1: *> \brief \b ZSYMV computes a matrix-vector product for a complex symmetric matrix.
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSYMV + dependencies
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11: *> [TGZ]</a>
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13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zsymv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INCX, INCY, LDA, N
26: * COMPLEX*16 ALPHA, BETA
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 A( LDA, * ), X( * ), Y( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZSYMV performs the matrix-vector operation
39: *>
40: *> y := alpha*A*x + beta*y,
41: *>
42: *> where alpha and beta are scalars, x and y are n element vectors and
43: *> A is an n by n symmetric matrix.
44: *> \endverbatim
45: *
46: * Arguments:
47: * ==========
48: *
49: *> \param[in] UPLO
50: *> \verbatim
51: *> UPLO is CHARACTER*1
52: *> On entry, UPLO specifies whether the upper or lower
53: *> triangular part of the array A is to be referenced as
54: *> follows:
55: *>
56: *> UPLO = 'U' or 'u' Only the upper triangular part of A
57: *> is to be referenced.
58: *>
59: *> UPLO = 'L' or 'l' Only the lower triangular part of A
60: *> is to be referenced.
61: *>
62: *> Unchanged on exit.
63: *> \endverbatim
64: *>
65: *> \param[in] N
66: *> \verbatim
67: *> N is INTEGER
68: *> On entry, N specifies the order of the matrix A.
69: *> N must be at least zero.
70: *> Unchanged on exit.
71: *> \endverbatim
72: *>
73: *> \param[in] ALPHA
74: *> \verbatim
75: *> ALPHA is COMPLEX*16
76: *> On entry, ALPHA specifies the scalar alpha.
77: *> Unchanged on exit.
78: *> \endverbatim
79: *>
80: *> \param[in] A
81: *> \verbatim
82: *> A is COMPLEX*16 array, dimension ( LDA, N )
83: *> Before entry, with UPLO = 'U' or 'u', the leading n by n
84: *> upper triangular part of the array A must contain the upper
85: *> triangular part of the symmetric matrix and the strictly
86: *> lower triangular part of A is not referenced.
87: *> Before entry, with UPLO = 'L' or 'l', the leading n by n
88: *> lower triangular part of the array A must contain the lower
89: *> triangular part of the symmetric matrix and the strictly
90: *> upper triangular part of A is not referenced.
91: *> Unchanged on exit.
92: *> \endverbatim
93: *>
94: *> \param[in] LDA
95: *> \verbatim
96: *> LDA is INTEGER
97: *> On entry, LDA specifies the first dimension of A as declared
98: *> in the calling (sub) program. LDA must be at least
99: *> max( 1, N ).
100: *> Unchanged on exit.
101: *> \endverbatim
102: *>
103: *> \param[in] X
104: *> \verbatim
105: *> X is COMPLEX*16 array, dimension at least
106: *> ( 1 + ( N - 1 )*abs( INCX ) ).
107: *> Before entry, the incremented array X must contain the N-
108: *> element vector x.
109: *> Unchanged on exit.
110: *> \endverbatim
111: *>
112: *> \param[in] INCX
113: *> \verbatim
114: *> INCX is INTEGER
115: *> On entry, INCX specifies the increment for the elements of
116: *> X. INCX must not be zero.
117: *> Unchanged on exit.
118: *> \endverbatim
119: *>
120: *> \param[in] BETA
121: *> \verbatim
122: *> BETA is COMPLEX*16
123: *> On entry, BETA specifies the scalar beta. When BETA is
124: *> supplied as zero then Y need not be set on input.
125: *> Unchanged on exit.
126: *> \endverbatim
127: *>
128: *> \param[in,out] Y
129: *> \verbatim
130: *> Y is COMPLEX*16 array, dimension at least
131: *> ( 1 + ( N - 1 )*abs( INCY ) ).
132: *> Before entry, the incremented array Y must contain the n
133: *> element vector y. On exit, Y is overwritten by the updated
134: *> vector y.
135: *> \endverbatim
136: *>
137: *> \param[in] INCY
138: *> \verbatim
139: *> INCY is INTEGER
140: *> On entry, INCY specifies the increment for the elements of
141: *> Y. INCY must not be zero.
142: *> Unchanged on exit.
143: *> \endverbatim
144: *
145: * Authors:
146: * ========
147: *
148: *> \author Univ. of Tennessee
149: *> \author Univ. of California Berkeley
150: *> \author Univ. of Colorado Denver
151: *> \author NAG Ltd.
152: *
153: *> \date December 2016
154: *
155: *> \ingroup complex16SYauxiliary
156: *
157: * =====================================================================
158: SUBROUTINE ZSYMV( UPLO, N, ALPHA, A, LDA, X, INCX, BETA, Y, INCY )
159: *
160: * -- LAPACK auxiliary routine (version 3.7.0) --
161: * -- LAPACK is a software package provided by Univ. of Tennessee, --
162: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
163: * December 2016
164: *
165: * .. Scalar Arguments ..
166: CHARACTER UPLO
167: INTEGER INCX, INCY, LDA, N
168: COMPLEX*16 ALPHA, BETA
169: * ..
170: * .. Array Arguments ..
171: COMPLEX*16 A( LDA, * ), X( * ), Y( * )
172: * ..
173: *
174: * =====================================================================
175: *
176: * .. Parameters ..
177: COMPLEX*16 ONE
178: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
179: COMPLEX*16 ZERO
180: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
181: * ..
182: * .. Local Scalars ..
183: INTEGER I, INFO, IX, IY, J, JX, JY, KX, KY
184: COMPLEX*16 TEMP1, TEMP2
185: * ..
186: * .. External Functions ..
187: LOGICAL LSAME
188: EXTERNAL LSAME
189: * ..
190: * .. External Subroutines ..
191: EXTERNAL XERBLA
192: * ..
193: * .. Intrinsic Functions ..
194: INTRINSIC MAX
195: * ..
196: * .. Executable Statements ..
197: *
198: * Test the input parameters.
199: *
200: INFO = 0
201: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
202: INFO = 1
203: ELSE IF( N.LT.0 ) THEN
204: INFO = 2
205: ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
206: INFO = 5
207: ELSE IF( INCX.EQ.0 ) THEN
208: INFO = 7
209: ELSE IF( INCY.EQ.0 ) THEN
210: INFO = 10
211: END IF
212: IF( INFO.NE.0 ) THEN
213: CALL XERBLA( 'ZSYMV ', INFO )
214: RETURN
215: END IF
216: *
217: * Quick return if possible.
218: *
219: IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
220: $ RETURN
221: *
222: * Set up the start points in X and Y.
223: *
224: IF( INCX.GT.0 ) THEN
225: KX = 1
226: ELSE
227: KX = 1 - ( N-1 )*INCX
228: END IF
229: IF( INCY.GT.0 ) THEN
230: KY = 1
231: ELSE
232: KY = 1 - ( N-1 )*INCY
233: END IF
234: *
235: * Start the operations. In this version the elements of A are
236: * accessed sequentially with one pass through the triangular part
237: * of A.
238: *
239: * First form y := beta*y.
240: *
241: IF( BETA.NE.ONE ) THEN
242: IF( INCY.EQ.1 ) THEN
243: IF( BETA.EQ.ZERO ) THEN
244: DO 10 I = 1, N
245: Y( I ) = ZERO
246: 10 CONTINUE
247: ELSE
248: DO 20 I = 1, N
249: Y( I ) = BETA*Y( I )
250: 20 CONTINUE
251: END IF
252: ELSE
253: IY = KY
254: IF( BETA.EQ.ZERO ) THEN
255: DO 30 I = 1, N
256: Y( IY ) = ZERO
257: IY = IY + INCY
258: 30 CONTINUE
259: ELSE
260: DO 40 I = 1, N
261: Y( IY ) = BETA*Y( IY )
262: IY = IY + INCY
263: 40 CONTINUE
264: END IF
265: END IF
266: END IF
267: IF( ALPHA.EQ.ZERO )
268: $ RETURN
269: IF( LSAME( UPLO, 'U' ) ) THEN
270: *
271: * Form y when A is stored in upper triangle.
272: *
273: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
274: DO 60 J = 1, N
275: TEMP1 = ALPHA*X( J )
276: TEMP2 = ZERO
277: DO 50 I = 1, J - 1
278: Y( I ) = Y( I ) + TEMP1*A( I, J )
279: TEMP2 = TEMP2 + A( I, J )*X( I )
280: 50 CONTINUE
281: Y( J ) = Y( J ) + TEMP1*A( J, J ) + ALPHA*TEMP2
282: 60 CONTINUE
283: ELSE
284: JX = KX
285: JY = KY
286: DO 80 J = 1, N
287: TEMP1 = ALPHA*X( JX )
288: TEMP2 = ZERO
289: IX = KX
290: IY = KY
291: DO 70 I = 1, J - 1
292: Y( IY ) = Y( IY ) + TEMP1*A( I, J )
293: TEMP2 = TEMP2 + A( I, J )*X( IX )
294: IX = IX + INCX
295: IY = IY + INCY
296: 70 CONTINUE
297: Y( JY ) = Y( JY ) + TEMP1*A( J, J ) + ALPHA*TEMP2
298: JX = JX + INCX
299: JY = JY + INCY
300: 80 CONTINUE
301: END IF
302: ELSE
303: *
304: * Form y when A is stored in lower triangle.
305: *
306: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
307: DO 100 J = 1, N
308: TEMP1 = ALPHA*X( J )
309: TEMP2 = ZERO
310: Y( J ) = Y( J ) + TEMP1*A( J, J )
311: DO 90 I = J + 1, N
312: Y( I ) = Y( I ) + TEMP1*A( I, J )
313: TEMP2 = TEMP2 + A( I, J )*X( I )
314: 90 CONTINUE
315: Y( J ) = Y( J ) + ALPHA*TEMP2
316: 100 CONTINUE
317: ELSE
318: JX = KX
319: JY = KY
320: DO 120 J = 1, N
321: TEMP1 = ALPHA*X( JX )
322: TEMP2 = ZERO
323: Y( JY ) = Y( JY ) + TEMP1*A( J, J )
324: IX = JX
325: IY = JY
326: DO 110 I = J + 1, N
327: IX = IX + INCX
328: IY = IY + INCY
329: Y( IY ) = Y( IY ) + TEMP1*A( I, J )
330: TEMP2 = TEMP2 + A( I, J )*X( IX )
331: 110 CONTINUE
332: Y( JY ) = Y( JY ) + ALPHA*TEMP2
333: JX = JX + INCX
334: JY = JY + INCY
335: 120 CONTINUE
336: END IF
337: END IF
338: *
339: RETURN
340: *
341: * End of ZSYMV
342: *
343: END
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