Title: Riemannian Metrics for Symmetric Positive Definite Matrices
Version: 0.1.0
Description: Implements various Riemannian metrics for symmetric positive definite matrices, including AIRM (Affine Invariant Riemannian Metric, see Pennec, Fillard, and Ayache (2006) <doi:10.1007/s11263-005-3222-z>), Log-Euclidean (see Arsigny, Fillard, Pennec, and Ayache (2006) <doi:10.1002/mrm.20965>), Euclidean, Log-Cholesky (see Lin (2019) <doi:10.1137/18M1221084>), and Bures-Wasserstein metrics (see Bhatia, Jain, and Lim (2019) <doi:10.1016/j.exmath.2018.01.002>). Provides functions for computing logarithmic and exponential maps, vectorization, and statistical operations on the manifold of positive definite matrices.
License: MIT + file LICENSE
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.3.2
Depends: R (≥ 4.3.0), Matrix
Imports: methods, expm, R6, purrr, MASS, furrr
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder: knitr
URL: https://nicoesve.github.io/riemtan/
BugReports: https://github.com/nicoesve/riemtan/issues
Config/testthat/edition: 3
Maintainer: Nicolas Escobar <nescoba@iu.edu>
NeedsCompilation: no
Packaged: 2025-04-19 21:30:24 UTC; nicolasescobar
Author: Nicolas Escobar ORCID iD [aut, cre], Jaroslaw Harezlak [ths]
Repository: CRAN
Date/Publication: 2025-04-23 10:10:02 UTC

riemtan: Riemannian Metrics for Symmetric Positive Definite Matrices

Description

Implements various Riemannian metrics for symmetric positive definite matrices, including AIRM (Affine Invariant Riemannian Metric, see Pennec, Fillard, and Ayache (2006) doi:10.1007/s11263-005-3222-z), Log-Euclidean (see Arsigny, Fillard, Pennec, and Ayache (2006) doi:10.1002/mrm.20965), Euclidean, Log-Cholesky (see Lin (2019) doi:10.1137/18M1221084), and Bures-Wasserstein metrics (see Bhatia, Jain, and Lim (2019) doi:10.1016/j.exmath.2018.01.002). Provides functions for computing logarithmic and exponential maps, vectorization, and statistical operations on the manifold of positive definite matrices.

Author(s)

Maintainer: Nicolas Escobar nescoba@iu.edu (ORCID)

Other contributors:

See Also

Useful links:

CSample Class

Description

This class represents a sample of connectomes, with various properties and methods to handle their tangent and vectorized images.

Active bindings

connectomes

Connectomes data

tangent_images

Tangent images data

vector_images

Vector images data

sample_size

Sample size

matrix_size

Matrix size

mfd_dim

Manifold dimension

is_centered

Centering status

frechet_mean

Frechet mean

riem_metric

Riemannian Metric used

variation

Variation of the sample

sample_cov

Sample covariance

ref_point

Reference point for tangent or vectorized images

Methods

Public methods

Method new()

Initialize a CSample object

Usage
CSample$new(
  conns = NULL,
  tan_imgs = NULL,
  vec_imgs = NULL,
  centered = NULL,
  ref_pt = NULL,
  metric_obj
)
Arguments
conns

A list of connectomes (default is NULL).

tan_imgs

A list of tangent images (default is NULL).

vec_imgs

A matrix whose rows are vectorized images (default is NULL).

centered

Boolean indicating whether tangent or vectorized images are centered (default is NULL).

ref_pt

A connectome (default is identity)

metric_obj

Object of class rmetric representing the Riemannian metric used.

Returns

A new CSample object.

Method compute_tangents()

This function computes the tangent images from the connectomes.

Usage
CSample$compute_tangents(ref_pt = default_ref_pt(private$p))
Arguments
ref_pt

A reference point, which must be a dppMatrix object (default is default_ref_pt).

Details

Error if ref_pt is not a dppMatrix object or if conns is not specified.

Returns

None

Method compute_conns()

This function computes the connectomes from the tangent images.

Usage
CSample$compute_conns()
Details

Error if tangent images are not specified.

Returns

None

Method compute_vecs()

This function computes the vectorized tangent images from the tangent images.

Usage
CSample$compute_vecs()
Details

Error if tangent images are not specified.

Returns

None

Method compute_unvecs()

This function computes the tangent images from the vector images.

Usage
CSample$compute_unvecs()
Details

Error if vec_imgs is not specified.

Returns

None

Method compute_fmean()

This function computes the Frechet mean of the sample.

Usage
CSample$compute_fmean(tol = 0.05, max_iter = 20, lr = 0.2)
Arguments
tol

Tolerance for the convergence of the mean (default is 0.05).

max_iter

Maximum number of iterations for the computation (default is 20).

lr

Learning rate for the optimization algorithm (default is 0.2).

Returns

None

Method change_ref_pt()

This function changes the reference point for the tangent images.

Usage
CSample$change_ref_pt(new_ref_pt)
Arguments
new_ref_pt

A new reference point, which must be a dppMatrix object.

Details

Error if tangent images have not been computed or if new_ref_pt is not a dppMatrix object.

Returns

None

Method center()

Center the sample

Usage
CSample$center()
Details

This function centers the sample by computing the Frechet mean if it is not already computed, and then changing the reference point to the computed Frechet mean. Error if tangent images are not specified. Error if the sample is already centered.

Returns

None. This function is called for its side effects.

Method compute_variation()

Compute Variation

Usage
CSample$compute_variation()
Details

This function computes the variation of the sample. It first checks if the vector images are null, and if so, it computes the vectors, computing first the tangent images if necessary. If the sample is not centered, it centers the sample and recomputes the vectors. Finally, it calculates the variation as the mean of the sum of squares of the vector images. Error if vec_imgs is not specified.

Returns

None. This function is called for its side effects.

Method compute_sample_cov()

Compute Sample Covariance

Usage
CSample$compute_sample_cov()
Details

This function computes the sample covariance matrix for the vector images. It first checks if the vector images are null, and if so, it computes the vectors, computing first the tangent images if necessary.

Returns

None. This function is called for its side effects.

Method clone()

The objects of this class are cloneable with this method.

Usage
CSample$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

TangentImageHandler Class

Description

TangentImageHandler Class

TangentImageHandler Class

Details

This class handles tangent images on a manifold. It provides methods to set a reference point, compute tangents, and perform various operations using a provided metric. Initialize the TangentImageHandler

Error if the tangent images have not been specified

Error if the reference point is not an object of class dppMatrix

Error if the matrix is not of type dspMatrix Tangent images getter

Active bindings

ref_point

A matrix of type dppMatrix

tangent_images

A list of dspMatrix objects

Methods

Public methods

Method new()

Usage
TangentImageHandler$new(metric_obj, reference_point = NULL)
Arguments
metric_obj

An rmetric object for operations.

reference_point

An optional reference point on the manifold.

Returns

A new instance of TangentImageHandler. Set a new reference point.

Method set_reference_point()

If tangent images have been created, it recomputes them by mapping to the manifold and then to the new tangent space.

Usage
TangentImageHandler$set_reference_point(new_ref_pt)
Arguments
new_ref_pt

A new reference point of class dppMatrix.

Returns

None. Computes the tangent images from the points in the manifold

Method compute_tangents()

Usage
TangentImageHandler$compute_tangents(manifold_points)
Arguments
manifold_points

A list of connectomes

Returns

None Computes vectorizations from tangent images

Method compute_vecs()

Usage
TangentImageHandler$compute_vecs()
Returns

A matrix, each row of which is a vectorization Computes connectomes from tangent images

Method compute_conns()

Usage
TangentImageHandler$compute_conns()
Returns

A list of connectomes Setter for the tangent images

Method set_tangent_images()

Usage
TangentImageHandler$set_tangent_images(reference_point, tangent_images)
Arguments
reference_point

A connectome

tangent_images

A list of tangent images

Returns

None Appends a matrix to the list of tangent images

Method add_tangent_image()

Usage
TangentImageHandler$add_tangent_image(image)
Arguments
image

Matrix to be added

Method get_tangent_images()

Usage
TangentImageHandler$get_tangent_images()
Returns

list of tangent matrices Wrapper for set_reference_point

Method relocate_tangents()

Usage
TangentImageHandler$relocate_tangents(new_ref_pt)
Arguments
new_ref_pt

The new reference point

Returns

None

Method clone()

The objects of this class are cloneable with this method.

Usage
TangentImageHandler$clone(deep = FALSE)
Arguments
deep

Whether to make a deep clone.

Compute the AIRM Exponential

Description

This function computes the Riemannian exponential map for the Affine-Invariant Riemannian Metric (AIRM).

Usage

airm_exp(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

v

A tangent vector of class dspMatrix, to be mapped back to the manifold at sigma.

Value

A symmetric positive-definite matrix of class dppMatrix.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  sigma <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  v <- diag(c(1, 0.5)) |>
    Matrix::symmpart() |>
    Matrix::pack()
  airm_exp(sigma, v)
}

Compute the AIRM Logarithm

Description

This function computes the Riemannian logarithmic map for the Affine-Invariant Riemannian Metric (AIRM).

Usage

airm_log(sigma, lambda)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

lambda

A symmetric positive-definite matrix of class dppMatrix, representing the target point.

Value

A symmetric matrix of class dspMatrix, representing the tangent space image of lambda at sigma.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  sigma <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  lambda <- diag(c(2, 3)) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  airm_log(sigma, lambda)
}

Compute the Inverse Vectorization (AIRM)

Description

Converts a vector back into a tangent matrix relative to a reference point using AIRM.

Usage

airm_unvec(sigma, w)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

w

A numeric vector, representing the vectorized tangent image.

Value

A symmetric matrix of class dspMatrix, representing the tangent vector.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  sigma <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  w <- c(1, sqrt(2), 2)
  airm_unvec(sigma, w)
}

Compute the AIRM Vectorization of Tangent Space

Description

Vectorizes a tangent matrix into a vector in Euclidean space using AIRM.

Usage

airm_vec(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

v

A symmetric matrix of class dspMatrix, representing a tangent vector.

Value

A numeric vector, representing the vectorized tangent image.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  sigma <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  v <- diag(c(1, 0.5)) |>
    Matrix::symmpart() |>
    Matrix::pack()
  airm_vec(sigma, v)
}

Compute the Bures-Wasserstein Exponential

Description

This function computes the Riemannian exponential map using the Bures-Wasserstein metric for symmetric positive-definite matrices. The map operates by solving a Lyapunov equation and then constructing the exponential.

Usage

bures_wasserstein_exp(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

v

A symmetric matrix of class dspMatrix, representing the tangent vector to be mapped.

Value

A symmetric positive-definite matrix of class dppMatrix, representing the point on the manifold.

Compute the Bures-Wasserstein Logarithm

Description

This function computes the Riemannian logarithmic map using the Bures-Wasserstein metric for symmetric positive-definite matrices.

Usage

bures_wasserstein_log(sigma, lambda)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

lambda

A symmetric positive-definite matrix of class dppMatrix, representing the target point.

Value

A symmetric matrix of class dspMatrix, representing the tangent space image of lambda at sigma.

Compute the Bures-Wasserstein Inverse Vectorization

Description

Compute the Bures-Wasserstein Inverse Vectorization

Usage

bures_wasserstein_unvec(sigma, w)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix

w

A numeric vector representing the vectorized tangent image

Value

A symmetric matrix of class dspMatrix

Compute the Bures-Wasserstein Vectorization

Description

Compute the Bures-Wasserstein Vectorization

Usage

bures_wasserstein_vec(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix

v

A symmetric matrix of class dspMatrix

Value

A numeric vector representing the vectorized tangent image

Compute the Frechet Mean

Description

This function computes the Frechet mean of a sample using an iterative algorithm.

Usage

compute_frechet_mean(sample, tol = 0.05, max_iter = 20, lr = 0.2)

Arguments

sample

An object of class CSample containing the sample data.

tol

A numeric value specifying the tolerance for convergence. Default is 0.05.

max_iter

An integer specifying the maximum number of iterations. Default is 20.

lr

A numeric value specifying the learning rate. Default is 0.2.

Details

The function iteratively updates the reference point of the sample until the change in the reference point is less than the specified tolerance or the maximum number of iterations is reached. If the tangent images are not already computed, they will be computed before starting the iterations.

Value

The computed Frechet mean.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  # Load the AIRM metric object
  data(airm)
  # Create a CSample object with example data
  conns <- list(
    diag(2) |> Matrix::nearPD() |> _$mat |> Matrix::pack(),
    diag(c(2, 3)) |> Matrix::nearPD() |> _$mat |> Matrix::pack()
  )
  sample <- CSample$new(conns = conns, metric_obj = airm)
  # Compute the Frechet mean
  compute_frechet_mean(sample, tol = 0.01, max_iter = 50, lr = 0.1)
}

Default reference point

Description

Default reference point

Usage

default_ref_pt(p)

Arguments

p

the dimension

Value

A diagonal matrix of the desired dimension

Differential of Matrix Exponential Map

Description

Computes the differential of the matrix exponential map located at a point a, evaluated at x

Usage

dexp(a, x)

Arguments

a

A symmetric matrix of class dspMatrix

x

A symmetric matrix representing tangent vector of class dspMatrix

Value

A positive definite symmetric matrix representing the differential located at a and evaluated at x, of class dppMatrix

Differential of Matrix Logarithm Map

Description

Computes the differential of the matrix logarithm map at a point Sigma, evaluated at H

Usage

dlog(sigma, h)

Arguments

sigma

A symmetric positive definite matrix of class dspMatrix

h

A symmetric matrix representing tangent vector of class dsyMatrix

Value

A symmetric matrix representing the differential evaluated at H of class dsyMatrix

Compute the Euclidean Exponential

Description

Compute the Euclidean Exponential

Usage

euclidean_exp(sigma, v)

Arguments

sigma

A reference point.

v

A tangent vector to be mapped back to the manifold at sigma.

Value

The point on the manifold corresponding to the tangent vector at sigma.

Compute the Euclidean Logarithm

Description

Compute the Euclidean Logarithm

Usage

euclidean_log(sigma, lambda)

Arguments

sigma

A reference point.

lambda

A point on the manifold.

Value

The tangent space image of lambda at sigma.

Compute the Inverse Vectorization (Euclidean)

Description

Converts a vector back into a tangent matrix relative to a reference point using Euclidean metric.

Usage

euclidean_unvec(sigma, w)

Arguments

sigma

A symmetric matrix.

w

A numeric vector, representing the vectorized tangent image.

Value

A symmetric matrix, representing the tangent vector.

Vectorize at Identity Matrix (Euclidean)

Description

Converts a symmetric matrix into a vector representation.

Usage

euclidean_vec(sigma, v)

Arguments

sigma

A symmetric matrix.

v

A vector.

Value

A numeric vector, representing the vectorized tangent image.

Half-underscore operation for use in the log-Cholesky metric

Description

Half-underscore operation for use in the log-Cholesky metric

Usage

half_underscore(x)

Arguments

x

A symmetric matrix (object of class dsyMatrix)

Value

The strictly lower triangular part of the matrix, plus half its diagonal part

Create an Identity Matrix

Description

Create an Identity Matrix

Usage

id_matr(sigma)

Arguments

sigma

A matrix.

Value

An identity matrix of the same dimensions as sigma.

Compute the Log-Cholesky Exponential

Description

This function computes the Riemannian exponential map using the Log-Cholesky metric for symmetric positive-definite matrices. The map operates by transforming the tangent vector via Cholesky decomposition of the reference point.

Usage

log_cholesky_exp(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

v

A symmetric matrix of class dspMatrix, representing the tangent vector to be mapped.

Value

A symmetric positive-definite matrix of class dppMatrix, representing the point on the manifold.

Compute the Log-Cholesky Logarithm

Description

This function computes the Riemannian logarithmic map using the Log-Cholesky metric for symmetric positive-definite matrices. The Log-Cholesky metric operates by transforming matrices via their Cholesky decomposition.

Usage

log_cholesky_log(sigma, lambda)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix, representing the reference point.

lambda

A symmetric positive-definite matrix of class dppMatrix, representing the target point.

Value

A symmetric matrix of class dspMatrix, representing the tangent space image of lambda at sigma.

Compute the Log-Cholesky Inverse Vectorization

Description

Compute the Log-Cholesky Inverse Vectorization

Usage

log_cholesky_unvec(sigma, w)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix

w

A numeric vector representing the vectorized tangent image

Value

A symmetric matrix of class dspMatrix

Compute the Log-Cholesky Vectorization

Description

Compute the Log-Cholesky Vectorization

Usage

log_cholesky_vec(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix

v

A symmetric matrix of class dspMatrix

Value

A numeric vector representing the vectorized tangent image

Compute the Log-Euclidean Exponential

Description

This function computes the Euclidean exponential map.

Usage

log_euclidean_exp(ref_pt, v)

Arguments

ref_pt

A reference point.

v

A tangent vector to be mapped back to the manifold at ref_pt.

Value

The point on the manifold corresponding to the tangent vector at ref_pt.

Compute the Log-Euclidean Logarithm

Description

Compute the Log-Euclidean Logarithm

Usage

log_euclidean_log(sigma, lambda)

Arguments

sigma

A reference point.

lambda

A point on the manifold.

Value

The tangent space image of lambda at sigma.

Compute the Inverse Vectorization (Euclidean)

Description

Converts a vector back into a tangent matrix relative to a reference point using Euclidean metric.

Usage

log_euclidean_unvec(sigma, w)

Arguments

sigma

A symmetric matrix.

w

A numeric vector, representing the vectorized tangent image.

Value

A symmetric matrix, representing the tangent vector.

Vectorize at Identity Matrix (Euclidean)

Description

Converts a symmetric matrix into a vector representation.

Usage

log_euclidean_vec(sigma, v)

Arguments

sigma

A symmetric matrix.

v

A vector.

Value

A numeric vector, representing the vectorized tangent image.

Metric Object Constructor

Description

Constructs a metric object that contains the necessary functions for Riemannian operations.

Usage

metric(log, exp, vec, unvec)

Arguments

log

A function representing the Riemannian logarithmic map. This function should accept a dppMatrix (the reference point) and another dppMatrix (the matrix whose logarithm is to be computed), and it outputs a dspMatrix (the tangent image).

exp

A function representing the Riemannian exponential map. This function should accept a dppMatrix (the reference point) and a dspMatrix (the matrix whose exponential is to be computed) and return a dppMatrix (the image on the manifold).

vec

A function representing the vectorization operation for tangent spaces. This function should accept a dppMatrix (the reference point) and a dspMatrix (the tangent image) and return a vector (the vectorized image).

unvec

A function representing the inverse of the vectorization operation. This function should accept a dppMatrix (the reference point) and a vector (the vectorized image), and it returns a dspMatrix (the tangent image).

Value

An object of class rmetric containing the specified functions.

Pre-configured Riemannian metrics for SPD matrices

Description

Ready-to-use metric objects for various Riemannian geometries on the manifold of symmetric positive definite matrices.

Usage

airm

log_euclidean

euclidean

log_cholesky

bures_wasserstein

Format

Objects of class rmetric containing four functions:

log

Computes the Riemannian logarithm

exp

Computes the Riemannian exponential

vec

Performs vectorization

unvec

Performs inverse vectorization

An object of class rmetric of length 4.

An object of class rmetric of length 4.

An object of class rmetric of length 4.

An object of class rmetric of length 4.

An object of class rmetric of length 4.

Relocate Tangent Representations to a New Reference Point

Description

Changes the reference point for tangent space representations on a Riemannian manifold.

Usage

relocate(old_ref, new_ref, images, met)

Arguments

old_ref

A reference point on the manifold to be replaced. Must be an object of class dppMatrix from the Matrix package.

new_ref

The new reference point on the manifold. Must be an object of class dppMatrix from the Matrix package.

images

A list of tangent representations relative to the old reference point. Each element in the list must be an object of class dspMatrix.

met

A metric object of class rmetric, containing functions for Riemannian operations (logarithmic map, exponential map, vectorization, and inverse vectorization).

Value

A list of tangent representations relative to the new reference point. Each element in the returned list will be an object of class dspMatrix.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  data(airm)
  old_ref <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  new_ref <- diag(c(2, 3)) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  images <- list(
    diag(2) |> Matrix::symmpart() |> Matrix::pack(),
    diag(c(1, 0.5)) |> Matrix::symmpart() |> Matrix::pack()
  )
  relocate(old_ref, new_ref, images, airm)
}

Generate Random Samples from a Riemannian Normal Distribution

Description

Simulates random samples from a Riemannian normal distribution on symmetric positive definite matrices.

Usage

rspdnorm(n, refpt, disp, met)

Arguments

n

Number of samples to generate.

refpt

Reference point on the manifold, represented as a symmetric positive definite matrix. Must be an object of class dppMatrix from the Matrix package.

disp

Dispersion matrix defining the spread of the distribution. Must be an object of class dppMatrix from the Matrix package.

met

A metric object of class rmetric.

Value

An object of class CSample containing the generated samples.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  data(airm)
  refpt <- diag(2) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  disp <- diag(3) |>
    Matrix::nearPD() |>
    _$mat |>
    Matrix::pack()
  rspdnorm(10, refpt, disp, airm)
}

Wrapper for the matrix logarithm

Description

Wrapper for the matrix logarithm

Usage

safe_logm(x)

Arguments

x

A matrix

Value

Its matrix logarithm

Solve the Lyapunov Equation

Description

Solves the Lyapunov equation L P + P L = V for L.

Usage

solve_lyapunov(p, v)

Arguments

p

A symmetric positive-definite matrix of class dppMatrix.

v

A symmetric matrix of class dspMatrix.

Value

A symmetric matrix of class dspMatrix, representing the solution L.

Reverse isometry from tangent space at identity to tangent space at P

Description

Reverse isometry from tangent space at identity to tangent space at P

Usage

spd_isometry_from_identity(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix

v

A symmetric matrix of class dspMatrix

Value

A symmetric matrix of class dspMatrix

Isometry from tangent space at P to tangent space at identity

Description

Isometry from tangent space at P to tangent space at identity

Usage

spd_isometry_to_identity(sigma, v)

Arguments

sigma

A symmetric positive-definite matrix of class dppMatrix

v

A symmetric matrix of class dspMatrix

Value

A symmetric matrix of class dspMatrix

Validate Connections

Description

Validates the connections input.

Usage

validate_conns(conns, tan_imgs, vec_imgs, centered)

Arguments

conns

List of connection matrices.

tan_imgs

List of tangent images.

vec_imgs

Matrix of vector images.

centered

Logical indicating if the data is centered.

Value

None. Throws an error if the validation fails.

Validate arguments for Riemannian logarithms

Description

Validate arguments for Riemannian logarithms

Usage

validate_exp_args(sigma, v)

Arguments

sigma

A dppMatrix object

v

A dspMatrix object

Details

Error if sigma and lambda are not of the same dimensions

Value

None

Validate arguments for Riemannian logarithms

Description

Validate arguments for Riemannian logarithms

Usage

validate_log_args(sigma, lambda)

Arguments

sigma

A dppMatrix object

lambda

A dppMatrix object

Details

Error if sigma and lambda are not of the same dimensions

Value

None

Validate Metric

Description

Validates that the metric is not NULL.

Usage

validate_metric(metric)

Arguments

metric

The metric to validate.

Value

None. Throws an error if the metric is NULL.

Validate Tangent Images

Description

Validates the tangent images input.

Usage

validate_tan_imgs(tan_imgs, vec_imgs, centered)

Arguments

tan_imgs

List of tangent images.

vec_imgs

List of vector images.

centered

Logical indicating if the data is centered.

Value

None. Throws an error if the validation fails.

Validate arguments for inverse vectorization

Description

Validate arguments for inverse vectorization

Usage

validate_unvec_args(sigma, w)

Arguments

sigma

A dppMatrix object

w

A numeric vector

Details

Error if the dimensionalities don't match

Value

None

Validate arguments for vectorization

Description

Validate arguments for vectorization

Usage

validate_vec_args(sigma, v)

Arguments

sigma

A dppMatrix object

v

A dspMatrix object

Details

Error if sigma and v are not of the same dimensions

Value

None

Validate Vector Images

Description

Validates the vector images input.

Usage

validate_vec_imgs(vec_imgs, centered)

Arguments

vec_imgs

List of vector images.

centered

Logical indicating if the data is centered.

Value

None. Throws an error if the validation fails.

Vectorize at Identity Matrix

Description

Converts a symmetric matrix into a vector representation specific to operations at the identity matrix.

Usage

vec_at_id(v)

Arguments

v

A symmetric matrix of class dspMatrix.

Value

A numeric vector, representing the vectorized tangent image.

Examples

if (requireNamespace("Matrix", quietly = TRUE)) {
  library(Matrix)
  v <- diag(c(1, sqrt(2))) |>
    Matrix::symmpart() |>
    Matrix::pack()
  vec_at_id(v)
}