Numerical Differentiation in Python/v3

Learn how to differentiate a sequence or list of values numerically

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ImportsÂ¶

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

Differentiate the Sine FunctionÂ¶

How to use numerical differentiation to plot the derivative of the sine function $y = sin(x)$:

In [2]:

x = np.linspace(0, 2*np.pi, 100)
y = np.sin(x)

dy = np.zeros(y.shape,np.float)
dy[0:-1] = np.diff(y)/np.diff(x)
dy[-1] = (y[-1] - y[-2])/(x[-1] - x[-2])

trace1 = go.Scatter(
    x=x,
    y=y,
    mode='lines',
    name='sin(x)'
)

trace2 = go.Scatter(
    x=x,
    y=dy,
    mode='lines',
    name='numerical derivative of sin(x)'
)

trace_data = [trace1, trace2]
py.iplot(trace_data, filename='numerical-differentiation')

Out[2]: