
- SciPy - Home
- SciPy - Introduction
- SciPy - Environment Setup
- SciPy - Basic Functionality
- SciPy - Relationship with NumPy
- SciPy Clusters
- SciPy - Clusters
- SciPy - Hierarchical Clustering
- SciPy - K-means Clustering
- SciPy - Distance Metrics
- SciPy Constants
- SciPy - Constants
- SciPy - Mathematical Constants
- SciPy - Physical Constants
- SciPy - Unit Conversion
- SciPy - Astronomical Constants
- SciPy - Fourier Transforms
- SciPy - FFTpack
- SciPy - Discrete Fourier Transform (DFT)
- SciPy - Fast Fourier Transform (FFT)
- SciPy Integration Equations
- SciPy - Integrate Module
- SciPy - Single Integration
- SciPy - Double Integration
- SciPy - Triple Integration
- SciPy - Multiple Integration
- SciPy Differential Equations
- SciPy - Differential Equations
- SciPy - Integration of Stochastic Differential Equations
- SciPy - Integration of Ordinary Differential Equations
- SciPy - Discontinuous Functions
- SciPy - Oscillatory Functions
- SciPy - Partial Differential Equations
- SciPy Interpolation
- SciPy - Interpolate
- SciPy - Linear 1-D Interpolation
- SciPy - Polynomial 1-D Interpolation
- SciPy - Spline 1-D Interpolation
- SciPy - Grid Data Multi-Dimensional Interpolation
- SciPy - RBF Multi-Dimensional Interpolation
- SciPy - Polynomial & Spline Interpolation
- SciPy Curve Fitting
- SciPy - Curve Fitting
- SciPy - Linear Curve Fitting
- SciPy - Non-Linear Curve Fitting
- SciPy - Input & Output
- SciPy - Input & Output
- SciPy - Reading & Writing Files
- SciPy - Working with Different File Formats
- SciPy - Efficient Data Storage with HDF5
- SciPy - Data Serialization
- SciPy Linear Algebra
- SciPy - Linalg
- SciPy - Matrix Creation & Basic Operations
- SciPy - Matrix LU Decomposition
- SciPy - Matrix QU Decomposition
- SciPy - Singular Value Decomposition
- SciPy - Cholesky Decomposition
- SciPy - Solving Linear Systems
- SciPy - Eigenvalues & Eigenvectors
- SciPy Image Processing
- SciPy - Ndimage
- SciPy - Reading & Writing Images
- SciPy - Image Transformation
- SciPy - Filtering & Edge Detection
- SciPy - Top Hat Filters
- SciPy - Morphological Filters
- SciPy - Low Pass Filters
- SciPy - High Pass Filters
- SciPy - Bilateral Filter
- SciPy - Median Filter
- SciPy - Non - Linear Filters in Image Processing
- SciPy - High Boost Filter
- SciPy - Laplacian Filter
- SciPy - Morphological Operations
- SciPy - Image Segmentation
- SciPy - Thresholding in Image Segmentation
- SciPy - Region-Based Segmentation
- SciPy - Connected Component Labeling
- SciPy Optimize
- SciPy - Optimize
- SciPy - Special Matrices & Functions
- SciPy - Unconstrained Optimization
- SciPy - Constrained Optimization
- SciPy - Matrix Norms
- SciPy - Sparse Matrix
- SciPy - Frobenius Norm
- SciPy - Spectral Norm
- SciPy Condition Numbers
- SciPy - Condition Numbers
- SciPy - Linear Least Squares
- SciPy - Non-Linear Least Squares
- SciPy - Finding Roots of Scalar Functions
- SciPy - Finding Roots of Multivariate Functions
- SciPy - Signal Processing
- SciPy - Signal Filtering & Smoothing
- SciPy - Short-Time Fourier Transform
- SciPy - Wavelet Transform
- SciPy - Continuous Wavelet Transform
- SciPy - Discrete Wavelet Transform
- SciPy - Wavelet Packet Transform
- SciPy - Multi-Resolution Analysis
- SciPy - Stationary Wavelet Transform
- SciPy - Statistical Functions
- SciPy - Stats
- SciPy - Descriptive Statistics
- SciPy - Continuous Probability Distributions
- SciPy - Discrete Probability Distributions
- SciPy - Statistical Tests & Inference
- SciPy - Generating Random Samples
- SciPy - Kaplan-Meier Estimator Survival Analysis
- SciPy - Cox Proportional Hazards Model Survival Analysis
- SciPy Spatial Data
- SciPy - Spatial
- SciPy - Special Functions
- SciPy - Special Package
- SciPy Advanced Topics
- SciPy - CSGraph
- SciPy - ODR
- SciPy Useful Resources
- SciPy - Reference
- SciPy - Quick Guide
- SciPy - Cheatsheet
- SciPy - Useful Resources
- SciPy - Discussion
SciPy - integrate.romb() Method
The SciPy integrate.romb() method is used to perform the task of numerical or romberg integration. This method also helps us to plot the graph based on sample/coordinates points.
Syntax
Following is the syntax of the SciPy integrate.romb() method −
romb(y, dx = int_val/float_val/1.0)
Parameters
This function accepts the following parameter −
- y: This parameter determine the array function which valued at discrete points and these points consider even spaces.
- dx: This parameter determine the spacing between the points and default value is 1.0 if not specify.
Return value
This method return the estimate value of type float.
Example 1
Following is the SciPy integrate.romb() method that shows the simple integration function f(x) = x2 over the interval between 0 and 1. The resultant value based on five discrete point.
import numpy as np from scipy import integrate # define the function values at discrete points x = np.linspace(0, 1, 5) y = x**2 # calculate the integral res_integral = integrate.romb(y, dx=x[1] - x[0]) # display the result print(res_integral)
Output
The above code produces the following result −
0.3333333333333333
Example 2
This program demonstrate the numerical integration of Gaussian function which is e-x2 over the interval between -2 to 2 and the function values are represented as nine points(x-axis).
import numpy as np from scipy.integrate import romb import matplotlib.pyplot as plt # define the function values at discrete points x = np.linspace(-2, 2, 9) y = np.exp(-x**2) # calculate the integral res_integral = romb(y, dx=x[1] - x[0]) # display the result print(f"Estimated integral: {res_integral}") # plot the Gaussian function and the points used in Romberg integration x_fine = np.linspace(-2, 2, 1000) y_fine = np.exp(-x_fine**2) plt.plot(x_fine, y_fine, label='Gaussian Function $e^{-x^2}$') plt.scatter(x, y, color='green', zorder=5, label='coords Points') plt.title('Gaussian Function and Sample Points for Romberg Integration') plt.xlabel('x') plt.ylabel('y') plt.legend() plt.grid(True) plt.show()
Output
The above code produces the following result −
