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