbatim
99: *> INCX is INTEGER
100: *> On entry, INCX specifies the increment for the elements of
101: *> X. INCX must not be zero.
102: *> \endverbatim
103: *>
104: *> \param[in] BETA
105: *> \verbatim
106: *> BETA is DOUBLE PRECISION.
107: *> On entry, BETA specifies the scalar beta. When BETA is
108: *> supplied as zero then Y need not be set on input.
109: *> \endverbatim
110: *>
111: *> \param[in,out] Y
112: *> \verbatim
113: *> Y is DOUBLE PRECISION array, dimension at least
114: *> ( 1 + ( m - 1 )*abs( INCY ) ) when TRANS = 'N' or 'n'
115: *> and at least
116: *> ( 1 + ( n - 1 )*abs( INCY ) ) otherwise.
117: *> Before entry with BETA non-zero, the incremented array Y
118: *> must contain the vector y. On exit, Y is overwritten by the
119: *> updated vector y.
120: *> \endverbatim
121: *>
122: *> \param[in] INCY
123: *> \verbatim
124: *> INCY is INTEGER
125: *> On entry, INCY specifies the increment for the elements of
126: *> Y. INCY must not be zero.
127: *> \endverbatim
128: *
129: * Authors:
130: * ========
131: *
132: *> \author Univ. of Tennessee
133: *> \author Univ. of California Berkeley
134: *> \author Univ. of Colorado Denver
135: *> \author NAG Ltd.
136: *
137: *> \ingroup double_blas_level2
138: *
139: *> \par Further Details:
140: * =====================
141: *>
142: *> \verbatim
143: *>
144: *> Level 2 Blas routine.
145: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
146: *>
147: *> -- Written on 22-October-1986.
148: *> Jack Dongarra, Argonne National Lab.
149: *> Jeremy Du Croz, Nag Central Office.
150: *> Sven Hammarling, Nag Central Office.
151: *> Richard Hanson, Sandia National Labs.
152: *> \endverbatim
153: *>
154: * =====================================================================
155: SUBROUTINE DGEMV(TRANS,M,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
156: *
157: * -- Reference BLAS level2 routine --
158: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
159: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
160: *
161: * .. Scalar Arguments ..
162: DOUBLE PRECISION ALPHA,BETA
163: INTEGER INCX,INCY,LDA,M,N
164: CHARACTER TRANS
165: * ..
166: * .. Array Arguments ..
167: DOUBLE PRECISION A(LDA,*),X(*),Y(*)
168: * ..
169: *
170: * =====================================================================
171: *
172: * .. Parameters ..
173: DOUBLE PRECISION ONE,ZERO
174: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
175: * ..
176: * .. Local Scalars ..
177: DOUBLE PRECISION TEMP
178: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY,LENX,LENY
179: * ..
180: * .. External Functions ..
181: LOGICAL LSAME
182: EXTERNAL LSAME
183: * ..
184: * .. External Subroutines ..
185: EXTERNAL XERBLA
186: * ..
187: * .. Intrinsic Functions ..
188: INTRINSIC MAX
189: * ..
190: *
191: * Test the input parameters.
192: *
193: INFO = 0
194: IF (.NOT.LSAME(TRANS,'N') .AND. .NOT.LSAME(TRANS,'T') .AND.
195: + .NOT.LSAME(TRANS,'C')) THEN
196: INFO = 1
197: ELSE IF (M.LT.0) THEN
198: INFO = 2
199: ELSE IF (N.LT.0) THEN
200: INFO = 3
201: ELSE IF (LDA.LT.MAX(1,M)) THEN
202: INFO = 6
203: ELSE IF (INCX.EQ.0) THEN
204: INFO = 8
205: ELSE IF (INCY.EQ.0) THEN
206: INFO = 11
207: END IF
208: IF (INFO.NE.0) THEN
209: CALL XERBLA('DGEMV ',INFO)
210: RETURN
211: END IF
212: *
213: * Quick return if possible.
214: *
215: IF ((M.EQ.0) .OR. (N.EQ.0) .OR.
216: + ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
217: *
218: * Set LENX and LENY, the lengths of the vectors x and y, and set
219: * up the start points in X and Y.
220: *
221: IF (LSAME(TRANS,'N')) THEN
222: LENX = N
223: LENY = M
224: ELSE
225: LENX = M
226: LENY = N
227: END IF
228: IF (INCX.GT.0) THEN
229: KX = 1
230: ELSE
231: KX = 1 - (LENX-1)*INCX
232: END IF
233: IF (INCY.GT.0) THEN
234: KY = 1
235: ELSE
236: KY = 1 - (LENY-1)*INCY
237: END IF
238: *
239: * Start the operations. In this version the elements of A are
240: * accessed sequentially with one pass through A.
241: *
242: * First form y := beta*y.
243: *
244: IF (BETA.NE.ONE) THEN
245: IF (INCY.EQ.1) THEN
246: IF (BETA.EQ.ZERO) THEN
247: DO 10 I = 1,LENY
248: Y(I) = ZERO
249: 10 CONTINUE
250: ELSE
251: DO 20 I = 1,LENY
252: Y(I) = BETA*Y(I)
253: 20 CONTINUE
254: END IF
255: ELSE
256: IY = KY
257: IF (BETA.EQ.ZERO) THEN
258: DO 30 I = 1,LENY
259: Y(IY) = ZERO
260: IY = IY + INCY
261: 30 CONTINUE
262: ELSE
263: DO 40 I = 1,LENY
264: Y(IY) = BETA*Y(IY)
265: IY = IY + INCY
266: 40 CONTINUE
267: END IF
268: END IF
269: END IF
270: IF (ALPHA.EQ.ZERO) RETURN
271: IF (LSAME(TRANS,'N')) THEN
272: *
273: * Form y := alpha*A*x + y.
274: *
275: JX = KX
276: IF (INCY.EQ.1) THEN
277: DO 60 J = 1,N
278: TEMP = ALPHA*X(JX)
279: DO 50 I = 1,M
280: Y(I) = Y(I) + TEMP*A(I,J)
281: 50 CONTINUE
282: JX = JX + INCX
283: 60 CONTINUE
284: ELSE
285: DO 80 J = 1,N
286: TEMP = ALPHA*X(JX)
287: IY = KY
288: DO 70 I = 1,M
289: Y(IY) = Y(IY) + TEMP*A(I,J)
290: IY = IY + INCY
291: 70 CONTINUE
292: JX = JX + INCX
293: 80 CONTINUE
294: END IF
295: ELSE
296: *
297: * Form y := alpha*A**T*x + y.
298: *
299: JY = KY
300: IF (INCX.EQ.1) THEN
301: DO 100 J = 1,N
302: TEMP = ZERO
303: DO 90 I = 1,M
304: TEMP = TEMP + A(I,J)*X(I)
305: 90 CONTINUE
306: Y(JY) = Y(JY) + ALPHA*TEMP
307: JY = JY + INCY
308: 100 CONTINUE
309: ELSE
310: DO 120 J = 1,N
311: TEMP = ZERO
312: IX = KX
313: DO 110 I = 1,M
314: TEMP = TEMP + A(I,J)*X(IX)
315: IX = IX + INCX
316: 110 CONTINUE
317: Y(JY) = Y(JY) + ALPHA*TEMP
318: JY = JY + INCY
319: 120 CONTINUE
320: END IF
321: END IF
322: *
323: RETURN
324: *
325: * End of DGEMV
326: *
327: END
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