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, 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, 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, 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: *> \ingroup double_blas_level2
134: *
135: *> \par Further Details:
136: * =====================
137: *>
138: *> \verbatim
139: *>
140: *> Level 2 Blas routine.
141: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
142: *>
143: *> -- Written on 22-October-1986.
144: *> Jack Dongarra, Argonne National Lab.
145: *> Jeremy Du Croz, Nag Central Office.
146: *> Sven Hammarling, Nag Central Office.
147: *> Richard Hanson, Sandia National Labs.
148: *> \endverbatim
149: *>
150: * =====================================================================
151: SUBROUTINE DSYMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
152: *
153: * -- Reference BLAS level2 routine --
154: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
155: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
156: *
157: * .. Scalar Arguments ..
158: DOUBLE PRECISION ALPHA,BETA
159: INTEGER INCX,INCY,LDA,N
160: CHARACTER UPLO
161: * ..
162: * .. Array Arguments ..
163: DOUBLE PRECISION A(LDA,*),X(*),Y(*)
164: * ..
165: *
166: * =====================================================================
167: *
168: * .. Parameters ..
169: DOUBLE PRECISION ONE,ZERO
170: PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
171: * ..
172: * .. Local Scalars ..
173: DOUBLE PRECISION TEMP1,TEMP2
174: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
175: * ..
176: * .. External Functions ..
177: LOGICAL LSAME
178: EXTERNAL LSAME
179: * ..
180: * .. External Subroutines ..
181: EXTERNAL XERBLA
182: * ..
183: * .. Intrinsic Functions ..
184: INTRINSIC MAX
185: * ..
186: *
187: * Test the input parameters.
188: *
189: INFO = 0
190: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
191: INFO = 1
192: ELSE IF (N.LT.0) THEN
193: INFO = 2
194: ELSE IF (LDA.LT.MAX(1,N)) THEN
195: INFO = 5
196: ELSE IF (INCX.EQ.0) THEN
197: INFO = 7
198: ELSE IF (INCY.EQ.0) THEN
199: INFO = 10
200: END IF
201: IF (INFO.NE.0) THEN
202: CALL XERBLA('DSYMV ',INFO)
203: RETURN
204: END IF
205: *
206: * Quick return if possible.
207: *
208: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
209: *
210: * Set up the start points in X and Y.
211: *
212: IF (INCX.GT.0) THEN
213: KX = 1
214: ELSE
215: KX = 1 - (N-1)*INCX
216: END IF
217: IF (INCY.GT.0) THEN
218: KY = 1
219: ELSE
220: KY = 1 - (N-1)*INCY
221: END IF
222: *
223: * Start the operations. In this version the elements of A are
224: * accessed sequentially with one pass through the triangular part
225: * of A.
226: *
227: * First form y := beta*y.
228: *
229: IF (BETA.NE.ONE) THEN
230: IF (INCY.EQ.1) THEN
231: IF (BETA.EQ.ZERO) THEN
232: DO 10 I = 1,N
233: Y(I) = ZERO
234: 10 CONTINUE
235: ELSE
236: DO 20 I = 1,N
237: Y(I) = BETA*Y(I)
238: 20 CONTINUE
239: END IF
240: ELSE
241: IY = KY
242: IF (BETA.EQ.ZERO) THEN
243: DO 30 I = 1,N
244: Y(IY) = ZERO
245: IY = IY + INCY
246: 30 CONTINUE
247: ELSE
248: DO 40 I = 1,N
249: Y(IY) = BETA*Y(IY)
250: IY = IY + INCY
251: 40 CONTINUE
252: END IF
253: END IF
254: END IF
255: IF (ALPHA.EQ.ZERO) RETURN
256: IF (LSAME(UPLO,'U')) THEN
257: *
258: * Form y when A is stored in upper triangle.
259: *
260: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
261: DO 60 J = 1,N
262: TEMP1 = ALPHA*X(J)
263: TEMP2 = ZERO
264: DO 50 I = 1,J - 1
265: Y(I) = Y(I) + TEMP1*A(I,J)
266: TEMP2 = TEMP2 + A(I,J)*X(I)
267: 50 CONTINUE
268: Y(J) = Y(J) + TEMP1*A(J,J) + ALPHA*TEMP2
269: 60 CONTINUE
270: ELSE
271: JX = KX
272: JY = KY
273: DO 80 J = 1,N
274: TEMP1 = ALPHA*X(JX)
275: TEMP2 = ZERO
276: IX = KX
277: IY = KY
278: DO 70 I = 1,J - 1
279: Y(IY) = Y(IY) + TEMP1*A(I,J)
280: TEMP2 = TEMP2 + A(I,J)*X(IX)
281: IX = IX + INCX
282: IY = IY + INCY
283: 70 CONTINUE
284: Y(JY) = Y(JY) + TEMP1*A(J,J) + ALPHA*TEMP2
285: JX = JX + INCX
286: JY = JY + INCY
287: 80 CONTINUE
288: END IF
289: ELSE
290: *
291: * Form y when A is stored in lower triangle.
292: *
293: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
294: DO 100 J = 1,N
295: TEMP1 = ALPHA*X(J)
296: TEMP2 = ZERO
297: Y(J) = Y(J) + TEMP1*A(J,J)
298: DO 90 I = J + 1,N
299: Y(I) = Y(I) + TEMP1*A(I,J)
300: TEMP2 = TEMP2 + A(I,J)*X(I)
301: 90 CONTINUE
302: Y(J) = Y(J) + ALPHA*TEMP2
303: 100 CONTINUE
304: ELSE
305: JX = KX
306: JY = KY
307: DO 120 J = 1,N
308: TEMP1 = ALPHA*X(JX)
309: TEMP2 = ZERO
310: Y(JY) = Y(JY) + TEMP1*A(J,J)
311: IX = JX
312: IY = JY
313: DO 110 I = J + 1,N
314: IX = IX + INCX
315: IY = IY + INCY
316: Y(IY) = Y(IY) + TEMP1*A(I,J)
317: TEMP2 = TEMP2 + A(I,J)*X(IX)
318: 110 CONTINUE
319: Y(JY) = Y(JY) + ALPHA*TEMP2
320: JX = JX + INCX
321: JY = JY + INCY
322: 120 CONTINUE
323: END IF
324: END IF
325: *
326: RETURN
327: *
328: * End of DSYMV
329: *
330: END
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