Annotation of rpl/lapack/lapack/zspmv.f, revision 1.18
1.11 bertrand 1: *> \brief \b ZSPMV computes a matrix-vector product for complex vectors using a complex symmetric packed matrix
1.8 bertrand 2: *
3: * =========== DOCUMENTATION ===========
4: *
1.15 bertrand 5: * Online html documentation available at
6: * http://www.netlib.org/lapack/explore-html/
1.8 bertrand 7: *
8: *> \htmlonly
1.15 bertrand 9: *> Download ZSPMV + dependencies
10: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zspmv.f">
11: *> [TGZ]</a>
12: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/zspmv.f">
13: *> [ZIP]</a>
14: *> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/zspmv.f">
1.8 bertrand 15: *> [TXT]</a>
1.15 bertrand 16: *> \endhtmlonly
1.8 bertrand 17: *
18: * Definition:
19: * ===========
20: *
21: * SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
1.15 bertrand 22: *
1.8 bertrand 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: * ..
1.15 bertrand 31: *
1.8 bertrand 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: *
1.15 bertrand 142: *> \author Univ. of Tennessee
143: *> \author Univ. of California Berkeley
144: *> \author Univ. of Colorado Denver
145: *> \author NAG Ltd.
1.8 bertrand 146: *
147: *> \ingroup complex16OTHERauxiliary
148: *
149: * =====================================================================
1.1 bertrand 150: SUBROUTINE ZSPMV( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
151: *
1.18 ! bertrand 152: * -- LAPACK auxiliary routine --
1.1 bertrand 153: * -- LAPACK is a software package provided by Univ. of Tennessee, --
154: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
155: *
156: * .. Scalar Arguments ..
157: CHARACTER UPLO
158: INTEGER INCX, INCY, N
159: COMPLEX*16 ALPHA, BETA
160: * ..
161: * .. Array Arguments ..
162: COMPLEX*16 AP( * ), X( * ), Y( * )
163: * ..
164: *
165: * =====================================================================
166: *
167: * .. Parameters ..
168: COMPLEX*16 ONE
169: PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ) )
170: COMPLEX*16 ZERO
171: PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) )
172: * ..
173: * .. Local Scalars ..
174: INTEGER I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
175: COMPLEX*16 TEMP1, TEMP2
176: * ..
177: * .. External Functions ..
178: LOGICAL LSAME
179: EXTERNAL LSAME
180: * ..
181: * .. External Subroutines ..
182: EXTERNAL XERBLA
183: * ..
184: * .. Executable Statements ..
185: *
186: * Test the input parameters.
187: *
188: INFO = 0
189: IF( .NOT.LSAME( UPLO, 'U' ) .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
190: INFO = 1
191: ELSE IF( N.LT.0 ) THEN
192: INFO = 2
193: ELSE IF( INCX.EQ.0 ) THEN
194: INFO = 6
195: ELSE IF( INCY.EQ.0 ) THEN
196: INFO = 9
197: END IF
198: IF( INFO.NE.0 ) THEN
199: CALL XERBLA( 'ZSPMV ', INFO )
200: RETURN
201: END IF
202: *
203: * Quick return if possible.
204: *
205: IF( ( N.EQ.0 ) .OR. ( ( ALPHA.EQ.ZERO ) .AND. ( BETA.EQ.ONE ) ) )
206: $ RETURN
207: *
208: * Set up the start points in X and Y.
209: *
210: IF( INCX.GT.0 ) THEN
211: KX = 1
212: ELSE
213: KX = 1 - ( N-1 )*INCX
214: END IF
215: IF( INCY.GT.0 ) THEN
216: KY = 1
217: ELSE
218: KY = 1 - ( N-1 )*INCY
219: END IF
220: *
221: * Start the operations. In this version the elements of the array AP
222: * are accessed sequentially with one pass through AP.
223: *
224: * First form y := beta*y.
225: *
226: IF( BETA.NE.ONE ) THEN
227: IF( INCY.EQ.1 ) THEN
228: IF( BETA.EQ.ZERO ) THEN
229: DO 10 I = 1, N
230: Y( I ) = ZERO
231: 10 CONTINUE
232: ELSE
233: DO 20 I = 1, N
234: Y( I ) = BETA*Y( I )
235: 20 CONTINUE
236: END IF
237: ELSE
238: IY = KY
239: IF( BETA.EQ.ZERO ) THEN
240: DO 30 I = 1, N
241: Y( IY ) = ZERO
242: IY = IY + INCY
243: 30 CONTINUE
244: ELSE
245: DO 40 I = 1, N
246: Y( IY ) = BETA*Y( IY )
247: IY = IY + INCY
248: 40 CONTINUE
249: END IF
250: END IF
251: END IF
252: IF( ALPHA.EQ.ZERO )
253: $ RETURN
254: KK = 1
255: IF( LSAME( UPLO, 'U' ) ) THEN
256: *
257: * Form y when AP contains the upper triangle.
258: *
259: IF( ( INCX.EQ.1 ) .AND. ( INCY.EQ.1 ) ) THEN
260: DO 60 J = 1, N
261: TEMP1 = ALPHA*X( J )
262: TEMP2 = ZERO
263: K = KK
264: DO 50 I = 1, J - 1
265: Y( I ) = Y( I ) + TEMP1*AP( K )
266: TEMP2 = TEMP2 + AP( K )*X( I )
267: K = K + 1
268: 50 CONTINUE
269: Y( J ) = Y( J ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
270: KK = KK + J
271: 60 CONTINUE
272: ELSE
273: JX = KX
274: JY = KY
275: DO 80 J = 1, N
276: TEMP1 = ALPHA*X( JX )
277: TEMP2 = ZERO
278: IX = KX
279: IY = KY
280: DO 70 K = KK, KK + J - 2
281: Y( IY ) = Y( IY ) + TEMP1*AP( K )
282: TEMP2 = TEMP2 + AP( K )*X( IX )
283: IX = IX + INCX
284: IY = IY + INCY
285: 70 CONTINUE
286: Y( JY ) = Y( JY ) + TEMP1*AP( KK+J-1 ) + ALPHA*TEMP2
287: JX = JX + INCX
288: JY = JY + INCY
289: KK = KK + J
290: 80 CONTINUE
291: END IF
292: ELSE
293: *
294: * Form y when AP contains the 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*AP( KK )
301: K = KK + 1
302: DO 90 I = J + 1, N
303: Y( I ) = Y( I ) + TEMP1*AP( K )
304: TEMP2 = TEMP2 + AP( K )*X( I )
305: K = K + 1
306: 90 CONTINUE
307: Y( J ) = Y( J ) + ALPHA*TEMP2
308: KK = KK + ( N-J+1 )
309: 100 CONTINUE
310: ELSE
311: JX = KX
312: JY = KY
313: DO 120 J = 1, N
314: TEMP1 = ALPHA*X( JX )
315: TEMP2 = ZERO
316: Y( JY ) = Y( JY ) + TEMP1*AP( KK )
317: IX = JX
318: IY = JY
319: DO 110 K = KK + 1, KK + N - J
320: IX = IX + INCX
321: IY = IY + INCY
322: Y( IY ) = Y( IY ) + TEMP1*AP( K )
323: TEMP2 = TEMP2 + AP( K )*X( IX )
324: 110 CONTINUE
325: Y( JY ) = Y( JY ) + ALPHA*TEMP2
326: JX = JX + INCX
327: JY = JY + INCY
328: KK = KK + ( N-J+1 )
329: 120 CONTINUE
330: END IF
331: END IF
332: *
333: RETURN
334: *
335: * End of ZSPMV
336: *
337: END
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