What Is Interpolation?

Continuous functions are interpolated on the basis of discrete data so that this continuous curve passes through all given discrete data points. ^[1]

As early as the 6th century, Liu Ye of China has used equidistant quadratic interpolation for astronomical calculations.

After the 17th century, I. Newton and J.-L. Lagrange discussed the general interpolation formulas of equidistant and non-equidistant respectively. In modern times,

Given n discrete data points (called nodes )

, K = 1,2, ..., n. for

, Finding the value of y for x is called interpolation. ^[2]

The formulation of the interpolation problem is:

Use interpolation function in matlab

The function of interpolation

interp1

Format of the calling function ( Syntax )

yi = interp1 (x, Y, xi)

yi = interp1 (Y, xi)

yi = interp1 (x, Y, xi, method)

yi = interp1 (x, Y, xi, method, 'extrap')

yi = interp1 (x, Y, xi, method, extrapval)

pp = interp1 (x, Y, method, 'pp')

Call Format Description ( Description )

yi = interp1 (x, Y, xi) returns the values of y determined by the vectors X and Y according to the input node xi. Vector Y is a function mapping of vector X.

If Y is a matrix, then the interpolation result is a corresponding matrix.

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yi = interp1 (x, Y, xi) returns vector yi containing elements corresponding to the elements of xi and determined by interpolation within vectors x and Y. The vector x specifies the points at which the data Y is given. If Y is a matrix , then the interpolation is performed for each column of Y and yi is length (xi) -by-size (Y, 2).

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yi = interp1 (x, Y, xi, method) interpolation methods:

Interpolation method	Description
nearest	Adjacent two-point interpolation
linear	Linear interpolation (default)
spline	Cubic spline interpolation
pchip	Piecewise cubic Hermite interpolation polynomial interpolation
cubic	(The same applies to pchip)
v5cubic	Interrupted cubic spline interpolation with matlab5 version

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yi = interp1 (x, Y, xi, method) interpolates using alternative methods:

methodDescription

nearestNearest neighbor interpolation

linearLinear interpolation (default)

splinesplineCubic spline interpolation

pchipPiecewise cubic Hermite interpolation

cubic (Same as 'pchip')

v5cubicCubic interpolation used in MATLAB 5

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Simple program example

>> x = [0.0 0.1 0.195 0.3 0.401 0.5];

>> y = [0.39849 0.39695 0.39142 0.38138 0.36812 0.35206];

>> plot (x, y);

>> T = interp1 (x, y, .25, 'linear')% linear interpolation

(Return result T = 0.3862)

>> T = interp1 (x, y, .25, 'nearest')% two-point interpolation

(Return result T = 0.3814)

>> T = interp1 (x, y, .25, 'spline')% cubic spline interpolation

(Return result T = 0.3867)

>> T = interp1 (x, y, .25, 'cubic')% cubic interpolation

(Return result T = 0.3867)