48 lines
1.5 KiB
Julia
48 lines
1.5 KiB
Julia
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using Random
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using Distributions
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using Plots
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# ===============================================================
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function max_conv_operator(samples, f_samples, input, L) # max convolution operator, with random uniform sampling
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return maximum(f_samples .- L .* abs.(input .- samples))
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end
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function sharktooth(f, domain, number_of_sharkteeth, L, plot_arg)
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samples = rand(Uniform(domain[1], domain[2]), number_of_sharkteeth) #samples are uniformly taken from domain
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f_samples = f.(samples) #y_i are f applied to samples componentwise
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x = LinRange(domain[1], domain[2], 10000) #approximant is plotted over a mesh of resolution 10000
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approximant = broadcast(x -> max_conv_operator(samples, f_samples, x, L), x)
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error = maximum(abs.(f.(x) - approximant))
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if plot_arg == 1
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plot(x, approximant)
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else
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return error
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end
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end
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function sharktooth_error_plot(L_values, sharktooth_upper_limit, f, domain)
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# Initialize an empty plot
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p = plot(legend=false, xlabel="Number of Sharkteeth", ylabel="Error")
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for L in L_values
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errors = Float64[] # Initialize an empty array to store errors
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for i in 1:sharktooth_upper_limit
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push!(errors, sharktooth(f, domain[1], domain[2], i, L, 0))
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end
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plot!(1:sharktooth_upper_limit, errors, label="L = $L") # Add the plot to the existing figure
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end
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# Show the legend
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plot!(legend=true)
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# Display the final plot
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display(p)
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end
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sharktooth_error_plot([1, 2, 3, 4], 150, sin, [0, 30])
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sharktooth(tanh, [-5, 5], 1500, 1, 1)
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