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First attempt at single precision tyeps * * * corrections to qrupdate single precision routines * * * prefer demotion to single over promotion to double * * * Add single precision support to log2 function * * * Trivial PROJECT file update * * * Cache optimized hermitian/transpose methods * * * Add tests for tranpose/hermitian and ChangeLog entry for new transpose code
author David Bateman <dbateman@free.fr>
date Sun, 27 Apr 2008 22:34:17 +0200
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7788:45f5faba05a2 7789:82be108cc558
1 SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
2 * .. Scalar Arguments ..
3 COMPLEX ALPHA,BETA
4 INTEGER INCX,INCY,LDA,N
5 CHARACTER UPLO
6 * ..
7 * .. Array Arguments ..
8 COMPLEX A(LDA,*),X(*),Y(*)
9 * ..
10 *
11 * Purpose
12 * =======
13 *
14 * CHEMV 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 .
43 * On entry, ALPHA specifies the scalar alpha.
44 * Unchanged on exit.
45 *
46 * A - COMPLEX 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 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 .
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 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 *
93 * Level 2 Blas routine.
94 *
95 * -- Written on 22-October-1986.
96 * Jack Dongarra, Argonne National Lab.
97 * Jeremy Du Croz, Nag Central Office.
98 * Sven Hammarling, Nag Central Office.
99 * Richard Hanson, Sandia National Labs.
100 *
101 *
102 * .. Parameters ..
103 COMPLEX ONE
104 PARAMETER (ONE= (1.0E+0,0.0E+0))
105 COMPLEX ZERO
106 PARAMETER (ZERO= (0.0E+0,0.0E+0))
107 * ..
108 * .. Local Scalars ..
109 COMPLEX TEMP1,TEMP2
110 INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
111 * ..
112 * .. External Functions ..
113 LOGICAL LSAME
114 EXTERNAL LSAME
115 * ..
116 * .. External Subroutines ..
117 EXTERNAL XERBLA
118 * ..
119 * .. Intrinsic Functions ..
120 INTRINSIC CONJG,MAX,REAL
121 * ..
122 *
123 * Test the input parameters.
124 *
125 INFO = 0
126 IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
127 INFO = 1
128 ELSE IF (N.LT.0) THEN
129 INFO = 2
130 ELSE IF (LDA.LT.MAX(1,N)) THEN
131 INFO = 5
132 ELSE IF (INCX.EQ.0) THEN
133 INFO = 7
134 ELSE IF (INCY.EQ.0) THEN
135 INFO = 10
136 END IF
137 IF (INFO.NE.0) THEN
138 CALL XERBLA('CHEMV ',INFO)
139 RETURN
140 END IF
141 *
142 * Quick return if possible.
143 *
144 IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
145 *
146 * Set up the start points in X and Y.
147 *
148 IF (INCX.GT.0) THEN
149 KX = 1
150 ELSE
151 KX = 1 - (N-1)*INCX
152 END IF
153 IF (INCY.GT.0) THEN
154 KY = 1
155 ELSE
156 KY = 1 - (N-1)*INCY
157 END IF
158 *
159 * Start the operations. In this version the elements of A are
160 * accessed sequentially with one pass through the triangular part
161 * of A.
162 *
163 * First form y := beta*y.
164 *
165 IF (BETA.NE.ONE) THEN
166 IF (INCY.EQ.1) THEN
167 IF (BETA.EQ.ZERO) THEN
168 DO 10 I = 1,N
169 Y(I) = ZERO
170 10 CONTINUE
171 ELSE
172 DO 20 I = 1,N
173 Y(I) = BETA*Y(I)
174 20 CONTINUE
175 END IF
176 ELSE
177 IY = KY
178 IF (BETA.EQ.ZERO) THEN
179 DO 30 I = 1,N
180 Y(IY) = ZERO
181 IY = IY + INCY
182 30 CONTINUE
183 ELSE
184 DO 40 I = 1,N
185 Y(IY) = BETA*Y(IY)
186 IY = IY + INCY
187 40 CONTINUE
188 END IF
189 END IF
190 END IF
191 IF (ALPHA.EQ.ZERO) RETURN
192 IF (LSAME(UPLO,'U')) THEN
193 *
194 * Form y when A is stored in upper triangle.
195 *
196 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
197 DO 60 J = 1,N
198 TEMP1 = ALPHA*X(J)
199 TEMP2 = ZERO
200 DO 50 I = 1,J - 1
201 Y(I) = Y(I) + TEMP1*A(I,J)
202 TEMP2 = TEMP2 + CONJG(A(I,J))*X(I)
203 50 CONTINUE
204 Y(J) = Y(J) + TEMP1*REAL(A(J,J)) + ALPHA*TEMP2
205 60 CONTINUE
206 ELSE
207 JX = KX
208 JY = KY
209 DO 80 J = 1,N
210 TEMP1 = ALPHA*X(JX)
211 TEMP2 = ZERO
212 IX = KX
213 IY = KY
214 DO 70 I = 1,J - 1
215 Y(IY) = Y(IY) + TEMP1*A(I,J)
216 TEMP2 = TEMP2 + CONJG(A(I,J))*X(IX)
217 IX = IX + INCX
218 IY = IY + INCY
219 70 CONTINUE
220 Y(JY) = Y(JY) + TEMP1*REAL(A(J,J)) + ALPHA*TEMP2
221 JX = JX + INCX
222 JY = JY + INCY
223 80 CONTINUE
224 END IF
225 ELSE
226 *
227 * Form y when A is stored in lower triangle.
228 *
229 IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
230 DO 100 J = 1,N
231 TEMP1 = ALPHA*X(J)
232 TEMP2 = ZERO
233 Y(J) = Y(J) + TEMP1*REAL(A(J,J))
234 DO 90 I = J + 1,N
235 Y(I) = Y(I) + TEMP1*A(I,J)
236 TEMP2 = TEMP2 + CONJG(A(I,J))*X(I)
237 90 CONTINUE
238 Y(J) = Y(J) + ALPHA*TEMP2
239 100 CONTINUE
240 ELSE
241 JX = KX
242 JY = KY
243 DO 120 J = 1,N
244 TEMP1 = ALPHA*X(JX)
245 TEMP2 = ZERO
246 Y(JY) = Y(JY) + TEMP1*REAL(A(J,J))
247 IX = JX
248 IY = JY
249 DO 110 I = J + 1,N
250 IX = IX + INCX
251 IY = IY + INCY
252 Y(IY) = Y(IY) + TEMP1*A(I,J)
253 TEMP2 = TEMP2 + CONJG(A(I,J))*X(IX)
254 110 CONTINUE
255 Y(JY) = Y(JY) + ALPHA*TEMP2
256 JX = JX + INCX
257 JY = JY + INCY
258 120 CONTINUE
259 END IF
260 END IF
261 *
262 RETURN
263 *
264 * End of CHEMV .
265 *
266 END