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
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.
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')
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.
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')