SciPy : Scientific Python

A framework for numerical computing using Python.

Special functions (scipy.special)
Integration (scipy.integrate)
Optimization (scipy.optimize)
Interpolation (scipy.interpolate)
Fourier Transforms (scipy.fftpack)
Signal Processing (scipy.signal)
Linear Algebra (scipy.linalg)
Sparse Eigenvalue Problems (scipy.sparse)
Statistics (scipy.stats)
Multi-dimensional image processing (scipy.ndimage)
File IO (scipy.io)

Some great examples are here: https://scipy-lectures.github.io/intro/scipy.html

Q. Import and explore the library.



In [18]:

    
import scipy.optimize



In [19]:

    
scipy.optimize??

Q. Find the minimum of the following function: $ f(x)= x^2 + 10\cdot\sin(x)$



In [20]:

    
import numpy as np
import matplotlib.pyplot as plt

def f(x):
    return x**2 + 10*np.sin(x)

Plot the function using matplotlib.



In [21]:

    
x = np.arange(-10, 10, 0.1)
fig, ax = plt.subplots(figsize=(10,5))
ax.plot(x, f(x));
ax.hlines(0,-10, 10, alpha=0.1);



In [22]:

    
initial_x = 5.0



In [23]:

    
minimum_x = scipy.optimize.fmin_bfgs(f, initial_x)









    



Optimization terminated successfully.
         Current function value: -7.945823
         Iterations: 5
         Function evaluations: 24
         Gradient evaluations: 8

Plot the found minimum.



In [24]:

    
%matplotlib inline

x = np.arange(-10, 10, 0.1)
fig, ax = plt.subplots(figsize=(10,5))
ax.plot(x, f(x));
ax.hlines(0,-10, 10, alpha=0.1);
ax.plot(initial_x, f(initial_x), 'or')
ax.plot(minimum_x, f(minimum_x), 'og')









    Out[24]:





[<matplotlib.lines.Line2D at 0x8649390>]

Q. Approximate the density of the following superposition of normals: $\mathcal{N}(-1.0, 0.5) + \mathcal{N}(1.0, 0.5)$



In [25]:

    
import scipy.stats as stats

N0 = stats.norm.rvs(loc=-1.0,scale=.5,size=1000)
N1 = stats.norm.rvs(loc=1.0,scale=.5,size=1000)
samp = np.hstack([N0, N1])

Plot the distribution of the data, using a histogram. Using the hist method.



In [26]:

    
fig, ax = plt.subplots(figsize=(10,5))
ax.hist(samp, 100, normed=1)
ax.set_xlim(-5, 5);
ax.grid()

Estimate the distribution of the data using a kernel density estimation.

http://en.wikipedia.org/wiki/Kernel_density_estimation



In [27]:

    
pdf = stats.gaussian_kde(samp)
fig, ax = plt.subplots(figsize=(10,5))
x = np.linspace(-5, 5, 100)
ax.plot(x, pdf(x),'r')
ax.hist(samp, 100, normed=1, alpha=.5);



In [28]:

    
pdf(0.)









    Out[28]:





array([ 0.14291297])



In [29]:

    
pdf(-1.), pdf(1.0)









    Out[29]:





(array([ 0.35811933]), array([ 0.34182221]))



In [ ]: