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Interpolation and Extrapolation in 1D in Python

Learn how to interpolation and extrapolate data in one dimension

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Imports

The tutorial below imports NumPy, Pandas, and SciPy.

In [1]:
import plotly.plotly as py
import plotly.graph_objs as go
from plotly.tools import FigureFactory as FF

import numpy as np
import pandas as pd
import scipy

Tips

Interpolation refers to the process of generating data points between already existing data points. Extrapolation is the process of generating points outside a given set of known data points.
(inter and extra are derived from Latin words meaning 'between' and 'outside' respectively)

Interpolation and Extrapolation

Interpolate and Extrapolate for a set of points and generate the curve of best fit that intersects all the points.

In [2]:
points = np.array([(1, 1), (2, 4), (3, 1), (9, 3)])

x = points[:,0]
y = points[:,1]

z = np.polyfit(x, y, 3)
f = np.poly1d(z)

x_new = np.linspace(0, 10, 50)
y_new = f(x_new)

trace1 = go.Scatter(
    x=x,
    y=y,
    mode='markers',
    name='Data',
    marker=dict(
        size=12
    )
)

trace2 = go.Scatter(
    x=x_new,
    y=y_new,
    mode='lines',
    name='Fit'
)

annotation = go.Annotation(
    x=6,
    y=-4.5,
    text='$0.43X^3 - 0.56X^2 + 16.78X + 10.61$',
    showarrow=False
)

layout = go.Layout(
    title='Polynomial Fit in Python',
    annotations=[annotation]
)

data = [trace1, trace2]
fig = go.Figure(data=data, layout=layout)

py.iplot(fig, filename='interpolation-and-extrapolation')
Out[2]:

Interpolation and Extrapolation of Y From X

Interpolation and Extrapolation of (x, y) points with pre-existant points and an array of specific x values.

In [3]:
points = np.array([(1, 1), (2, 4), (3, 1), (9, 3)])

# get x and y vectors
x = points[:,0]
y = points[:,1]

# calculate polynomial
z = np.polyfit(x, y, 3)
f = np.poly1d(z)

# other x values
other_x = np.array([1.2, 1.34, 1.57, 1.7, 3.6, 3.8, 3.9, 4.0, 5.4, 6.6, 7.2, 7.3, 7.7, 8, 8.9, 9.1, 9.3])
other_y = f(other_x)

# calculate new x's and y's
x_new = np.linspace(0, 10, 50)
y_new = f(x_new)

# Creating the dataset, and generating the plot
trace1 = go.Scatter(
    x=x,
    y=y,
    mode='markers',
    name='Data',
    marker=dict(
        size=12
    )
)

trace2 = go.Scatter(
    x=other_x,
    y=other_y,
    name='Interpolated/Extrapolated Data',
    mode='markers',
    marker=dict(
        symbol='square-open',
        size=12
    )
)

layout = go.Layout(
    title='Interpolation and Extrapolation of Y From X',
)

data2 = [trace1, trace2]
fig2 = go.Figure(data=data2, layout=layout)

py.iplot(fig2, filename='interpolation-and-extrapolation-of-y-from-x')
Out[3]:
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