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