1: SUBROUTINE ZHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
2: * .. Scalar Arguments ..
3: DOUBLE COMPLEX ALPHA,BETA
4: INTEGER INCX,INCY,LDA,N
5: CHARACTER UPLO
6: * ..
7: * .. Array Arguments ..
8: DOUBLE COMPLEX A(LDA,*),X(*),Y(*)
9: * ..
10: *
11: * Purpose
12: * =======
13: *
14: * ZHEMV performs the matrix-vector operation
15: *
16: * y := alpha*A*x + beta*y,
17: *
18: * where alpha and beta are scalars, x and y are n element vectors and
19: * A is an n by n hermitian matrix.
20: *
21: * Arguments
22: * ==========
23: *
24: * UPLO - CHARACTER*1.
25: * On entry, UPLO specifies whether the upper or lower
26: * triangular part of the array A is to be referenced as
27: * follows:
28: *
29: * UPLO = 'U' or 'u' Only the upper triangular part of A
30: * is to be referenced.
31: *
32: * UPLO = 'L' or 'l' Only the lower triangular part of A
33: * is to be referenced.
34: *
35: * Unchanged on exit.
36: *
37: * N - INTEGER.
38: * On entry, N specifies the order of the matrix A.
39: * N must be at least zero.
40: * Unchanged on exit.
41: *
42: * ALPHA - COMPLEX*16 .
43: * On entry, ALPHA specifies the scalar alpha.
44: * Unchanged on exit.
45: *
46: * A - COMPLEX*16 array of DIMENSION ( LDA, n ).
47: * Before entry with UPLO = 'U' or 'u', the leading n by n
48: * upper triangular part of the array A must contain the upper
49: * triangular part of the hermitian matrix and the strictly
50: * lower triangular part of A is not referenced.
51: * Before entry with UPLO = 'L' or 'l', the leading n by n
52: * lower triangular part of the array A must contain the lower
53: * triangular part of the hermitian matrix and the strictly
54: * upper triangular part of A is not referenced.
55: * Note that the imaginary parts of the diagonal elements need
56: * not be set and are assumed to be zero.
57: * Unchanged on exit.
58: *
59: * LDA - INTEGER.
60: * On entry, LDA specifies the first dimension of A as declared
61: * in the calling (sub) program. LDA must be at least
62: * max( 1, n ).
63: * Unchanged on exit.
64: *
65: * X - COMPLEX*16 array of dimension at least
66: * ( 1 + ( n - 1 )*abs( INCX ) ).
67: * Before entry, the incremented array X must contain the n
68: * element vector x.
69: * Unchanged on exit.
70: *
71: * INCX - INTEGER.
72: * On entry, INCX specifies the increment for the elements of
73: * X. INCX must not be zero.
74: * Unchanged on exit.
75: *
76: * BETA - COMPLEX*16 .
77: * On entry, BETA specifies the scalar beta. When BETA is
78: * supplied as zero then Y need not be set on input.
79: * Unchanged on exit.
80: *
81: * Y - COMPLEX*16 array of dimension at least
82: * ( 1 + ( n - 1 )*abs( INCY ) ).
83: * Before entry, the incremented array Y must contain the n
84: * element vector y. On exit, Y is overwritten by the updated
85: * vector y.
86: *
87: * INCY - INTEGER.
88: * On entry, INCY specifies the increment for the elements of
89: * Y. INCY must not be zero.
90: * Unchanged on exit.
91: *
92: * Further Details
93: * ===============
94: *
95: * Level 2 Blas routine.
96: *
97: * -- Written on 22-October-1986.
98: * Jack Dongarra, Argonne National Lab.
99: * Jeremy Du Croz, Nag Central Office.
100: * Sven Hammarling, Nag Central Office.
101: * Richard Hanson, Sandia National Labs.
102: *
103: * =====================================================================
104: *
105: * .. Parameters ..
106: DOUBLE COMPLEX ONE
107: PARAMETER (ONE= (1.0D+0,0.0D+0))
108: DOUBLE COMPLEX ZERO
109: PARAMETER (ZERO= (0.0D+0,0.0D+0))
110: * ..
111: * .. Local Scalars ..
112: DOUBLE COMPLEX TEMP1,TEMP2
113: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
114: * ..
115: * .. External Functions ..
116: LOGICAL LSAME
117: EXTERNAL LSAME
118: * ..
119: * .. External Subroutines ..
120: EXTERNAL XERBLA
121: * ..
122: * .. Intrinsic Functions ..
123: INTRINSIC DBLE,DCONJG,MAX
124: * ..
125: *
126: * Test the input parameters.
127: *
128: INFO = 0
129: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
130: INFO = 1
131: ELSE IF (N.LT.0) THEN
132: INFO = 2
133: ELSE IF (LDA.LT.MAX(1,N)) THEN
134: INFO = 5
135: ELSE IF (INCX.EQ.0) THEN
136: INFO = 7
137: ELSE IF (INCY.EQ.0) THEN
138: INFO = 10
139: END IF
140: IF (INFO.NE.0) THEN
141: CALL XERBLA('ZHEMV ',INFO)
142: RETURN
143: END IF
144: *
145: * Quick return if possible.
146: *
147: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
148: *
149: * Set up the start points in X and Y.
150: *
151: IF (INCX.GT.0) THEN
152: KX = 1
153: ELSE
154: KX = 1 - (N-1)*INCX
155: END IF
156: IF (INCY.GT.0) THEN
157: KY = 1
158: ELSE
159: KY = 1 - (N-1)*INCY
160: END IF
161: *
162: * Start the operations. In this version the elements of A are
163: * accessed sequentially with one pass through the triangular part
164: * of A.
165: *
166: * First form y := beta*y.
167: *
168: IF (BETA.NE.ONE) THEN
169: IF (INCY.EQ.1) THEN
170: IF (BETA.EQ.ZERO) THEN
171: DO 10 I = 1,N
172: Y(I) = ZERO
173: 10 CONTINUE
174: ELSE
175: DO 20 I = 1,N
176: Y(I) = BETA*Y(I)
177: 20 CONTINUE
178: END IF
179: ELSE
180: IY = KY
181: IF (BETA.EQ.ZERO) THEN
182: DO 30 I = 1,N
183: Y(IY) = ZERO
184: IY = IY + INCY
185: 30 CONTINUE
186: ELSE
187: DO 40 I = 1,N
188: Y(IY) = BETA*Y(IY)
189: IY = IY + INCY
190: 40 CONTINUE
191: END IF
192: END IF
193: END IF
194: IF (ALPHA.EQ.ZERO) RETURN
195: IF (LSAME(UPLO,'U')) THEN
196: *
197: * Form y when A is stored in upper triangle.
198: *
199: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
200: DO 60 J = 1,N
201: TEMP1 = ALPHA*X(J)
202: TEMP2 = ZERO
203: DO 50 I = 1,J - 1
204: Y(I) = Y(I) + TEMP1*A(I,J)
205: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
206: 50 CONTINUE
207: Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
208: 60 CONTINUE
209: ELSE
210: JX = KX
211: JY = KY
212: DO 80 J = 1,N
213: TEMP1 = ALPHA*X(JX)
214: TEMP2 = ZERO
215: IX = KX
216: IY = KY
217: DO 70 I = 1,J - 1
218: Y(IY) = Y(IY) + TEMP1*A(I,J)
219: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
220: IX = IX + INCX
221: IY = IY + INCY
222: 70 CONTINUE
223: Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
224: JX = JX + INCX
225: JY = JY + INCY
226: 80 CONTINUE
227: END IF
228: ELSE
229: *
230: * Form y when A is stored in lower triangle.
231: *
232: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
233: DO 100 J = 1,N
234: TEMP1 = ALPHA*X(J)
235: TEMP2 = ZERO
236: Y(J) = Y(J) + TEMP1*DBLE(A(J,J))
237: DO 90 I = J + 1,N
238: Y(I) = Y(I) + TEMP1*A(I,J)
239: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
240: 90 CONTINUE
241: Y(J) = Y(J) + ALPHA*TEMP2
242: 100 CONTINUE
243: ELSE
244: JX = KX
245: JY = KY
246: DO 120 J = 1,N
247: TEMP1 = ALPHA*X(JX)
248: TEMP2 = ZERO
249: Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J))
250: IX = JX
251: IY = JY
252: DO 110 I = J + 1,N
253: IX = IX + INCX
254: IY = IY + INCY
255: Y(IY) = Y(IY) + TEMP1*A(I,J)
256: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
257: 110 CONTINUE
258: Y(JY) = Y(JY) + ALPHA*TEMP2
259: JX = JX + INCX
260: JY = JY + INCY
261: 120 CONTINUE
262: END IF
263: END IF
264: *
265: RETURN
266: *
267: * End of ZHEMV .
268: *
269: END
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