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Integrating a function over multiple dimensions using SciPy's nquad function

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by sneha@openweaver.com dot icon Updated: Mar 29, 2023

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Integrating a function over multiple dimensions means taking the integral of the function concerning each of the variables in the function. This means that the integral is being taken concerning all of the dimensions of the function, not just one variable. This can be used to find a multidimensional object's volume or calculate the average of a function over a certain region in multiple dimensions. 



Scipy is an open-source library of scientific computing tools for Python. It is built on the NumPy library and provides tools for numerical integration, optimization, linear algebra, signal processing, and more. It is widely used in scientific and engineering applications. 



Scipy's nquad function is a numerical integration function that performs double and triple integration. 

  • It can integrate a function of multiple variables over multiple intervals. 
  • It is an improved version of the scipy.integrate.quad function, which is used to integrate a single variable over a single interval. 


Here is an example of Integrating a function over multiple dimensions using SciPy's nquad function 



Fig1: Preview of the Output when the code is run in IDE.

Code


In this solution, we will use SciPy's nquad function to Integrate a function over multiple dimensions.

Python: Integration over Multiple Dimensions of function taking an array input

PythondotLines of Code : 19dotLicense : Strong Copyleft (CC BY-SA 4.0)

Dependent Libraries : 
from scipy.integrate import nquad
from scipy.stats import multivariate_normal

mean = [0., 0.]
cov = np.array([[1., 0.],
                [0., 1.]])

bivariate_normal = multivariate_normal(mean=mean, cov=cov)

def pdf(*args):
    x = np.array(args)
    return bivariate_normal.pdf(x)

integration_range = [[-18, 18], [-18, 18]]

nquad(pdf, integration_range)

Output: (1.000000000000001, 1.3429066352690133e-08)

Instructions


  1. Install Jupyter Notebook on your computer.
  2. Open terminal and install the required libraries with following commands.
  3. Install Scipy- pip install scipy
  4. Copy the snippet using the 'copy' button and paste it into that file.
  5. Run the file using run button.


I hope you found this useful. I have added the link to dependent libraries, version information in the following sections.



I found this code snippet by searching for "Integration over Multiple Dimensions of function using scipy" in kandi. You can try any such use case!

Dependent Libraries

scipyby scipy

Python doticonstar image 11340 doticonVersion:v1.11.0rc1doticon
License: Permissive (BSD-3-Clause)

SciPy library main repository

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            scipyby scipy

            Python doticon star image 11340 doticonVersion:v1.11.0rc1doticon License: Permissive (BSD-3-Clause)

            SciPy library main repository
            Support
              Quality
                Security
                  License
                    Reuse

                      If you do not have SciPy that is required to run this code, you can install it by clicking on the above link and copying the pip Install command from the numpy page in kandi.


                      You can search for any dependent library on kandi like SciPy.

                      Environment Tested


                      I tested this solution in the following versions. Be mindful of changes when working with other versions.

                      1. The solution is created in Python3.9.6
                      2. The solution is tested on SciPy-Python 1.9.1 version.


                      Using this solution, we are able to Integrate a function over multiple dimensions using SciPy's nquad function.


                      This process also facilities an easy to use, hassle free method to create a hands-on working version of code which would help us to Integrate a function over multiple dimensions using SciPy's nquad function

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