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
|
#include "fourier.hpp"
#include <getopt.h>
#include <iostream>
#include <fstream>
int main(int argc, char* argv[]) {
unsigned p = 2;
unsigned s = 2;
Real λ = 0.5;
Real τ₀ = 0;
Real y₀ = 0;
Real yₘₐₓ = 0.5;
Real Δy = 0.05;
unsigned log2n = 8;
Real τₘₐₓ = 20;
unsigned maxIterations = 1000;
Real ε = 1e-14;
Real γ = 0;
bool loadData = false;
int opt;
while ((opt = getopt(argc, argv, "p:s:2:T:t:0:y:d:I:g:l")) != -1) {
switch (opt) {
case 'p':
p = atoi(optarg);
break;
case 's':
s = atoi(optarg);
break;
case '2':
log2n = atoi(optarg);
break;
case 'T':
τₘₐₓ = atof(optarg);
break;
case 't':
τ₀ = atof(optarg);
break;
case '0':
y₀ = atof(optarg);
break;
case 'y':
yₘₐₓ = atof(optarg);
break;
case 'd':
Δy = atof(optarg);
break;
case 'I':
maxIterations = (unsigned)atof(optarg);
break;
case 'g':
γ = atof(optarg);
break;
case 'l':
loadData = true;
break;
default:
exit(1);
}
}
unsigned n = pow(2, log2n);
Real Δτ = τₘₐₓ / M_PI / n;
Real Δω = M_PI / τₘₐₓ;
Real z = (-1+sqrt(1+2*τ₀)) / (2 * τ₀);
Real Γ₀ = 1;
std::vector<Real> C(2 * n);
std::vector<Real> R(2 * n);
FourierTransform fft(n, Δω, Δτ);
std::vector<Complex> Ct;
std::vector<Complex> Rt;
Real y = y₀;
if (!loadData) {
// start from the exact solution for τ₀ = 0
for (unsigned i = 0; i < n; i++) {
Real τ = i * Δτ * M_PI;
C[i] = Γ₀ / 2 * (exp(-z * τ) - z * τ₀ * exp(-τ / τ₀)) / (z - pow(z, 3) * pow(τ₀, 2));
if (i > 0) {
C[2 * n - i] = C[i];
}
R[i] = exp(-z * τ);
}
Ct = fft.fourier(C);
Rt = fft.fourier(R);
} else {
std::ifstream cfile(fourierFile("C", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
cfile.read((char*)(C.data()), C.size() * sizeof(Real));
cfile.close();
std::ifstream rfile(fourierFile("R", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::binary);
rfile.read((char*)(R.data()), R.size() * sizeof(Real));
rfile.close();
Ct = fft.fourier(C);
Rt = fft.fourier(R);
z = estimateZ(fft, C, Ct, R, Rt, p, s, λ, y);
}
while (y += Δy, y <= yₘₐₓ) {
Real ΔC = 1;
Real ΔCprev = 1000;
unsigned it = 0;
while (sqrt(2 * ΔC / C.size()) > ε) {
it++;
auto [RddfCt, dfCt] = RddfCtdfCt(fft, C, R, p, s, λ);
for (unsigned i = 0; i < Rt.size(); i++) {
Real ω = i * Δω;
Rt[i] = (1.0 + pow(y, 2) * RddfCt[i] * Rt[i]) / (z + 1i * ω);
}
for (unsigned i = 0; i < Ct.size(); i++) {
Real ω = i * Δω;
Ct[i] = (Γ₀ * std::conj(Rt[i]) / (1 + pow(τ₀ * ω, 2)) + pow(y, 2) * (RddfCt[i] * Ct[i] + dfCt[i] * std::conj(Rt[i]))) / (z + 1i * ω);
}
std::vector<Real> Cnew = fft.inverse(Ct);
std::vector<Real> Rnew = fft.inverse(Rt);
for (unsigned i = n; i < 2 * n; i++) {
Rnew[i] = 0;
}
ΔC = 0;
for (unsigned i = 0; i < Cnew.size() / 2; i++) {
ΔC += pow(Cnew[i] - C[i], 2);
ΔC += pow(Rnew[i] - R[i], 2);
}
for (unsigned i = 0; i < Cnew.size(); i++) {
C[i] += γ * (Cnew[i] - C[i]);
}
for (unsigned i = 0; i < Rnew.size() / 2; i++) {
R[i] += γ * (Rnew[i] - R[i]);
}
z *= Cnew[0];
if (it % maxIterations == 0) {
if (ΔC < ΔCprev) {
γ = std::min(1.1 * γ, 1.0);
} else {
γ /= 2;
}
ΔCprev = ΔC;
}
std::cerr << it << " " << p << " " << s << " " << τ₀ << " " << y << " " << sqrt(2 * ΔC / C.size()) << " " << γ << std::endl;
}
Real e = energy(C, R, p, s, λ, y, Δτ);
std::cerr << "y " << y << " " << e << " " << z << std::endl;
std::ofstream outfile(fourierFile("C", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
outfile.write((const char*)(C.data()), C.size() * sizeof(Real));
outfile.close();
std::ofstream outfileR(fourierFile("R", p, s, λ, τ₀, y, log2n, τₘₐₓ), std::ios::out | std::ios::binary);
outfileR.write((const char*)(R.data()), R.size() * sizeof(Real));
outfileR.close();
}
return 0;
}
|
