uniform: A uniform continuous random variable.norm: A normal continuous random variable.beta: A beta continuous random variable.gamma: A gamma continuous random variable.t: A Student’s T continuous random variable.chi2: A chi-squared continuous random variable.f: An F continuous random variable.multivariate_normal: A multivariate normal random variable.dirichlet: A Dirichlet random variable.wishart: A Wishart random variable.bernoulli: A Bernoulli discrete random variable.binom: A binomial discrete random variable.boltzmann: A Boltzmann (Truncated Discrete Exponential) random variable.rvs: 샘플 생성pdf or pmf: Probability Density Functioncdf: Cumulative Distribution Functionstats: Return mean, variance, (Fisher’s) skew, or (Fisher’s) kurtosismoment: non-central moments of the distributionfit: parameter estimation random_state: seedsize: 생성하려는 샘플의 shapeloc: 일반적으로 평균의 값scale: 일반적으로 표준편차의 값
In [1]:
rv = sp.stats.norm(loc=10, scale=10)
rv.rvs(size=(3, 10), random_state=1)
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In [2]:
sns.distplot(rv.rvs(size=10000, random_state=1))
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In [3]:
xx = np.linspace(-40, 60, 1000)
pdf = rv.pdf(xx)
plt.plot(xx, pdf)
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In [4]:
cdf = rv.cdf(xx)
plt.plot(xx, cdf)
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In [5]:
sp.pi
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In [6]:
import scipy.constants
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sp.constants.c # speed of light
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In [8]:
x = np.linspace(-3, 3, 1000)
y1 = sp.special.erf(x)
a = plt.subplot(211)
plt.plot(x, y1)
plt.title("elf")
a.xaxis.set_ticklabels([])
y2 = sp.special.expit(x)
plt.subplot(212)
plt.plot(x, y2)
plt.title("logistic")
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In [9]:
A = np.array([[1, 2],
[3, 4]])
sp.linalg.inv(A)
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In [10]:
sp.linalg.det(A)
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In [11]:
from scipy.interpolate import interp1d
In [12]:
x = np.linspace(0, 10, num=11, endpoint=True)
y = np.cos(-x**2/9.0)
f = interp1d(x, y)
f2 = interp1d(x, y, kind='cubic')
xnew = np.linspace(0, 10, num=41)
plt.plot(x, y, 'o', xnew, f(xnew), '-', xnew, f2(xnew), '--')
plt.legend(['data', 'linear', 'cubic'])
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In [13]:
x, y = np.mgrid[-1:1:20j, -1:1:20j]
z = (x+y) * np.exp(-6.0*(x*x+y*y))
plt.pcolormesh(x, y, z)
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In [14]:
xnew, ynew = np.mgrid[-1:1:100j, -1:1:100j]
tck = sp.interpolate.bisplrep(x, y, z, s=0)
znew = sp.interpolate.bisplev(xnew[:, 0], ynew[0, :], tck)
plt.pcolormesh(xnew, ynew, znew)
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In [15]:
from scipy import optimize
In [16]:
def f(x):
return x**2 + 10*np.sin(x)
x = np.arange(-10, 10, 0.1)
plt.plot(x, f(x))
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In [28]:
result = optimize.minimize(f, 4)
print(result)
x0 = result['x']
x0
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In [29]:
plt.plot(x, f(x));
plt.hold(True)
plt.scatter(x0, f(x0), s=200)
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In [31]:
def sixhump(x):
return (4 - 2.1*x[0]**2 + x[0]**4 / 3.) * x[0]**2 + x[0] * x[1] + (-4 + \
4*x[1]**2) * x[1] **2
In [34]:
x = np.linspace(-2, 2)
y = np.linspace(-1, 1)
xg, yg = np.meshgrid(x, y)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
In [35]:
x = np.linspace(-2, 2)
y = np.linspace(-1, 1)
xg, yg = np.meshgrid(x, y)
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
surf = ax.plot_surface(xg, yg, sixhump([xg, yg]), rstride=1, cstride=1,
cmap=plt.cm.jet, linewidth=0, antialiased=False)
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_zlabel('f(x, y)')
ax.set_title('Six-hump Camelback function')
plt.show()
In [36]:
x1 = optimize.minimize(sixhump, (1, 1))['x']
x2 = optimize.minimize(sixhump, (-1, -1))['x']
print(x1, x2)
In [37]:
time_step = 0.02
period = 5.
time_vec = np.arange(0, 20, time_step)
sig = np.sin(2 * np.pi / period * time_vec) + 0.5 * np.random.randn(time_vec.size)
plt.plot(sig)
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In [38]:
import scipy.fftpack
sample_freq = sp.fftpack.fftfreq(sig.size, d=time_step)
sig_fft = sp.fftpack.fft(sig)
pidxs = np.where(sample_freq > 0)
freqs, power = sample_freq[pidxs], np.abs(sig_fft)[pidxs]
freq = freqs[power.argmax()]
plt.stem(freqs[:50], power[:50])
plt.xlabel('Frequency [Hz]')
plt.ylabel('plower')
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