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
|
/*
* Copyright © 2005 Ondra Kamenik
* Copyright © 2019 Dynare Team
*
* This file is part of Dynare.
*
* Dynare is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* Dynare is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with Dynare. If not, see <http://www.gnu.org/licenses/>.
*/
#include "smolyak.hh"
#include "symmetry.hh"
#include <iostream>
#include <iomanip>
/* This constructs a beginning of ‘isum’ summand in ‘smolq’. We must be careful
here, since ‘isum’ can be past-the-end, so no reference to vectors in
‘smolq’ by ‘isum’ must be done in this case. */
smolpit::smolpit(const SmolyakQuadrature &q, unsigned int isum)
: smolq(q), isummand(isum),
jseq(q.dimen(), 0),
sig{q.dimen()},
p{q.dimen()}
{
if (isummand < q.numSummands())
setPointAndWeight();
}
bool
smolpit::operator==(const smolpit &spit) const
{
return &smolq == &spit.smolq && isummand == spit.isummand && jseq == spit.jseq;
}
/* We first try to increase index within the current summand. If we are at
maximum, we go to a subsequent summand. Note that in this case all indices
in ‘jseq’ will be zero, so no change is needed. */
smolpit &
smolpit::operator++()
{
const IntSequence &levpts = smolq.levpoints[isummand];
int i = smolq.dimen()-1;
jseq[i]++;
while (i >= 0 && jseq[i] == levpts[i])
{
jseq[i] = 0;
i--;
if (i >= 0)
jseq[i]++;
}
sig.signalAfter(std::max(i, 0));
if (i < 0)
isummand++;
if (isummand < smolq.numSummands())
setPointAndWeight();
return *this;
}
/* Here we set the point coordinates according to ‘jseq’ and
‘isummand’. Also the weight is set here. */
void
smolpit::setPointAndWeight()
{
// todo: raise if isummand ≥ smolq.numSummands()
int l = smolq.level;
int d = smolq.dimen();
int sumk = (smolq.levels[isummand]).sum();
int m1exp = l + d - sumk - 1;
w = (2*(m1exp/2) == m1exp) ? 1.0 : -1.0;
w *= PascalTriangle::noverk(d-1, sumk-l);
for (int i = 0; i < d; i++)
{
int ki = (smolq.levels[isummand])[i];
p[i] = (smolq.uquad).point(ki, jseq[i]);
w *= (smolq.uquad).weight(ki, jseq[i]);
}
}
/* Debug print. */
void
smolpit::print() const
{
auto ff = std::cout.flags();
std::cout << "isum=" << std::left << std::setw(3) << isummand << std::right << ": [";
for (int i = 0; i < smolq.dimen(); i++)
std::cout << std::setw(2) << (smolq.levels[isummand])[i] << ' ';
std::cout << "] j=[";
for (int i = 0; i < smolq.dimen(); i++)
std::cout << std::setw(2) << jseq[i] << ' ';
std::cout << std::showpos << std::fixed << std::setprecision(3)
<< "] " << std::setw(4) << w << "*(";
for (int i = 0; i < smolq.dimen()-1; i++)
std::cout << std::setw(4) << p[i] << ' ';
std::cout << std::setw(4) << p[smolq.dimen()-1] << ')' << std::endl;
std::cout.flags(ff);
}
/* Here is the constructor of SmolyakQuadrature. We have to setup ‘levels’,
‘levpoints’ and ‘cumevals’. We have to go through all d-dimensional
sequences k, such that l≤|k|≤l+d−1 and all kᵢ are positive integers. This is
equivalent to going through all k such that l−d≤|k|≤l−1 and all kᵢ are
non-negative integers. This is equivalent to going through d+1 dimensional
sequences (k,x) such that |(k,x)|=l−1 and x=0,…,d−1. The resulting sequence
of positive integers is obtained by adding 1 to all kᵢ. */
SmolyakQuadrature::SmolyakQuadrature(int d, int l, const OneDQuadrature &uq)
: QuadratureImpl<smolpit>(d), level(l), uquad(uq)
{
// TODO: check l>1, l≥d
// TODO: check l≥uquad.miLevel(), l≤uquad.maxLevel()
int cum = 0;
for (const auto &si : SymmetrySet(l-1, d+1))
{
if (si[d] <= d-1)
{
IntSequence lev(si, 0, d);
lev.add(1);
levels.push_back(lev);
IntSequence levpts(d);
for (int i = 0; i < d; i++)
levpts[i] = uquad.numPoints(lev[i]);
levpoints.push_back(levpts);
cum += levpts.mult();
cumevals.push_back(cum);
}
}
}
/* Here we return a number of evalutions of the quadrature for the given level.
If the given level is the current one, we simply return the maximum
cumulative number of evaluations. Otherwise we call costly
calcNumEvaluations() method. */
int
SmolyakQuadrature::numEvals(int l) const
{
if (l != level)
return calcNumEvaluations(l);
else
return cumevals[numSummands()-1];
}
/* This divides all the evaluations to ‘tn’ approximately equal groups, and
returns the beginning of the specified group ‘ti’. The granularity of
divisions are summands as listed by ‘levels’. */
smolpit
SmolyakQuadrature::begin(int ti, int tn, int l) const
{
// TODO: raise is level≠l
if (ti == tn)
return smolpit(*this, numSummands());
int totevals = cumevals[numSummands()-1];
int evals = (totevals*ti)/tn;
unsigned int isum = 0;
while (isum+1 < numSummands() && cumevals[isum+1] < evals)
isum++;
return smolpit(*this, isum);
}
/* This is the same in a structure as SmolyakQuadrature constructor. We have to
go through all summands and calculate a number of evaluations in each
summand. */
int
SmolyakQuadrature::calcNumEvaluations(int lev) const
{
int cum = 0;
for (const auto &si : SymmetrySet(lev-1, dim+1))
{
if (si[dim] <= dim-1)
{
IntSequence lev(si, 0, dim);
lev.add(1);
IntSequence levpts(dim);
for (int i = 0; i < dim; i++)
levpts[i] = uquad.numPoints(lev[i]);
cum += levpts.mult();
}
}
return cum;
}
/* This returns a maximum level such that the number of evaluations is less
than the given number. */
void
SmolyakQuadrature::designLevelForEvals(int max_evals, int &lev, int &evals) const
{
int last_evals;
evals = 1;
lev = 1;
do
{
lev++;
last_evals = evals;
evals = calcNumEvaluations(lev);
}
while (lev < uquad.numLevels() && evals <= max_evals);
lev--;
evals = last_evals;
}
|
