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1: *> \brief \b DSYMV
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 DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * DOUBLE PRECISION ALPHA,BETA
15: * INTEGER INCX,INCY,LDA,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * DOUBLE PRECISION A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> DSYMV performs the matrix-vector operation
29: *>
30: *> y := alpha*A*x + beta*y,
31: *>
32: *> where alpha and beta are scalars, x and y are n element vectors and
33: *> A is an n by n symmetric matrix.
34: *> \endverbatim
35: *
36: * Arguments:
37: * ==========
38: *
39: *> \param[in] UPLO
40: *> \verbatim
41: *> UPLO is CHARACTER*1
42: *> On entry, UPLO specifies whether the upper or lower
43: *> triangular part of the array A is to be referenced as
44: *> follows:
45: *>
46: *> UPLO = 'U' or 'u' Only the upper triangular part of A
47: *> is to be referenced.
48: *>
49: *> UPLO = 'L' or 'l' Only the lower triangular part of A
50: *> is to be referenced.
51: *> \endverbatim
52: *>
53: *> \param[in] N
54: *> \verbatim
55: *> N is INTEGER
56: *> On entry, N specifies the order of the matrix A.
57: *> N must be at least zero.
58: *> \endverbatim
59: *>
60: *> \param[in] ALPHA
61: *> \verbatim
62: *> ALPHA is DOUBLE PRECISION.
63: *> On entry, ALPHA specifies the scalar alpha.
64: *> \endverbatim
65: *>
66: *> \param[in] A
67: *> \verbatim
68: *> A is DOUBLE PRECISION array of DIMENSION ( LDA, n ).
69: *> Before entry with UPLO = 'U' or 'u', the leading n by n
70: *> upper triangular part of the array A must contain the upper
71: *> triangular part of the symmetric matrix and the strictly
72: *> lower triangular part of A is not referenced.
73: *> Before entry with UPLO = 'L' or 'l', the leading n by n
74: *> lower triangular part of the array A must contain the lower
75: *> triangular part of the symmetric matrix and the strictly
76: *> upper triangular part of A is not referenced.
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, n ).
85: *> \endverbatim
86: *>
87: *> \param[in] X
88: *> \verbatim
89: *> X is DOUBLE PRECISION array of dimension at least
90: *> ( 1 + ( n - 1 )*abs( INCX ) ).
91: *> Before entry, the incremented array X must contain the n
92: *> element vector x.
93: *> \endverbatim
94: *>
95: *> \param[in] INCX
96: *> \verbatim
97: *> INCX is INTEGER
98: *> On entry, INCX specifies the increment for the elements of
99: *> X. INCX must not be zero.
100: *> \endverbatim
101: *>
102: *> \param[in] BETA
103: *> \verbatim
104: *> BETA is DOUBLE PRECISION.
105: *> On entry, BETA specifies the scalar beta. When BETA is
106: *> supplied as zero then Y need not be set on input.
107: *> \endverbatim
108: *>
109: *> \param[in,out] Y
110: *> \verbatim
111: *> Y is DOUBLE PRECISION array of dimension at least
112: *> ( 1 + ( n - 1 )*abs( INCY ) ).
113: *> Before entry, the incremented array Y must contain the n
114: *> element vector y. On exit, Y is overwritten by the updated
115: *> vector y.
116: *> \endverbatim
117: *>
118: *> \param[in] INCY
119: *> \verbatim
120: *> INCY is INTEGER
121: *> On entry, INCY specifies the increment for the elements of
122: *> Y. INCY must not be zero.
123: *> \endverbatim
124: *
125: * Authors:
126: * ========
127: *
128: *> \author Univ. of Tennessee
129: *> \author Univ. of California Berkeley
130: *> \author Univ. of Colorado Denver
131: *> \author NAG Ltd.
132: *
133: *> \date November 2011
134: *
135: *> \ingroup double_blas_level2
136: *
137: *> \par Further Details:
138: * =====================
139: *>
140: *> \verbatim
141: *>
142: *> Level 2 Blas routine.
143: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
144: *>
145: *> -- Written on 22-October-1986.
146: *> Jack Dongarra, Argonne National Lab.
147: *> Jeremy Du Croz, Nag Central Office.
148: *> Sven Hammarling, Nag Central Office.
149: *> Richard Hanson, Sandia National Labs.
150: *> \endverbatim
151: *>
152: * =====================================================================
153: SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
154: *
155: * -- Reference BLAS level2 routine (version 3.4.0) --
156: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
157: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158: * November 2011
159: *
160: * .. Scalar Arguments ..
161: DOUBLE PRECISION ALPHA,BETA
162: INTEGER INCX,INCY,LDA,N
163: CHARACTER UPLO
164: * ..
165: * .. Array Arguments ..
166: DOUBLE PRECISION A(LDA,*),X(*),Y(*)
167: * ..
168: *
169: * =====================================================================
170: *
171: * .. Parameters ..
172: DOUBLE PRECISION ONE,ZERO
173: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
174: * ..
175: * .. Local Scalars ..
176: DOUBLE PRECISION TEMP1,TEMP2
177: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
178: * ..
179: * .. External Functions ..
180: LOGICAL LSAME
181: EXTERNAL LSAME
182: * ..
183: * .. External Subroutines ..
184: EXTERNAL XERBLA
185: * ..
186: * .. Intrinsic Functions ..
187: INTRINSIC MAX
188: * ..
189: *
190: * Test the input parameters.
191: *
192: INFO = 0
193: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
194: INFO = 1
195: ELSE IF (N.LT.0) THEN
196: INFO = 2
197: ELSE IF (LDA.LT.MAX(1,N)) THEN
198: INFO = 5
199: ELSE IF (INCX.EQ.0) THEN
200: INFO = 7
201: ELSE IF (INCY.EQ.0) THEN
202: INFO = 10
203: END IF
204: IF (INFO.NE.0) THEN
205: CALL XERBLA('DSYMV ',INFO)
206: RETURN
207: END IF
208: *
209: * Quick return if possible.
210: *
211: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
212: *
213: * Set up the start points in X and Y.
214: *
215: IF (INCX.GT.0) THEN
216: KX = 1
217: ELSE
218: KX = 1 - (N-1)*INCX
219: END IF
220: IF (INCY.GT.0) THEN
221: KY = 1
222: ELSE
223: KY = 1 - (N-1)*INCY
224: END IF
225: *
226: * Start the operations. In this version the elements of A are
227: * accessed sequentially with one pass through the triangular part
228: * of A.
229: *
230: * First form y := beta*y.
231: *
232: IF (BETA.NE.ONE) THEN
233: IF (INCY.EQ.1) THEN
234: IF (BETA.EQ.ZERO) THEN
235: DO 10 I = 1,N
236: Y(I) = ZERO
237: 10 CONTINUE
238: ELSE
239: DO 20 I = 1,N
240: Y(I) = BETA*Y(I)
241: 20 CONTINUE
242: END IF
243: ELSE
244: IY = KY
245: IF (BETA.EQ.ZERO) THEN
246: DO 30 I = 1,N
247: Y(IY) = ZERO
248: IY = IY + INCY
249: 30 CONTINUE
250: ELSE
251: DO 40 I = 1,N
252: Y(IY) = BETA*Y(IY)
253: IY = IY + INCY
254: 40 CONTINUE
255: END IF
256: END IF
257: END IF
258: IF (ALPHA.EQ.ZERO) RETURN
259: IF (LSAME(UPLO,'U')) THEN
260: *
261: * Form y when A is stored in upper triangle.
262: *
263: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
264: DO 60 J = 1,N
265: TEMP1 = ALPHA*X(J)
266: TEMP2 = ZERO
267: DO 50 I = 1,J - 1
268: Y(I) = Y(I) + TEMP1*A(I,J)
269: TEMP2 = TEMP2 + A(I,J)*X(I)
270: 50 CONTINUE
271: Y(J) = Y(J) + TEMP1*A(J,J) + ALPHA*TEMP2
272: 60 CONTINUE
273: ELSE
274: JX = KX
275: JY = KY
276: DO 80 J = 1,N
277: TEMP1 = ALPHA*X(JX)
278: TEMP2 = ZERO
279: IX = KX
280: IY = KY
281: DO 70 I = 1,J - 1
282: Y(IY) = Y(IY) + TEMP1*A(I,J)
283: TEMP2 = TEMP2 + A(I,J)*X(IX)
284: IX = IX + INCX
285: IY = IY + INCY
286: 70 CONTINUE
287: Y(JY) = Y(JY) + TEMP1*A(J,J) + ALPHA*TEMP2
288: JX = JX + INCX
289: JY = JY + INCY
290: 80 CONTINUE
291: END IF
292: ELSE
293: *
294: * Form y when A is stored in lower triangle.
295: *
296: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
297: DO 100 J = 1,N
298: TEMP1 = ALPHA*X(J)
299: TEMP2 = ZERO
300: Y(J) = Y(J) + TEMP1*A(J,J)
301: DO 90 I = J + 1,N
302: Y(I) = Y(I) + TEMP1*A(I,J)
303: TEMP2 = TEMP2 + A(I,J)*X(I)
304: 90 CONTINUE
305: Y(J) = Y(J) + ALPHA*TEMP2
306: 100 CONTINUE
307: ELSE
308: JX = KX
309: JY = KY
310: DO 120 J = 1,N
311: TEMP1 = ALPHA*X(JX)
312: TEMP2 = ZERO
313: Y(JY) = Y(JY) + TEMP1*A(J,J)
314: IX = JX
315: IY = JY
316: DO 110 I = J + 1,N
317: IX = IX + INCX
318: IY = IY + INCY
319: Y(IY) = Y(IY) + TEMP1*A(I,J)
320: TEMP2 = TEMP2 + A(I,J)*X(IX)
321: 110 CONTINUE
322: Y(JY) = Y(JY) + ALPHA*TEMP2
323: JX = JX + INCX
324: JY = JY + INCY
325: 120 CONTINUE
326: END IF
327: END IF
328: *
329: RETURN
330: *
331: * End of DSYMV .
332: *
333: END
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