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test_hermitefunction.py
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test_hermitefunction.py
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import numpy as np
from hermitefunction import HermiteFunction
from scipy.integrate import cumulative_trapezoid
if __name__ == '__main__':
x = np.linspace(-4, +4, 1000)
#HermiteFunction
#HermiteFunction.random
#fitting
for _ in range(100):
deg = np.random.randint(0, 20)
f = HermiteFunction.random(deg)
y = f(x)
fit = HermiteFunction.fit(x, y, deg)
assert np.allclose(f.coef, fit.coef)
f = HermiteFunction.random(20)
#length
assert len(f) == 21
#indexing
f[5]
assert f[999] == 0
#iterating
for c in f:
pass
#comparison
assert f != HermiteFunction(21)
#shifting
assert (f<<1).deg == 19 and (f>>1).deg == 21
#norm
assert np.isclose(abs(f), 1)
#dot
assert np.isclose(f @ HermiteFunction(21), 0)
#addition & subtraction
for _ in range(100):
f = HermiteFunction.random(np.random.randint(0, 20))
g = HermiteFunction.random(np.random.randint(0, 20))
assert np.allclose((f+g)(x), f(x)+g(x))
assert np.allclose((f-g)(x), f(x)-g(x))
#scalar multiplication and division
for _ in range(100):
f = HermiteFunction.random(np.random.randint(0, 20))
c = np.random.rand()
assert np.allclose((c*f)(x), c*(f(x)))
assert np.allclose((f/c)(x), (f(x))/c)
f = HermiteFunction.random(20)
#degree
assert f.deg == 20
#calling
f(x)
#derivative
def der_num(x, y, n=1):
"""Nummerical differentiation."""
for _ in range(n):
y = np.diff(y) / np.diff(x)
x = (x[1:] + x[:-1]) / 2
return x, y
for _ in range(100):
f = HermiteFunction.random(np.random.randint(0, 20))
assert np.allclose(f.der()(der_num(x, f(x))[0]),
der_num(x, f(x))[1], atol=1e-3)
#antiderivative
for _ in range(100):
f = HermiteFunction.random(np.random.randint(0, 5))
F, r = f.antider()
assert np.allclose(F(x) + r * HermiteFunction.zeroth_antiderivative(x),
cumulative_trapezoid(f(x), x, initial=0), atol=1e-1)
#fourier
def fourier(y, x):
#https://stackoverflow.com/a/24077914
dx = (max(x)-min(x)) / len(x)
w = np.fft.fftshift(np.fft.fftfreq(len(x), dx)) * 2*np.pi
g = np.fft.fftshift(np.fft.fft(y))
g *= dx * np.exp(-complex(0,1)*w*min(x)) / np.sqrt(2*np.pi)
return w, g
for _ in range(100):
f = HermiteFunction.random(np.random.randint(0, 5))
Fx, Ff = fourier(f(x), x)
assert np.allclose(f.fourier()(Fx), Ff, atol=1e-1)
#kinetic energy
def kin_num(x, y):
"""Nummeric kinetic energy."""
x, y_lapl = der_num(x, y, 2)
y = (y[2:] + 2*y[1:-1] + y[:-2]) / 4 #mid y twice to broadcast to y_lapl
return -np.trapz(y*y_lapl, x) / 2
for _ in range(100):
f = HermiteFunction.random(5)
assert np.isclose(f.kin, kin_num(x, f(x)), atol=1e-2)
#python stuff
str(f)