Nothing
R/riemannian-metric.R
In rgeomstats: Interface to 'Geomstats'
#' Abstract Class for Riemannian Metrics
#'
#' @description An [R6::R6Class] object implementing the base
#' [`RiemannianMetric`] class. This is an abstract class for Riemannian and
#' pseudo-Riemannian metrics which are the associated Levi-Civita connection
#' on the tangent bundle.
#'
#' @param base_point A numeric array of shape `dim` specifying a point on
#' the manifold. Defaults to `NULL`.
#' @param vector A numeric array of shape `dim` specifying a vector.
#'
#' @author Nina Miolane
#'
#' @keywords internal
RiemannianMetric <- R6::R6Class(
classname = "RiemannianMetric",
inherit = Connection,
public = list(
#' @field signature An integer vector specifying the signature of the
#' metric.
signature = NULL,
#' @description The [`RiemannianMetric`] class constructor.
#'
#' @param dim An integer value specifying the dimension of the manifold.
#' @param shape An integer vector specifying the shape of one element of the
#' manifold. Defaults to `NULL`.
#' @param signature An integer vector specifying the signature of the
#' metric. Defaults to `c(dim, 0L)`.
#' @param default_coords_type A string specifying the coordinate type.
#' Choices are `extrensic` or `intrinsic`. Defaults to `intrinsic`.
#' @param py_cls A Python object of class `RiemannianMetric`. Defaults to
#' `NULL` in which case it is instantiated on the fly using the other
#' input arguments.
#'
#' @return An object of class [`RiemannianMetric`].
initialize = function(dim, shape = NULL, signature = NULL,
default_coords_type = "intrinsic", py_cls = NULL) {
if (is.null(py_cls)) {
dim <- as.integer(dim)
if (!is.null(shape)) shape <- dim
if (!is.null(signature)) signature <- as.integer(signature)
py_cls <- gs$geometry$riemannian_metric$RiemannianMetric(
dim = dim,
shape = shape,
signature = signature,
default_coords_type = default_coords_type
)
}
super$set_python_class(py_cls)
private$set_fields()
},
#' @description Metric matrix at the tangent space at a base point.
#'
#' @return A numeric array of shape `dim x dim` storing the inner-product
#' matrix.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$metric_matrix()
#' }
metric_matrix = function(base_point = NULL) {
super$get_python_class()$metric_matrix(base_point)
},
#' @description Inner co-product matrix at the cotangent space at a base
#' point. This represents the cometric matrix, i.e. the inverse of the
#' metric matrix.
#'
#' @return A numeric array of shape `dim x dim` storing the inverse of the
#' inner-product matrix.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$cometric_matrix()
#' }
cometric_matrix = function(base_point = NULL) {
super$get_python_class()$cometric_matrix(base_point)
},
#' @description Compute derivative of the inner prod matrix at base point.
#'
#' @return A numeric array of shape `dim x dim` storing the derivative of
#' the inverse of the inner-product matrix.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$inner_product_derivative_matrix()
#' }
inner_product_derivative_matrix = function(base_point) {
super$get_python_class()$inner_product_derivative_matrix(base_point)
},
#' @description Inner product between two tangent vectors at a base point.
#'
#' @param tangent_vec_a A numeric array of shape `dim` specifying a tangent
#' vector at base point.
#' @param tangent_vec_b A numeric array of shape `dim` specifying a tangent
#' vector at base point.
#'
#' @return A scalar value representing the inner product between the two
#' input tangent vectors at the input base point.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$inner_product(diag(0, 3), diag(1, 3), base_point = diag(1, 3))
#' }
inner_product = function(tangent_vec_a, tangent_vec_b, base_point) {
super$get_python_class()$inner_product(
tangent_vec_a = tangent_vec_a,
tangent_vec_b = tangent_vec_b,
base_point = base_point
)
},
#' @description Computes inner coproduct between two cotangent vectors at
#' base point. This is the inner product associated to the cometric
#' matrix.
#'
#' @param cotangent_vec_a A numeric array of shape `dim` specifying a
#' cotangent vector at base point.
#' @param cotangent_vec_b A numeric array of shape `dim` specifying a
#' cotangent vector at base point.
#'
#' @return A scalar value representing the inner coproduct between the two
#' input cotangent vectors at the input base point.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$inner_coproduct(diag(0, 3), diag(1, 3), base_point = diag(1, 3))
#' }
inner_coproduct = function(cotangent_vec_a, cotangent_vec_b, base_point = NULL) {
super$get_python_class()$inner_coproduct(
cotangent_vec_a = cotangent_vec_a,
cotangent_vec_b = cotangent_vec_b,
base_point = base_point
)
},
#' @description Computes the Hamiltonian energy associated to the cometric.
#' The Hamiltonian at state \eqn{(q, p)} is defined by \deqn{H(q, p) =
#' \frac{1}{2} \langle p, p \rangle_q,} where \eqn{\langle \cdot, \cdot
#' \rangle_q} is the cometric at \eqn{q}.
#'
#' @param state A list with two components: (i) a numeric array of shape
#' `dim` specifying the *position* which is a point on the manifold and
#' (ii) a numeric array of shape `dim` specifying the *momentum* which is
#' a cotangent vector.
#'
#' @return A numeric value representing the Hamiltonian energy at `state`.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$hamiltonian()
#' }
hamiltonian = function(state) {
super$get_python_class()$hamiltonian(state)
},
#' @description Computes the square of the norm of a vector. Squared norm of
#' a vector associated to the inner product at the tangent space at a base
#' point.
#'
#' @return A numeric value representing the squared norm of the input
#' vector.
#'
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$squared_norm(diag(0, 3), diag(1, 3))
#' }
squared_norm = function(vector, base_point = NULL) {
super$get_python_class()$squared_norm(
vector = vector,
base_point = base_point
)
},
#' @description Computes the norm of a vector associated to the inner
#' product at the tangent space at a base point.
#'
#' @details This only works for positive-definite Riemannian metrics and
#' inner products.
#'
#' @return A numeric value representing the norm of the input vector.
#'
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$norm(diag(0, 3), diag(1, 3))
#' }
norm = function(vector, base_point = NULL) {
super$get_python_class()$norm(
vector = vector,
base_point = base_point
)
},
#' @description Normalizes a tangent vector at a given point.
#'
#' @return A numeric array of shape `dim` storing the normalized version of
#' the input tangent vector.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$normalize(diag(2, 3), diag(1, 3))
#' }
normalize = function(vector, base_point = NULL) {
super$get_python_class()$normalize(
vector = vector,
base_point = base_point
)
},
#' @description Generates a random unit tangent vector at a given point.
#'
#' @param n_vectors An integer value specifying the number of vectors to be
#' generated at `base_point`. For vectorization purposes, `n_vectors` can
#' be greater than 1 *iff* `base_point` corresponds to a single point.
#' Defaults to `1L`.
#'
#' @return A numeric array of shape `c(n_vectors, dim)` storing random unit
#' tangent vectors at `base_point`.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$random_unit_tangent_vec(diag(1, 3))
#' }
random_unit_tangent_vec = function(base_point = NULL, n_vectors = 1) {
n_vectors <- as.integer(n_vectors)
super$get_python_class()$random_unit_tangent_vec(
base_point = base_point,
n_vectors = n_vectors
)
},
#' @description Squared geodesic distance between two points.
#'
#' @param point_a A numeric array of shape `dim` on the manifold.
#' @param point_b A numeric array of shape `dim` on the manifold.
#' @param ... Extra parameters to be passed to the `$log()` method of the
#' parent [`Connection`] class.
#'
#' @return A numeric value storing the squared geodesic distance between the
#' two input points.
#'
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$squared_dist(diag(1, 3), diag(1, 3))
#' }
squared_dist = function(point_a, point_b, ...) {
dots <- capture_extra_params(...)
dots$point_a <- point_a
dots$point_b <- point_b
do.call(super$get_python_class()$squared_dist, dots)
},
#' @description Geodesic distance between two points.
#'
#' @details It only works for positive definite Riemannian metrics.
#'
#' @param point_a A numeric array of shape `dim` on the manifold.
#' @param point_b A numeric array of shape `dim` on the manifold.
#' @param ... Extra parameters to be passed to the `$log()` method of the
#' parent [`Connection`] class.
#'
#' @return A numeric value storing the geodesic distance between the two
#' input points.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$dist(diag(1, 3), diag(1, 3))
#' }
dist = function(point_a, point_b, ...) {
dots <- capture_extra_params(...)
dots$point_a <- point_a
dots$point_b <- point_b
do.call(super$get_python_class()$dist, dots)
},
#' @description Computes the geodesic distance between points.
#'
#' @details If `n_samples_a == n_samples_b` then `dist` is the element-wise
#' distance result of a point in `points_a` with the point from `points_b`
#' of the same index. If `n_samples_a != n_samples_b` then `dist` is the
#' result of applying geodesic distance for each point from `points_a` to
#' all points from `points_b`.
#'
#' @param points_a A numeric array of shape `c(n_samples_a, dim)` specifying
#' a set of points on the manifold.
#' @param points_b A numeric array of shape `c(n_samples_b, dim)` specifying
#' a set of points on the manifold.
#'
#' @return A numeric array of shape `c(n_samples_a, dim)` if `n_samples_a ==
#' n_samples_b` or of shape `c(n_samples_a, n_samples_b, dim)` if
#' `n_samples_a != n_samples_b` storing the geodesic distance between
#' points in set A and points in set B.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$dist(diag(1, 3), diag(1, 3))
#' }
dist_broadcast = function(points_a, points_b) {
super$get_python_class()$dist_broadcast(
point_a = points_a,
point_b = points_b
)
},
#' @description Computes the pairwise distance between points.
#'
#' @param points A numeric array of shape `c(n_samples, dim)` specifying a
#' set of points on the manifold.
#' @param n_jobs An integer value specifying the number of cores for
#' parallel computation. Defaults to `1L`.
#' @param ... Extra parameters to be passed tothe `joblib.Parallel` Python
#' class. See [joblib
#' documentation](https://joblib.readthedocs.io/en/latest/) for details.
#'
#' @return A numeric matrix of shape `c(n_samples, n_samples)` storing the
#' pairwise geodesic distances between all the points.
dist_pairwise = function(points, n_jobs = 1, ...) {
dots <- capture_extra_params(...)
dots$points <- points
dots$n_jobs <- as.integer(n_jobs)
do.call(super$get_python_class()$dist_pairwise, dots)
},
#' @description Computes the diameter of set of points on a manifold.
#'
#' @details The diameter is the maximum over all pairwise distances.
#'
#' @param points A numeric array of shape `c(n_samples, dim)` specifying a
#' set of points on the manifold.
#'
#' @return A numeric value representing the largest distance between any two
#' points in the input set.
diameter = function(points) {
super$get_python_class()$diameter(points)
},
#' @description Finds the closest neighbor to a point among a set of
#' neighbors.
#'
#' @param point A numeric array of shape `dim` specifying a point on the
#' manifold.
#' @param neighbors A numeric array of shape `c(n_neighbors, dim)`
#' specifying a set of neighboring points for the input `point`.
#'
#' @return An integer value representing the index of the neighbor in
#' `neighbors` that is closest to `point`.
closest_neighbor_index = function(point, neighbors) {
super$get_python_class()$closest_neighbor_index(
point = point,
neighbors = neighbors
)
},
#' @description Normalizes the basis with respect to the metric. This
#' corresponds to a renormalization of each basis vector.
#'
#' @param basis A numeric array of shape `c(dim, dim)` specifying a basis.
#'
#' @return A numeric array of shape `c(dim, n, n)` storing the normal basis.
normal_basis = function(basis, base_point = NULL) {
super$get_python_class()$normal_basis(
basis = basis,
base_point = base_point
)
},
#' @description Computes the sectional curvature.
#'
#' @details For two orthonormal tangent vectors \eqn{x} and \eqn{y} at a
#' base point, the sectional curvature is defined by \deqn{\langle R(x,
#' y)x, y \rangle = \langle R_x(y), y \rangle.} For non-orthonormal
#' vectors, it is \deqn{\langle R(x, y)x, y \rangle / \\|x \wedge y\\|^2.}
#' See also https://en.wikipedia.org/wiki/Sectional_curvature.
#'
#' @param tangent_vec_a A numeric array of shape `c(n, n)` specifying a
#' tangent vector at `base_point`.
#' @param tangent_vec_b A numeric array of shape `c(n, n)` specifying a
#' tangent vector at `base_point`.
#'
#' @return A numeric value representing the sectional curvature at
#' `base_point`.
sectional_curvature = function(tangent_vec_a, tangent_vec_b, base_point = NULL) {
super$get_python_class()$sectional_curvature(
tangent_vec_a = tangent_vec_a,
tangent_vec_b = tangent_vec_b,
base_point = base_point
)
}
),
private = list(
set_fields = function() {
super$set_fields()
self$signature <- super$get_python_class()$signature
}
)
)
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#' Abstract Class for Riemannian Metrics
#'
#' @description An [R6::R6Class] object implementing the base
#' [`RiemannianMetric`] class. This is an abstract class for Riemannian and
#' pseudo-Riemannian metrics which are the associated Levi-Civita connection
#' on the tangent bundle.
#'
#' @param base_point A numeric array of shape `dim` specifying a point on
#' the manifold. Defaults to `NULL`.
#' @param vector A numeric array of shape `dim` specifying a vector.
#'
#' @author Nina Miolane
#'
#' @keywords internal
RiemannianMetric <- R6::R6Class(
classname = "RiemannianMetric",
inherit = Connection,
public = list(
#' @field signature An integer vector specifying the signature of the
#' metric.
signature = NULL,
#' @description The [`RiemannianMetric`] class constructor.
#'
#' @param dim An integer value specifying the dimension of the manifold.
#' @param shape An integer vector specifying the shape of one element of the
#' manifold. Defaults to `NULL`.
#' @param signature An integer vector specifying the signature of the
#' metric. Defaults to `c(dim, 0L)`.
#' @param default_coords_type A string specifying the coordinate type.
#' Choices are `extrensic` or `intrinsic`. Defaults to `intrinsic`.
#' @param py_cls A Python object of class `RiemannianMetric`. Defaults to
#' `NULL` in which case it is instantiated on the fly using the other
#' input arguments.
#'
#' @return An object of class [`RiemannianMetric`].
initialize = function(dim, shape = NULL, signature = NULL,
default_coords_type = "intrinsic", py_cls = NULL) {
if (is.null(py_cls)) {
dim <- as.integer(dim)
if (!is.null(shape)) shape <- dim
if (!is.null(signature)) signature <- as.integer(signature)
py_cls <- gs$geometry$riemannian_metric$RiemannianMetric(
dim = dim,
shape = shape,
signature = signature,
default_coords_type = default_coords_type
)
}
super$set_python_class(py_cls)
private$set_fields()
},
#' @description Metric matrix at the tangent space at a base point.
#'
#' @return A numeric array of shape `dim x dim` storing the inner-product
#' matrix.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$metric_matrix()
#' }
metric_matrix = function(base_point = NULL) {
super$get_python_class()$metric_matrix(base_point)
},
#' @description Inner co-product matrix at the cotangent space at a base
#' point. This represents the cometric matrix, i.e. the inverse of the
#' metric matrix.
#'
#' @return A numeric array of shape `dim x dim` storing the inverse of the
#' inner-product matrix.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$cometric_matrix()
#' }
cometric_matrix = function(base_point = NULL) {
super$get_python_class()$cometric_matrix(base_point)
},
#' @description Compute derivative of the inner prod matrix at base point.
#'
#' @return A numeric array of shape `dim x dim` storing the derivative of
#' the inverse of the inner-product matrix.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$inner_product_derivative_matrix()
#' }
inner_product_derivative_matrix = function(base_point) {
super$get_python_class()$inner_product_derivative_matrix(base_point)
},
#' @description Inner product between two tangent vectors at a base point.
#'
#' @param tangent_vec_a A numeric array of shape `dim` specifying a tangent
#' vector at base point.
#' @param tangent_vec_b A numeric array of shape `dim` specifying a tangent
#' vector at base point.
#'
#' @return A scalar value representing the inner product between the two
#' input tangent vectors at the input base point.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$inner_product(diag(0, 3), diag(1, 3), base_point = diag(1, 3))
#' }
inner_product = function(tangent_vec_a, tangent_vec_b, base_point) {
super$get_python_class()$inner_product(
tangent_vec_a = tangent_vec_a,
tangent_vec_b = tangent_vec_b,
base_point = base_point
)
},
#' @description Computes inner coproduct between two cotangent vectors at
#' base point. This is the inner product associated to the cometric
#' matrix.
#'
#' @param cotangent_vec_a A numeric array of shape `dim` specifying a
#' cotangent vector at base point.
#' @param cotangent_vec_b A numeric array of shape `dim` specifying a
#' cotangent vector at base point.
#'
#' @return A scalar value representing the inner coproduct between the two
#' input cotangent vectors at the input base point.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$inner_coproduct(diag(0, 3), diag(1, 3), base_point = diag(1, 3))
#' }
inner_coproduct = function(cotangent_vec_a, cotangent_vec_b, base_point = NULL) {
super$get_python_class()$inner_coproduct(
cotangent_vec_a = cotangent_vec_a,
cotangent_vec_b = cotangent_vec_b,
base_point = base_point
)
},
#' @description Computes the Hamiltonian energy associated to the cometric.
#' The Hamiltonian at state \eqn{(q, p)} is defined by \deqn{H(q, p) =
#' \frac{1}{2} \langle p, p \rangle_q,} where \eqn{\langle \cdot, \cdot
#' \rangle_q} is the cometric at \eqn{q}.
#'
#' @param state A list with two components: (i) a numeric array of shape
#' `dim` specifying the *position* which is a point on the manifold and
#' (ii) a numeric array of shape `dim` specifying the *momentum* which is
#' a cotangent vector.
#'
#' @return A numeric value representing the Hamiltonian energy at `state`.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$hamiltonian()
#' }
hamiltonian = function(state) {
super$get_python_class()$hamiltonian(state)
},
#' @description Computes the square of the norm of a vector. Squared norm of
#' a vector associated to the inner product at the tangent space at a base
#' point.
#'
#' @return A numeric value representing the squared norm of the input
#' vector.
#'
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$squared_norm(diag(0, 3), diag(1, 3))
#' }
squared_norm = function(vector, base_point = NULL) {
super$get_python_class()$squared_norm(
vector = vector,
base_point = base_point
)
},
#' @description Computes the norm of a vector associated to the inner
#' product at the tangent space at a base point.
#'
#' @details This only works for positive-definite Riemannian metrics and
#' inner products.
#'
#' @return A numeric value representing the norm of the input vector.
#'
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$norm(diag(0, 3), diag(1, 3))
#' }
norm = function(vector, base_point = NULL) {
super$get_python_class()$norm(
vector = vector,
base_point = base_point
)
},
#' @description Normalizes a tangent vector at a given point.
#'
#' @return A numeric array of shape `dim` storing the normalized version of
#' the input tangent vector.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$normalize(diag(2, 3), diag(1, 3))
#' }
normalize = function(vector, base_point = NULL) {
super$get_python_class()$normalize(
vector = vector,
base_point = base_point
)
},
#' @description Generates a random unit tangent vector at a given point.
#'
#' @param n_vectors An integer value specifying the number of vectors to be
#' generated at `base_point`. For vectorization purposes, `n_vectors` can
#' be greater than 1 *iff* `base_point` corresponds to a single point.
#' Defaults to `1L`.
#'
#' @return A numeric array of shape `c(n_vectors, dim)` storing random unit
#' tangent vectors at `base_point`.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' # mt <- SPDMetricLogEuclidean$new(n = 3)
#' # mt$random_unit_tangent_vec(diag(1, 3))
#' }
random_unit_tangent_vec = function(base_point = NULL, n_vectors = 1) {
n_vectors <- as.integer(n_vectors)
super$get_python_class()$random_unit_tangent_vec(
base_point = base_point,
n_vectors = n_vectors
)
},
#' @description Squared geodesic distance between two points.
#'
#' @param point_a A numeric array of shape `dim` on the manifold.
#' @param point_b A numeric array of shape `dim` on the manifold.
#' @param ... Extra parameters to be passed to the `$log()` method of the
#' parent [`Connection`] class.
#'
#' @return A numeric value storing the squared geodesic distance between the
#' two input points.
#'
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$squared_dist(diag(1, 3), diag(1, 3))
#' }
squared_dist = function(point_a, point_b, ...) {
dots <- capture_extra_params(...)
dots$point_a <- point_a
dots$point_b <- point_b
do.call(super$get_python_class()$squared_dist, dots)
},
#' @description Geodesic distance between two points.
#'
#' @details It only works for positive definite Riemannian metrics.
#'
#' @param point_a A numeric array of shape `dim` on the manifold.
#' @param point_b A numeric array of shape `dim` on the manifold.
#' @param ... Extra parameters to be passed to the `$log()` method of the
#' parent [`Connection`] class.
#'
#' @return A numeric value storing the geodesic distance between the two
#' input points.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$dist(diag(1, 3), diag(1, 3))
#' }
dist = function(point_a, point_b, ...) {
dots <- capture_extra_params(...)
dots$point_a <- point_a
dots$point_b <- point_b
do.call(super$get_python_class()$dist, dots)
},
#' @description Computes the geodesic distance between points.
#'
#' @details If `n_samples_a == n_samples_b` then `dist` is the element-wise
#' distance result of a point in `points_a` with the point from `points_b`
#' of the same index. If `n_samples_a != n_samples_b` then `dist` is the
#' result of applying geodesic distance for each point from `points_a` to
#' all points from `points_b`.
#'
#' @param points_a A numeric array of shape `c(n_samples_a, dim)` specifying
#' a set of points on the manifold.
#' @param points_b A numeric array of shape `c(n_samples_b, dim)` specifying
#' a set of points on the manifold.
#'
#' @return A numeric array of shape `c(n_samples_a, dim)` if `n_samples_a ==
#' n_samples_b` or of shape `c(n_samples_a, n_samples_b, dim)` if
#' `n_samples_a != n_samples_b` storing the geodesic distance between
#' points in set A and points in set B.
#'
#' @examples
#' if (reticulate::py_module_available("geomstats")) {
#' mt <- SPDMetricLogEuclidean$new(n = 3)
#' mt$dist(diag(1, 3), diag(1, 3))
#' }
dist_broadcast = function(points_a, points_b) {
super$get_python_class()$dist_broadcast(
point_a = points_a,
point_b = points_b
)
},
#' @description Computes the pairwise distance between points.
#'
#' @param points A numeric array of shape `c(n_samples, dim)` specifying a
#' set of points on the manifold.
#' @param n_jobs An integer value specifying the number of cores for
#' parallel computation. Defaults to `1L`.
#' @param ... Extra parameters to be passed tothe `joblib.Parallel` Python
#' class. See [joblib
#' documentation](https://joblib.readthedocs.io/en/latest/) for details.
#'
#' @return A numeric matrix of shape `c(n_samples, n_samples)` storing the
#' pairwise geodesic distances between all the points.
dist_pairwise = function(points, n_jobs = 1, ...) {
dots <- capture_extra_params(...)
dots$points <- points
dots$n_jobs <- as.integer(n_jobs)
do.call(super$get_python_class()$dist_pairwise, dots)
},
#' @description Computes the diameter of set of points on a manifold.
#'
#' @details The diameter is the maximum over all pairwise distances.
#'
#' @param points A numeric array of shape `c(n_samples, dim)` specifying a
#' set of points on the manifold.
#'
#' @return A numeric value representing the largest distance between any two
#' points in the input set.
diameter = function(points) {
super$get_python_class()$diameter(points)
},
#' @description Finds the closest neighbor to a point among a set of
#' neighbors.
#'
#' @param point A numeric array of shape `dim` specifying a point on the
#' manifold.
#' @param neighbors A numeric array of shape `c(n_neighbors, dim)`
#' specifying a set of neighboring points for the input `point`.
#'
#' @return An integer value representing the index of the neighbor in
#' `neighbors` that is closest to `point`.
closest_neighbor_index = function(point, neighbors) {
super$get_python_class()$closest_neighbor_index(
point = point,
neighbors = neighbors
)
},
#' @description Normalizes the basis with respect to the metric. This
#' corresponds to a renormalization of each basis vector.
#'
#' @param basis A numeric array of shape `c(dim, dim)` specifying a basis.
#'
#' @return A numeric array of shape `c(dim, n, n)` storing the normal basis.
normal_basis = function(basis, base_point = NULL) {
super$get_python_class()$normal_basis(
basis = basis,
base_point = base_point
)
},
#' @description Computes the sectional curvature.
#'
#' @details For two orthonormal tangent vectors \eqn{x} and \eqn{y} at a
#' base point, the sectional curvature is defined by \deqn{\langle R(x,
#' y)x, y \rangle = \langle R_x(y), y \rangle.} For non-orthonormal
#' vectors, it is \deqn{\langle R(x, y)x, y \rangle / \\|x \wedge y\\|^2.}
#' See also https://en.wikipedia.org/wiki/Sectional_curvature.
#'
#' @param tangent_vec_a A numeric array of shape `c(n, n)` specifying a
#' tangent vector at `base_point`.
#' @param tangent_vec_b A numeric array of shape `c(n, n)` specifying a
#' tangent vector at `base_point`.
#'
#' @return A numeric value representing the sectional curvature at
#' `base_point`.
sectional_curvature = function(tangent_vec_a, tangent_vec_b, base_point = NULL) {
super$get_python_class()$sectional_curvature(
tangent_vec_a = tangent_vec_a,
tangent_vec_b = tangent_vec_b,
base_point = base_point
)
}
),
private = list(
set_fields = function() {
super$set_fields()
self$signature <- super$get_python_class()$signature
}
)
)
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