1: *> \brief \b ZHEMV
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 ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
12: *
13: * .. Scalar Arguments ..
14: * COMPLEX*16 ALPHA,BETA
15: * INTEGER INCX,INCY,LDA,N
16: * CHARACTER UPLO
17: * ..
18: * .. Array Arguments ..
19: * COMPLEX*16 A(LDA,*),X(*),Y(*)
20: * ..
21: *
22: *
23: *> \par Purpose:
24: * =============
25: *>
26: *> \verbatim
27: *>
28: *> ZHEMV 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.
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 COMPLEX*16
63: *> On entry, ALPHA specifies the scalar alpha.
64: *> \endverbatim
65: *>
66: *> \param[in] A
67: *> \verbatim
68: *> A is COMPLEX*16 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 hermitian 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 hermitian matrix and the strictly
76: *> upper triangular part of A is not referenced.
77: *> Note that the imaginary parts of the diagonal elements need
78: *> not be set and are assumed to be zero.
79: *> \endverbatim
80: *>
81: *> \param[in] LDA
82: *> \verbatim
83: *> LDA is INTEGER
84: *> On entry, LDA specifies the first dimension of A as declared
85: *> in the calling (sub) program. LDA must be at least
86: *> max( 1, n ).
87: *> \endverbatim
88: *>
89: *> \param[in] X
90: *> \verbatim
91: *> X is COMPLEX*16 array, dimension at least
92: *> ( 1 + ( n - 1 )*abs( INCX ) ).
93: *> Before entry, the incremented array X must contain the n
94: *> element vector x.
95: *> \endverbatim
96: *>
97: *> \param[in] INCX
98: *> \verbatim
99: *> INCX is INTEGER
100: *> On entry, INCX specifies the increment for the elements of
101: *> X. INCX must not be zero.
102: *> \endverbatim
103: *>
104: *> \param[in] BETA
105: *> \verbatim
106: *> BETA is COMPLEX*16
107: *> On entry, BETA specifies the scalar beta. When BETA is
108: *> supplied as zero then Y need not be set on input.
109: *> \endverbatim
110: *>
111: *> \param[in,out] Y
112: *> \verbatim
113: *> Y is COMPLEX*16 array, dimension at least
114: *> ( 1 + ( n - 1 )*abs( INCY ) ).
115: *> Before entry, the incremented array Y must contain the n
116: *> element vector y. On exit, Y is overwritten by the updated
117: *> vector y.
118: *> \endverbatim
119: *>
120: *> \param[in] INCY
121: *> \verbatim
122: *> INCY is INTEGER
123: *> On entry, INCY specifies the increment for the elements of
124: *> Y. INCY must not be zero.
125: *> \endverbatim
126: *
127: * Authors:
128: * ========
129: *
130: *> \author Univ. of Tennessee
131: *> \author Univ. of California Berkeley
132: *> \author Univ. of Colorado Denver
133: *> \author NAG Ltd.
134: *
135: *> \ingroup complex16_blas_level2
136: *
137: *> \par Further Details:
138: * =====================
139: *>
140: *> \verbatim
141: *>
142: *> Level 2 Blas routine.
143: *> The vector and matrix arguments are not referenced when N = 0, or M = 0
144: *>
145: *> -- Written on 22-October-1986.
146: *> Jack Dongarra, Argonne National Lab.
147: *> Jeremy Du Croz, Nag Central Office.
148: *> Sven Hammarling, Nag Central Office.
149: *> Richard Hanson, Sandia National Labs.
150: *> \endverbatim
151: *>
152: * =====================================================================
153: SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
154: *
155: * -- Reference BLAS level2 routine --
156: * -- Reference BLAS is a software package provided by Univ. of Tennessee, --
157: * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
158: *
159: * .. Scalar Arguments ..
160: COMPLEX*16 ALPHA,BETA
161: INTEGER INCX,INCY,LDA,N
162: CHARACTER UPLO
163: * ..
164: * .. Array Arguments ..
165: COMPLEX*16 A(LDA,*),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: COMPLEX*16 TEMP1,TEMP2
178: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
179: * ..
180: * .. External Functions ..
181: LOGICAL LSAME
182: EXTERNAL LSAME
183: * ..
184: * .. External Subroutines ..
185: EXTERNAL XERBLA
186: * ..
187: * .. Intrinsic Functions ..
188: INTRINSIC DBLE,DCONJG,MAX
189: * ..
190: *
191: * Test the input parameters.
192: *
193: INFO = 0
194: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
195: INFO = 1
196: ELSE IF (N.LT.0) THEN
197: INFO = 2
198: ELSE IF (LDA.LT.MAX(1,N)) THEN
199: INFO = 5
200: ELSE IF (INCX.EQ.0) THEN
201: INFO = 7
202: ELSE IF (INCY.EQ.0) THEN
203: INFO = 10
204: END IF
205: IF (INFO.NE.0) THEN
206: CALL XERBLA('ZHEMV ',INFO)
207: RETURN
208: END IF
209: *
210: * Quick return if possible.
211: *
212: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
213: *
214: * Set up the start points in X and Y.
215: *
216: IF (INCX.GT.0) THEN
217: KX = 1
218: ELSE
219: KX = 1 - (N-1)*INCX
220: END IF
221: IF (INCY.GT.0) THEN
222: KY = 1
223: ELSE
224: KY = 1 - (N-1)*INCY
225: END IF
226: *
227: * Start the operations. In this version the elements of A are
228: * accessed sequentially with one pass through the triangular part
229: * of A.
230: *
231: * First form y := beta*y.
232: *
233: IF (BETA.NE.ONE) THEN
234: IF (INCY.EQ.1) THEN
235: IF (BETA.EQ.ZERO) THEN
236: DO 10 I = 1,N
237: Y(I) = ZERO
238: 10 CONTINUE
239: ELSE
240: DO 20 I = 1,N
241: Y(I) = BETA*Y(I)
242: 20 CONTINUE
243: END IF
244: ELSE
245: IY = KY
246: IF (BETA.EQ.ZERO) THEN
247: DO 30 I = 1,N
248: Y(IY) = ZERO
249: IY = IY + INCY
250: 30 CONTINUE
251: ELSE
252: DO 40 I = 1,N
253: Y(IY) = BETA*Y(IY)
254: IY = IY + INCY
255: 40 CONTINUE
256: END IF
257: END IF
258: END IF
259: IF (ALPHA.EQ.ZERO) RETURN
260: IF (LSAME(UPLO,'U')) THEN
261: *
262: * Form y when A is stored in upper triangle.
263: *
264: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
265: DO 60 J = 1,N
266: TEMP1 = ALPHA*X(J)
267: TEMP2 = ZERO
268: DO 50 I = 1,J - 1
269: Y(I) = Y(I) + TEMP1*A(I,J)
270: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
271: 50 CONTINUE
272: Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
273: 60 CONTINUE
274: ELSE
275: JX = KX
276: JY = KY
277: DO 80 J = 1,N
278: TEMP1 = ALPHA*X(JX)
279: TEMP2 = ZERO
280: IX = KX
281: IY = KY
282: DO 70 I = 1,J - 1
283: Y(IY) = Y(IY) + TEMP1*A(I,J)
284: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
285: IX = IX + INCX
286: IY = IY + INCY
287: 70 CONTINUE
288: Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
289: JX = JX + INCX
290: JY = JY + INCY
291: 80 CONTINUE
292: END IF
293: ELSE
294: *
295: * Form y when A is stored in lower triangle.
296: *
297: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
298: DO 100 J = 1,N
299: TEMP1 = ALPHA*X(J)
300: TEMP2 = ZERO
301: Y(J) = Y(J) + TEMP1*DBLE(A(J,J))
302: DO 90 I = J + 1,N
303: Y(I) = Y(I) + TEMP1*A(I,J)
304: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
305: 90 CONTINUE
306: Y(J) = Y(J) + ALPHA*TEMP2
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(A(J,J))
315: IX = JX
316: IY = JY
317: DO 110 I = J + 1,N
318: IX = IX + INCX
319: IY = IY + INCY
320: Y(IY) = Y(IY) + TEMP1*A(I,J)
321: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
322: 110 CONTINUE
323: Y(JY) = Y(JY) + ALPHA*TEMP2
324: JX = JX + INCX
325: JY = JY + INCY
326: 120 CONTINUE
327: END IF
328: END IF
329: *
330: RETURN
331: *
332: * End of ZHEMV
333: *
334: END
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