PHP Class MathPHP\NumericalAnalysis\Interpolation\LagrangePolynomial
In numerical analysis, the Lagrange Polynomials are used for polynomial
interpolation.
"Given a set of distinct points {xⱼ,yⱼ}, the Lagrange Polynomial is the
[unique] polynomial of least degree such that at each point xⱼ assumes the
corresponding value yⱼ (i.e. the functions coincide at each point)."
The lagrange polynomials belong to a collection of techniques that
interpolate a function or a set of values, producing a continuous polynomial.
We can either directly supply a set of inputs and their corresponding outputs
for said function, or if we explicitly know the function, we can define it as
a callback function and then generate a set of points by evaluating that
function at n points between a start and end point. We then use these values
to interpolate a Lagrange polynomial.
https://en.wikipedia.org/wiki/Lagrange_polynomial
http://mathworld.wolfram.com/LagrangeInterpolatingPolynomial.html
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Class Usage Examples
Public Methods
Method Details
interpolate()
public static method
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public static interpolate ( $source, $args ) : callable |
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$source |
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The source of our approximation. Should be either
a callback function or a set of arrays. Each array
(point) contains precisely two numbers, an x and y.
Example array: [[1,2], [2,3], [3,4]].
Example callback: function($x) {return $x**2;} |
| return |
callable |
The lagrange polynomial p(x) |