marando/interp

A PHP data interpolation package

0.1.1 2016-08-15 05:41 UTC

Requires

• php: >=5.5

Requires (Dev)

• phpunit/phpunit: ^5.0

GNU2

• Ashley Marando

README

Interp is a PHP data interpolation package that can interpolate data using difference interpolation as well as the Lagrange interpolation formula.

Installation

Interp can be installed with composer like so:

$ composer require marando/interp

Usage

Difference Interpolation with Interp3 and Interp5

Both the Interp3 and Interp5 objects can interpolate data using the second and third difference interpolation methods respectively. This method requires that all data points are equidistant.

Initialization

An Interp3 or Interp5 object can be created by either calling the default constructor or the init() static constructor. You must supply the first and last x-values as well as the full table of y-values:

$i3 = new Interp3(1, 7, [1, 2, 3, 4, 5, 6, 7]);
$i3 = Interp3::init(1, 7, [1, 2, 3, 4, 5, 6, 7]);

Interpolation by x Value

Call upon the x() method to interpolate an x value second argument returns by reference the interpolated value of y:

$i3 = new Interp3(1, 7, [1, 2, 3, 4, 5, 6, 7]);

$i3->x(1.0, $y);  // Result: y = 1
$i3->x(2.3, $y);  // Result: y = 2.3

The value you provide must be within the range of the initialized data or an OutOfRangeException will occur:

$i3 = new Interp3(1, 7, [1, 2, 3, 4, 5, 6, 7]);

$i3->x(100, $y);  

OutOfRangeException: The x value '12.3' is out of the range [1, 7].

The third argument returns the last difference from the table of differences:

$i3 = new Interp3(1, 7, [1.234, 2.45, 3.345, 4.231, 5.56, 6.233, 7.653]);

$i3->x(2.3, $y, $c);
print $c;

Output:

0.321

Interpolation by n Interpolation Factor

You can also interpolate data by providing an interplation factor as seen here:

$i3 = new Interp3(1, 3, [1, 2, 3]);
$i3->n(0, $x, $y);

print $x;
print $y;

Output:

2
2

If the initialized data has more than three values, you must also specify an x-value to focus around, otherwise an IncorrectCountException will be thrown:

$i3 = new Interp3(1, 6, [1, 2, 3, 4, 5, 6]);
$i3->n(0.5, $x, $y, $c, 5);

print $x;
print $y;

Output:

5.5
5.5

Also, as seen before, the last difference from the table of differences is returned, but as the fourth value here.

Interpolation of Extrema

The extremum of the data can be found by calling the extremum() function. Both the x and y value at the extremum are returned by reference as well as the last difference from the table of differences:

$i3 = new Interp3(1, 3, [0.71, 0.68, 0.79]);
$i3->extremum($x, $y, $c);

print $x;
print $y;
print $c;

Output:

1.7142857142857
0.67428571428571
0.1

If no extremum can be found a NoExtremumException will be thrown.

Interpolation of the Zero

Interpolation at y = 0 can be found by using the zero() function which works exactly the same as the extremum() function. If no zero can be found a NoZeroException will be thrown.

$i3 = new Interp3(1, 6, [-2, -1, 0, 1, 2, 3]);
$i3->zero($x, $y, $c);

print $x;
print $y;
print $c;

Output:

3
0
0

Strictness

The Interp3 and Interp5 objects have a property called strict which if set to true restricts all interpolation factors to safe values between -0.5 and 0.5, otherwise the limit is set to [-1, 1]

Lagrange Interpolation

Lagrange interpolation can be performed with the Lagrange object. You must provide the object a table of x and y values by using either the default constructor or the init() method:

// Initialize Lagrange object with data
$l = Lagrange::init($data = [
  [29.43, .4913598528],
  [30.97, .5145891926],
  [27.69, .4646875083],
  [28.11, .4711658342],
  [31.58, .5236885653],
  [33.05, .5453707057],
]);

Then use the x() method to interpolate a given x-value. The value of y is returned by reference:

$l->x(30, $y);
print $y

Output:

0.5