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ex1-refl.jl
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include(joinpath(@__DIR__, "src", "bp.jl"));
using Cubature;
s = ArgParseSettings();
@add_arg_table! s begin
"--C1", "-a"
help = "coefficient 1"
arg_type = Float64
default = 1.0
"--C2", "-b"
help = "coefficient 2"
arg_type = Float64
default = 3.0
"--x0", "-X"
help = "initial configuration"
arg_type = String
default = "(::Any) -> 0.0"
"--force", "-f"
help = "applied force"
arg_type = Float64
default = 0.0
"--umbrella-b"
help = "pseudopotential 'b'"
arg_type = Float64
default = 0.5
"--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)
kT = pargs["kT"];
a = pargs["C1"];
b = pargs["C2"];
f = pargs["force"];
wt = pargs["weight"];
U = (x) -> a*x^4 - b*x^2 - f*x;
x = pargs["x0"](pargs);
xstep = pargs["dx"];
dx_dist = Uniform(-xstep, xstep);
orbf = (pargs["orbit"]) ? x -> rand([-1; 1])*x : x -> x;
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[];
traj_file = if pargs["do-trajectory"]
mkpath(pargs["outdir"]);
open(joinpath(pargs["outdir"], "trajectory.csv"), "w");
else
nothing;
end
natt = 0;
nacc = 0;
nacc_total = 0;
start = time();
last_update = start;
for s = 1:nsteps
xtrial = orbf(x + rand(dx_dist));
Utrial = U(xtrial);
wt_trial = wt(xtrial);
if 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)));
if pargs["do-trajectory"]
writedlm(traj_file, [x Ucurr x*x Ucurr*Ucurr ar s]);
end
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 &&
pargs["steps-per-adjust"] != 0 &&
s % pargs["steps-per-adjust"] == 0
) # adjust step size?
ar = nacc / natt;
if (ar > pargs["step-adjust-ub"])
nacc = 0;
natt = 0;
xstep *= pargs["step-adjust-scale"];
@info "acceptance ratio is high; increasing step size", xstep;
elseif ar < pargs["step-adjust-lb"]
nacc = 0;
natt = 0;
xstep /= pargs["step-adjust-scale"];
@info "acceptance ratio is low; decreasing step size", xstep;
end
dx_dist = Uniform(-xstep, xstep);
end
end
if pargs["do-trajectory"]
close(traj_file);
end
return Dict(:xavg => xtotal / inv_wt_total,
:Uavg => Utotal / inv_wt_total,
:xrolling => copy(xrolling), :Urolling => copy(Urolling),
:x2avg => x2total / inv_wt_total,
:U2avg => U2total / inv_wt_total,
:x2rolling => copy(x2rolling), :U2rolling => copy(U2rolling),
:xstd_rolling => copy(xstd_rolling),
:Ustd_rolling => copy(Ustd_rolling),
:rolls => rolls,
:ar => nacc / natt,
:AR => nacc_total / nsteps
);
end
src_include("wrap_main_runs.jl");
results_std, results_polya = wrap_main_runs(pargs);
uC, ub = pargs["umbrella-C"], pargs["umbrella-b"];
pargs_umb = copy(pargs);
pargs_umb["weight"] = x -> uC*exp(-ub*x^2);
pargs_umb["outdir"] = joinpath(pargs["outdir"], "umb");
results_umb_std, results_umb_polya = wrap_main_runs(pargs_umb);
kT = pargs["kT"];
a = pargs["C1"];
b = pargs["C2"];
f = pargs["force"];
wt = pargs["weight"];
U = (x) -> a*x^4 - b*x^2 - f*x;
meq = 25000;
ℓ = 4*sqrt(b / a);
(Zquad, Zquad_err) = (
collect(hquadrature(t -> -exp(-U(1/t)/kT) / t^2, 0.0, -1/ℓ; maxevals=meq)) +
collect(hquadrature(x -> exp(-U(x)/kT), -ℓ, ℓ; maxevals=meq)) +
collect(hquadrature(t -> -exp(-U(1/t)/kT) / t^2, 1/ℓ, 0.0; maxevals=meq))
);
(xquad, xquad_err) = (f == 0) ? [0.0; 0.0] : (
(
collect(hquadrature(t -> -(1/t)*exp(-U(1/t)/kT) / t^2 / Zquad, 0.0, -1/ℓ; maxevals=meq)) +
collect(hquadrature(x -> x*exp(-U(x)/kT) / Zquad, -ℓ, ℓ; maxevals=meq)) +
collect(hquadrature(t -> -(1/t)*exp(-U(1/t)/kT) / t^2 / Zquad, 1/ℓ, 0.0; maxevals=meq))
)
);
(Uquad, Uquad_err) = (
collect(hquadrature(t -> -U(1/t)*exp(-U(1/t)/kT) / t^2 / Zquad, 0.0, -1/ℓ; maxevals=meq)) +
collect(hquadrature(x -> U(x)*exp(-U(x)/kT) / Zquad, -ℓ, ℓ; maxevals=meq)) +
collect(hquadrature(t -> -U(1/t)*exp(-U(1/t)/kT) / t^2 / Zquad, 1/ℓ, 0.0; maxevals=meq))
);
(x2quad, x2quad_err) = (
collect(hquadrature(t -> -(1/t)^2*exp(-U(1/t)/kT) / t^2 / Zquad, 0.0, -1/ℓ; maxevals=meq)) +
collect(hquadrature(x -> x^2*exp(-U(x)/kT) / Zquad, -ℓ, ℓ; maxevals=meq)) +
collect(hquadrature(t -> -(1/t)^2*exp(-U(1/t)/kT) / t^2 / Zquad, 1/ℓ, 0.0; maxevals=meq))
);
(U2quad, U2quad_err) = (
collect(hquadrature(t -> -(U(1/t))^2*exp(-U(1/t)/kT) / t^2 / Zquad, 0.0, -1/ℓ; maxevals=meq)) +
collect(hquadrature(x -> (U(x))^2*exp(-U(x)/kT) / Zquad, -ℓ, ℓ; maxevals=meq)) +
collect(hquadrature(t -> -(U(1/t))^2*exp(-U(1/t)/kT) / t^2 / Zquad, 1/ℓ, 0.0; maxevals=meq))
);
idx = rand(1:pargs["num-runs"]);
@info "std ar = $(results_std[idx][:ar])";
@info "polya ar = $(results_polya[idx][:ar])";
@info "umb std ar = $(results_umb_std[idx][:ar])";
@info "umb polya ar = $(results_umb_polya[idx][:ar])";
@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])";
@info "<U^2> via quadrature = $U2quad; error = $U2quad_err";
@info "<U^2> via std = $(results_std[idx][:U2avg])";
@info "<U^2> via polya = $(results_polya[idx][:U2avg])";
@info "<U^2> via umb std = $(results_umb_std[idx][:U2avg])";
@info "<U^2> via umb polya = $(results_umb_polya[idx][:U2avg])";
#@info "<Urolling> via std = $(results_std[idx][:Urolling])";
#@info "<Urolling> via polya = $(results_polya[idx][:Urolling])";
#@info "<Urolling> via umb std = $(results_umb_std[idx][:Urolling])";
#@info "<Urolling> via umb polya = $(results_umb_polya[idx][:Urolling])";
L1_error_std, L1_error_polya = post_process_main_runs(results_std,
results_polya,
pargs;
xrolling=xquad,
Urolling=Uquad,
x2rolling=x2quad,
U2rolling=U2quad);
L1_err_umb_std, L1_err_umb_polya = post_process_main_runs(results_umb_std,
results_umb_polya,
pargs_umb;
xrolling=xquad,
Urolling=Uquad,
x2rolling=x2quad,
U2rolling=U2quad);
if pargs["do-csvs"]
for k in keys(L1_error_std)
writedlm(joinpath(pargs["outdir"], "L1_$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"]
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");
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");
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");
display(p);
println();
println("Press RETURN to exit...");
readline();
end