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# SciPy Interpolation ### What is Interpolation? In the field of numerical analysis in mathematics, interpolation is a process or method for estimating new data points within a range based on known, discrete data points. Simply put, interpolation is a method for generating points between given points. **For example:** For two points 1 and 2, we can interpolate and find points 1.33 and 1.66. Interpolation has many uses. In machine learning we often deal with missing data, and interpolation can usually be used to replace these values. This method of filling values is called imputation. Besides imputation, interpolation is often used where we need to smooth discrete points in a dataset. ### How to Implement Interpolation in SciPy? SciPy provides the scipy.interpolate module to handle interpolation. ### One-Dimensional Interpolation The interpolation operation for one-dimensional data can be done through the interp1d() method. This method takes two parameters: x points and y points. The return value is a callable function that can be called with new x and returns the corresponding y, i.e., y = f(x). For the given xs and ys, interpolate from 2.1, 2.2... to 2.9: ## Example from scipy.interpolate import interp1d import numpy as np xs = np.arange(10) ys =2*xs + 1 interp_func = interp1d(xs, ys) newarr = interp_func(np.arange(2.1,3,0.1)) print(newarr) The output is: [5.2 5.4 5.6 5.8 6. 6.2 6.4 6.6 6.8] **Note:** The new xs should be in the same range as the old xs, which means we cannot call interp_func() with values greater than 10 or less than 0. ### Univariate Interpolation In one-dimensional interpolation, points are fitted against a single curve, while in spline interpolation, points are fitted against a function defined using piecewise polynomials. Un