1: *> \brief \b ZHPMV
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 ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA,BETA
15: * INTEGER INCX,INCY,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 AP(*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZHPMV 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 hermitian matrix, supplied in packed form.
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 matrix A is supplied in the packed
44: *> array AP as follows:
45: *>
46: *> UPLO = 'U' or 'u' The upper triangular part of A is
47: *> supplied in AP.
48: *>
49: *> UPLO = 'L' or 'l' The lower triangular part of A is
50: *> supplied in AP.
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 COMPLEX*16
63: *> On entry, ALPHA specifies the scalar alpha.
64: *> \endverbatim
65: *>
66: *> \param[in] AP
67: *> \verbatim
68: *> AP is COMPLEX*16 array, dimension at least
69: *> ( ( n*( n + 1 ) )/2 ).
70: *> Before entry with UPLO = 'U' or 'u', the array AP must
71: *> contain the upper triangular part of the hermitian matrix
72: *> packed sequentially, column by column, so that AP( 1 )
73: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
74: *> and a( 2, 2 ) respectively, and so on.
75: *> Before entry with UPLO = 'L' or 'l', the array AP must
76: *> contain the lower triangular part of the hermitian matrix
77: *> packed sequentially, column by column, so that AP( 1 )
78: *> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
79: *> and a( 3, 1 ) respectively, and so on.
80: *> Note that the imaginary parts of the diagonal elements need
81: *> not be set and are assumed to be zero.
82: *> \endverbatim
83: *>
84: *> \param[in] X
85: *> \verbatim
86: *> X is COMPLEX*16 array, dimension at least
87: *> ( 1 + ( n - 1 )*abs( INCX ) ).
88: *> Before entry, the incremented array X must contain the n
89: *> element vector x.
90: *> \endverbatim
91: *>
92: *> \param[in] INCX
93: *> \verbatim
94: *> INCX is INTEGER
95: *> On entry, INCX specifies the increment for the elements of
96: *> X. INCX must not be zero.
97: *> \endverbatim
98: *>
99: *> \param[in] BETA
100: *> \verbatim
101: *> BETA is COMPLEX*16
102: *> On entry, BETA specifies the scalar beta. When BETA is
103: *> supplied as zero then Y need not be set on input.
104: *> \endverbatim
105: *>
106: *> \param[in,out] Y
107: *> \verbatim
108: *> Y is COMPLEX*16 array, dimension at least
109: *> ( 1 + ( n - 1 )*abs( INCY ) ).
110: *> Before entry, the incremented array Y must contain the n
111: *> element vector y. On exit, Y is overwritten by the updated
112: *> vector y.
113: *> \endverbatim
114: *>
115: *> \param[in] INCY
116: *> \verbatim
117: *> INCY is INTEGER
118: *> On entry, INCY specifies the increment for the elements of
119: *> Y. INCY must not be zero.
120: *> \endverbatim
121: *
122: * Authors:
123: * ========
124: *
125: *> \author Univ. of Tennessee
126: *> \author Univ. of California Berkeley
127: *> \author Univ. of Colorado Denver
128: *> \author NAG Ltd.
129: *
130: *> \ingroup complex16_blas_level2
131: *
132: *> \par Further Details:
133: * =====================
134: *>
135: *> \verbatim
136: *>
137: *> Level 2 Blas routine.
138: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
139: *>
140: *> -- Written on 22-October-1986.
141: *> Jack Dongarra, Argonne National Lab.
142: *> Jeremy Du Croz, Nag Central Office.
143: *> Sven Hammarling, Nag Central Office.
144: *> Richard Hanson, Sandia National Labs.
145: *> \endverbatim
146: *>
147: * =====================================================================
148: SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
149: *
150: * -- Reference BLAS level2 routine --
151: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
152: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
153: *
154: * .. Scalar Arguments ..
155: COMPLEX*16 ALPHA,BETA
156: INTEGER INCX,INCY,N
157: CHARACTER UPLO
158: * ..
159: * .. Array Arguments ..
160: COMPLEX*16 AP(*),X(*),Y(*)
161: * ..
162: *
163: * =====================================================================
164: *
165: * .. Parameters ..
166: COMPLEX*16 ONE
167: PARAMETER (ONE= (1.0D+0,0.0D+0))
168: COMPLEX*16 ZERO
169: PARAMETER (ZERO= (0.0D+0,0.0D+0))
170: * ..
171: * .. Local Scalars ..
172: COMPLEX*16 TEMP1,TEMP2
173: INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
174: * ..
175: * .. External Functions ..
176: LOGICAL LSAME
177: EXTERNAL LSAME
178: * ..
179: * .. External Subroutines ..
180: EXTERNAL XERBLA
181: * ..
182: * .. Intrinsic Functions ..
183: INTRINSIC DBLE,DCONJG
184: * ..
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('ZHPMV ',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))) RETURN
206: *
207: * Set up the start points in X and Y.
208: *
209: IF (INCX.GT.0) THEN
210: KX = 1
211: ELSE
212: KX = 1 - (N-1)*INCX
213: END IF
214: IF (INCY.GT.0) THEN
215: KY = 1
216: ELSE
217: KY = 1 - (N-1)*INCY
218: END IF
219: *
220: * Start the operations. In this version the elements of the array AP
221: * are accessed sequentially with one pass through AP.
222: *
223: * First form y := beta*y.
224: *
225: IF (BETA.NE.ONE) THEN
226: IF (INCY.EQ.1) THEN
227: IF (BETA.EQ.ZERO) THEN
228: DO 10 I = 1,N
229: Y(I) = ZERO
230: 10 CONTINUE
231: ELSE
232: DO 20 I = 1,N
233: Y(I) = BETA*Y(I)
234: 20 CONTINUE
235: END IF
236: ELSE
237: IY = KY
238: IF (BETA.EQ.ZERO) THEN
239: DO 30 I = 1,N
240: Y(IY) = ZERO
241: IY = IY + INCY
242: 30 CONTINUE
243: ELSE
244: DO 40 I = 1,N
245: Y(IY) = BETA*Y(IY)
246: IY = IY + INCY
247: 40 CONTINUE
248: END IF
249: END IF
250: END IF
251: IF (ALPHA.EQ.ZERO) RETURN
252: KK = 1
253: IF (LSAME(UPLO,'U')) THEN
254: *
255: * Form y when AP contains the upper triangle.
256: *
257: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
258: DO 60 J = 1,N
259: TEMP1 = ALPHA*X(J)
260: TEMP2 = ZERO
261: K = KK
262: DO 50 I = 1,J - 1
263: Y(I) = Y(I) + TEMP1*AP(K)
264: TEMP2 = TEMP2 + DCONJG(AP(K))*X(I)
265: K = K + 1
266: 50 CONTINUE
267: Y(J) = Y(J) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2
268: KK = KK + J
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 K = KK,KK + J - 2
279: Y(IY) = Y(IY) + TEMP1*AP(K)
280: TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX)
281: IX = IX + INCX
282: IY = IY + INCY
283: 70 CONTINUE
284: Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK+J-1)) + ALPHA*TEMP2
285: JX = JX + INCX
286: JY = JY + INCY
287: KK = KK + J
288: 80 CONTINUE
289: END IF
290: ELSE
291: *
292: * Form y when AP contains the lower triangle.
293: *
294: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
295: DO 100 J = 1,N
296: TEMP1 = ALPHA*X(J)
297: TEMP2 = ZERO
298: Y(J) = Y(J) + TEMP1*DBLE(AP(KK))
299: K = KK + 1
300: DO 90 I = J + 1,N
301: Y(I) = Y(I) + TEMP1*AP(K)
302: TEMP2 = TEMP2 + DCONJG(AP(K))*X(I)
303: K = K + 1
304: 90 CONTINUE
305: Y(J) = Y(J) + ALPHA*TEMP2
306: KK = KK + (N-J+1)
307: 100 CONTINUE
308: ELSE
309: JX = KX
310: JY = KY
311: DO 120 J = 1,N
312: TEMP1 = ALPHA*X(JX)
313: TEMP2 = ZERO
314: Y(JY) = Y(JY) + TEMP1*DBLE(AP(KK))
315: IX = JX
316: IY = JY
317: DO 110 K = KK + 1,KK + N - J
318: IX = IX + INCX
319: IY = IY + INCY
320: Y(IY) = Y(IY) + TEMP1*AP(K)
321: TEMP2 = TEMP2 + DCONJG(AP(K))*X(IX)
322: 110 CONTINUE
323: Y(JY) = Y(JY) + ALPHA*TEMP2
324: JX = JX + INCX
325: JY = JY + INCY
326: KK = KK + (N-J+1)
327: 120 CONTINUE
328: END IF
329: END IF
330: *
331: RETURN
332: *
333: * End of ZHPMV
334: *
335: END
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