Linear Algebra Methods

Reference for linear algebra operations.

norm()

public function norm(
    float|int|string|null $ord = null,
    ?int $axis = null,
    bool $keepdims = false
): float|NDArray

Compute vector or matrix norm.

Parameters

Parameter	Type	Description
$ord	float|int|string|null	Norm order. Optional. Default: null.
$axis	int|null	Reduction axis. If null, reduces all elements. Optional. Default: null.
$keepdims	bool	Keep reduced axis with size 1 (axis mode only). Optional. Default: false.

Returns

• float|NDArray - Scalar if axis is null, otherwise an NDArray.

Raises

• InvalidArgumentException - If norm order is unsupported or incompatible with array dimensions.

Supported Orders

Order	Description
null	L2 norm (Euclidean), or Frobenius for 2D matrices
1	L1 norm (sum of absolute values)
2	L2 norm (Euclidean)
INF	Infinity norm (maximum absolute value)
-INF	Negative infinity norm (minimum absolute value)
'fro'	Frobenius norm (matrix only, axis must be null)

Examples

$vector = NDArray::array([3, 4]);

// L2 norm (Euclidean)
echo $vector->norm();
// Output: 5.0

// L1 norm
echo $vector->norm(1);
// Output: 7.0

// Infinity norm
echo $vector->norm('inf');
// Output: 4.0

// Matrix norm
$matrix = NDArray::array([
    [1, 2],
    [3, 4]
]);
echo $matrix->norm();
// Output: 5.477... (Frobenius norm)

dot()

public function dot(NDArray $other): NDArray

Compute dot product of two arrays.

For 1D arrays: returns scalar For 2D arrays: returns matrix multiplication

Parameters

Parameter	Type	Description
$other	NDArray	The other array.

Returns

• NDArray - Dot product result.

Examples

// Matrix multiplication
$a = NDArray::array([
    [1, 2],
    [3, 4]
]);

$b = NDArray::array([
    [5, 6],
    [7, 8]
]);

$c = $a->dot($b);
print_r($c->toArray());
// Output: [[19, 22], [43, 50]]

// Vector dot product
$v1 = NDArray::array([1, 2, 3]);
$v2 = NDArray::array([4, 5, 6]);
$result = $v1->dot($v2);
print_r($result->toArray());
// Output: 32

matmul()

public function matmul(NDArray $other): NDArray

Compute matrix multiplication.

Requires both arrays to be at least 2D.

Parameters

Parameter	Type	Description
$other	NDArray	The other array.

Returns

• NDArray - Matrix multiplication result.

Examples

$a = NDArray::array([
    [1, 2],
    [3, 4]
]);

$b = NDArray::array([
    [5, 6],
    [7, 8]
]);

$c = $a->matmul($b);
print_r($c->toArray());
// Output: [[19, 22], [43, 50]]

diagonal()

public function diagonal(): NDArray

Extract diagonal elements from a 2D array.

Returns a 1D array containing the diagonal.

Returns

• NDArray - 1D array of diagonal elements.

Examples

$matrix = NDArray::array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]);

$diag = $matrix->diagonal();
print_r($diag->toArray());
// Output: [1, 5, 9]

trace()

public function trace(): NDArray

Compute trace (sum of diagonal elements).

Returns a scalar array.

Returns

• NDArray - Scalar array containing the trace.

Examples

$matrix = NDArray::array([
    [1, 2, 3],
    [4, 5, 6],
    [7, 8, 9]
]);

$tr = $matrix->trace();
print_r($tr->toArray());
// Output: 15 (1 + 5 + 9)