Learn (Python) SciPy

SciPy

• SciPy stands for Scientific Python.
• It is a free and open-source Python library.
• It is used for scientific computing and technical computing. Also, it's used in mathematics, scientific computing, Engineering, and technical computing.
• SciPy contains modules for complex mathematical and technical operations like:- optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering.
• SciPy builds on the NumPy array (to understand NumPy you can refer to- https://www.c-sharpcorner.com/article/getting-started-with-numpy/ and https://www.c-sharpcorner.com/article/numpy-array/ ) object and is part of the NumPy stack.
• It includes tools like Matplotlib, pandas and symPy (library for symbolic mathematics).

SciPy has various sub-packages to perform different mathematical and scientific functions, which are as follows,

 

SPECIAL FUNCTION PACKAGE: (scipy.special)

 

This package includes basic mathematical physics’ functions like,

 

FUNCTION	SYNTAX	DESCRIPTION
Cubic Root	scipy.special.cbrt()	Finds the cube root of values
Exponential	scipy.special.exp10()	Computes the 10**x element-wise
Combinations	scipy.special.comb()	Calculates the Combination
Permutations	scipy.special.perm()	Calculates the Permutation
Log Sum Exponential	scipy.special.logsumexp()	Computes the log of sum exponential input element.
Bessel Function	scipy.special.jn()	Nth integer order calculation function
Relative Error Exponential	scipy.special.exprel()	It generates the relative error exponential, (exp(x) - 1)/x.
Lambert Function W(z)	scipy.special.lambertw()	The value of W(z) is such that z = W(z) * exp(W(z)) for any complex number z.
Gamma Function	scipy.special.gamma()	The gamma function is often referred to as the generalized factorial.

 

EXAMPLE

from scipy.special import exprel
from scipy.special import cbrt
from scipy.special import exp10
from scipy.special import lambertw
from scipy.special import comb
from scipy.special import perm
from scipy.special import gamma

cb = cbrt([27, 64, 0.1254])
print(cb)

exp = exp10([4,10])
print(exp)

com = comb(5, 2)
print(com)

per = perm(5, 2)
print(per)

res = exprel([-0.25, -0.1, 0, 0.1, 0.25])
print (res)

w = lambertw(1)
print (w)

gm = gamma([0, 0.5, 1, 5])
print (gm)

OUTPUT

 

 

SCIPY CONSTANT PACKAGE(scipy.constants)

 

This package provides many constants which we use in daily mathematical problems or SI units or any measuring units.

 

 

EXAMPLE

import scipy.constants

print("sciPy - pi = %.16f"%scipy.constants.pi)
print("Gravitational constant- G = %.16f"%scipy.constants.G)
print("sciPy - micro = %.16f"%scipy.constants.micro)

OUTPUT

 

 

LINERA ALGEBRA PACKAGE: (scipy.linalg)

 

Linear algebra block accepts two-dimensional array object and output is also a two-dimensional array.

 

EXAMPLE

from scipy import linalg
import numpy as np

a = np.array([ [4,5], [3,2] ])

linalg.det(a)    #Calculating determinant of a two-dimensional matrix

linalg.inv(a)    #Calculates the inverse of square matrix

eg_val, eg_vect = linalg.eig(a)    #Calculates the eigenValues and eigenVectors

print(eg_val)
print(eg_vect)

OUTPUT

 

DICRETE FOURIER TRANSFORMATION PACKAGE:(scipy.fftpack)

 

Discrete Fourier Transformation is used to convert Spatial data into Frequency data. Fourier Transformation is computed on a time domain signal to check its behavior in the frequency domain. FFT(Fast Fourier Transformation) is an algorithm to implement DFT

 

EXAMPLE

import numpy as np
from scipy.fftpack import fft

x = np.array([1.0, 2.0, 1.0, -1.0, 1.5])
y = fft(x)
print (y)

OUTPUT

IMAGE PROCESSING PACKAGE:(scipy.misc, scipy,ndimage)

• scipy.ndimage is a submodule of SciPy which is mostly used for performing an image related operation. You can find numerous functions involved in ndimage package you can find these in the attachment- Scipy(ndimage,Misc)
• scipy.misc; MISC is a package which contains prebuilt images which can be used to perform image manipulation task. You can find numerous functions involved in misc package you can find these in the attachment- Scipy(ndimage,Misc)

By using these packages, we can zoom, flip, blurr, rotate, crop, sharpen or add filters to an image ; and many more operations can be done.

 

To understand Matplotlib you can refer to my previous article.

 

EXAMPLE: (Display an image)

from scipy import misc
from matplotlib import pyplot as plt
import numpy as np

panda = misc.face()    #get face image of panda from misc package
plt.imshow( panda )     #plot or show image of face
plt.show()

OUTPUT

EXAMPLE: (Flip down the Image)

from scipy import misc
from matplotlib import pyplot as plt
import numpy as np

panda = misc.face()
flip_down = np.flipud(misc.face())

plt.imshow(flip_down)
plt.show()

OUTPUT

EXAMPLE: (Rotation of the Image)

from scipy import misc, ndimage
from matplotlib import pyplot as plt
import numpy as np

panda = misc.face()
panda_rotate = ndimage.rotate(panda, 135)

plt.imshow(panda_rotate)
plt.show()

OUTPUT

INTEGRATION PACKAGE(scipy.integrate)

 

This package has single integration, double, triple, multiple, Gaussian quadrate, Romberg, Trapezoidal and Simpson's rules.

 

To understand functions in Python refer to my previous article.

 

EXAMPLE: (Single Integration)

#single integration with a = 0 & b = 1 on function f(x)
from scipy.integrate import quad

def f(x):
return x**2

ans, err = quad(f, 0, 1)
print (ans)

OUTPUT

EXAMPLE - (Double Integration)

1. Double integration- we use Lambda function here because we want that function to have to return constants
2. For double integration we use, dblquad
3. Also order of arguments in the integrand is different than in Matlab.
   

   from scipy.integrate import dblquad
   import numpy as np
   
   def f(y, x):    #y must be the first argument, and x the second.
   return y * np.sin(x) + x * np.cos(y)
   
   #First integral is from a=pi and b=2*pi on f(x)
   #Second integral is from a=0 and b=pi on f(y)
   
   ans, err = dblquad(f, np.pi, 2*np.pi,
   lambda x: 0,
   lambda x: np.pi)
   print (ans)

OUTPUT

 

INTERPOLATE PACKAGE:(scipy.interpolate)

 

Interpolation is the process of finding a value between two points on a line or a curve.

 

EXAMPLE

import numpy as np
from scipy import interpolate
import matplotlib.pyplot as plt

x = np.linspace(0, 4, 12)
y = np.cos(x**2/3+4)

print (x,y)
plt.plot(x, y,'o')
plt.show()

OUTPUT

 

When we want to interpolate between two fixed points then we use 1D interpolation,

 

interp1d(x, y,kind = 'linear')

 

We can also draw mechanical splines using interpolate.

 

INPUT/OUTPUT PACKAGE:(scipy. io)

 

This would help us to read or write data in a particular file. Also, we can read a data from file1 and write it in file2 and many more. We would learn more such file handling under the topic CSV.

 

We have few more packages under SciPy,

• CLUSTER PACKAGE
  
  
• These are Compressed sparse graphs.
• Focuses on Fast graph algorithms based on sparse matrix representations.
  
  scipy.sparse.csgraph
  
  
• STATS PACKAGE
  
  
• All statistics’ functions are found in this package.
• We can calculate harmonic mean, geometric mean, mode, kurtosis, median, skewness, interquartile range etc.
  
  scipy.stats
  
  
• CS GRAPH PACKAGE/ SPARSE
  
  
• These are Compressed Sparse Graphs.
• It is used to store large sparse matrices and provide the functionality to perform complex matrix computations.
  
  scipy.sparse.csgraph
  
  
• ODR PACKAGE
  
  
• These are Orthogonal Distance Regressions which are used for regression studies.
• This is to calculate relationship between the two variables y and x by drawing the line of the best fit in the graph
  
  scipy.odr

SUMMARY

 

We learned what is SciPy and how it is used, and what its sub-packages are. We know how to solve mathematical complex problems through Python now. Also you can now proceed with Scientific and Technical computations using SciPy in Python.

 

Practice!

 

Feedback or queries related to this article are most welcome.

 

Thanks for reading.