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Data Analysis with SciPy

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Scipy is a Python library useful for solving many mathematical equations and algorithms. It is designed on the top of Numpy library that gives more extension of finding scientific mathematical formulae like Matrix Rank, Inverse, polynomial equations, LU Decomposition, etc. Using its high-level functions will significantly reduce the complexity of the code and helps better in analyzing the data.

In this article, we will explore What is SciPy, the Installation of SciPy, and How Data Analysis with SciPy works and Compute pivoted LU decomposition.

What is SciPy?

SciPy is an interactive Python session used as a data-processing library that is made to compete with its rivalries such as MATLAB, Octave, R-Lab, etc. It has many user-friendly, efficient, and easy-to-use functions that help to solve problems like numerical integration, interpolation, optimization, linear algebra, and statistics. The benefit of using the SciPy library in Python while making ML models is that it makes a strong programming language available for developing fewer complex programs and applications.

Installation of SciPy

To install SciPy in your system, you can use Python package manager pip. Before proceeding, make sure that you have Python already installed in your system. Here’s the step to install Python in your system.

Step 1: Firstly, Open terminal and Command Prompt in your system.

Step 2: Run the installation Command to install SciPy in your system.

pip install scipy

Step 3: Pip will be download and install SciPy along with dependencies. This process will may take some time depends on internet connection.

Step 4: To verify installation, you need to import SciPy in a Python script or interactive shell.

import scipy print(scipy.__version__)

Now the installation of SciPy is successfully completed.

How does Data Analysis work with SciPy?

Data Preparation

  • Import the necessary libraries: import numpy as np and import scipy as sp.
  • Load or generate your dataset using NumPy or pandas.

Exploratory Data Analysis (EDA)

  • Use descriptive statistics from SciPy’s stats module to gain insights into the dataset.
  • Calculate measures such as mean, median, standard deviation, skewness, kurtosis, etc.

Python3

from scipy import stats
data = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9])
# Calculate mean and standard deviation
mean_val = np.mean(data)
std_dev = np.std(data)
# Perform basic statistical tests
t_stat, p_value = stats.ttest_1samp(data, popmean=5)
print("t_stat:" , t_stat)
print("p_value:", p_value)

                    

Output:

t_stat: 0.0
p_value: 1.0

Statistical Hypothesis Testing

Use SciPy’s stats module for various hypothesis tests such as t-tests, chi-square tests, ANOVA, etc.

# Example of a t-test

t_stat, p_value = stats.ttest_ind(group1, group2)

Regression Analysis

Utilize the linregress function for linear regression analysis.

# Linear regression

slope, intercept, r_value, p_value, std_err = stats.linregress(x, y)

Signal and Image Processing

  • Use the scipy.signal module for signal processing operations.
  • Explore scipy.ndimage for image processing.

from scipy import signal, ndimage

# Example of convolution using signal processing

result = signal.convolve2d(image, kernel, mode=’same’, boundary=’wrap’)

Optimization

Employ the optimization functions in SciPy to find optimal parameter values.

from scipy.optimize import minimize

# Define an objective function

def objective_function(x):

return x[0]**2 + x[1]**2

result = minimize(objective_function, [0, 0])

Import SciPy

Once SciPy is installed , you need to import the SciPy module(s)

Python3

# import numpy library
import numpy as np
A= [[1, 2,],
    [5, 6,]]

                    

Linear Algebra

Determinant of a Matrix

Python3

# importing linalg function from scipy
from scipy import linalg
A= [[1, 2,],
    [5, 6,]]
 
# Compute the determinant of a matrix
linalg.det(A)

                    

Output:

-4.0

Compute pivoted LU decomposition of a Matrix

LU decomposition is a method that reduce matrix into constituent parts that helps in easier calculation of complex matrix operations. The decomposition methods are also called matrix factorization methods, are base of linear algebra in computers, even for basic operations such as solving systems of linear equations, calculating the inverse, and calculating the determinant of a matrix. The decomposition is: A = P L U where P is a permutation matrix, L lower triangular with unit diagonal elements, and U upper triangular.

Python3

P, L, U = linalg.lu(A)
print(P)
print(L)
print(U)
# print LU decomposition
print(np.dot(L,U))

                    

Output:

[[0. 1. 0.]  
[0. 0. 1.]  
[1. 0. 0.]] 
[[1.         0.         0.        ] 
 [0.14285714 1.         0.        ]  
 [0.57142857 0.5        1.        ]] 
[[7.         8.         8.        ]  
 [0.         0.85714286 1.85714286]  
 [0.         0.         0.5       ]] 
[[0.14285714 1.         0.        ] 
 [0.57142857 0.5        1.        ]  
  [1.         0.         0.        ]]

Eigen values and Eigen vectors of this matrix

Python3

eigen_values, eigen_vectors = linalg.eig(A)
print(eigen_values)
print(eigen_vectors)

                    

Output:

array([ 15.55528261+0.j,  -1.41940876+0.j,  -0.13587385+0.j])
array([[-0.24043423, -0.67468642,  0.51853459],
       [-0.54694322, -0.23391616, -0.78895962],
       [-0.80190056,  0.70005819,  0.32964312]])

Solving systems of linear equations can also be done

Python3

v = np.array([[2, 4],[3,8]])
print(v)
s = linalg.solve(A,v)
print(s)

                    

Output:

[[2 4]
 [3 8]]
[[-1.5  -2.  ]
 [ 1.75  3.  ]]

Sparse Linear Algebra

SciPy has some routines for computing with sparse and potentially very large matrices. The necessary tools are in the submodule scipy.sparse.

Let’s look on how to construct a large sparse matrix

Python3

# import necessary modules
from scipy import sparse
# Row-based linked list sparse matrix
A = sparse.lil_matrix((1000, 1000))
print(A)
A[0,:100] = np.random.rand(100)
A[1,100:200] = A[0,:100]
A.setdiag(np.random.rand(1000))
print(A)

                    

Output:

  (0, 0)    0.7948113035416484
  (0, 1)    0.22210781047073025
  (0, 2)    0.1198653673336828
  (0, 3)    0.33761517140362796
  (0, 4)    0.9429097039125192
  (0, 5)    0.32320293202075523
  (0, 6)    0.5187906217433661
  (0, 7)    0.7030189588951778
  (0, 8)    0.363629602379294
  (0, 9)    0.9717820827209607
  (0, 10)    0.9624472949421112
  (0, 11)    0.25178229582536416
  (0, 12)    0.49724850589238545
  (0, 13)    0.30087830981676966
  (0, 14)    0.2848404943774676
  (0, 15)    0.036886947354532795

Linear Algebra for Sparse Matrices

Python3

from scipy.sparse import linalg
# Convert this matrix to Compressed Sparse Row format.
A.tocsr()
A = A.tocsr()
b = np.random.rand(1000)
ans = linalg.spsolve(A, b)
# it will print ans array of 1000 size
print(ans)

                    

Output:

[-4.67207136e+01 -3.69332972e+02  3.69393775e-01  6.32141409e-02
  3.33772205e+00  5.10104872e-01  3.07850190e+00  1.94608719e+01
  1.49997674e+00  1.04751174e+00  9.23616608e-01  8.14103772e-01
  8.42662424e-01  2.28221903e+00  4.92361307e+01  6.74574814e-01
  3.06515031e-01  3.36481843e-02  9.55613073e-01  7.22911464e-01
  2.70518013e+00  1.25039001e+00  1.37825326e-01  3.95005049e-01
  4.04480605e+00  7.72817743e-01  2.14200400e-01  7.06283767e-01
  1.12635170e-01  5.98880840e+00  4.37382510e-01  8.05571435e-01
..............................................................................................................................]

Python3

from scipy import integrate
f = lambda y, x: x*y**2
i = integrate.dblquad(f, 0, 2, lambda x: 0, lambda x: 1)
# print the results
print(i)

                    

Output:

(0.6666666666666667, 7.401486830834377e-15)

There is a lot more that SciPy is capable of, such as Fourier Transforms, Bessel Functions, etc.



Last Updated : 19 Feb, 2024
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