# Interpolation and Extrapolation in 1D in Python/v3

Learn how to interpolation and extrapolate data in one dimension

See our Version 4 Migration Guide for information about how to upgrade.

#### New to Plotly?¶

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#### Imports¶

The tutorial below imports NumPy, Pandas, and SciPy.

In :
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 :
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:

#### 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 :
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: 