---
icon: package
label: linalg
---

Provide `mat3x3`, `vec2`, `vec3` and `vec4` types.

This classes adopt `torch`'s naming convention. Methods with `_` suffix will modify the instance itself.

https://github.com/pocketpy/pocketpy/blob/main/include/typings/linalg.pyi

```python
from typing import overload
from c import _StructLike, float_p

class vec2:
    x: float
    y: float

    def __init__(self, x: float, y: float) -> None: ...
    def __add__(self, other: vec2) -> vec2: ...
    def __sub__(self, other: vec2) -> vec2: ...
    def __getitem__(self, index: int) -> float: ...

    @overload
    def __mul__(self, other: float) -> vec2: ...
    @overload
    def __mul__(self, other: vec2) -> vec2: ...

    def __rmul__(self, other: float) -> vec2: ...
    def __truediv__(self, other: float) -> vec2: ...
    def dot(self, other: vec2) -> float: ...
    def cross(self, other: vec2) -> float: ...
    def length(self) -> float: ...
    def length_squared(self) -> float: ...
    def normalize(self) -> vec2: ...
    def rotate(self, radians: float) -> vec2: ...

    @staticmethod
    def angle(__from: vec2, __to: vec2) -> float:
        """Returns the angle in radians between vectors `from` and `to`.

        The result range is `[-pi, pi]`.
        
        + if y axis is top to bottom, positive value means clockwise
        + if y axis is bottom to top, positive value means counter-clockwise
        """

    @staticmethod
    def smooth_damp(current: vec2, target: vec2, current_velocity: vec2, smooth_time: float, max_speed: float, delta_time: float) -> tuple[vec2, vec2]:
        ...

class vec3:
    x: float
    y: float
    z: float

    def __init__(self, x: float, y: float, z: float) -> None: ...
    def __add__(self, other: vec3) -> vec3: ...
    def __sub__(self, other: vec3) -> vec3: ...
    def __getitem__(self, index: int) -> float: ...

    @overload
    def __mul__(self, other: float) -> vec3: ...
    @overload
    def __mul__(self, other: vec3) -> vec3: ...

    def __rmul__(self, other: float) -> vec3: ...
    def __truediv__(self, other: float) -> vec3: ...
    def dot(self, other: vec3) -> float: ...
    def cross(self, other: vec3) -> float: ...
    def length(self) -> float: ...
    def length_squared(self) -> float: ...
    def normalize(self) -> vec3: ...

class vec4(_StructLike['vec4']):
    x: float
    y: float
    z: float
    w: float

    def __init__(self, x: float, y: float, z: float, w: float) -> None: ...
    def __add__(self, other: vec4) -> vec4: ...
    def __sub__(self, other: vec4) -> vec4: ...
    def __getitem__(self, index: int) -> float: ...

    @overload
    def __mul__(self, other: float) -> vec4: ...
    @overload
    def __mul__(self, other: vec4) -> vec4: ...

    def __rmul__(self, other: float) -> vec4: ...
    def __truediv__(self, other: float) -> vec4: ...
    def dot(self, other: vec4) -> float: ...
    def length(self) -> float: ...
    def length_squared(self) -> float: ...
    def normalize(self) -> vec4: ...

    def copy_(self, other: vec4) -> None: ...
    def normalize_(self) -> None: ...

class mat3x3(_StructLike['mat3x3']):
    _11: float
    _12: float
    _13: float
    _21: float
    _22: float
    _23: float
    _31: float
    _32: float
    _33: float

    @overload
    def __init__(self) -> None: ...
    @overload
    def __init__(self, _11, _12, _13, _21, _22, _23, _31, _32, _33) -> None: ...
    @overload
    def __init__(self, a: list[float]): ...

    def determinant(self) -> float: ...
    def inverse(self) -> mat3x3: ...
    def transpose(self) -> mat3x3: ...

    def __getitem__(self, index: tuple[int, int]) -> float: ...
    def __setitem__(self, index: tuple[int, int], value: float) -> None: ...
    def __add__(self, other: mat3x3) -> mat3x3: ...
    def __sub__(self, other: mat3x3) -> mat3x3: ...
    def __mul__(self, other: float) -> mat3x3: ...
    def __rmul__(self, other: float) -> mat3x3: ...
    def __truediv__(self, other: float) -> mat3x3: ...

    def __invert__(self) -> mat3x3: ...
    @overload
    def __matmul__(self, other: mat3x3) -> mat3x3: ...
    @overload
    def __matmul__(self, other: vec3) -> vec3: ...

    def matmul(self, other: mat3x3, out: mat3x3 = None) -> mat3x3 | None: ...

    def copy_(self, other: mat3x3) -> None: ...
    def inverse_(self) -> None: ...
    def transpose_(self) -> None: ...

    @staticmethod
    def zeros() -> mat3x3: ...
    @staticmethod
    def ones() -> mat3x3: ...
    @staticmethod
    def identity() -> mat3x3: ...

    # affine transformations
    @staticmethod
    def trs(t: vec2, r: float, s: vec2) -> mat3x3: ...

    def copy_trs_(self, t: vec2, r: float, s: vec2) -> None: ...
    def copy_t_(self, t: vec2) -> None: ...
    def copy_r_(self, r: float) -> None: ...
    def copy_s_(self, s: vec2) -> None: ...

    def _t(self) -> vec2: ...
    def _r(self) -> float: ...
    def _s(self) -> vec2: ...

    def is_affine(self) -> bool: ...

    def transform_point(self, p: vec2) -> vec2: ...
    def transform_vector(self, v: vec2) -> vec2: ...
    def inverse_transform_point(self, p: vec2) -> vec2: ...
    def inverse_transform_vector(self, v: vec2) -> vec2: ...

vec4_p = float_p
mat3x3_p = float_p

```
