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examples/fractures_quantum_amplitude_estimation_for_uq/ex.jl
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import DelimitedFiles | ||
import DPFEHM | ||
import PyPlot | ||
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function addfractures!(logks, fracture_logk, fracture_scales; beta=0.5) | ||
#this recursively defines a formula where fracture_logk ∝ length ^ beta as in equation 5 from Jeffrey's paper (10.1002/2016WR018806) | ||
if fracture_scales > 0 | ||
if fracture_logk < 0.0 | ||
@show fracture_logk | ||
@show fracture_scales | ||
error("you need to increase fracture_logk so that the permeability of the small fractures is greater than the permeability of the matrix") | ||
end | ||
logks[div(end, 2), 1:div(3 * end, 4) + 1] .= fracture_logk + log(1.5 ^ beta)#this fracture is 1.5 times longer than the next fracture | ||
logks[div(end, 4):div(3 * end, 4), div(end, 2)] .= fracture_logk | ||
n = size(logks, 1) | ||
#addfractures!(view(logks, 1:div(n, 2), 1:div(n, 2)))#upper left | ||
addfractures!(view(logks, 1:div(n, 2), div(n, 2) + 1:n), fracture_logk - log(2 ^ beta), fracture_scales - 1; beta=beta)#upper right | ||
#addfractures!(view(logks, div(n, 2) + 1:n, 1:div(n, 2)))#lower left | ||
addfractures!(view(logks, div(n, 2) + 1:n, div(n, 2) + 1:n), fracture_logk - log(2 ^ beta), fracture_scales - 1; beta=beta)#lower right | ||
end | ||
end | ||
addboundaries(logks) = hcat(logks[:, 1], logks, logks[:, end]) | ||
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function fractal_fractures(N, fracture_scales; doplot=false, matrix_logk=0.0, fracture_logk=1.0, kwargs...) | ||
mins = [0.0, 0.0] | ||
maxs = [1, 1] | ||
ns = [N + 2, N] | ||
xs = range(mins[1], maxs[1]; length=ns[1]) | ||
ys = range(mins[2], maxs[2]; length=ns[2]) | ||
logks = fill(matrix_logk, N, N) | ||
addfractures!(logks, fracture_logk, fracture_scales; kwargs...) | ||
logks = addboundaries(logks) | ||
if doplot | ||
fig, ax = PyPlot.subplots() | ||
img = ax.imshow(logks) | ||
fig.colorbar(img) | ||
display(fig) | ||
println() | ||
PyPlot.close(fig) | ||
end | ||
coords, neighbors, areasoverlengths, _ = DPFEHM.regulargrid2d(mins, maxs, ns, 1.0) | ||
logKs2Ks_neighbors(Ks) = exp.(0.5 * (Ks[map(p->p[1], neighbors)] .+ Ks[map(p->p[2], neighbors)])) | ||
Ks_neighbors = logKs2Ks_neighbors(logks) | ||
dirichletnodes = [collect(1:2 * N); collect(prod(ns) - 2 * N + 1:prod(ns))] | ||
dirichleths = zeros(size(coords, 2)) | ||
dirichleths[1:2 * N] .= 1.0 | ||
Qs = zeros(size(coords, 2)) | ||
A = DPFEHM.groundwater_h(zeros(size(coords, 2) - length(dirichletnodes)), Ks_neighbors, neighbors, areasoverlengths, dirichletnodes, dirichleths, Qs, ones(size(coords, 2)), ones(size(coords, 2))) | ||
b = -DPFEHM.groundwater_residuals(zeros(size(coords, 2) - length(dirichletnodes)), Ks_neighbors, neighbors, areasoverlengths, dirichletnodes, dirichleths, Qs, ones(size(coords, 2)), ones(size(coords, 2))) | ||
x = A \ b | ||
isfreenode, nodei2freenodei, freenodei2nodei = DPFEHM.getfreenodes(prod(ns), dirichletnodes) | ||
h = DPFEHM.addboundaryconditions(x, dirichletnodes, dirichleths, isfreenode, nodei2freenodei) | ||
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if doplot | ||
fig, axs = PyPlot.subplots(1, 2) | ||
axs[1].imshow(reshape(h, reverse(ns)...), origin="lower", extent=[mins[1], maxs[1], mins[2], maxs[2]]) | ||
axs[2].imshow(reshape(h, reverse(ns)...) .- [1 - x for x in xs, y in ys]', origin="lower", extent=[mins[1], maxs[1], mins[2], maxs[2]]) | ||
display(fig) | ||
println() | ||
PyPlot.close(fig) | ||
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fig, ax = PyPlot.subplots() | ||
nx(n) = 0.5 * (coords[1, n[1]] + coords[1, n[2]]) | ||
ny(n) = 0.5 * (coords[2, n[1]] + coords[2, n[2]]) | ||
ax.scatter(map(nx, neighbors), map(ny, neighbors), c=Ks_neighbors, s=30, alpha=0.25) | ||
display(fig) | ||
println() | ||
PyPlot.close(fig) | ||
end | ||
return x, h, logks | ||
end | ||
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betas = collect(range(0.25, 0.75; length=2 ^ 6)) | ||
fracture_logks = collect(range(4, 6; length=2 ^ 6)) | ||
matrix_logks = collect(range(-1, 3; length=2 ^ 6)) | ||
i = 1 | ||
j = 1 | ||
k = 1 | ||
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#z = randn(length(x)) | ||
values = Float64[] | ||
for i = 1:length(betas), j = 1:length(fracture_logks), k = 1:length(matrix_logks) | ||
x, h, logks = fractal_fractures(2 ^ 4, 2; matrix_logk=matrix_logks[k], fracture_logk=fracture_logks[j], beta=betas[i], doplot=false) | ||
matrix_k = exp(matrix_logks[k]) | ||
#z = matrix_k * reshape(x, 16, 14)[:, end] | ||
z = zeros(16, 14) | ||
z[:, end] .= matrix_k | ||
z = z[:] | ||
z = z / sqrt(sum(z .^ 2)) | ||
x = x / sqrt(sum(x .^ 2)) | ||
value = sum(x .* z) | ||
value | ||
push!(values, value) | ||
end | ||
DelimitedFiles.writedlm("values.csv", values, ',') | ||
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fig, ax = PyPlot.subplots() | ||
ax.hist(values, bins=50) | ||
display(fig) | ||
println() | ||
PyPlot.close(fig) | ||
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#= | ||
for i = 4:7, fracture_scales = 1:i - 1 | ||
A_with_fractures, x_with_fractures, b_with_fractures = fractal_fractures(2 ^ i, fracture_scales; fracture_logk=5.0, doplot=true) | ||
end | ||
=# | ||
nothing |