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