PHP Class MathPHP\NumericalAnalysis\Interpolation\ClampedCubicSpline

In numerical analysis, cubic splines are used for polynomial interpolation. A cubic spline is a spline constructed of piecewise third-order polynomials which pass through a set of m control points." In the case of the Clamped cubic spline, the first derivative of piecewise polynomial is set to equal the first derivative of our input at the endpoints. Cubic spline interpolation belongs to a collection of techniques that interpolate a function or a set of values, producing a continuous polynomial. In the case of the cubic spline, a piecewise function (polynomial) is produced. 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 our piecewise polynomial. https://en.wikipedia.org/wiki/Spline_interpolation http://mathworld.wolfram.com/CubicSpline.html

Inheritance: extends Interpolation

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Public Methods

Method	Description
getSplinePoints ( $source, array $args = [] ) : array	Determine where the input $source argument is a callback function, a set of arrays, or neither. If $source is a callback function, run it through the functionToPoints() method with the input $args, and set $points to output array. If $source is a set of arrays, simply set $points to $source. If $source is neither, throw an Exception.
interpolate ( $source, $args ) : Piecewise	Interpolate
validateSpline ( array $points, number $degree = 2 ) : boolean	Validate that there are enough input arrays (points), that each point array has precisely three numbers, and that no two points share the same first number (x-component)

Protected Methods

Method	Description
functionToSplinePoints ( callable $function, callable $derivative, number $start, number $end, number $n ) : array	Evaluate our callback function and derivative at n evenly spaced points on the interval between start and end

Method Details

functionToSplinePoints() protected static method

Evaluate our callback function and derivative at n evenly spaced points on the interval between start and end

protected static functionToSplinePoints ( callable $function, callable $derivative, number $start, number $end, number $n ) : array
$function	callable	f(x) callback function
$derivative	callable	f'(x) callback function
$start	number	the start of the interval
$end	number	the end of the interval
$n	number	the number of function evaluations
return	array

getSplinePoints() public static method

Determine where the input $source argument is a callback function, a set of arrays, or neither. If $source is a callback function, run it through the functionToPoints() method with the input $args, and set $points to output array. If $source is a set of arrays, simply set $points to $source. If $source is neither, throw an Exception.

public static getSplinePoints ( $source, array $args = [] ) : array
$source		The source of our approximation. Should be either a callback function or a set of arrays.
$args	array	The arguments of our callback function: derivative, start, end, and n. Example: [$derivative, 0, 8, 5]. If $source is a set of arrays, $args will default to [].
return	array

interpolate() public static method

Interpolate

public static interpolate ( $source, $args ) : Piecewise
$source		The source of our approximation. Should be either a callback function or a set of arrays. Each array (point) contains precisely three numbers: x, y, and y' Example array: [[1,2,1], [2,3,0], [3,4,2]]. Example callback: function($x) {return $x**2;}
return	MathPHP\Functions\Piecewise	The interpolting (piecewise) polynomial, as an instance of Piecewise.

validateSpline() public static method

Validate that there are enough input arrays (points), that each point array has precisely three numbers, and that no two points share the same first number (x-component)

public static validateSpline ( array $points, number $degree = 2 ) : boolean
$points	array	Array of arrays (points)
$degree	number	The miminum number of input arrays
return	boolean