In [1]:
%autosave 60
%matplotlib inline
In [5]:
import matplotlib.pyplot as plt
import numpy as np
import scipy.misc
In [6]:
from scipy import special
In [12]:
x = np.r_[0:20:101j]
n_zeros = 6
zeros = special.jn_zeros(1, n_zeros)
plt.plot(x, special.jn(1, x), label=r'$J_1$')
plt.scatter(zeros, np.zeros_like(zeros), marker='x', label='zeros')
plt.grid()
plt.legend()
Out[12]:
In [14]:
from scipy import signal, ndimage
In [27]:
y = np.r_[np.ones(5), np.zeros(5), np.ones(5)]
x = np.arange(7)
k = np.exp(- (x - np.mean(x))**2)
plt.plot(y, 'x', label='signal')
plt.plot(k, '*', label='kernel')
y1 = signal.convolve(y, k, mode='valid')
plt.plot(y1, 'v', label='convolved')
plt.legend()
Out[27]:
In [36]:
y = scipy.misc.face(gray=True)
plt.imshow(y, cmap='gray')
k = np.zeros((50, 50))
k[0, 0] = 1
k[-1, -1] = 1
convolved = signal.fftconvolve(y, k)
plt.figure()
plt.imshow(convolved, cmap='gray')
X, Y = np.mgrid[0:50, 0:50]
k = np.exp(- ((X-25)**2 + (Y-25)) / 10**2)
convolved = signal.fftconvolve(y, k)
plt.figure()
plt.imshow(convolved, cmap='gray')
Out[36]:
In [41]:
x = np.arange(100)
y = np.sin(x * 2*np.pi / 7)
plt.plot(x, y)
plt.figure()
plt.plot(*signal.periodogram(y))
Out[41]:
In [50]:
# import gatspy
x = np.random.rand(100)
y = np.sin(x * 2*np.pi / 0.3)
freq = np.linspace(1, 100, 100)
p = signal.lombscargle(x, y, freq)
plt.xlabel('Period')
plt.plot(2*np.pi / freq, p)
plt.xlim([0, 1])
Out[50]:
In [51]:
from scipy import stats
In [58]:
rng = np.random.default_rng()
x = rng.normal(size=10000)
stats.anderson(x)
Out[58]:
In [60]:
dist = stats.norm(-1, 2)
dir(dist)
Out[60]:
In [64]:
dist.a, dist.b
Out[64]:
In [65]:
dist.mean()
Out[65]:
In [66]:
dist.std()
Out[66]:
In [68]:
dist.stats(moments='mvk')
Out[68]:
In [78]:
dist.rvs((5, 2), random_state=0)
Out[78]:
In [79]:
dist.rvs((5, 2), random_state=0)
Out[79]:
In [85]:
plt.hist(dist.rvs(10000), bins=100, density=True, alpha=0.3)
x = np.r_[-10:10:100j]
plt.plot(x, dist.pdf(x))
Out[85]:
In [88]:
x = np.r_[-10:10:100j]
plt.plot(x, dist.cdf(x))
plt.plot(x, dist.sf(x))
Out[88]:
In [89]:
x = np.r_[-1:1:100j]
plt.plot(x, dist.ppf(x))
plt.plot(x, dist.isf(x))
Out[89]:
In [91]:
stats.norm.rvs(-1, 2, (5, 2), random_state=0)
Out[91]:
In [92]:
from scipy.io import netcdf
In [93]:
from scipy import optimize
In [101]:
# import mcmc
# import lmfit
def f(x):
return np.cbrt(x - np.sqrt(2))
result = optimize.bisect(f, 0, 2, xtol=1e-6, full_output=True)
print(result)
result = optimize.brentq(f, 0, 2, xtol=1e-6, full_output=True)
print(result)
In [102]:
def f(x):
return (x - 0.5) ** 2
result = optimize.newton(f, 0, tol=1e-6, full_output=True)
print(result)
In [106]:
optimize.root
Out[106]:
In [107]:
def f(x):
return x**2 + 3*x + 5
optimize.fmin(f, x0=0, xtol=1e-6, full_output=1)
Out[107]:
In [110]:
def f(x, a, b, c):
return a * np.exp(x / c) + b
p_true = (3.0, 5.0, -2.0)
noise = 0.2
x = np.r_[0:10:50j]
y = f(x, *p_true) + np.random.normal(0, noise, x.shape)
plt.plot(x, y, 'x')
Out[110]:
In [118]:
p0 = (2.5, 4.5, -1.5)
x_ = np.r_[0:10:100j]
In [119]:
# Не надо так
result = optimize.minimize(
lambda p: np.sum(np.square(f(x, *p) - y)),
x0=p0,
)
print(result)
plt.plot(x, y, 'x')
plt.plot(x_, f(x_, *result.x))
Out[119]:
In [130]:
def jac(x, a, b, c):
"""Jacobian of a * np.exp(x / c) + b"""
dfda = np.exp(x / c)
dfdb = np.ones_like(x)
dfdc = -a * np.exp(x / c) * x / c**2
return np.stack([dfda, dfdb, dfdc]).T
result = optimize.least_squares(
lambda p: f(x, *p) - y,
x0=p0,
jac=lambda p: jac(x, *p),
)
print(result)
plt.plot(x, y, 'x')
plt.plot(x_, f(x_, *result.x))
Out[130]:
In [135]:
p, sigma = optimize.curve_fit(f, xdata=x, ydata=y, p0=p0)
plt.plot(x, y, 'x')
plt.plot(x_, f(x_, *p))
Out[135]:
In [149]:
from scipy import ndimage
from PIL import Image
with Image.open('sombrero.png') as img:
x = np.array(img)
plt.imshow(x)
# x_median = ndimage.filters.median_filter(x, size=3)
# plt.imshow(x - x_median)
x_rotated = ndimage.rotate(x, 30, reshape=False)
plt.figure()
plt.imshow(-x_rotated)
Out[149]:
In [ ]: