MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation Class Reference

Base class for numerical differentiation techniques. More...

Inheritance diagram for MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation:

Static Public Member Functions
static	differentiate ($target, $source,... $args)
static	getPoints ($source, array $args=[])
	Determine where the input $source argument is a callback function, a set of arrays, or neither. More...
static	validate (array $points, $degree)
	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) More...
static	isSpacingConstant (array $sorted)
	Ensures that the length of each subinterval is equal, or equivalently, that the spacing between each point is equal. More...
static	isTargetInPoints ($target, array $sorted)
	Ensures that our target is the x-component of one of the points we supply. More...

Public Attributes
const	X = 0
const	Y = 1

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

Detailed Description

Base class for numerical differentiation techniques.

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.

Member Function Documentation

functionToPoints()

static MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation::functionToPoints ( callable  $function,   $start,   $end,   $n  )

staticprotected

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

Parameters

callable	$function	f(x) callback function
number	$start	the start of the interval
number	$end	the end of the interval
number	$n	the number of function evaluations

Returns

array

getPoints()

static MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation::getPoints (   $source, array  $args = []  )

static

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.

Todo:

Add method to verify function is continuous on our interval.

Add method to verify input arguments are valid. Verify $start and $end are numbers, $end > $start, and $points is an integer > 1

Parameters

callable | array	$source	The source of our approximation. Should be either a callback function or a set of arrays.
array	$args	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 [].

Returns

array

Exceptions

Exception

if $source is not callable or a set of arrays

isSpacingConstant()

static MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation::isSpacingConstant ( array  $sorted )

static

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

Parameters

array

$sorted

Points sorted by (increasing) x-component

Exceptions

Exception

if the spacing between any two points is not equal to the average spacing between every point

isTargetInPoints()

static MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation::isTargetInPoints (   $target, array  $sorted  )

static

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

Parameters

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

Exceptions

Exception

if $target is not contained in the array of our x-components

sort()

static MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation::sort ( array  $points )

staticprotected

Sorts our coordinates (arrays) by their x-component (first number) such that consecutive coordinates have an increasing x-component.

Parameters

array

$points

Returns

array

validate()

static MathPHP\NumericalAnalysis\NumericalDifferentiation\NumericalDifferentiation::validate ( array  $points,   $degree  )

static

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)

Parameters

array	$points	Array of arrays (points)
number	$degree	The number of input arrays

Returns

bool

Exceptions

Exception	if there are not enough input arrays
Exception	if any point does not contain two numbers
Exception	if two points share the same first number (x-component)

---

The documentation for this class was generated from the following file:

• src/NumericalAnalysis/NumericalDifferentiation/NumericalDifferentiation.php