SPDMatrices: Class for the Manifold of Symmetric Positive Definite...
In rgeomstats: Interface to 'Geomstats'
SPDMatrices R Documentation
Class for the Manifold of Symmetric Positive Definite Matrices
Description
Class for the manifold of symmetric positive definite (SPD)
matrices.
Super classes
rgeomstats::PythonClass -> rgeomstats::Manifold -> rgeomstats::OpenSet -> SPDMatrices
Public fields
nAn integer value specifying the number of rows and columns of the
matrices.
Methods
Public methods
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Inherited methods
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$to_tangent()rgeomstats::OpenSet$projection()
Method new()
The SPDMatrices class constructor.
Usage
SPDMatrices$new(n, ..., py_cls = NULL)
Arguments
nAn integer value specifying the number of rows and columns of the
matrices.
...Extra arguments to be passed to parent class constructors. See
OpenSet and Manifold classes.
py_clsA Python object of class SPDMatrices. Defaults to NULL
in which case it is instantiated on the fly using the other input
arguments.
Returns
An object of class SPDMatrices.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3
}
Method cholesky_factor()
Computes Cholesky factor for a symmetric positive definite
matrix.
Usage
SPDMatrices$cholesky_factor(mat)
Arguments
matA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices.
Returns
A numeric array of the same shape storing the corresponding
Cholesky factors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$cholesky_factor(A)
}
Method differential_cholesky_factor()
Computes the differential of the Cholesky factor map.
Usage
SPDMatrices$differential_cholesky_factor(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices specifying base points for the input
tangent vectors.
Returns
A numeric array of shape [… \times n \times n] storing
the differentials of the corresponding Cholesky factor maps.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_cholesky_factor(diag(1, 3), A)
}
Method expm()
Computes the matrix exponential for a symmetric matrix.
Usage
SPDMatrices$expm(mat)
Arguments
matA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices.
Returns
A numeric array of the same shape storing the corresponding
matrix exponentials.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$expm(diag(-1, 3))
}
Method differential_exp()
Computes the differential of the matrix exponential.
Usage
SPDMatrices$differential_exp(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices specifying base points for the input
tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing
the differentials of matrix exponential at corresponding base points
applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_exp(diag(1, 3), A)
}
Method inverse_differential_exp()
Computes the inverse of the differential of the matrix
exponential.
Usage
SPDMatrices$inverse_differential_exp(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices specifying base points for the input
tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing
the inverse of the differentials of matrix exponential at corresponding
base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_exp(diag(1, 3), A)
}
Method logm()
Computes the matrix logarithm of an SPD matrix.
Usage
SPDMatrices$logm(mat)
Arguments
matA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices.
Returns
A numeric array of the same shape storing the logarithms of the
input SPD matrices.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$logm(diag(1, 3))
}
Method differential_log()
Computes the differential of the matrix logarithm.
Usage
SPDMatrices$differential_log(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices specifying base points for the input
tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing
the differentials of matrix logarithm at corresponding base points
applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_log(diag(1, 3), A)
}
Method inverse_differential_log()
Computes the inverse of the differential of the matrix
logarithm.
Usage
SPDMatrices$inverse_differential_log(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices specifying base points for the input
tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing
the inverse of the differentials of matrix logarithm at corresponding
base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_log(diag(1, 3), A)
}
Method powerm()
Computes the matrix power of an SPD matrix.
Usage
SPDMatrices$powerm(mat, power)
Arguments
matA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices.
powerA numeric value or vector specifying the desired power(s).
Returns
A numeric array of the same shape as mat storing the
corresponding matrix powers computed as:
A^p = \exp(p \log(A)).
If power is a vector, a list of such arrays is returned.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$powerm(diag(1, 3), 2)
}
Method differential_power()
Computes the differential of the matrix power function.
Usage
SPDMatrices$differential_power(power, tangent_vec, base_point)
Arguments
powerAn integer value specifying the desired power.
tangent_vecA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices specifying base points for the input
tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing
the differential of the power function
A^p = \exp(p \log(A))
at
corresponding base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_power(2, diag(1, 3), A)
}
Method inverse_differential_power()
Computes the inverse of the differential of the matrix power
function.
Usage
SPDMatrices$inverse_differential_power(power, tangent_vec, base_point)
Arguments
powerAn integer value specifying the desired power.
tangent_vecA numeric array of shape [… \times n \times n]
specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n]
specifying one or more SPD matrices specifying base points for the input
tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing
the inverse of the differential of the power function
A^p =
\exp(p \log(A))
at corresponding base points applied to corresponding
tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_power(2, diag(1, 3), A)
}
Method clone()
The objects of this class are cloneable with this method.
Usage
SPDMatrices$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Yann Thanwerdas
See Also
Other symmetric positive definite matrix classes:
SPDMatrix()
Examples
## ------------------------------------------------
## Method `SPDMatrices$new`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3
}
## ------------------------------------------------
## Method `SPDMatrices$cholesky_factor`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$cholesky_factor(A)
}
## ------------------------------------------------
## Method `SPDMatrices$differential_cholesky_factor`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_cholesky_factor(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$expm`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$expm(diag(-1, 3))
}
## ------------------------------------------------
## Method `SPDMatrices$differential_exp`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_exp(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$inverse_differential_exp`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_exp(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$logm`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$logm(diag(1, 3))
}
## ------------------------------------------------
## Method `SPDMatrices$differential_log`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_log(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$inverse_differential_log`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_log(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$powerm`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$powerm(diag(1, 3), 2)
}
## ------------------------------------------------
## Method `SPDMatrices$differential_power`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_power(2, diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$inverse_differential_power`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_power(2, diag(1, 3), A)
}
rgeomstats documentation built on Nov. 4, 2022, 5:09 p.m.
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| SPDMatrices | R Documentation |
Class for the Manifold of Symmetric Positive Definite Matrices
Description
Class for the manifold of symmetric positive definite (SPD) matrices.
Super classes
rgeomstats::PythonClass -> rgeomstats::Manifold -> rgeomstats::OpenSet -> SPDMatrices
Public fields
nAn integer value specifying the number of rows and columns of the matrices.
Methods
Public methods
Inherited methods
rgeomstats::PythonClass$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::OpenSet$projection()
Method new()
The SPDMatrices class constructor.
Usage
SPDMatrices$new(n, ..., py_cls = NULL)
Arguments
nAn integer value specifying the number of rows and columns of the matrices.
...Extra arguments to be passed to parent class constructors. See
OpenSetandManifoldclasses.py_clsA Python object of class
SPDMatrices. Defaults toNULLin which case it is instantiated on the fly using the other input arguments.
Returns
An object of class SPDMatrices.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3
}
Method cholesky_factor()
Computes Cholesky factor for a symmetric positive definite matrix.
Usage
SPDMatrices$cholesky_factor(mat)
Arguments
matA numeric array of shape [… \times n \times n] specifying one or more SPD matrices.
Returns
A numeric array of the same shape storing the corresponding Cholesky factors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$cholesky_factor(A)
}
Method differential_cholesky_factor()
Computes the differential of the Cholesky factor map.
Usage
SPDMatrices$differential_cholesky_factor(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n] specifying one or more SPD matrices specifying base points for the input tangent vectors.
Returns
A numeric array of shape [… \times n \times n] storing the differentials of the corresponding Cholesky factor maps.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_cholesky_factor(diag(1, 3), A)
}
Method expm()
Computes the matrix exponential for a symmetric matrix.
Usage
SPDMatrices$expm(mat)
Arguments
matA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices.
Returns
A numeric array of the same shape storing the corresponding matrix exponentials.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$expm(diag(-1, 3))
}
Method differential_exp()
Computes the differential of the matrix exponential.
Usage
SPDMatrices$differential_exp(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n] specifying one or more SPD matrices specifying base points for the input tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing the differentials of matrix exponential at corresponding base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_exp(diag(1, 3), A)
}
Method inverse_differential_exp()
Computes the inverse of the differential of the matrix exponential.
Usage
SPDMatrices$inverse_differential_exp(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n] specifying one or more SPD matrices specifying base points for the input tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing the inverse of the differentials of matrix exponential at corresponding base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_exp(diag(1, 3), A)
}
Method logm()
Computes the matrix logarithm of an SPD matrix.
Usage
SPDMatrices$logm(mat)
Arguments
matA numeric array of shape [… \times n \times n] specifying one or more SPD matrices.
Returns
A numeric array of the same shape storing the logarithms of the input SPD matrices.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$logm(diag(1, 3))
}
Method differential_log()
Computes the differential of the matrix logarithm.
Usage
SPDMatrices$differential_log(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n] specifying one or more SPD matrices specifying base points for the input tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing the differentials of matrix logarithm at corresponding base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_log(diag(1, 3), A)
}
Method inverse_differential_log()
Computes the inverse of the differential of the matrix logarithm.
Usage
SPDMatrices$inverse_differential_log(tangent_vec, base_point)
Arguments
tangent_vecA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n] specifying one or more SPD matrices specifying base points for the input tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing the inverse of the differentials of matrix logarithm at corresponding base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_log(diag(1, 3), A)
}
Method powerm()
Computes the matrix power of an SPD matrix.
Usage
SPDMatrices$powerm(mat, power)
Arguments
matA numeric array of shape [… \times n \times n] specifying one or more SPD matrices.
powerA numeric value or vector specifying the desired power(s).
Returns
A numeric array of the same shape as mat storing the
corresponding matrix powers computed as:
A^p = \exp(p \log(A)).
If power is a vector, a list of such arrays is returned.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$powerm(diag(1, 3), 2)
}
Method differential_power()
Computes the differential of the matrix power function.
Usage
SPDMatrices$differential_power(power, tangent_vec, base_point)
Arguments
powerAn integer value specifying the desired power.
tangent_vecA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n] specifying one or more SPD matrices specifying base points for the input tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing the differential of the power function
A^p = \exp(p \log(A))
at corresponding base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_power(2, diag(1, 3), A)
}
Method inverse_differential_power()
Computes the inverse of the differential of the matrix power function.
Usage
SPDMatrices$inverse_differential_power(power, tangent_vec, base_point)
Arguments
powerAn integer value specifying the desired power.
tangent_vecA numeric array of shape [… \times n \times n] specifying one or more symmetric matrices at corresponding base points.
base_pointA numeric array of shape [… \times n \times n] specifying one or more SPD matrices specifying base points for the input tangent vectors.
Returns
A numeric array of shape [… \times n \times] storing the inverse of the differential of the power function
A^p = \exp(p \log(A))
at corresponding base points applied to corresponding tangent vectors.
Examples
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_power(2, diag(1, 3), A)
}
Method clone()
The objects of this class are cloneable with this method.
Usage
SPDMatrices$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Yann Thanwerdas
See Also
Other symmetric positive definite matrix classes:
SPDMatrix()
Examples
## ------------------------------------------------
## Method `SPDMatrices$new`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3
}
## ------------------------------------------------
## Method `SPDMatrices$cholesky_factor`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$cholesky_factor(A)
}
## ------------------------------------------------
## Method `SPDMatrices$differential_cholesky_factor`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_cholesky_factor(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$expm`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$expm(diag(-1, 3))
}
## ------------------------------------------------
## Method `SPDMatrices$differential_exp`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_exp(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$inverse_differential_exp`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_exp(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$logm`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$logm(diag(1, 3))
}
## ------------------------------------------------
## Method `SPDMatrices$differential_log`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_log(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$inverse_differential_log`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_log(diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$powerm`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
spd3$powerm(diag(1, 3), 2)
}
## ------------------------------------------------
## Method `SPDMatrices$differential_power`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$differential_power(2, diag(1, 3), A)
}
## ------------------------------------------------
## Method `SPDMatrices$inverse_differential_power`
## ------------------------------------------------
if (reticulate::py_module_available("geomstats")) {
spd3 <- SPDMatrix(n = 3)
V <- cbind(
c(sqrt(2) / 2, -sqrt(2) / 2, 0),
c(sqrt(2) / 2, sqrt(2) / 2, 0),
c(0, 0, 1)
)
A <- V %*% diag(1:3) %*% t(V)
spd3$inverse_differential_power(2, diag(1, 3), A)
}
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