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[Utility & Helpers](/categories/utility) 4. / 5. mcordingley/linearalgebra ActiveLibrary[Utility & Helpers](/categories/utility) mcordingley/linearalgebra ========================= Matrix math for PHP. 3.0.0(3y ago)85146.3k—6.3%111MITPHPPHP ^8.0.0 Since Apr 3Pushed 3y ago5 watchersCompare [ Source](https://github.com/mcordingley/LinearAlgebra)[ Packagist](https://packagist.org/packages/mcordingley/linearalgebra)[ RSS](/packages/mcordingley-linearalgebra/feed)WikiDiscussions master Synced 1mo ago READMEChangelog (10)Dependencies (1)Versions (19)Used By (1) Matrix ====== [](#matrix) [![Build Status](https://camo.githubusercontent.com/0e042703fa3a543d9943a38890e94cc678a14d34786020f659ca571c256b5a00/68747470733a2f2f6170692e7472617669732d63692e636f6d2f7265706f7369746f726965732f6d636f7264696e676c65792f4c696e656172416c67656272612e737667)](https://travis-ci.com/github/mcordingley/LinearAlgebra)[![Code Climate](https://camo.githubusercontent.com/f0b9450543e86c0b8ee0ac5a365bb27d41d74318d553e8e1f06f4b571f5dc6f1/68747470733a2f2f636f6465636c696d6174652e636f6d2f6769746875622f6d636f7264696e676c65792f4c696e656172416c67656272612f6261646765732f6770612e737667)](https://codeclimate.com/github/mcordingley/LinearAlgebra)[![Code Coverage](https://camo.githubusercontent.com/391105ce2c15902aab8cd4ba2ef9fc581a0df6e68b45dcfb388bf1da78f5a014/68747470733a2f2f636f6465636c696d6174652e636f6d2f6769746875622f6d636f7264696e676c65792f4c696e656172416c67656272612f6261646765732f636f7665726167652e737667)](https://codeclimate.com/github/mcordingley/LinearAlgebra) Stand-alone Linear Algebra Library for PHP Installation ------------ [](#installation) ``` composer require mcordingley/LinearAlgebra ``` Alternately, include this in your composer.json and then update: ``` "mcordingley/linearalgebra": "^3.0.0" ``` If Composer isn't an option for you, clone this repository and run `build-phar.php` to generate a phar archive that you can include into your project. PHP will autoload classes from inside the archive as needed. Usage ----- [](#usage) ### Matrix [](#matrix-1) Start with a `use` statement for the class: ``` use MCordingley\LinearAlgebra\Matrix; ``` Then, instantiate a new instance of the matrix class like so: ``` $matrix = new Matrix([ [0, 1, 2], [3, 4, 5], [6, 7, 8] ]); ``` You can also generate an identity matrix with the `identity` factory function: ``` $threeByThreeIdentityMatrix = Matrix::identity(3); ``` With the matrix instance, you can retrieve individual elements with `get` using the zero-based indices of the row and column that you want: ``` $element = $matrix->get($row, $column); ``` It's also possible to find out how large the matrix is with `getRowCount()` and `getColumnCount()`: ``` $rows = $matrix->getRowCount(); $columns = $matrix->getColumnCount(); ``` You can also add, subtract, and multiply the matrix with scalar values and other matrices. All operations return a new Matrix and do not modify the underlying matrix: ``` $addedScalar = $matrix->addScalar(3); $addedMatrix = $matrix->addMatrix($anotherMatrix); $subtractedScalar = $matrix->subtractScalar(2); $subtractedMatrix = $matrix->subtractMatrix($anotherMatrix); $multipliedByScalar = $matrix->multiplyScalar(4); $multipliedByMatrix = $matrix->multiplyMatrix($anotherMatrix); ``` Matrices can be compared with `equals` to see if they're equal: ``` if ($matrix1->equals($matrix2)) { // Equality for all! } ``` In addition to these basic operations, the Matrix class offers other common matrix operations: ``` $matrix->inverse() $matrix->adjugate() $matrix->determinant() $matrix->trace() $matrix->transpose() ``` You can get the upper and lower triangular matrices by calling `upper(bool)` and `lower(bool)`. The lone argument tells whether the main diagonal of the triangular matrix should be set to ones (`true`) or the value of the parent matrix (`false`). It's also possible to run a map over the matrix: ``` $squaredElements = $matrix->map(function($element, $row, $column, $matrix) { return $element * $element }); ``` Submatrices may be extracted with `sliceColumns($offset, $length)` and `sliceRows($offset, $length)`. The semantics of the arguments are the same as PHP's `array_slice`. Similarly, `spliceColumns($offset, $length, $replacement)` and `spliceRows($offset, $length, $replacement)` can be used to create new matrices with specific rows or columns removed or replaced. Unlike the native PHP `array_splice`, these operations do not modify the matrix in place and return the removed elements, but instead return a new matrix with the splice applied. If you need to combine together matrices, you can do so by calling the concatenation methods: ``` $m1 = new Matrix([ [1,2,3], [4,5,6], ]); $m2 = new Matrix([ [7], [8], ]); $m3 = new Matrix([[3,2,1]]); $m4 = $m1->concatenateRight($m2); // [ // [1,2,3,7], // [4,5,6,8], // ] $m5 = $m1->concatenateBottom($m3); // [ // [1,2,3], // [4,5,6], // [3,2,1], // ] ``` LU and LUP decomposition methods are available as separate classes and both expose `lower()` and `upper()` for the L and U portions of the decompositions, respectively. The LUP decomposition additionally exposes `permutationMatrix` and `permutationArray` to fetch the P component of the decomposition as well as `parity` to return the total number of pivots performed. ### Vector [](#vector) As with `Matrix`, import the class into your current namespace: ``` use MCordingley\LinearAlgebra\Vector; ``` Since a `Vector` is a special case of a `Matrix`, `Vector` inherits from `Matrix`. As such, every method available on `Matrix` is also available on `Vector`. `Vector` also exposes additional methods specific to working with vectors. Creating a `Vector` differs from creating a `Matrix` only in that the constructor takes an array of scalars, rather than an array of arrays: ``` $vector = new Vector([1, 2, 3, 4]); ``` Note that `Vector` instances are all row vectors. If you need a column vector, `transpose()` the vector to get a `Matrix` with a single column. If you need to cast a `Matrix` into a `Vector`, call the factory method `fromMatrix()`: ``` $vector = Vector::fromMatrix($matrix); ``` `toArray()` is overridden to return an array of scalars to mirror how the constructor works. It is equivalent to calling `$matrix->toArray()[0]` on a `Matrix` instance. `getSize()` is provided as an alias for `getColumnCount()`. `sum()` will return the sum of the `Vector` elements, while `dotProduct($otherVector)` will return the sum of the pair-wise products of `$vector` and `$otherVector`, and is also availabe aliased as `innerProduct($otherVector)`. `outerProduct($otherVector)` will return a new Matrix representing the outer product of the two vectors. `crossProduct($otherVector)` is also available. Vectors may be normalized with `normalize()`. They may also be projected onto other vectors with `project($otherVector)`. The Euclidean distance may also be calculated between two vectors with `euclideanDistance($otherVector)`. For measures of vector magnitude, `l1Norm()`, `l2Norm()`, and `maxNorm()` are all available, with `length()` as an alias for `l2Norm()`. Links to relevant Wikipedia articles are provided in the function documentation for additional detail. Change-log ---------- [](#change-log) - 3.0.0 - Update to PHP 8 to start taking advantage of new features. - Adds some previously-missing type assertions enabled by PHP 8. - Adds `euclideanDistance` to `Vector`. - 2.2.0 - Implement the `ArrayAccess` interface on `Matrix` to return row vectors. - Implement the `ArrayAccess` interface on `Vector` to return scalars. - Add `addVector()` and `subtractVector()` to `Vector` - Add `magnitude()` as an alias to `length()` on `Vector` - 2.1.1 - Fix a bug involving inheritance with `map()` on `Vector`. - 2.1.0 - Add `Vector` as a subclass of `Matrix`. Thanks to battlecook for this contribution. - 2.0.0 - Drop support for PHP 5.x - Introduce strict scalar type hints - Drop deprecated functions and properties. - Tighten up interface with the `final` and `private` keywords. - `diagonal()` now returns a full matrix, not a vector. - Rename `adjoint()` to `adjugate()` for clarity. - Add `entrywise()` to compute the Hadamard product. - Add `upper()` and `lower()` - Add `sliceColumns()` and `sliceRows()` - Add `spliceColumns()` and `spliceRows()` - Add `LU` and `LUP` decompositions as classes. - 1.3.2 - Deprecate `__toString()` magic method. - Deprecate `isSymmetric()`. - 1.3.1 - Deprecate use of the `ArrayAccess` interface. - More internal code style fixes. - 1.3.0 - Fix typo in names of `concatenateRight()` and `concatenateBottom()` - Remove generated Phar file. Users who need it should use the `build-phar.php` script to generate one. - Refactor LUDecomposition to have a less awkward constructor. - Split `add()` into `addMatrix()` and `addScalar()`. Deprecate `add()`. - Split `subtract()` into `subtractMatrix()` and `subtractScalar()`. Deprecate `subtract()`. - Split `multiply()` into `multiplyMatrix()` and `multiplyScalar()`. Deprecate `multiply()`. - Add `getRowCount()` and `getColumnCount()` accessors. - Deprecate `rows` and `columns` properties. - 1.2.0 - Added `concatenateBottom($other)` - Added `concatencateRight($other)` - 1.1.0 - Added `diagonal()`. - 1.0.0 - Switch to PSR-4 from PSR-0. - Take `isSymmetric()` public. - Rearrange source in `Matrix.php` to be more readable and PSR-compliant. - 0.9.1 - Fix several bugs with the Cholesky decomposition and inverse. - 0.9.0 - Bump version up to represent that this is close to it's final form. - Merged PR for faster `inverse` calculations - KISS `Vector` class good-bye. - Renamed `eq` to `equals`. - Removed `set` function, so instantiated objects are immutable. - 0.3.0 - Added the `identity` factory function - Using Cholesky decomposition for faster matrix inversions for applicable matrices - Added `eq` function to test equality of matrices - Implemented the ArrayAccess interface - 0.2.0 - Created the Vector type - `\MCordingley` namespace is now `\mcordingley` - Matrix functions that return a new Matrix now return a new instance of the called class - 0.1.0 - Created the Matrix type - Scalar Addition - Scalar Subtraction - Scalar Multiplication - Matrix Addition - Matrix Subtraction - Matrix Multiplication - Inverse - Adjoint - Determinant - Trace - Transpose - Submatrix - Map ### Health Score 45 — FairBetter than 93% of packages Maintenance20 Infrequent updates — may be unmaintained Popularity47 Moderate usage in the ecosystem Community21 Small or concentrated contributor base Maturity77 Established project with proven stability Bus Factor1 Top contributor holds 91.9% of commits — single point of failure How is this calculated?**Maintenance (25%)** — Last commit recency, latest release date, and issue-to-star ratio. Uses a 2-year decay window. **Popularity (30%)** — Total and monthly downloads, GitHub stars, and forks. Logarithmic scaling prevents top-heavy scores. **Community (15%)** — Contributors, dependents, forks, watchers, and maintainers. Measures real ecosystem engagement. **Maturity (30%)** — Project age, version count, PHP version support, and release stability. ### Release Activity Cadence Every ~180 days Recently: every ~466 days Total 18 Last Release 1360d ago Major Versions 0.9.1 → 1.0.02015-11-07 1.3.2 → 2.0.02016-11-27 2.3.0 → 3.0.02022-08-27 PHP version history (3 changes)0.1.0PHP >=5.4.0 2.0.0PHP ^7.0.0 3.0.0PHP ^8.0.0 ### Community Maintainers ![](https://www.gravatar.com/avatar/292870c77b057996c6d7ebb96381529d5aba3829e8a9a220328a408039e80d70?d=identicon)[mcordingley](/maintainers/mcordingley) --- Top Contributors [![mcordingley](https://avatars.githubusercontent.com/u/1084253?v=4)](https://github.com/mcordingley "mcordingley (285 commits)")[![thominj](https://avatars.githubusercontent.com/u/3819908?v=4)](https://github.com/thominj "thominj (19 commits)")[![battlecook](https://avatars.githubusercontent.com/u/9781396?v=4)](https://github.com/battlecook "battlecook (4 commits)")[![brad-jones](https://avatars.githubusercontent.com/u/2754772?v=4)](https://github.com/brad-jones "brad-jones (1 commits)")[![rreynier](https://avatars.githubusercontent.com/u/1953114?v=4)](https://github.com/rreynier "rreynier (1 commits)") --- Tags linear-algebra-librarylinearalgebramatrixphpmatrixlinear algebra ### Code Quality TestsPHPUnit ### Embed Badge ![Health badge](/badges/mcordingley-linearalgebra/health.svg) ``` [![Health](https://phpackages.com/badges/mcordingley-linearalgebra/health.svg)](https://phpackages.com/packages/mcordingley-linearalgebra) ``` ### Alternatives [markrogoyski/math-php Math Library for PHP. 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