Parametrization of Rotations
Matrix Parametrization
- e3nn.o3.rand_matrix(*shape, requires_grad=False, dtype=None, device=None)[source]
random rotation matrix
- Parameters
*shape (int) –
- Returns
tensor of shape \((\mathrm{shape}, 3, 3)\)
- Return type
- e3nn.o3.matrix_x(angle: torch.Tensor) torch.Tensor[source]
matrix of rotation around X axis
- Parameters
angle (
torch.Tensor) – tensor of any shape \((...)\)- Returns
matrices of shape \((..., 3, 3)\)
- Return type
- e3nn.o3.matrix_y(angle: torch.Tensor) torch.Tensor[source]
matrix of rotation around Y axis
- Parameters
angle (
torch.Tensor) – tensor of any shape \((...)\)- Returns
matrices of shape \((..., 3, 3)\)
- Return type
- e3nn.o3.matrix_z(angle: torch.Tensor) torch.Tensor[source]
matrix of rotation around Z axis
- Parameters
angle (
torch.Tensor) – tensor of any shape \((...)\)- Returns
matrices of shape \((..., 3, 3)\)
- Return type
Euler Angles Parametrization
- e3nn.o3.identity_angles(*shape, requires_grad=False, dtype=None, device=None)[source]
angles of the identity rotation
- Parameters
*shape (int) –
- Returns
alpha (
torch.Tensor) – tensor of shape \((\mathrm{shape})\)beta (
torch.Tensor) – tensor of shape \((\mathrm{shape})\)gamma (
torch.Tensor) – tensor of shape \((\mathrm{shape})\)
- e3nn.o3.rand_angles(*shape, requires_grad=False, dtype=None, device=None)[source]
random rotation angles
- Parameters
*shape (int) –
- Returns
alpha (
torch.Tensor) – tensor of shape \((\mathrm{shape})\)beta (
torch.Tensor) – tensor of shape \((\mathrm{shape})\)gamma (
torch.Tensor) – tensor of shape \((\mathrm{shape})\)
- e3nn.o3.compose_angles(a1, b1, c1, a2, b2, c2)[source]
compose angles
Computes \((a, b, c)\) such that \(R(a, b, c) = R(a_1, b_1, c_1) \circ R(a_2, b_2, c_2)\)
- Parameters
a1 (
torch.Tensor) – tensor of shape \((...)\), (applied second)b1 (
torch.Tensor) – tensor of shape \((...)\), (applied second)c1 (
torch.Tensor) – tensor of shape \((...)\), (applied second)a2 (
torch.Tensor) – tensor of shape \((...)\), (applied first)b2 (
torch.Tensor) – tensor of shape \((...)\), (applied first)c2 (
torch.Tensor) – tensor of shape \((...)\), (applied first)
- Returns
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
- e3nn.o3.inverse_angles(a, b, c)[source]
angles of the inverse rotation
- Parameters
a (
torch.Tensor) – tensor of shape \((...)\)b (
torch.Tensor) – tensor of shape \((...)\)c (
torch.Tensor) – tensor of shape \((...)\)
- Returns
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
Quaternion Parametrization
- e3nn.o3.identity_quaternion(*shape, requires_grad=False, dtype=None, device=None)[source]
quaternion of identity rotation
- Parameters
*shape (int) –
- Returns
tensor of shape \((\mathrm{shape}, 4)\)
- Return type
- e3nn.o3.rand_quaternion(*shape, requires_grad=False, dtype=None, device=None)[source]
generate random quaternion
- Parameters
*shape (int) –
- Returns
tensor of shape \((\mathrm{shape}, 4)\)
- Return type
- e3nn.o3.compose_quaternion(q1, q2)[source]
compose two quaternions: \(q_1 \circ q_2\)
- Parameters
q1 (
torch.Tensor) – tensor of shape \((..., 4)\), (applied second)q2 (
torch.Tensor) – tensor of shape \((..., 4)\), (applied first)
- Returns
tensor of shape \((..., 4)\)
- Return type
- e3nn.o3.inverse_quaternion(q)[source]
inverse of a quaternion
Works only for unit quaternions.
- Parameters
q (
torch.Tensor) – tensor of shape \((..., 4)\)- Returns
tensor of shape \((..., 4)\)
- Return type
Axis-Angle Parametrization
- e3nn.o3.rand_axis_angle(*shape, requires_grad=False, dtype=None, device=None)[source]
generate random rotation as axis-angle
- Parameters
*shape (int) –
- Returns
axis (
torch.Tensor) – tensor of shape \((\mathrm{shape}, 3)\)angle (
torch.Tensor) – tensor of shape \((\mathrm{shape})\)
- e3nn.o3.compose_axis_angle(axis1, angle1, axis2, angle2)[source]
compose \((\vec x_1, \alpha_1)\) with \((\vec x_2, \alpha_2)\)
- Parameters
axis1 (
torch.Tensor) – tensor of shape \((..., 3)\), (applied second)angle1 (
torch.Tensor) – tensor of shape \((...)\), (applied second)axis2 (
torch.Tensor) – tensor of shape \((..., 3)\), (applied first)angle2 (
torch.Tensor) – tensor of shape \((...)\), (applied first)
- Returns
axis (
torch.Tensor) – tensor of shape \((..., 3)\)angle (
torch.Tensor) – tensor of shape \((...)\)
Convertions
- e3nn.o3.angles_to_matrix(alpha, beta, gamma)[source]
conversion from angles to matrix
- Parameters
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
- Returns
matrices of shape \((..., 3, 3)\)
- Return type
- e3nn.o3.matrix_to_angles(R)[source]
conversion from matrix to angles
- Parameters
R (
torch.Tensor) – matrices of shape \((..., 3, 3)\)- Returns
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
- e3nn.o3.angles_to_quaternion(alpha, beta, gamma)[source]
conversion from angles to quaternion
- Parameters
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
- Returns
matrices of shape \((..., 4)\)
- Return type
- e3nn.o3.matrix_to_quaternion(R)[source]
conversion from matrix \(R\) to quaternion \(q\)
- Parameters
R (
torch.Tensor) – tensor of shape \((..., 3, 3)\)- Returns
tensor of shape \((..., 4)\)
- Return type
- e3nn.o3.axis_angle_to_quaternion(xyz, angle)[source]
convertion from axis-angle to quaternion
- Parameters
xyz (
torch.Tensor) – tensor of shape \((..., 3)\)angle (
torch.Tensor) – tensor of shape \((...)\)
- Returns
tensor of shape \((..., 4)\)
- Return type
- e3nn.o3.quaternion_to_axis_angle(q)[source]
convertion from quaternion to axis-angle
- Parameters
q (
torch.Tensor) – tensor of shape \((..., 4)\)- Returns
axis (
torch.Tensor) – tensor of shape \((..., 3)\)angle (
torch.Tensor) – tensor of shape \((...)\)
- e3nn.o3.matrix_to_axis_angle(R)[source]
conversion from matrix to axis-angle
- Parameters
R (
torch.Tensor) – tensor of shape \((..., 3, 3)\)- Returns
axis (
torch.Tensor) – tensor of shape \((..., 3)\)angle (
torch.Tensor) – tensor of shape \((...)\)
- e3nn.o3.angles_to_axis_angle(alpha, beta, gamma)[source]
conversion from angles to axis-angle
- Parameters
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
- Returns
axis (
torch.Tensor) – tensor of shape \((..., 3)\)angle (
torch.Tensor) – tensor of shape \((...)\)
- e3nn.o3.axis_angle_to_matrix(axis, angle)[source]
conversion from axis-angle to matrix
- Parameters
axis (
torch.Tensor) – tensor of shape \((..., 3)\)angle (
torch.Tensor) – tensor of shape \((...)\)
- Returns
tensor of shape \((..., 3, 3)\)
- Return type
- e3nn.o3.quaternion_to_matrix(q)[source]
convertion from quaternion to matrix
- Parameters
q (
torch.Tensor) – tensor of shape \((..., 4)\)- Returns
tensor of shape \((..., 3, 3)\)
- Return type
- e3nn.o3.quaternion_to_angles(q)[source]
convertion from quaternion to angles
- Parameters
q (
torch.Tensor) – tensor of shape \((..., 4)\)- Returns
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
- e3nn.o3.axis_angle_to_angles(axis, angle)[source]
convertion from axis-angle to angles
- Parameters
axis (
torch.Tensor) – tensor of shape \((..., 3)\)angle (
torch.Tensor) – tensor of shape \((...)\)
- Returns
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)gamma (
torch.Tensor) – tensor of shape \((...)\)
Convertions to point on the sphere
- e3nn.o3.angles_to_xyz(alpha, beta)[source]
convert \((\alpha, \beta)\) into a point \((x, y, z)\) on the sphere
- Parameters
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)
- Returns
tensor of shape \((..., 3)\)
- Return type
Examples
>>> angles_to_xyz(torch.tensor(1.7), torch.tensor(0.0)).abs() tensor([0., 1., 0.])
- e3nn.o3.xyz_to_angles(xyz)[source]
convert a point \(\vec r = (x, y, z)\) on the sphere into angles \((\alpha, \beta)\)
\[\vec r = R(\alpha, \beta, 0) \vec e_z\]- Parameters
xyz (
torch.Tensor) – tensor of shape \((..., 3)\)- Returns
alpha (
torch.Tensor) – tensor of shape \((...)\)beta (
torch.Tensor) – tensor of shape \((...)\)