1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
|
*> \brief \b DSPR
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
*
* .. Scalar Arguments ..
* DOUBLE PRECISION ALPHA
* INTEGER INCX,N
* CHARACTER UPLO
* ..
* .. Array Arguments ..
* DOUBLE PRECISION AP(*),X(*)
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> DSPR performs the symmetric rank 1 operation
*>
*> A := alpha*x*x**T + A,
*>
*> where alpha is a real scalar, x is an n element vector and A is an
*> n by n symmetric matrix, supplied in packed form.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] UPLO
*> \verbatim
*> UPLO is CHARACTER*1
*> On entry, UPLO specifies whether the upper or lower
*> triangular part of the matrix A is supplied in the packed
*> array AP as follows:
*>
*> UPLO = 'U' or 'u' The upper triangular part of A is
*> supplied in AP.
*>
*> UPLO = 'L' or 'l' The lower triangular part of A is
*> supplied in AP.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> On entry, N specifies the order of the matrix A.
*> N must be at least zero.
*> \endverbatim
*>
*> \param[in] ALPHA
*> \verbatim
*> ALPHA is DOUBLE PRECISION.
*> On entry, ALPHA specifies the scalar alpha.
*> \endverbatim
*>
*> \param[in] X
*> \verbatim
*> X is DOUBLE PRECISION array, dimension at least
*> ( 1 + ( n - 1 )*abs( INCX ) ).
*> Before entry, the incremented array X must contain the n
*> element vector x.
*> \endverbatim
*>
*> \param[in] INCX
*> \verbatim
*> INCX is INTEGER
*> On entry, INCX specifies the increment for the elements of
*> X. INCX must not be zero.
*> \endverbatim
*>
*> \param[in,out] AP
*> \verbatim
*> AP is DOUBLE PRECISION array, dimension at least
*> ( ( n*( n + 1 ) )/2 ).
*> Before entry with UPLO = 'U' or 'u', the array AP must
*> contain the upper triangular part of the symmetric matrix
*> packed sequentially, column by column, so that AP( 1 )
*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
*> and a( 2, 2 ) respectively, and so on. On exit, the array
*> AP is overwritten by the upper triangular part of the
*> updated matrix.
*> Before entry with UPLO = 'L' or 'l', the array AP must
*> contain the lower triangular part of the symmetric matrix
*> packed sequentially, column by column, so that AP( 1 )
*> contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
*> and a( 3, 1 ) respectively, and so on. On exit, the array
*> AP is overwritten by the lower triangular part of the
*> updated matrix.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_blas_level2
*
*> \par Further Details:
* =====================
*>
*> \verbatim
*>
*> Level 2 Blas routine.
*>
*> -- Written on 22-October-1986.
*> Jack Dongarra, Argonne National Lab.
*> Jeremy Du Croz, Nag Central Office.
*> Sven Hammarling, Nag Central Office.
*> Richard Hanson, Sandia National Labs.
*> \endverbatim
*>
* =====================================================================
SUBROUTINE DSPR(UPLO,N,ALPHA,X,INCX,AP)
*
* -- Reference BLAS level2 routine (version 3.7.0) --
* -- Reference BLAS is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
DOUBLE PRECISION ALPHA
INTEGER INCX,N
CHARACTER UPLO
* ..
* .. Array Arguments ..
DOUBLE PRECISION AP(*),X(*)
* ..
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER (ZERO=0.0D+0)
* ..
* .. Local Scalars ..
DOUBLE PRECISION TEMP
INTEGER I,INFO,IX,J,JX,K,KK,KX
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA
* ..
*
* Test the input parameters.
*
INFO = 0
IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
INFO = 1
ELSE IF (N.LT.0) THEN
INFO = 2
ELSE IF (INCX.EQ.0) THEN
INFO = 5
END IF
IF (INFO.NE.0) THEN
CALL XERBLA('DSPR ',INFO)
RETURN
END IF
*
* Quick return if possible.
*
IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
*
* Set the start point in X if the increment is not unity.
*
IF (INCX.LE.0) THEN
KX = 1 - (N-1)*INCX
ELSE IF (INCX.NE.1) THEN
KX = 1
END IF
*
* Start the operations. In this version the elements of the array AP
* are accessed sequentially with one pass through AP.
*
KK = 1
IF (LSAME(UPLO,'U')) THEN
*
* Form A when upper triangle is stored in AP.
*
IF (INCX.EQ.1) THEN
DO 20 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = ALPHA*X(J)
K = KK
DO 10 I = 1,J
AP(K) = AP(K) + X(I)*TEMP
K = K + 1
10 CONTINUE
END IF
KK = KK + J
20 CONTINUE
ELSE
JX = KX
DO 40 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*X(JX)
IX = KX
DO 30 K = KK,KK + J - 1
AP(K) = AP(K) + X(IX)*TEMP
IX = IX + INCX
30 CONTINUE
END IF
JX = JX + INCX
KK = KK + J
40 CONTINUE
END IF
ELSE
*
* Form A when lower triangle is stored in AP.
*
IF (INCX.EQ.1) THEN
DO 60 J = 1,N
IF (X(J).NE.ZERO) THEN
TEMP = ALPHA*X(J)
K = KK
DO 50 I = J,N
AP(K) = AP(K) + X(I)*TEMP
K = K + 1
50 CONTINUE
END IF
KK = KK + N - J + 1
60 CONTINUE
ELSE
JX = KX
DO 80 J = 1,N
IF (X(JX).NE.ZERO) THEN
TEMP = ALPHA*X(JX)
IX = JX
DO 70 K = KK,KK + N - J
AP(K) = AP(K) + X(IX)*TEMP
IX = IX + INCX
70 CONTINUE
END IF
JX = JX + INCX
KK = KK + N - J + 1
80 CONTINUE
END IF
END IF
*
RETURN
*
* End of DSPR .
*
END
|
