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: * The vector and matrix arguments are not referenced when N = 0, or M = 0
97: *
98: * -- Written on 22-October-1986.
99: * Jack Dongarra, Argonne National Lab.
100: * Jeremy Du Croz, Nag Central Office.
101: * Sven Hammarling, Nag Central Office.
102: * Richard Hanson, Sandia National Labs.
103: *
104: * =====================================================================
105: *
106: * .. Parameters ..
107: DOUBLE COMPLEX ONE
108: PARAMETER (ONE= (1.0D+0,0.0D+0))
109: DOUBLE COMPLEX ZERO
110: PARAMETER (ZERO= (0.0D+0,0.0D+0))
111: * ..
112: * .. Local Scalars ..
113: DOUBLE COMPLEX TEMP1,TEMP2
114: INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
115: * ..
116: * .. External Functions ..
117: LOGICAL LSAME
118: EXTERNAL LSAME
119: * ..
120: * .. External Subroutines ..
121: EXTERNAL XERBLA
122: * ..
123: * .. Intrinsic Functions ..
124: INTRINSIC DBLE,DCONJG,MAX
125: * ..
126: *
127: * Test the input parameters.
128: *
129: INFO = 0
130: IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
131: INFO = 1
132: ELSE IF (N.LT.0) THEN
133: INFO = 2
134: ELSE IF (LDA.LT.MAX(1,N)) THEN
135: INFO = 5
136: ELSE IF (INCX.EQ.0) THEN
137: INFO = 7
138: ELSE IF (INCY.EQ.0) THEN
139: INFO = 10
140: END IF
141: IF (INFO.NE.0) THEN
142: CALL XERBLA('ZHEMV ',INFO)
143: RETURN
144: END IF
145: *
146: * Quick return if possible.
147: *
148: IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
149: *
150: * Set up the start points in X and Y.
151: *
152: IF (INCX.GT.0) THEN
153: KX = 1
154: ELSE
155: KX = 1 - (N-1)*INCX
156: END IF
157: IF (INCY.GT.0) THEN
158: KY = 1
159: ELSE
160: KY = 1 - (N-1)*INCY
161: END IF
162: *
163: * Start the operations. In this version the elements of A are
164: * accessed sequentially with one pass through the triangular part
165: * of A.
166: *
167: * First form y := beta*y.
168: *
169: IF (BETA.NE.ONE) THEN
170: IF (INCY.EQ.1) THEN
171: IF (BETA.EQ.ZERO) THEN
172: DO 10 I = 1,N
173: Y(I) = ZERO
174: 10 CONTINUE
175: ELSE
176: DO 20 I = 1,N
177: Y(I) = BETA*Y(I)
178: 20 CONTINUE
179: END IF
180: ELSE
181: IY = KY
182: IF (BETA.EQ.ZERO) THEN
183: DO 30 I = 1,N
184: Y(IY) = ZERO
185: IY = IY + INCY
186: 30 CONTINUE
187: ELSE
188: DO 40 I = 1,N
189: Y(IY) = BETA*Y(IY)
190: IY = IY + INCY
191: 40 CONTINUE
192: END IF
193: END IF
194: END IF
195: IF (ALPHA.EQ.ZERO) RETURN
196: IF (LSAME(UPLO,'U')) THEN
197: *
198: * Form y when A is stored in upper triangle.
199: *
200: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
201: DO 60 J = 1,N
202: TEMP1 = ALPHA*X(J)
203: TEMP2 = ZERO
204: DO 50 I = 1,J - 1
205: Y(I) = Y(I) + TEMP1*A(I,J)
206: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
207: 50 CONTINUE
208: Y(J) = Y(J) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
209: 60 CONTINUE
210: ELSE
211: JX = KX
212: JY = KY
213: DO 80 J = 1,N
214: TEMP1 = ALPHA*X(JX)
215: TEMP2 = ZERO
216: IX = KX
217: IY = KY
218: DO 70 I = 1,J - 1
219: Y(IY) = Y(IY) + TEMP1*A(I,J)
220: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
221: IX = IX + INCX
222: IY = IY + INCY
223: 70 CONTINUE
224: Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J)) + ALPHA*TEMP2
225: JX = JX + INCX
226: JY = JY + INCY
227: 80 CONTINUE
228: END IF
229: ELSE
230: *
231: * Form y when A is stored in lower triangle.
232: *
233: IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
234: DO 100 J = 1,N
235: TEMP1 = ALPHA*X(J)
236: TEMP2 = ZERO
237: Y(J) = Y(J) + TEMP1*DBLE(A(J,J))
238: DO 90 I = J + 1,N
239: Y(I) = Y(I) + TEMP1*A(I,J)
240: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(I)
241: 90 CONTINUE
242: Y(J) = Y(J) + ALPHA*TEMP2
243: 100 CONTINUE
244: ELSE
245: JX = KX
246: JY = KY
247: DO 120 J = 1,N
248: TEMP1 = ALPHA*X(JX)
249: TEMP2 = ZERO
250: Y(JY) = Y(JY) + TEMP1*DBLE(A(J,J))
251: IX = JX
252: IY = JY
253: DO 110 I = J + 1,N
254: IX = IX + INCX
255: IY = IY + INCY
256: Y(IY) = Y(IY) + TEMP1*A(I,J)
257: TEMP2 = TEMP2 + DCONJG(A(I,J))*X(IX)
258: 110 CONTINUE
259: Y(JY) = Y(JY) + ALPHA*TEMP2
260: JX = JX + INCX
261: JY = JY + INCY
262: 120 CONTINUE
263: END IF
264: END IF
265: *
266: RETURN
267: *
268: * End of ZHEMV .
269: *
270: END
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