Matrix
, (*1)
Stand-alone Linear Algebra Library for PHP, (*2)
Installation
composer require mcordingley/LinearAlgebra
Alternately, include this in your composer.json and then update:, (*3)
"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., (*4)
Usage
Matrix
Start with a use statement for the class:, (*5)
use MCordingley\LinearAlgebra\Matrix;
Then, instantiate a new instance of the matrix class like so:, (*6)
$matrix = new Matrix([
[0, 1, 2],
[3, 4, 5],
[6, 7, 8]
]);
You can also generate an identity matrix with the identity factory function:, (*7)
$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:, (*8)
$element = $matrix->get($row, $column);
It's also possible to find out how large the matrix is with getRowCount() and getColumnCount():, (*9)
$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:, (*10)
$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:, (*11)
if ($matrix1->equals($matrix2)) {
// Equality for all!
}
In addition to these basic operations, the Matrix class offers other common
matrix operations:, (*12)
$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)., (*13)
It's also possible to run a map over the matrix:, (*14)
$squaredElements = $matrix->map(function($element, $row, $column, $matrix) {
return $element * $element
});
Submatrices may be extracted with sliceColumns($offset, $length) and sliceRows($offset, $length). The semantics of
the arguments are the same as PHP's array_slice., (*15)
Similarly, spliceColumns($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., (*16)
If you need to combine together matrices, you can do so by calling the concatenation methods:, (*17)
$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., (*18)
Vector
As with Matrix, import the class into your current namespace:, (*19)
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., (*20)
Creating a Vector differs from creating a Matrix only in that the constructor takes an array of scalars, rather
than an array of arrays:, (*21)
$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., (*22)
If you need to cast a Matrix into a Vector, call the factory method fromMatrix():, (*23)
$vector = Vector::fromMatrix($matrix);
toArray() is overridden to return an array of scalars to mirror how the constructor works. It is equivalent to
calling $matrix->toArray()[0] on a Matrix instance., (*24)
getSize() is provided as an alias for getColumnCount(). sum() will return the sum of the Vector elements,
while dotProduct($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)., (*25)
For measures of vector magnitude, l1Norm(), l2Norm(), and maxNorm() are all available, with length() as
an alias for l2Norm()., (*26)
Links to relevant Wikipedia articles are provided in the function documentation for additional detail., (*27)
Change-log
-
3.0.0, (*28)
- 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, (*29)
- 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, (*30)
- Fix a bug involving inheritance with
map() on Vector.
-
2.1.0, (*31)
- Add
Vector as a subclass of Matrix. Thanks to battlecook for this contribution.
-
2.0.0, (*32)
- 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, (*33)
- Deprecate
__toString() magic method.
- Deprecate
isSymmetric().
-
1.3.1, (*34)
- Deprecate use of the
ArrayAccess interface.
- More internal code style fixes.
-
1.3.0, (*35)
- 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, (*36)
- Added
concatenateBottom($other)
- Added
concatencateRight($other)
-
1.1.0, (*37)
-
1.0.0, (*38)
- 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, (*39)
- Fix several bugs with the Cholesky decomposition and inverse.
-
0.9.0, (*40)
- 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, (*41)
- 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, (*42)
- 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, (*43)
- Created the Matrix type
- Scalar Addition
- Scalar Subtraction
- Scalar Multiplication
- Matrix Addition
- Matrix Subtraction
- Matrix Multiplication
- Inverse
- Adjoint
- Determinant
- Trace
- Transpose
- Submatrix
- Map
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