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import math
import numpy as np
import matplotlib.pyplot as plt
from finitediff.grid import locate_discontinuity, pool_discontinuity_approx, adapted_grid, plot_convergence
%matplotlib inline


    

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n = 50
x = np.linspace(0, 10, n*2)
y = np.empty_like(x)
y[:n] = np.exp(-x[:n])
y[n:] = np.exp(-(x[n:]-x[n]))
print(x[n])


    

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def plot_discont(x, y, ref, n=None, dn=7, consider=5):
    loc_res = locate_discontinuity(x, y, consider)
    avg, s = pool_discontinuity_approx(loc_res)
    fig, axes = plt.subplots(1, 2, figsize=(14, 4))
    for ax in axes:
        ax.axvline(ref, color='k', linestyle='-')
        ax.axvline(avg, color='r', linestyle=':')
        ax.axvline(avg-s, color='g', linestyle='--')
        ax.axvline(avg+s, color='g', linestyle='--')
    x, y = map(lambda a: np.asarray(a, dtype=np.float64), [x, y])
    axes[0].plot(x, y)
    if n is None:
        n = np.argmin(np.abs(x - ref))
    axes[1].plot(x[n-dn:n+dn], y[n-dn:n+dn])
    return avg, s


    

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plot_discont(x, y, x[n])


    

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f = np.vectorize(lambda t: math.exp(-t) if t < 5 else math.exp(5-t))
plt.plot(x, f(x))


    

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g, v = adapted_grid(0, 10, f, grid_additions=(8,)*4)


    

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plot_convergence(None, [None], f, grid_additions=(8,)*8, xstart=0, xstop=10)


    

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plot_discont(g, v, x[n], n)


    

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f2 = np.vectorize(lambda t: (math.exp(-t) + (.2 if int(round(t*1234567)) % 3 == 0 else 0)) if t < 5 else 0.5*math.exp(5-t))
plot_convergence(None, [None], f2, grid_additions=(16,)*8, xstart=0, xstop=10)


    

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plot_convergence(None, [None], f2, grid_additions=(16,)*8, xstart=0, xstop=10, snr=True)


    

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plot_discont(*adapted_grid(0, 10, f2, grid_additions=(22,)*12, snr=True), ref=5, consider=5)


    

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pool_discontinuity_approx(locate_discontinuity(*adapted_grid(0, 10, f2, grid_additions=(16,)*8, snr=True), consider=5))