# Source code for kornia.geometry.linalg

from __future__ import annotations

import torch

from kornia.core import Tensor, zeros_like
from kornia.core.check import KORNIA_CHECK, KORNIA_CHECK_IS_TENSOR, KORNIA_CHECK_SHAPE
from kornia.geometry.conversions import convert_points_from_homogeneous, convert_points_to_homogeneous

__all__ = [
"compose_transformations",
"relative_transformation",
"inverse_transformation",
"transform_points",
"point_line_distance",
"squared_norm",
"batched_squared_norm",
"batched_dot_product",
"euclidean_distance",
]

[docs]def compose_transformations(trans_01: Tensor, trans_12: Tensor) -> Tensor:
r"""Function that composes two homogeneous transformations.

.. math::
T_0^{2} = \begin{bmatrix} R_0^1 R_1^{2} & R_0^{1} t_1^{2} + t_0^{1} \\
\mathbf{0} & 1\end{bmatrix}

Args:
trans_01: tensor with the homogeneous transformation from
a reference frame 1 respect to a frame 0. The tensor has must have a
shape of :math:(N, 4, 4) or :math:(4, 4).
trans_12: tensor with the homogeneous transformation from
a reference frame 2 respect to a frame 1. The tensor has must have a
shape of :math:(N, 4, 4) or :math:(4, 4).

Returns:
the transformation between the two frames with shape :math:(N, 4, 4) or :math:(4, 4).

Example::
>>> trans_01 = torch.eye(4)  # 4x4
>>> trans_12 = torch.eye(4)  # 4x4
>>> trans_02 = compose_transformations(trans_01, trans_12)  # 4x4
"""
KORNIA_CHECK_IS_TENSOR(trans_01)
KORNIA_CHECK_IS_TENSOR(trans_12)

if not ((trans_01.dim() in (2, 3)) and (trans_01.shape[-2:] == (4, 4))):
raise ValueError(f"Input trans_01 must be a of the shape Nx4x4 or 4x4. Got {trans_01.shape}")

if not ((trans_12.dim() in (2, 3)) and (trans_12.shape[-2:] == (4, 4))):
raise ValueError(f"Input trans_12 must be a of the shape Nx4x4 or 4x4. Got {trans_12.shape}")

if not trans_01.dim() == trans_12.dim():
raise ValueError(f"Input number of dims must match. Got {trans_01.dim()} and {trans_12.dim()}")

# unpack input data
rmat_01: Tensor = trans_01[..., :3, :3]  # Nx3x3
rmat_12: Tensor = trans_12[..., :3, :3]  # Nx3x3
tvec_01: Tensor = trans_01[..., :3, -1:]  # Nx3x1
tvec_12: Tensor = trans_12[..., :3, -1:]  # Nx3x1

# compute the actual transforms composition
rmat_02: Tensor = torch.matmul(rmat_01, rmat_12)
tvec_02: Tensor = torch.matmul(rmat_01, tvec_12) + tvec_01

# pack output tensor
trans_02: Tensor = zeros_like(trans_01)
trans_02[..., :3, 0:3] += rmat_02
trans_02[..., :3, -1:] += tvec_02
trans_02[..., -1, -1:] += 1.0
return trans_02

[docs]def inverse_transformation(trans_12: Tensor) -> Tensor:
r"""Function that inverts a 4x4 homogeneous transformation.

:math:T_1^{2} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1 \end{bmatrix}

The inverse transformation is computed as follows:

.. math::

T_2^{1} = (T_1^{2})^{-1} = \begin{bmatrix} R_1^T & -R_1^T t_1 \\
\mathbf{0} & 1\end{bmatrix}

Args:
trans_12: transformation tensor of shape :math:(N, 4, 4) or :math:(4, 4).

Returns:
tensor with inverted transformations with shape :math:(N, 4, 4) or :math:(4, 4).

Example:
>>> trans_12 = torch.rand(1, 4, 4)  # Nx4x4
>>> trans_21 = inverse_transformation(trans_12)  # Nx4x4
"""
KORNIA_CHECK_IS_TENSOR(trans_12)

if not ((trans_12.dim() in (2, 3)) and (trans_12.shape[-2:] == (4, 4))):
raise ValueError(f"Input size must be a Nx4x4 or 4x4. Got {trans_12.shape}")
# unpack input tensor
rmat_12 = trans_12[..., :3, 0:3]  # Nx3x3
tvec_12 = trans_12[..., :3, 3:4]  # Nx3x1

# compute the actual inverse
rmat_21 = torch.transpose(rmat_12, -1, -2)
tvec_21 = torch.matmul(-rmat_21, tvec_12)

# pack to output tensor
trans_21 = zeros_like(trans_12)
trans_21[..., :3, 0:3] += rmat_21
trans_21[..., :3, -1:] += tvec_21
trans_21[..., -1, -1:] += 1.0
return trans_21

[docs]def relative_transformation(trans_01: Tensor, trans_02: Tensor) -> Tensor:
r"""Function that computes the relative homogeneous transformation from a reference transformation.

:math:T_1^{0} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1 \end{bmatrix} to destination :math:T_2^{0} =
\begin{bmatrix} R_2 & t_2 \\ \mathbf{0} & 1 \end{bmatrix}.

The relative transformation is computed as follows:

.. math::

T_1^{2} = (T_0^{1})^{-1} \cdot T_0^{2}

Args:
trans_01: reference transformation tensor of shape :math:(N, 4, 4) or :math:(4, 4).
trans_02: destination transformation tensor of shape :math:(N, 4, 4) or :math:(4, 4).

Returns:
the relative transformation between the transformations with shape :math:(N, 4, 4) or :math:(4, 4).

Example::
>>> trans_01 = torch.eye(4)  # 4x4
>>> trans_02 = torch.eye(4)  # 4x4
>>> trans_12 = relative_transformation(trans_01, trans_02)  # 4x4
"""
KORNIA_CHECK_IS_TENSOR(trans_01)
KORNIA_CHECK_IS_TENSOR(trans_02)
if not ((trans_01.dim() in (2, 3)) and (trans_01.shape[-2:] == (4, 4))):
raise ValueError(f"Input must be a of the shape Nx4x4 or 4x4. Got {trans_01.shape}")
if not ((trans_02.dim() in (2, 3)) and (trans_02.shape[-2:] == (4, 4))):
raise ValueError(f"Input must be a of the shape Nx4x4 or 4x4. Got {trans_02.shape}")
if not trans_01.dim() == trans_02.dim():
raise ValueError(f"Input number of dims must match. Got {trans_01.dim()} and {trans_02.dim()}")

trans_10 = inverse_transformation(trans_01)
trans_12 = compose_transformations(trans_10, trans_02)
return trans_12

[docs]def transform_points(trans_01: Tensor, points_1: Tensor) -> Tensor:
r"""Function that applies transformations to a set of points.

Args:
trans_01: tensor for transformations of shape
:math:(B, D+1, D+1).
points_1: tensor of points of shape :math:(B, N, D).
Returns:
a tensor of N-dimensional points.

Shape:
- Output: :math:(B, N, D)

Examples:

>>> points_1 = torch.rand(2, 4, 3)  # BxNx3
>>> trans_01 = torch.eye(4).view(1, 4, 4)  # Bx4x4
>>> points_0 = transform_points(trans_01, points_1)  # BxNx3
"""
KORNIA_CHECK_IS_TENSOR(trans_01)
KORNIA_CHECK_IS_TENSOR(points_1)
if not trans_01.shape[0] == points_1.shape[0] and trans_01.shape[0] != 1:
raise ValueError(
f"Input batch size must be the same for both tensors or 1. Got {trans_01.shape} and {points_1.shape}"
)
if not trans_01.shape[-1] == (points_1.shape[-1] + 1):
raise ValueError(f"Last input dimensions must differ by one unit Got{trans_01} and {points_1}")

# We reshape to BxNxD in case we get more dimensions, e.g., MxBxNxD
shape_inp = list(points_1.shape)
points_1 = points_1.reshape(-1, points_1.shape[-2], points_1.shape[-1])
trans_01 = trans_01.reshape(-1, trans_01.shape[-2], trans_01.shape[-1])
# We expand trans_01 to match the dimensions needed for bmm
trans_01 = torch.repeat_interleave(trans_01, repeats=points_1.shape[0] // trans_01.shape[0], dim=0)
# to homogeneous
points_1_h = convert_points_to_homogeneous(points_1)  # BxNxD+1
# transform coordinates
points_0_h = torch.bmm(points_1_h, trans_01.permute(0, 2, 1))
points_0_h = torch.squeeze(points_0_h, dim=-1)
# to euclidean
points_0 = convert_points_from_homogeneous(points_0_h)  # BxNxD
# reshape to the input shape
shape_inp[-2] = points_0.shape[-2]
shape_inp[-1] = points_0.shape[-1]
points_0 = points_0.reshape(shape_inp)
return points_0

[docs]def point_line_distance(point: Tensor, line: Tensor, eps: float = 1e-9) -> Tensor:
r"""Return the distance from points to lines.

Args:
point: (possibly homogeneous) points :math:(*, N, 2 or 3).
line: lines coefficients :math:(a, b, c) with shape :math:(*, N, 3), where :math:ax + by + c = 0.
eps: Small constant for safe sqrt.

Returns:
the computed distance with shape :math:(*, N).
"""
KORNIA_CHECK_IS_TENSOR(point)
KORNIA_CHECK_IS_TENSOR(line)

if point.shape[-1] not in (2, 3):
raise ValueError(f"pts must be a (*, 2 or 3) tensor. Got {point.shape}")

if not line.shape[-1] == 3:
raise ValueError(f"lines must be a (*, 3) tensor. Got {line.shape}")

numerator = (line[..., 0] * point[..., 0] + line[..., 1] * point[..., 1] + line[..., 2]).abs()
denominator = line[..., :2].norm(dim=-1)

return numerator / (denominator + eps)

[docs]def batched_dot_product(x: Tensor, y: Tensor, keepdim: bool = False) -> Tensor:
"""Return a batched version of .dot()"""
KORNIA_CHECK_SHAPE(x, ["*", "N"])
KORNIA_CHECK_SHAPE(y, ["*", "N"])
return (x * y).sum(-1, keepdim)

def batched_squared_norm(x: Tensor, keepdim: bool = False) -> Tensor:
"""Return the squared norm of a vector."""
return batched_dot_product(x, x, keepdim)

[docs]def euclidean_distance(x: Tensor, y: Tensor, keepdim: bool = False, eps: float = 1e-6) -> Tensor:
"""Compute the Euclidean distance between two set of n-dimensional points.

More: https://en.wikipedia.org/wiki/Euclidean_distance

Args:
x: first set of points of shape :math:(*, N).
y: second set of points of shape :math:(*, N).
keepdim: whether to keep the dimension after reduction.
eps: small value to have numerical stability.
"""
KORNIA_CHECK_SHAPE(x, ["*", "N"])
KORNIA_CHECK_SHAPE(y, ["*", "N"])
KORNIA_CHECK(x.shape == y.shape)

return (x - y + eps).pow(2).sum(-1, keepdim).sqrt()

# aliases
squared_norm = batched_squared_norm

# TODO:
# - project_points: from opencv