SpecialOrthogonal2Vectors | R Documentation |
Class for the special orthogonal group \mathrm{SO}(2) in
vector form, i.e. the Lie group of planar rotations. This class is
specific to the vector representation of rotations. For the matrix
representation, use the SpecialOrthogonal
class and set n = 2
.
rgeomstats::PythonClass
-> rgeomstats::Manifold
-> rgeomstats::LieGroup
-> rgeomstats::SpecialOrthogonalVectors
-> SpecialOrthogonal2Vectors
rgeomstats::PythonClass$get_python_class()
rgeomstats::PythonClass$set_python_class()
rgeomstats::Manifold$belongs()
rgeomstats::Manifold$is_tangent()
rgeomstats::Manifold$random_point()
rgeomstats::Manifold$random_tangent_vec()
rgeomstats::Manifold$regularize()
rgeomstats::Manifold$set_metric()
rgeomstats::Manifold$to_tangent()
rgeomstats::LieGroup$add_metric()
rgeomstats::LieGroup$compose()
rgeomstats::LieGroup$exp()
rgeomstats::LieGroup$exp_from_identity()
rgeomstats::LieGroup$exp_not_from_identity()
rgeomstats::LieGroup$get_identity()
rgeomstats::LieGroup$inverse()
rgeomstats::LieGroup$jacobian_translation()
rgeomstats::LieGroup$lie_bracket()
rgeomstats::LieGroup$log()
rgeomstats::LieGroup$log_from_identity()
rgeomstats::LieGroup$log_not_from_identity()
rgeomstats::LieGroup$tangent_translation_map()
rgeomstats::SpecialOrthogonalVectors$projection()
rgeomstats::SpecialOrthogonalVectors$regularize_tangent_vec()
rgeomstats::SpecialOrthogonalVectors$regularize_tangent_vec_at_identity()
rgeomstats::SpecialOrthogonalVectors$skew_matrix_from_vector()
rgeomstats::SpecialOrthogonalVectors$vector_from_skew_matrix()
new()
The SpecialOrthogonal2Vectors
class constructor.
SpecialOrthogonal2Vectors$new(epsilon = 0, py_cls = NULL)
epsilon
A numeric value specifying the precision to use for
calculations involving potential division by 0 in rotations. Defaults to
0
.
py_cls
A Python object of class SpecialOrthogonal2Vectors
.
Defaults to NULL
in which case it is instantiated on the fly using
the other input arguments.
An object of class SpecialOrthogonal2Vectors
.
rotation_vector_from_matrix()
Converts rotation matrix (in 2D) to rotation vector
(axis-angle) getting the angle through the atan2()
function.
SpecialOrthogonal2Vectors$rotation_vector_from_matrix(rot_mat)
rot_mat
A numeric array of shape [… \times 2 \times 2] specifying one or more 2D rotation matrices.
A numeric array of shape [… \times 1] storing the corresponding axis-angle representations.
if (reticulate::py_module_available("geomstats")) { so2 <- SpecialOrthogonal(n = 2, point_type = "vector") so2$rotation_vector_from_matrix(diag(1, 2)) }
matrix_from_rotation_vector()
Convert a 2D rotation from vector to matrix representation.
SpecialOrthogonal2Vectors$matrix_from_rotation_vector(rot_vec)
rot_vec
A numeric array of shape ... \times 1 specifying one or more 2D rotations in vector representation.
A numeric array of shape ... \times 2 \times 2 storing the corresponding 2D rotation matrices.
if (reticulate::py_module_available("geomstats")) { so2 <- SpecialOrthogonal(n = 2, point_type = "vector") so2$matrix_from_rotation_vector(array(0)) }
random_uniform()
Samples in \mathrm{SO}(2) from a uniform distribution.
SpecialOrthogonal2Vectors$random_uniform(n_samples = 1)
n_samples
An integer value specifying the sample size. Defaults to
1L
.
A numeric array of shape ... \times 1 storing a sample of 2D rotations in axis-angle representation uniformly sampled in \mathrm{SO}(2).
clone()
The objects of this class are cloneable with this method.
SpecialOrthogonal2Vectors$clone(deep = FALSE)
deep
Whether to make a deep clone.
Nicolas Guigui and Nina Miolane
Other special orthogonal classes:
SpecialOrthogonal3Vectors
,
SpecialOrthogonalMatrices
,
SpecialOrthogonal()
## ------------------------------------------------ ## Method `SpecialOrthogonal2Vectors$rotation_vector_from_matrix` ## ------------------------------------------------ if (reticulate::py_module_available("geomstats")) { so2 <- SpecialOrthogonal(n = 2, point_type = "vector") so2$rotation_vector_from_matrix(diag(1, 2)) } ## ------------------------------------------------ ## Method `SpecialOrthogonal2Vectors$matrix_from_rotation_vector` ## ------------------------------------------------ if (reticulate::py_module_available("geomstats")) { so2 <- SpecialOrthogonal(n = 2, point_type = "vector") so2$matrix_from_rotation_vector(array(0)) }
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