Mathematical Functions

Reference for mathematical operations including arithmetic, transcendental functions, powers, and rounding.

---

add()

public function add(float|int|NDArray $other): NDArray

Add another array or scalar to this array element-wise.

Parameters

Parameter	Type	Description
$other	float|int|NDArray	Array or scalar to add.

Returns

• NDArray - New array with element-wise sum.

Examples

// Array + Array
$a = NDArray::array([1, 2, 3]);
$b = NDArray::array([4, 5, 6]);
$result = $a->add($b);
print_r($result->toArray());
// Output: [5, 7, 9]

// Array + Scalar
$result = $a->add(10);
print_r($result->toArray());
// Output: [11, 12, 13]

---

subtract()

public function subtract(float|int|NDArray $other): NDArray

Subtract another array or scalar from this array element-wise.

Parameters

Parameter	Type	Description
$other	float|int|NDArray	Array or scalar to subtract.

Returns

• NDArray - New array with element-wise difference.

Examples

$a = NDArray::array([10, 20, 30]);
$b = NDArray::array([1, 2, 3]);
$result = $a->subtract($b);
print_r($result->toArray());
// Output: [9, 18, 27]

// Scalar subtraction
$result = $a->subtract(5);
print_r($result->toArray());
// Output: [5, 15, 25]

---

multiply()

public function multiply(float|int|NDArray $other): NDArray

Multiply this array by another array or scalar element-wise.

Parameters

Parameter	Type	Description
$other	float|int|NDArray	Array or scalar to multiply by.

Returns

• NDArray - New array with element-wise product.

Examples

$a = NDArray::array([2, 3, 4]);
$b = NDArray::array([5, 6, 7]);
$result = $a->multiply($b);
print_r($result->toArray());
// Output: [10, 18, 28]

// Scalar multiplication
$result = $a->multiply(3);
print_r($result->toArray());
// Output: [6, 9, 12]

---

divide()

public function divide(float|int|NDArray $other): NDArray

Divide this array by another array or scalar element-wise.

Parameters

Parameter	Type	Description
$other	float|int|NDArray	Array or scalar to divide by.

Returns

• NDArray - New array with element-wise quotient.

Examples

$a = NDArray::array([10.0, 20.0, 30.0]);
$b = NDArray::array([2.0, 4.0, 5.0]);
$result = $a->divide($b);
print_r($result->toArray());
// Output: [5.0, 5.0, 6.0]

// Scalar division
$result = $a->divide(2);
print_r($result->toArray());
// Output: [5.0, 10.0, 15.0]

---

rem()

public function rem(float|int|NDArray $other): NDArray

Compute remainder (modulo) with another array or scalar element-wise.

Parameters

Parameter	Type	Description
$other	float|int|NDArray	Array or scalar.

Returns

• NDArray - New array with element-wise remainder.

Examples

$a = NDArray::array([10, 15, 20]);
$b = NDArray::array([3, 4, 6]);
$result = $a->rem($b);
print_r($result->toArray());
// Output: [1, 3, 2]

// Scalar modulo
$result = $a->rem(7);
print_r($result->toArray());
// Output: [3, 1, 6]

---

mod()

public function mod(float|int|NDArray $other): NDArray

Compute modulo with another array or scalar element-wise.

Alias for rem().

Parameters

Parameter	Type	Description
$other	float|int|NDArray	Array or scalar.

Returns

• NDArray - New array with element-wise modulo.

Examples

$a = NDArray::array([10, 15, 20]);
$result = $a->mod(7);
print_r($result->toArray());
// Output: [3, 1, 6]

---

abs()

public function abs(): NDArray

Compute absolute value element-wise.

Returns

• NDArray - New array with absolute values.

Examples

$arr = NDArray::array([-1, -2, 3, -4]);
$result = $arr->abs();
print_r($result->toArray());
// Output: [1, 2, 3, 4]

---

negative()

public function negative(): NDArray

Compute negation element-wise (-$a).

Not supported for unsigned integers or bool.

Returns

• NDArray - New array with negated values.

Raises

• InvalidArgumentException - For unsigned integer or boolean arrays.

Examples

$arr = NDArray::array([1, -2, 3, -4]);
$result = $arr->negative();
print_r($result->toArray());
// Output: [-1, 2, -3, 4]

---

sqrt()

public function sqrt(): NDArray

Compute square root element-wise.

Returns

• NDArray - New array with square roots.

Examples

$arr = NDArray::array([1.0, 4.0, 9.0, 16.0]);
$result = $arr->sqrt();
print_r($result->toArray());
// Output: [1.0, 2.0, 3.0, 4.0]

---

cbrt()

public function cbrt(): NDArray

Compute cube root element-wise.

Returns

• NDArray - New array with cube roots.

Examples

$arr = NDArray::array([1.0, 8.0, 27.0, 64.0]);
$result = $arr->cbrt();
print_r($result->toArray());
// Output: [1.0, 2.0, 3.0, 4.0]

---

exp()

public function exp(): NDArray

Compute exponential (e^x) element-wise.

Returns

• NDArray - New array with exponential values.

Examples

$arr = NDArray::array([0.0, 1.0, 2.0]);
$result = $arr->exp();
print_r($result->toArray());
// Output: [1.0, 2.718..., 7.389...]

---

exp2()

public function exp2(): NDArray

Compute base-2 exponential (2^x) element-wise.

Returns

• NDArray - New array with base-2 exponential values.

Examples

$arr = NDArray::array([0, 1, 2, 3]);
$result = $arr->exp2();
print_r($result->toArray());
// Output: [1, 2, 4, 8]

---

log()

public function log(): NDArray

Compute natural logarithm element-wise.

Returns

• NDArray - New array with natural logarithm values.

Examples

$arr = NDArray::array([1.0, 2.718, 7.389]);
$result = $arr->log();
print_r($result->toArray());
// Output: [0.0, 1.0, 2.0]

---

ln()

public function ln(): NDArray

Compute natural logarithm element-wise.

Alias for log().

Returns

• NDArray - New array with natural logarithm values.

Examples

$arr = NDArray::array([1.0, 2.718, 7.389]);
$result = $arr->ln();
print_r($result->toArray());
// Output: [0.0, 1.0, 2.0]

---

log2()

public function log2(): NDArray

Compute base-2 logarithm element-wise.

Returns

• NDArray - New array with base-2 logarithm values.

Examples

$arr = NDArray::array([1, 2, 4, 8, 16]);
$result = $arr->log2();
print_r($result->toArray());
// Output: [0, 1, 2, 3, 4]

---

log10()

public function log10(): NDArray

Compute base-10 logarithm element-wise.

Returns

• NDArray - New array with base-10 logarithm values.

Examples

$arr = NDArray::array([1, 10, 100, 1000]);
$result = $arr->log10();
print_r($result->toArray());
// Output: [0, 1, 2, 3]

---

ln1p()

public function ln1p(): NDArray

Compute ln(1+x) element-wise.

More accurate than log(1+x) for small x.

Returns

• NDArray - New array with ln(1+x) values.

Examples

$arr = NDArray::array([0.0, 0.1, 0.01]);
$result = $arr->ln1p();
print_r($result->toArray());
// Output: [0.0, 0.0953..., 0.00995...]

---

sin()

public function sin(): NDArray

Compute sine element-wise.

Returns

• NDArray - New array with sine values.

Examples

$arr = NDArray::array([0, M_PI/2, M_PI]);
$result = $arr->sin();
print_r($result->toArray());
// Output: [0.0, 1.0, 0.0]

---

cos()

public function cos(): NDArray

Compute cosine element-wise.

Returns

• NDArray - New array with cosine values.

Examples

$arr = NDArray::array([0, M_PI/2, M_PI]);
$result = $arr->cos();
print_r($result->toArray());
// Output: [1.0, 0.0, -1.0]

---

tan()

public function tan(): NDArray

Compute tangent element-wise.

Returns

• NDArray - New array with tangent values.

Examples

$arr = NDArray::array([0, M_PI/4, M_PI/2]);
$result = $arr->tan();
print_r($result->toArray());
// Output: [0.0, 1.0, very large number]

---

asin()

public function asin(): NDArray

Compute arc sine element-wise.

Returns

• NDArray - New array with arc sine values.

Examples

$arr = NDArray::array([0.0, 0.5, 1.0]);
$result = $arr->asin();
print_r($result->toArray());
// Output: [0.0, 0.523..., 1.570...]

---

acos()

public function acos(): NDArray

Compute arc cosine element-wise.

Returns

• NDArray - New array with arc cosine values.

Examples

$arr = NDArray::array([0.0, 0.5, 1.0]);
$result = $arr->acos();
print_r($result->toArray());
// Output: [1.570..., 1.047..., 0.0]

---

atan()

public function atan(): NDArray

Compute arc tangent element-wise.

Returns

• NDArray - New array with arc tangent values.

Examples

$arr = NDArray::array([0.0, 1.0, -1.0]);
$result = $arr->atan();
print_r($result->toArray());
// Output: [0.0, 0.785..., -0.785...]

---

sinh()

public function sinh(): NDArray

Compute hyperbolic sine element-wise.

Returns

• NDArray - New array with hyperbolic sine values.

Examples

$arr = NDArray::array([0.0, 1.0, 2.0]);
$result = $arr->sinh();
print_r($result->toArray());
// Output: [0.0, 1.175..., 3.626...]

---

cosh()

public function cosh(): NDArray

Compute hyperbolic cosine element-wise.

Returns

• NDArray - New array with hyperbolic cosine values.

Examples

$arr = NDArray::array([0.0, 1.0, 2.0]);
$result = $arr->cosh();
print_r($result->toArray());
// Output: [1.0, 1.543..., 3.762...]

---

tanh()

public function tanh(): NDArray

Compute hyperbolic tangent element-wise.

Returns

• NDArray - New array with hyperbolic tangent values.

Examples

$arr = NDArray::array([0.0, 1.0, 2.0]);
$result = $arr->tanh();
print_r($result->toArray());
// Output: [0.0, 0.761..., 0.964...]

---

toDegrees()

public function toDegrees(): NDArray

Convert radians to degrees element-wise.

Returns

• NDArray - New array with degree values.

Examples

$arr = NDArray::array([0, M_PI/2, M_PI]);
$result = $arr->toDegrees();
print_r($result->toArray());
// Output: [0, 90, 180]

---

toRadians()

public function toRadians(): NDArray

Convert degrees to radians element-wise.

Returns

• NDArray - New array with radian values.

Examples

$arr = NDArray::array([0, 90, 180]);
$result = $arr->toRadians();
print_r($result->toArray());
// Output: [0, 1.570..., 3.141...]

---

floor()

public function floor(): NDArray

Compute floor element-wise (round down to nearest integer).

Returns

• NDArray - New array with floor values.

Examples

$arr = NDArray::array([1.2, 2.5, 3.7, -1.2]);
$result = $arr->floor();
print_r($result->toArray());
// Output: [1, 2, 3, -2]

---

ceil()

public function ceil(): NDArray

Compute ceiling element-wise (round up to nearest integer).

Returns

• NDArray - New array with ceiling values.

Examples

$arr = NDArray::array([1.2, 2.5, 3.7, -1.2]);
$result = $arr->ceil();
print_r($result->toArray());
// Output: [2, 3, 4, -1]

---

round()

public function round(): NDArray

Compute round element-wise (round to nearest integer).

Returns

• NDArray - New array with rounded values.

Examples

$arr = NDArray::array([1.2, 2.5, 3.7, -1.5]);
$result = $arr->round();
print_r($result->toArray());
// Output: [1, 2, 4, -2]

---

pow2()

public function pow2(): NDArray

Compute x^2 (square) element-wise.

Returns

• NDArray - New array with squared values.

Examples

$arr = NDArray::array([1, 2, 3, 4]);
$result = $arr->pow2();
print_r($result->toArray());
// Output: [1, 4, 9, 16]

---

powi()

public function powi(int $exp): NDArray

Compute x^n where n is an integer, element-wise.

Generally faster than powf() for integer exponents.

Parameters

Parameter	Type	Description
$exp	int	Integer exponent.

Returns

• NDArray - New array with x^n values.

Examples

$arr = NDArray::array([2, 3, 4]);
$result = $arr->powi(3);
print_r($result->toArray());
// Output: [8, 27, 64]

---

powf()

public function powf(float $exp): NDArray

Compute x^y where y is a float, element-wise.

Parameters

Parameter	Type	Description
$exp	float	Float exponent.

Returns

• NDArray - New array with x^y values.

Examples

$arr = NDArray::array([4.0, 9.0, 16.0]);
$result = $arr->powf(0.5);
print_r($result->toArray());
// Output: [2.0, 3.0, 4.0]

---

recip()

public function recip(): NDArray

Compute reciprocal (1/x) element-wise.

Returns

• NDArray - New array with reciprocal values.

Examples

$arr = NDArray::array([1.0, 2.0, 4.0, 0.5]);
$result = $arr->recip();
print_r($result->toArray());
// Output: [1.0, 0.5, 0.25, 2.0]

---

signum()

public function signum(): NDArray

Compute signum element-wise.

Returns -1 for negative values, 0 for zero, and 1 for positive values.

Returns

• NDArray - New array with signum values.

Examples

$arr = NDArray::array([-5, -1, 0, 1, 5]);
$result = $arr->signum();
print_r($result->toArray());
// Output: [-1, -1, 0, 1, 1]

---

hypot()

public function hypot(float $other): NDArray

Compute hypotenuse element-wise with a scalar value.

Parameters

Parameter	Type	Description
$other	float	Scalar value.

Returns

• NDArray - New array with hypotenuse values (sqrt(x^2 + y^2)).

Examples

$arr = NDArray::array([3.0, 4.0, 5.0]);
$result = $arr->hypot(4.0);
print_r($result->toArray());
// Output: [5.0, 5.656..., 6.403...]

---

clamp()

public function clamp(float|int $min, float|int $max): NDArray

Clamp (clip) array values to a specified range.

Values outside [min, max] are set to the nearest boundary.

Parameters

Parameter	Type	Description
$min	float|int	Minimum value.
$max	float|int	Maximum value.

Returns

• NDArray - New array with clamped values.

Raises

• InvalidArgumentException - If min > max.

Examples

$arr = NDArray::array([-5, 0, 5, 10, 15]);
$result = $arr->clamp(0, 10);
print_r($result->toArray());
// Output: [0, 0, 5, 10, 10]

---

clip()

public function clip(float|int $min, float|int $max): NDArray

Clip array values to a specified range.

Alias for clamp().

Parameters

Parameter	Type	Description
$min	float|int	Minimum value.
$max	float|int	Maximum value.

Returns

• NDArray - New array with clipped values.

Raises

• InvalidArgumentException - If min > max.

Examples

$arr = NDArray::array([-5, 0, 5, 10, 15]);
$result = $arr->clip(0, 10);
print_r($result->toArray());
// Output: [0, 0, 5, 10, 10]

---

minimum()

public function minimum(NDArray $other): NDArray

Element-wise minimum of two arrays.

Compares two arrays element-wise and returns a new array containing the smaller value at each position. Supports broadcasting.

Parameters

Parameter	Type	Description
$other	NDArray	The array to compare with.

Returns

• NDArray - New array with element-wise minimum values.

Examples

$a = NDArray::array([1, 5, 3, 8]);
$b = NDArray::array([2, 4, 6, 7]);
$result = $a->minimum($b);
print_r($result->toArray());
// Output: [1, 4, 3, 7]

// With broadcasting
$a = NDArray::array([[1, 2, 3], [4, 5, 6]]);
$b = NDArray::array([2, 2, 2]);
$result = $a->minimum($b);
print_r($result->toArray());
// Output: [[1, 2, 2], [2, 2, 2]]

---

maximum()

public function maximum(NDArray $other): NDArray

Element-wise maximum of two arrays.

Compares two arrays element-wise and returns a new array containing the larger value at each position. Supports broadcasting.

Parameters

Parameter	Type	Description
$other	NDArray	The array to compare with.

Returns

• NDArray - New array with element-wise maximum values.

Examples

$a = NDArray::array([1, 5, 3, 8]);
$b = NDArray::array([2, 4, 6, 7]);
$result = $a->maximum($b);
print_r($result->toArray());
// Output: [2, 5, 6, 8]

// With broadcasting
$a = NDArray::array([[1, 2, 3], [4, 5, 6]]);
$b = NDArray::array([2, 2, 2]);
$result = $a->maximum($b);
print_r($result->toArray());
// Output: [[2, 2, 3], [4, 5, 6]]

---

sigmoid()

public function sigmoid(): NDArray

Compute sigmoid element-wise: 1 / (1 + exp(-x)).

Returns

• NDArray - New array with sigmoid values.

Examples

$arr = NDArray::array([0.0, 1.0, -1.0, 2.0, -2.0]);
$result = $arr->sigmoid();
print_r($result->toArray());
// Output: [0.5, 0.731..., 0.268..., 0.880..., 0.119...]

---

softmax()

public function softmax(int $axis = -1): NDArray

Compute softmax along axis: exp(x - max) / sum(exp(x - max)).

Numerically stable. Default axis -1 (last axis) for typical logits.

Parameters

Parameter	Type	Description
$axis	int	Axis along which to compute softmax. Optional. Default: -1.

Returns

• NDArray - New array with softmax values (sums to 1 along axis).

Examples

$arr = NDArray::array([[1.0, 2.0, 3.0], [1.0, 2.0, 3.0]]);
$result = $arr->softmax(axis: 1);
print_r($result->toArray());
// Output: [[0.090..., 0.244..., 0.665...], [0.090..., 0.244..., 0.665...]]

---

Summary Table

Arithmetic Operations

Method	Operation	Example
add()	Addition	[1, 2] + [3, 4] → [4, 6]
subtract()	Subtraction	[5, 6] - [1, 2] → [4, 4]
multiply()	Multiplication	[2, 3] * [4, 5] → [8, 15]
divide()	Division	[10, 20] / [2, 4] → [5, 5]
rem() / mod()	Modulo	[10, 15] % [3, 4] → [1, 3]
abs()	Absolute value	abs([-1, -2]) → [1, 2]
negative()	Negation	-[1, -2] → [-1, 2]

Powers and Roots

Method	Operation	Example
sqrt()	Square root	sqrt([4, 9]) → [2, 3]
cbrt()	Cube root	cbrt([8, 27]) → [2, 3]
pow2()	Square	pow2([2, 3]) → [4, 9]
powi()	Integer power	powi([2, 3], 3) → [8, 27]
powf()	Float power	powf([4, 9], 0.5) → [2, 3]
recip()	Reciprocal	recip([2, 4]) → [0.5, 0.25]

Exponentials and Logarithms

Method	Operation	Example
exp()	e^x	exp([0, 1]) → [1, 2.718]
exp2()	2^x	exp2([0, 3]) → [1, 8]
log() / ln()	Natural log	log([1, 2.718]) → [0, 1]
log2()	Base-2 log	log2([1, 8]) → [0, 3]
log10()	Base-10 log	log10([1, 100]) → [0, 2]
ln1p()	ln(1+x)	ln1p([0, 0.1]) → [0, 0.095]

Trigonometric Functions

Method	Operation	Example
sin()	Sine	sin([0, π/2]) → [0, 1]
cos()	Cosine	cos([0, π]) → [1, -1]
tan()	Tangent	tan([0, π/4]) → [0, 1]
asin()	Arc sine	asin([0, 1]) → [0, π/2]
acos()	Arc cosine	acos([1, 0]) → [0, π/2]
atan()	Arc tangent	atan([0, 1]) → [0, π/4]
sinh()	Hyperbolic sine	sinh([0, 1]) → [0, 1.175]
cosh()	Hyperbolic cosine	cosh([0, 1]) → [1, 1.543]
tanh()	Hyperbolic tangent	tanh([0, 1]) → [0, 0.762]
toDegrees()	Radians to degrees	toDegrees([0, π]) → [0, 180]
toRadians()	Degrees to radians	toRadians([0, 90]) → [0, π/2]

Rounding Functions

Method	Operation	Example
floor()	Round down	floor([1.7, -1.2]) → [1, -2]
ceil()	Round up	ceil([1.2, -1.7]) → [2, -1]
round()	Round nearest	round([1.4, 1.5]) → [1, 2]

Miscellaneous

Method	Operation	Example
signum()	Sign	signum([-5, 0, 3]) → [-1, 0, 1]
hypot()	Hypotenuse	hypot([3, 4], 4) → [5, 5.657]
clamp() / clip()	Clip range	clamp([-5, 5, 15], 0, 10) → [0, 5, 10]
minimum()	Element-wise minimum	minimum([1, 5], [2, 4]) → [1, 4]
maximum()	Element-wise maximum	maximum([1, 5], [2, 4]) → [2, 5]
sigmoid()	Sigmoid	sigmoid([0, 1]) → [0.5, 0.731]
softmax()	Softmax	softmax([1, 2, 3]) → [0.09, 0.24, 0.67]

---

Next Steps

• Logic Functions - Comparison operations
• Bitwise Operations - Bitwise operations on integers
• Statistics - Statistical reductions