PHP Matrix data structure support package

2.5.0 2017-03-21 23:13 UTC


Quality Assurance

PHP 5.4 PHP 5.5 PHP 5.6 PHP 7 Build Status Test Coverage Code Climate

The above badges represent the current development branch. As a rule, I don't push to GitHub unless tests, coverage and usability are acceptable. This may not be true for short periods of time; on holiday, need code for some other downstream project etc. If you need stable code, use a tagged version. Read 'Further Documentation' and 'Installation'.

Test Contract in the docs directory.


This library aims to provide matrix transformation functionality given that:

  • Everything has a test case
  • It's PHP 5.4+

The matrix supplied in this library is a generic one. It treats a matrix as a data structure giving the ability to create matrices and carry out transformations.

The library is released under the GNU GPL V3 or later license


I finally got round, after too may years, to investigate TDD as a serious methodology. Always interested in something a bit maths related, I thought that having a go at matrices would brush up on old forgotten things and provide a bit of entertainment. So this library is as much about using TDD as it is about matrices. The bonus for taking the TDD approach is that as I've (re)learnt something about matrices, I've been able to refactor in safety.


The current library covers basic matrix manipulation. The library will cover most well known generic matrix transformations and derivatives.

If you want more, either suggest it, or better still, fork it and provide a pull request.

Check out chippyash/Logical-Matrix for logical matrix operations

Check out chippyash/Math-Matrix for mathematical matrix operations

Check out chippyash/Strong-Type for strong type including numeric, rational and complex type support

Check out chippyash/Math-Type-Calculator for arithmetic operations on aforementioned strong types

Check out ZF4 Packages for more packages


Coding Basics

In PHP terms a matrix is an array of arrays, 2 dimensional i.e

  • [[]]

A shortcut for a single item matrix is to supply a single array

    use Chippyash/Matrix/Matrix;

    $mA = new Matrix([]);  //empty matrix
    $mA = new Matrix([[]]);  //empty matrix
    $mA = new Matrix([1]);  //single item matrix

As with any TDD application, the tests tell you everything you need to know about the SUT. Read them! However for the short of temper amongst us, the salient points are:

A basic Matrix type is supplied

  • Matrix(array $source, bool $complete = false, bool $normalize= false, bool $normalizeDefault = null)

Matrices are 1 based, not 0 (zero) based

The following methods on a matrix are supported:

  • toArray() : array - return matrix data as an array
  • rows(): int - number of rows (n) in the matrix
  • columns(): int - number of columns (m) in the matrix
  • vertices(): int - number of entries in matrix (== n * m)
  • get(int $row >= 0, int $col >= 0): mixed - if either row or col are zero, then return a row vector if col == 0, column vector if row == 0, else return single vertex from matrix indictated by row, col.
  • is(string $attribute): boolean - see attributes below
  • test(string $attribute): boolean - Raw form of is() method. You can use this to test for attributes not supplied with the library by passing in $attribute conforming to AttributeInterface
  • transform(TransformationInterface $transformation, $extra = null): Matrix - see transformations below
  • setFormatter(FormatterInterface $formatter): fluent - set a display formatter
  • display(): mixed - Return the matrix in some displayable format
  • equality(Matrix $mB, boolean $strict = true): boolean - Is the matrix equal to matrix mB?
    • mA->rows() == mB->rows()
    • mA->columns() == mB->columns()
    • mA->get(i,j) ==[=] mB->get(i,j) If strict then type and value checked else only equivalence of value

Matrices are immutable

No operation on a matrix will change the internal structure of the matrix. Any transformation or similar will return another matrix, leaving the original alone. This allows for arithmetic stability.

However, a Mutability trait is provided for you to create a mutable matrix for special purposes.

use Chippyash\Matrix\Traits\Mutability;

class MutableMatrix extends Matrix
    use Mutability;

This provides a set() method:

     * Set a matrix vertex, row or column vector
     * If row == 0 && col > 0, then set the column vector indicated by col
     * If col == 0 && row > 0, then set the row vector indicated by row
     * if row > 0 && col > 0, set the vertex
     * row == col == 0 is an error
     * @param int $row
     * @param int $col
     * @param mixed|Matrix $data If setting a vector, supply the correct vector matrix
     * @return Matrix
     * @throws VerticeOutOfBoundsException
     * @throws MatrixException
    public function set($row, $col, $data);

Matrices have attributes

  • Attributes always return a boolean.
  • Attributes implement the Chippyash\Matrix\Interfaces\AttributeInterface
  • You can use the is() method of a Matrix to test for an attribute
    if ($mA->is('square')) {}
    //is the same as
    $attr = new Matrix/Attribute/IsSquare();
    if ($attr($mA) {}

Attributes supported:

  • IsColumnvector() - Is the matrix a column vector?
  • IsComplete() - Does the matrix have all its entries present?
  • IsDiagonal() - Are only entries on the main diagonal non-zero?
  • IsEmpty() - Is the matrix an empty one?
  • IsRectangle() - Is matrix non-empty and non-square?
  • IsRowVector() - Is the matrix a row vector?
  • IsSquare() - Is the matrix square? i.e. n == m & n >= 0
  • IsVector() - Is the matrix a row vector or a column vector?

Matrices can be transformed

  • Transformation always returns a Matrix
  • The original matrix is untouched
  • You can use the magic __invoke functionality
  • Transformations implement the Chippyash\Matrix\Interfaces\TransformationInterface
    $mB = $mA("Transpose");
    //same as :
    $comp = new Matrix\Transformation\Transpose;
    $mB = $comp($mA);
    $mB = $mA->transform($comp);

Transformations supported:

  • Circshift - shift columns in matrix left or right (default) around the Y axis
  • Cofactor - return the cofactor matrix of a vertice
  • Colreduce - return matrix reduced by 1+ columns
  • Colslice - return a slice (1+) of the matrix columns
  • Concatenate - return matrix with extra matrix appended to the right
  • Diagonal - reduce a matrix to its diagonal elements substituting non diagonal entries with zero
  • MFunction - apply a function to every entry in the matrix
  • Reflect - reflect matrix on X plane, Y plane, y=x plane and through origin
  • Resize - resize a matrix by adding or subtracting rows and columns from bottom and right side respectively
  • Rotate - rotate matrix through 90, 180 or 270 degrees
  • Rowreduce - return matrix reduced by 1+ rows
  • Rowslice - return a slice (1+) of matrix rows
  • Shift - shift matrix rows columns left or right across the matrix replacing new columns with a value
  • Stack - return matrix stacked on top of extra matrix
  • Transpose - return matrix with rows and columns swapped around the diagonal

The magic invoke methods allow you to write in a functional way

For example (taken from Transformation\Cofactor):

        $fC = new Colreduce();
        $fR = new Rowreduce();
        return $fR($fC($mA,[$col]),[$row]);

or this (from Transformation\Colreduce):

        $fT = new Transpose();
        $fR = new Rowreduce();

        return $fT($fR($fT($mA), [$col, $numCols]));

Matrices can be output for display

You can supply a formatter to create output via the display() method. The library currently has an Ascii formatter. To use it

    use Chippyash\Matrix\Formatter\Ascii;
    use Chippyash\Matrix\Matrix;

    $mA = new Matrix([[1,2,3],['a','b','c'],[true, false, 'foo']]);
    echo $mA->setFormatter(new Asciii())->display();
  • Formatters implement the Chippyash\Matrix\Interfaces\FormatterInterface
  • The Matrix::display() method accepts an optional array of options that are passed to the formatter
  • Formatters are not limited to string output. You could for instance, write a formatter to output an SVG file

You can debug a Matrix

If you find something weird happening, utilise the Debug trait to dump out the matrix to screen using the Ascii formatter.

Changing the library

  1. fork it
  2. write the test
  3. amend it
  4. do a pull request

Found a bug you can't figure out?

  1. fork it
  2. write the test
  3. do a pull request

NB. Make sure you rebase to HEAD before your pull request


The library is hosted at Github. It is available at


Install Composer

For production


    "chippyash/matrix": "~2"

to your composer.json "requires" section

For development

Clone this repo, and then run Composer in local repo root to pull in dependencies

    git clone Matrix
    cd Matrix
    composer update

To run the tests:

    cd Matrix
    vendor/bin/phpunit -c test/phpunit.xml test/


This software library is released under the GNU GPL V3 or later license

This software library is Copyright (c) 2014-2016, Ashley Kitson, UK

A commercial license is available for this software library, please contact the author. It is normally free to deserving causes, but gets you around the limitation of the GPL license, which does not allow unrestricted inclusion of this code in commercial works.


V1.0.0 Original release

V1.0.1 Minor bug fixes

V1.1.0 New transformations

  • Concatenate
  • Stack
  • Rotate

V1.1.1 Code analysis conformance

V1.1.2 Update readme

V1.2.0 New transformation

  • Reflect

V1.2.1 Code analysis conformance

V1.2.2 Fix Ascii formatter to work with descendent matrices

V1.2.3 Fix transformations to work with descendent matrices

V1.2.4 Amend IsSquare attribute test to accept empty matrix as square

Update documentation

V1.2.5 Add equality() method

V1.2.6 Add ability to set the formatter on Debug trait

V1.2.7 Add ability to set the formatter options for debug

V1.2.8 update phpunit to ~V4.3.0

V2.0.0 BC Break: change chippyash\Matrix namespace to Chippyash\Matrix

V2.0.1 remove duplicated tests

V2.0.2 Add link to packages

V2.0.3 code cleanup

V2.1.0 Add Circshift transformation

V2.2.0 Add Shift transformation

V2.3.0 Add IsVector attribute

V2.3.1 Add ability to get() method to return vectors

V2.4.0 Add Mutable Set Trait

V2.4.1 code cleanup

V2.4.2 remove user config files

V2.5.0 add Resize transformation