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What is Interpolation in SCIPY:-

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

This tool, interpolation, is not only useful in statistics, but is also useful in science, business, or when there is a need to predict values that fall within two existing data points.

scipy.interpolate package will be used for interpolation

Without interpolation first we show plot using x and y co-ordinate

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()

## 1-D Interpolation

he interp1d class in the scipy.interpolate is a convenient method to create a function based on fixed data points, which can be evaluated anywhere within the domain defined by the given data using linear interpolation.

Using the interp1d function, we created two functions f1 and f2. These functions, for a given input x returns y. The third variable kind represents the type of interpolation technique. 'Linear', 'Nearest', 'Zero', 'Linear', 'Quadratic', 'Cubic' are a few techniques of interpolation.

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)
f1 = interpolate.interp1d(x, y,kind = 'linear')
f2 = interpolate.interp1d(x, y, kind = 'cubic')
xnew = np.linspace(0, 4,30)
plt.plot(x,y,'o',xnew, f1(xnew), '-',xnew, f2(xnew), '--')
plt.legend(['data', 'linear', 'cubic','nearest'], loc = 'best')
plt.show()

Interpolation with UnivariateSpline

import matplotlib.pyplot as plt
from scipy.interpolate import UnivariateSpline

x = np.linspace(-3, 3, 50)
y = np.exp(-x**2) + 0.1 * np.random.randn(50)
spl = UnivariateSpline(x, y)
xs = np.linspace(-3, 3, 1000)
plt.plot(xs, spl(xs), 'r', lw = 10)
plt.show()

Spline Interpolation

In 1D interpolation the points are fitted for a single curve whereas in Spline interpolation the points are fitted against a piecewise function defined with polynomials called splines.

The UnivariateSpline() function takes xs and ys and produce a callable funciton that can be called with new xs.

Piecewise function: A function that has different definition for different ranges.

Example
Find univariate spline interpolation for 2.1, 2.2... 2.9 for the following non linear points:

from scipy.interpolate import UnivariateSpline
import numpy as np

xs = np.arange(10)
ys = xs**2 + np.sin(xs) + 1

interp_func = UnivariateSpline(xs, ys)

newarr = interp_func(np.arange(2.1, 3, 0.1))

print(newarr)
Result:

[5.62826474 6.03987348 6.47131994 6.92265019 7.3939103  7.88514634
8.39640439 8.92773053 9.47917082]

Interpolation with Radial Basis Function
Radial basis function is a function that is defined corresponding to a fixed reference point.

The Rbf() function also takes xs and ys as arguments and produces a callable function that can be called with new xs.

Example
Interpolate following xs and ys using rbf and find values for 2.1, 2.2 ... 2.9:

from scipy.interpolate import Rbf
import numpy as np

xs = np.arange(10)
ys = xs**2 + np.sin(xs) + 1

interp_func = Rbf(xs, ys)

newarr = interp_func(np.arange(2.1, 3, 0.1))

print(newarr)