PHP Class MathPHP\NumericalAnalysis\NumericalIntegration\NumericalIntegration

Numerical integration techniques are used to approximate the value of an indefinite intergal. This calss gives each technique a set of common tools, and requires each technique to define an approximate() method to approximate an indefinite integral.
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Méthodes publiques

Méthode Description
approximate ( $source, $args )
getPoints ( $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.
validate ( array $points, number $degree = 2 ) : boolean Validate that there are enough input arrays (points), that each point array has precisely two numbers, and that no two points share the same first number (x-component)

Méthodes protégées

Méthode Description
functionToPoints ( callable $function, number $start, number $end, number $n ) : array Evaluate our callback function at n evenly spaced points on the interval between start and end
sort ( array $points ) : array Sorts our coordinates (arrays) by their x-component (first number) such that consecutive coordinates have an increasing x-component.

Method Details

approximate() abstract public static méthode

abstract public static approximate ( $source, $args )

functionToPoints() protected static méthode

Evaluate our callback function at n evenly spaced points on the interval between start and end
protected static functionToPoints ( callable $function, number $start, number $end, number $n ) : array
$function 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
Résultat array

getPoints() public static méthode

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 getPoints ( $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: start, end, and n. Example: [0, 8, 5]. If $source is a set of arrays, $args will default to [].
Résultat array

sort() protected static méthode

Sorts our coordinates (arrays) by their x-component (first number) such that consecutive coordinates have an increasing x-component.
protected static sort ( array $points ) : array
$points array
Résultat array

validate() public static méthode

Validate that there are enough input arrays (points), that each point array has precisely two numbers, and that no two points share the same first number (x-component)
public static validate ( array $points, number $degree = 2 ) : boolean
$points array Array of arrays (points)
$degree number The miminum number of input arrays
Résultat boolean