PHP Класс MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation

Numerical differentiation techniques are used to approximate the derivative of a function at an input value. This class gives each technique a set of common tools, and requires each technique to define a differentiate() method to approximate the derivative of a function at an input value.

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Открытые методы

Метод	Описание
differentiate ( $target, $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.
isSpacingConstant ( array $sorted )	Ensures that the length of each subinterval is equal, or equivalently, that the spacing between each point is equal
isTargetInPoints ( number $target, array $sorted )	Ensures that our target is the x-component of one of the points we supply
validate ( array $points, number $degree ) : boolean	Validate that there are a set number of input arrays (points), that each point array has precisely two numbers, and that no two points share the same first number (x-component)

Защищенные методы

Метод	Описание
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.

Описание методов

differentiate() абстрактный публичный статический Метод

abstract public static differentiate ( $target, $source, $args )

functionToPoints() защищенный статический Метод

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
Результат	array

getPoints() публичный статический Метод

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 [].
Результат	array

isSpacingConstant() публичный статический Метод

Ensures that the length of each subinterval is equal, or equivalently, that the spacing between each point is equal

public static isSpacingConstant ( array $sorted )
$sorted	array	Points sorted by (increasing) x-component

isTargetInPoints() публичный статический Метод

Ensures that our target is the x-component of one of the points we supply

public static isTargetInPoints ( number $target, array $sorted )
$target	number	The value at which we are approximating the derivative
$sorted	array	Points sorted by (increasing) x-component

sort() защищенный статический Метод

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
Результат	array

validate() публичный статический Метод

Validate that there are a set number of 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 ) : boolean
$points	array	Array of arrays (points)
$degree	number	The number of input arrays
Результат	boolean