-
Notifications
You must be signed in to change notification settings - Fork 0
/
ex2-trans.jl
269 lines (245 loc) · 9.82 KB
/
ex2-trans.jl
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
262
263
264
265
266
267
268
269
include(joinpath(@__DIR__, "src", "bp.jl"));
using Cubature;
s = ArgParseSettings();
@add_arg_table! s begin
"--x0", "-X"
help = "initial configuration (Function, i.e. rand)"
arg_type = String
default = "(::Any) -> 0.0"
"--C1", "-a"
help = "coefficient 1"
arg_type = Float64
default = 1.0
"--C2", "-n"
help = "coefficient 2"
arg_type = Int
default = 4
"--force", "-f"
help = "applied force"
arg_type = Float64
default = 0.0
"--periodic-bcs", "-p"
help = "enforce periodic boundary conditions"
action = :store_true
"--umbrella-C"
help = "pseudopotential 'C'"
arg_type = Float64
default = 1.0
end
default_options = src_include("default_options.jl");
ArgParse.import_settings!(s, default_options);
pargs = src_include("parse_args.jl");
@everywhere function mcmc(nsteps::Int, pargs::Dict)
kT = pargs["kT"];
a = pargs["C1"];
n = pargs["C2"];
f = pargs["force"];
wt = pargs["weight"];
U = (x) -> a*cos(n*x) - f*x;
x = pargs["x0"](pargs);
xstep = pargs["dx"];
dx_dist = Uniform(-xstep, xstep);
orbf = (pargs["orbit"]) ? x -> x + rand([-1; 0; 1])*(2*π / n) : x -> x;
bcf = if pargs["periodic-bcs"]
x -> begin;
if x > π # apply periodic boundary conditions
-π + (x - π);
elseif x < -π
π - (-π - x);
else
x;
end
end
else
x -> x;
end
nacc = 0;
wt_curr = wt(x);
inv_wt_total = 1 / wt_curr;
xtotal = x / wt_curr;
xrolling = Float64[];
Ucurr = U(x);
Utotal = Ucurr / wt_curr;
Urolling = Float64[];
x2total = x*x / wt_curr;
x2rolling = Float64[];
xstd_rolling = Float64[];
U2total = Ucurr*Ucurr / wt_curr;
U2rolling = Float64[];
Ustd_rolling = Float64[];
stepout = pargs["stepout"];
rolls = Int[];
natt = 0;
nacc = 0;
nacc_total = 0;
start = time();
last_update = start;
for s = 1:nsteps
xtrial = bcf(orbf(x + rand(dx_dist)));
Utrial = U(xtrial);
wt_trial = wt(xtrial);
if (
(-π <= xtrial <= π) &&
(rand() <= ( exp(-(Utrial - Ucurr) / kT) * wt_trial / wt_curr ))
)
x = xtrial;
Ucurr = Utrial;
wt_curr = wt_trial;
nacc += 1;
nacc_total += 1;
end
natt += 1;
inv_wt_total += 1 / wt_curr;
xtotal += x / wt_curr;
Utotal += Ucurr / wt_curr;
x2total += x*x / wt_curr;
U2total += Ucurr*Ucurr / wt_curr;
ar = nacc_total / s; # rolling acceptance ratio
if s % stepout == 0
push!(rolls, s);
push!(xrolling, xtotal / inv_wt_total);
push!(Urolling, Utotal / inv_wt_total);
push!(x2rolling, x2total / inv_wt_total);
push!(U2rolling, U2total / inv_wt_total);
push!(xstd_rolling, sqrt(max(0.0, x2total / inv_wt_total -
(xtotal / inv_wt_total)^2)));
push!(Ustd_rolling, sqrt(max(0.0, U2total / inv_wt_total -
(Utotal / inv_wt_total)^2)));
end
if time() - last_update > pargs["update-freq"]
@info "elapsed: $(time() - start)";
@info "step: $s / $nsteps";
last_update = time();
end
if (
pargs["step-adjust-scale"] != 1.0 &&
s % pargs["steps-per-adjust"] == 0
) # adjust step size?
ar = nacc / natt;
if (ar > pargs["step-adjust-ub"])
@info "acceptance ratio is high; increasing step size", xstep;
nacc = 0;
natt = 0;
xstep *= pargs["step-adjust-scale"];
elseif ar < pargs["step-adjust-lb"]
@info "acceptance ratio is low; decreasing step size", xstep;
nacc = 0;
natt = 0;
xstep /= pargs["step-adjust-scale"];
end
dx_dist = Uniform(-xstep, xstep);
end
end
return Dict(:xavg => xtotal / inv_wt_total,
:Uavg => Utotal / inv_wt_total,
:xrolling => xrolling,
:Urolling => Urolling,
:x2avg => x2total / inv_wt_total,
:U2avg => U2total / inv_wt_total,
:x2rolling => x2rolling,
:U2rolling => U2rolling,
:xstd_rolling => xstd_rolling,
:Ustd_rolling => Ustd_rolling,
:rolls => rolls,
:ar => nacc / nsteps, :AR => nacc_total / nsteps);
end
maxevals = convert(Int, 1e6);
kT = pargs["kT"];
a = pargs["C1"];
n = pargs["C2"];
f = pargs["force"];
U = (x) -> a*cos(n*x) - f*x;
Zquad, Zquad_err = hquadrature(x -> exp(-U(x)/kT), -π, π; maxevals=maxevals);
xquad, xquad_err = hquadrature(x -> x * exp(-U(x)/kT) / Zquad, -π, π; maxevals=maxevals);
Uquad, Uquad_err = hquadrature(x -> U(x) * exp(-U(x)/kT) / Zquad, -π, π; maxevals=maxevals);
x2quad, x2quad_err = hquadrature(x -> x*x * exp(-U(x)/kT) / Zquad, -π, π; maxevals=maxevals);
U2quad, U2quad_err = hquadrature(x -> (U(x))^2 * exp(-U(x)/kT) / Zquad, -π, π; maxevals=maxevals);
src_include("wrap_main_runs.jl");
results_std, results_polya = wrap_main_runs(pargs);
L1_error_std, L1_error_polya = post_process_main_runs(results_std,
results_polya,
pargs;
xrolling=xquad,
Urolling=Uquad,
x2rolling=x2quad,
U2rolling=U2quad);
μs = vcat(range(0.0, -π; step=-2*π/n), range(0.0, π; step=2*π/n)[2:end]);
pargs_umb = copy(pargs);
pargs_umb["weight"] = x -> a * sum(map(μ -> exp(-n^2*(x-μ)^2 / 2), μs));
pargs_umb["outdir"] = joinpath(pargs["outdir"], "umb");
results_umb_std, results_umb_polya = wrap_main_runs(pargs_umb);
L1_err_umb_std, L1_err_umb_polya = post_process_main_runs(results_umb_std,
results_umb_polya,
pargs_umb,
xrolling=xquad,
Urolling=Uquad,
x2rolling=x2quad,
U2rolling=U2quad);
idx = rand(1:pargs["num-runs"]);
@info "Z via quadrature = $Zquad; error = $Zquad_err";
@info "<x> via quadrature = $xquad; error = $xquad_err";
@info "<x> via std = $(results_std[idx][:xavg])";
@info "<x> via polya = $(results_polya[idx][:xavg])";
@info "<x> via umb std = $(results_umb_std[idx][:xavg])";
@info "<x> via umb polya = $(results_umb_polya[idx][:xavg])";
@info "<U> via quadrature = $Uquad; error = $Uquad_err";
@info "<U> via std = $(results_std[idx][:Uavg])";
@info "<U> via polya = $(results_polya[idx][:Uavg])";
@info "<U> via umb std = $(results_umb_std[idx][:Uavg])";
@info "<U> via umb polya = $(results_umb_polya[idx][:Uavg])";
@info "<x^2> via quadrature = $x2quad; error = $x2quad_err";
@info "<x^2> via std = $(results_std[idx][:x2avg])";
@info "<x^2> via polya = $(results_polya[idx][:x2avg])";
@info "<x^2> via umb std = $(results_umb_std[idx][:x2avg])";
@info "<x^2> via umb polya = $(results_umb_polya[idx][:x2avg])";
if pargs["do-csvs"]
for k in keys(L1_error_std)
writedlm(joinpath(pargs["outdir"], "L1_$k.csv"), hcat(
results_std[1][:rolls],
L1_error_std[k],
L1_error_polya[k],
L1_err_umb_std[k],
L1_err_umb_polya[k]
), ',');
end
end
if pargs["do-conv-rates"]
println("αs via std = $(convergence_rates(L1_error_std, results_std[1][:rolls]))");
println("αs via polya = $(convergence_rates(L1_error_polya, results_std[1][:rolls]))");
println("αs via umb = $(convergence_rates(L1_err_umb_std, results_std[1][:rolls]))");
println("αs via gu = $(convergence_rates(L1_err_umb_polya, results_std[1][:rolls]))");
end
if pargs["do-plots"]
nsamples = length(results_polya[idx][:rolls])
idx = rand(1:pargs["num-runs"]);
p = plot(results_std[idx][:rolls], results_std[idx][:xrolling]; label="std mcmc",
xlabel = "step", ylabel = "\$\\langle x \\rangle\$");
plot!(results_polya[idx][:rolls], results_polya[idx][:xrolling]; label="polya");
plot!(results_umb_std[idx][:rolls], results_umb_std[idx][:xrolling]; label="umb");
plot!(results_umb_polya[idx][:rolls], results_umb_polya[idx][:xrolling]; label="umb + polya");
plot!(results_polya[idx][:rolls], fill(xquad, nsamples); label="quad", linestyle=:dash);
display(p);
println();
println("Press RETURN to exit...");
readline();
p = plot(results_std[idx][:rolls], results_std[idx][:Urolling]; label="std mcmc",
xlabel = "step", ylabel = "\$\\langle U \\rangle\$");
plot!(results_polya[idx][:rolls], results_polya[idx][:Urolling]; label="polya");
plot!(results_umb_std[idx][:rolls], results_umb_std[idx][:Urolling]; label="umb");
plot!(results_umb_polya[idx][:rolls], results_umb_polya[idx][:Urolling]; label="umb + polya");
plot!(results_polya[idx][:rolls], fill(Uquad, nsamples); label="quad", linestyle=:dash);
display(p);
println();
println("Press RETURN to exit...");
readline();
p = plot(results_std[idx][:rolls], results_std[idx][:x2rolling]; label="std mcmc",
xlabel = "step", ylabel = "\$\\langle x^2 \\rangle\$");
plot!(results_polya[idx][:rolls], results_polya[idx][:x2rolling]; label="polya");
plot!(results_umb_std[idx][:rolls], results_umb_std[idx][:x2rolling]; label="umb");
plot!(results_umb_polya[idx][:rolls], results_umb_polya[idx][:x2rolling]; label="umb + polya");
plot!(results_polya[idx][:rolls], fill(x2quad, nsamples); label="quad", linestyle=:dash);
display(p);
println();
println("Press RETURN to exit...");
readline();
end