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ex6-D2h.jl
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ex6-D2h.jl
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include(joinpath(@__DIR__, "src", "bp.jl"));
using Cubature;
s = ArgParseSettings();
@add_arg_table! s begin
"--len-x", "-a"
help = "length in the x-direction"
arg_type = Float64
default = 1.0
"--len-y", "-b"
help = "length in the y-direction"
arg_type = Float64
default = 0.5
"--len-z", "-c"
help = "length in the z-direction"
arg_type = Float64
default = 2.0
"--charge", "-q"
help = "charge of ion"
arg_type = Float64
default = 1.0
"--x0", "-X"
help = "initial configuration"
arg_type = String
default = "(args::Any) -> [rand(Uniform(-args[\"len-x\"], args[\"len-x\"])), rand(Uniform(-args[\"len-y\"], args[\"len-y\"])), rand(Uniform(-args[\"len-z\"], args[\"len-z\"]))]"
"--umbrella-sigma-a"
help = "umbrella weight width"
arg_type = Float64
default = 1.0
"--umbrella-sigma-b"
help = "umbrella weight width"
arg_type = Float64
default = 1.0
"--umbrella-sigma-c"
help = "umbrella weight width"
arg_type = Float64
default = 1.0
"--umbrella-C"
help = "umbrella peak height"
arg_type = Float64
default = 1.0
"--force", "-f"
help = "applied force"
arg_type = String
default = "[0.0; 0.0; 0.0]"
end
default_options = src_include("default_options.jl");
ArgParse.import_settings!(s, default_options);
pargs = src_include("parse_args.jl");
pargs["force"] = eval(Meta.parse(pargs["force"]));
@everywhere function pbc!(xs::Vector{Float64}, ℓs::Vector{Float64})
xs[:] = map(pair -> begin
x, ℓ = pair;
return if x <= -3*ℓ/2
3*ℓ + x;
elseif x >= 3*ℓ/2
x - 3*ℓ;
else
x
end
end, zip(xs, ℓs))
end
@everywhere function mcmc(nsteps::Int, pargs)
basis_vectors = [1 0 0; 0 1 0; 0 0 1];
kT = pargs["kT"];
a = pargs["len-x"];
b = pargs["len-y"];
c = pargs["len-z"];
f = pargs["force"];
q = pargs["charge"];
wt = pargs["weight"];
latvecs = [
[0; 0; 0],
[-a; 0; 0],
[a; 0; 0],
[0; -b; 0],
[0; b; 0],
[0; 0; -c],
[0; 0; c]
];
U = (x) -> q*sum(map(v -> 1/norm(x - v, 2), latvecs)) - dot(f, x)
x = pargs["x0"](pargs);
xstep = pargs["dx"];
dx_dist = Uniform(-xstep, xstep);
orbf! = if (pargs["orbit"])
x -> begin;
choice = rand(1:4);
if choice == 1
x[1] = -x[1];
elseif choice == 2
x[2] = -x[2];
elseif choice == 3
x[3] = -x[3];
end
end
else
x -> x;
end
wt_curr = wt(x);
inv_wt_total = 1 / wt_curr;
xtotal = x[:] / wt_curr;
xrolling = Vector{Float64}[];
Ucurr = U(x);
Utotal = Ucurr / wt_curr;
Urolling = Float64[];
x2total = (x[:] .* x[:]) / wt_curr;
x2rolling = Vector{Float64}[];
xstd_rolling = Vector{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 = x[:] + rand(dx_dist, 3);
orbf!(xtrial);
Utrial = U(xtrial);
wt_trial = wt(xtrial);
if (
(abs(xtrial[1]) <= a) &&
(abs(xtrial[2]) <= b) &&
(abs(xtrial[3]) <= c) &&
(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;
@assert((abs(x[1]) <= a) &&
(abs(x[2]) <= b) &&
(abs(x[3]) <= c));
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,
map(i -> sqrt(max(0.0, x2total[i] / inv_wt_total
- (xtotal[i] / inv_wt_total)^2)), 1:3)
);
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 / natt,
:AR => nacc_total / inv_wt_total
);
end
src_include("wrap_main_runs.jl");
results_std, results_polya = wrap_main_runs(pargs);
uC = pargs["umbrella-C"];
uΣ = 1/2*[1/(pargs["umbrella-sigma-a"]^2) 0 0;
0 1/(pargs["umbrella-sigma-b"]^2) 0;
0 0 1/(pargs["umbrella-sigma-c"]^2)];
pargs_umb = copy(pargs);
pargs_umb["weight"] = x -> uC*exp(-dot(x, uΣ*x));
pargs_umb["outdir"] = joinpath(pargs["outdir"], "umb");
results_umb_std, results_umb_polya = wrap_main_runs(pargs_umb);
kT = pargs["kT"];
a = pargs["len-x"];
b = pargs["len-y"];
c = pargs["len-z"];
q = pargs["charge"];
f = pargs["force"];
latvecs = [
[0; 0; 0],
[-a; 0; 0],
[a; 0; 0],
[0; -b; 0],
[0; b; 0],
[0; 0; -c],
[0; 0; c]
];
U = (x) -> q*sum(map(v -> 1/norm(x - v, 2), latvecs)) - dot(f, x)
meq = 25000;
(Zquad, Zquad_err) = hcubature(x -> exp(-U(x) / kT), [-a, -b, -c], [a, b, c]; maxevals=meq);
(xquad, xquad_err) = hcubature(3, (x, v) -> (v[:] = x*exp(-U(x) / kT) / Zquad), [-a, -b, -c], [a, b, c]; maxevals=meq);
(Uquad, Uquad_err) = (
collect(hcubature(x -> U(x)*exp(-U(x) / kT) / Zquad, [0, -b, -c], [a, b, c]; maxevals=meq)) +
collect(hcubature(x -> U(x)*exp(-U(x) / kT) / Zquad, [-a, -b, -c], [0, b, c]; maxevals=meq))
);
(x2quad, x2quad_err) = hcubature(3, (x, v) -> (v[:] = x .* x *exp(-U(x) / kT) / Zquad), [-a, -b, -c], [a, b, c]; maxevals=meq);
(U2quad, U2quad_err) = (
collect(hcubature(x -> (U(x)^2)*exp(-U(x) / kT) / Zquad, [0, -b, -c], [a, b, c]; maxevals=meq)) +
collect(hcubature(x -> (U(x)^2)*exp(-U(x) / kT) / Zquad, [-a, -b, -c], [0, b, c]; 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 "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"]);
xrolling_std = transpose(hcat(results_std[idx][:xrolling]...));
p = plot(results_std[idx][:rolls], xrolling_std[:, 1]; label="std mcmc",
xlabel = "step", ylabel = "\$\\langle x_1 \\rangle\$");
xrolling_polya = transpose(hcat(results_polya[idx][:xrolling]...));
plot!(results_polya[idx][:rolls], xrolling_polya[:, 1]; label="polya");
display(p);
println();
println("Press RETURN to exit...");
readline();
p = plot(results_std[idx][:rolls], xrolling_std[:, 2]; label="std mcmc",
xlabel = "step", ylabel = "\$\\langle x_2 \\rangle\$");
plot!(results_polya[idx][:rolls], xrolling_polya[:, 2]; label="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");
display(p);
println();
println("Press RETURN to exit...");
readline();
end