1: *> \brief \b ZSPMV
2: *
3: * =========== DOCUMENTATION ===========
4: *
5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
7: *
8: *> \htmlonly
9: *> Download ZSPMV + 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/zspmv.f">
15: *> [TXT]</a>
16: *> \endhtmlonly
17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
22: *
23: * .. Scalar Arguments ..
24: * CHARACTER UPLO
25: * INTEGER INCX, INCY, N
26: * COMPLEX*16 ALPHA, BETA
27: * ..
28: * .. Array Arguments ..
29: * COMPLEX*16 AP( * ), X( * ), Y( * )
30: * ..
31: *
32: *
33: *> \par Purpose:
34: * =============
35: *>
36: *> \verbatim
37: *>
38: *> ZSPMV 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, supplied in packed form.
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 matrix A is supplied in the packed
54: *> array AP as follows:
55: *>
56: *> UPLO = 'U' or 'u' The upper triangular part of A is
57: *> supplied in AP.
58: *>
59: *> UPLO = 'L' or 'l' The lower triangular part of A is
60: *> supplied in AP.
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] AP
81: *> \verbatim
82: *> AP is COMPLEX*16 array, dimension at least
83: *> ( ( N*( N + 1 ) )/2 ).
84: *> Before entry, with UPLO = 'U' or 'u', the array AP must
85: *> contain the upper triangular part of the symmetric matrix
86: *> packed sequentially, column by column, so that AP( 1 )
87: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
88: *> and a( 2, 2 ) respectively, and so on.
89: *> Before entry, with UPLO = 'L' or 'l', the array AP must
90: *> contain the lower triangular part of the symmetric matrix
91: *> packed sequentially, column by column, so that AP( 1 )
92: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
93: *> and a( 3, 1 ) respectively, and so on.
94: *> Unchanged on exit.
95: *> \endverbatim
96: *>
97: *> \param[in] X
98: *> \verbatim
99: *> X is COMPLEX*16 array, dimension at least
100: *> ( 1 + ( N - 1 )*abs( INCX ) ).
101: *> Before entry, the incremented array X must contain the N-
102: *> element vector x.
103: *> Unchanged on exit.
104: *> \endverbatim
105: *>
106: *> \param[in] INCX
107: *> \verbatim
108: *> INCX is INTEGER
109: *> On entry, INCX specifies the increment for the elements of
110: *> X. INCX must not be zero.
111: *> Unchanged on exit.
112: *> \endverbatim
113: *>
114: *> \param[in] BETA
115: *> \verbatim
116: *> BETA is COMPLEX*16
117: *> On entry, BETA specifies the scalar beta. When BETA is
118: *> supplied as zero then Y need not be set on input.
119: *> Unchanged on exit.
120: *> \endverbatim
121: *>
122: *> \param[in,out] Y
123: *> \verbatim
124: *> Y is COMPLEX*16 array, dimension at least
125: *> ( 1 + ( N - 1 )*abs( INCY ) ).
126: *> Before entry, the incremented array Y must contain the n
127: *> element vector y. On exit, Y is overwritten by the updated
128: *> vector y.
129: *> \endverbatim
130: *>
131: *> \param[in] INCY
132: *> \verbatim
133: *> INCY is INTEGER
134: *> On entry, INCY specifies the increment for the elements of
135: *> Y. INCY must not be zero.
136: *> Unchanged on exit.
137: *> \endverbatim
138: *
139: * Authors:
140: * ========
141: *
142: *> \author Univ. of Tennessee
143: *> \author Univ. of California Berkeley
144: *> \author Univ. of Colorado Denver
145: *> \author NAG Ltd.
146: *
147: *> \date November 2011
148: *
149: *> \ingroup complex16OTHERauxiliary
150: *
151: * =====================================================================
152: SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
153: *
154: * -- LAPACK auxiliary routine (version 3.4.0) --
155: * -- LAPACK is a software package provided by Univ. of Tennessee, --
156: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
157: * November 2011
158: *
159: * .. Scalar Arguments ..
160: CHARACTER UPLO
161: INTEGER INCX, INCY, N
162: COMPLEX*16 ALPHA, BETA
163: * ..
164: * .. Array Arguments ..
165: COMPLEX*16 AP( * ), X( * ), Y( * )
166: * ..
167: *
168: * =====================================================================
169: *
170: * .. Parameters ..
171: COMPLEX*16 ONE
172: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
173: COMPLEX*16 ZERO
174: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
175: * ..
176: * .. Local Scalars ..
177: INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
178: COMPLEX*16 TEMP1, TEMP2
179: * ..
180: * .. External Functions ..
181: LOGICAL LSAME
182: EXTERNAL LSAME
183: * ..
184: * .. External Subroutines ..
185: EXTERNAL XERBLA
186: * ..
187: * .. Executable Statements ..
188: *
189: * Test the input parameters.
190: *
191: INFO = 0
192: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
193: INFO = 1
194: ELSE IF( N.LT.0 ) THEN
195: INFO = 2
196: ELSE IF( INCX.EQ.0 ) THEN
197: INFO = 6
198: ELSE IF( INCY.EQ.0 ) THEN
199: INFO = 9
200: END IF
201: IF( INFO.NE.0 ) THEN
202: CALL XERBLA( 'ZSPMV ', 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 ) ) )
209: $ RETURN
210: *
211: * Set up the start points in X and Y.
212: *
213: IF( INCX.GT.0 ) THEN
214: KX = 1
215: ELSE
216: KX = 1 - ( N-1 )*INCX
217: END IF
218: IF( INCY.GT.0 ) THEN
219: KY = 1
220: ELSE
221: KY = 1 - ( N-1 )*INCY
222: END IF
223: *
224: * Start the operations. In this version the elements of the array AP
225: * are accessed sequentially with one pass through AP.
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 )
256: $ RETURN
257: KK = 1
258: IF( LSAME( UPLO, 'U' ) ) THEN
259: *
260: * Form y when AP contains the upper triangle.
261: *
262: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
263: DO 60 J = 1, N
264: TEMP1 = ALPHA*X( J )
265: TEMP2 = ZERO
266: K = KK
267: DO 50 I = 1, J - 1
268: Y( I ) = Y( I ) + TEMP1*AP( K )
269: TEMP2 = TEMP2 + AP( K )*X( I )
270: K = K + 1
271: 50 CONTINUE
272: Y( J ) = Y( J ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
273: KK = KK + J
274: 60 CONTINUE
275: ELSE
276: JX = KX
277: JY = KY
278: DO 80 J = 1, N
279: TEMP1 = ALPHA*X( JX )
280: TEMP2 = ZERO
281: IX = KX
282: IY = KY
283: DO 70 K = KK, KK + J - 2
284: Y( IY ) = Y( IY ) + TEMP1*AP( K )
285: TEMP2 = TEMP2 + AP( K )*X( IX )
286: IX = IX + INCX
287: IY = IY + INCY
288: 70 CONTINUE
289: Y( JY ) = Y( JY ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
290: JX = JX + INCX
291: JY = JY + INCY
292: KK = KK + J
293: 80 CONTINUE
294: END IF
295: ELSE
296: *
297: * Form y when AP contains the lower triangle.
298: *
299: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
300: DO 100 J = 1, N
301: TEMP1 = ALPHA*X( J )
302: TEMP2 = ZERO
303: Y( J ) = Y( J ) + TEMP1*AP( KK )
304: K = KK + 1
305: DO 90 I = J + 1, N
306: Y( I ) = Y( I ) + TEMP1*AP( K )
307: TEMP2 = TEMP2 + AP( K )*X( I )
308: K = K + 1
309: 90 CONTINUE
310: Y( J ) = Y( J ) + ALPHA*TEMP2
311: KK = KK + ( N-J+1 )
312: 100 CONTINUE
313: ELSE
314: JX = KX
315: JY = KY
316: DO 120 J = 1, N
317: TEMP1 = ALPHA*X( JX )
318: TEMP2 = ZERO
319: Y( JY ) = Y( JY ) + TEMP1*AP( KK )
320: IX = JX
321: IY = JY
322: DO 110 K = KK + 1, KK + N - J
323: IX = IX + INCX
324: IY = IY + INCY
325: Y( IY ) = Y( IY ) + TEMP1*AP( K )
326: TEMP2 = TEMP2 + AP( K )*X( IX )
327: 110 CONTINUE
328: Y( JY ) = Y( JY ) + ALPHA*TEMP2
329: JX = JX + INCX
330: JY = JY + INCY
331: KK = KK + ( N-J+1 )
332: 120 CONTINUE
333: END IF
334: END IF
335: *
336: RETURN
337: *
338: * End of ZSPMV
339: *
340: END
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