TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace
¶
Module Contents¶
Classes¶
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Multivariate Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\) |
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Multivariate Gaussian distribution \(\pi({\bf x}\vert{\bf y}) \sim \mathcal{N}(\mu({\bf y}), \Sigma({\bf y}))\) |
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Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\) |
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Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\) |
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Transition probability distribution \(g(\theta,{\bf x}_{k-1},{\bf x}_k) = \pi_{{\bf X}_k \vert {\bf X}_{k-1}={\bf x}_{k-1}}({\bf x}_k, \Theta=\theta) = \pi({\bf x}_k - F_k(\theta) {\bf x}_{k-1} - {\bf c}_k(\theta))\) where \(\pi \sim \mathcal{N}(\mu_k(\theta),Q_k(\theta))\). |
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Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\) |
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Define the log-likelihood for the additive linear Gaussian model |
Functions¶
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Attributes¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw1[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw1dot[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw1[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw1dot[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw2[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw2dot[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw2[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw2dot[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yb[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Ybdot[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pb[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pbdot[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yc[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Ycdot[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.D1[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.D2[source]¶
- TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.DEFAULTS[source]¶
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Coradia175Vehicle(v, observables=[Ybdot, Pb, Ycdot], dt=0.01, Ar=2 * 0.33 * 1e-06, init_noise=1e-06, obs_noise={'Yw1dot': 0.0001 * 10.0, 'Yw2dot': 0.0001 * 10.0, 'Ybdot': 4.11 * 0.0001 * 10.0, 'Pb': 3.75 * 1e-07 * 10.0, 'Ycdot': 7.62 * 0.001 * 10.0})[source]¶
Bases:
object
- Parameters:
v (float) – Longitudinal vehicle velocity (m/s)
- get_system_matrix(L_Ky=DEFAULTS['L_Ky'], T_Ky=DEFAULTS['T_Ky'], L_KPsi=DEFAULTS['L_KPsi'], T_KPsi=DEFAULTS['T_KPsi'], Kyb=DEFAULTS['Kyb'], Cyb=DEFAULTS['Cyb'], CPb=DEFAULTS['CPb'], f11=DEFAULTS['f11'], f22=DEFAULTS['f22'])[source]¶
- get_grad_system_matrix(par_name_list, L_Ky=DEFAULTS['L_Ky'], T_Ky=DEFAULTS['T_Ky'], L_KPsi=DEFAULTS['L_KPsi'], T_KPsi=DEFAULTS['T_KPsi'], Kyb=DEFAULTS['Kyb'], Cyb=DEFAULTS['Cyb'], CPb=DEFAULTS['CPb'], f11=DEFAULTS['f11'], f22=DEFAULTS['f22'])[source]¶
- get_observation_matrix(L_Ky=DEFAULTS['L_Ky'], T_Ky=DEFAULTS['T_Ky'], L_KPsi=DEFAULTS['L_KPsi'], T_KPsi=DEFAULTS['T_KPsi'], Kyb=DEFAULTS['Kyb'], Cyb=DEFAULTS['Cyb'], CPb=DEFAULTS['CPb'], f11=DEFAULTS['f11'], f22=DEFAULTS['f22'])[source]¶
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.ParametersPrior(par_name_list)[source]¶
Bases:
TransportMaps.Distributions.NormalDistribution
Multivariate Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\)
- Parameters:
mu (
ndarray
[\(d\)]) – mean vector \(\mu\)covariance (
ndarray
[\(d,d\)]) – covariance matrix \(\Sigma\)precision (
ndarray
[\(d,d\)]) – precision matrix \(\Sigma^{-1}\)square_root_covariance (
ndarray
[\(d,d\)]) – square root \(\Sigma^{\frac{1}{2}}\)square_root_precision (
ndarray
[\(d,d\)]) – square root \(\Sigma^{-\frac{1}{2}}\)square_root_type (str) – type of square root to be used in case
covariance
orprecision``were provided. For ``square_root_type=='sym'
, \(L=U\Lambda^{\frac{1}{2}}U^T\) where \(\Sigma = U\Lambda U^T\) is the eigenvalue decomposition of \(\Sigma\). Forsquare_root_type=='tri'
orsquare_root_type=='chol'
, :maht:`L=C` where \(\Sigma=CC^T\) is the Cholesky decomposition of \(\Sigma\). Forsquare_root_type=='kl'
, \(L=U\Lambda^{\frac{1}{2}}\) where \(\Sigma = U\Lambda U^T\) is the eigenvalue decomposition of \(\Sigma\) (this corresponds to the Karuenen-Loeve expansion). The eigenvalues and eigenvectors are ordered with \(\lambda_i\geq\lambda_{i+1}\). If the parametersquare_root
is provided, then thesquare_root_type
attribute will be setuser
.
Note
The arguments
covariance
,precision
andsquare_root
are mutually exclusive.
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.StateSpacePrior(vehicle, par_name_list=[], init_coeffs=None)[source]¶
Bases:
TransportMaps.Distributions.ConditionallyGaussianDistribution
Multivariate Gaussian distribution \(\pi({\bf x}\vert{\bf y}) \sim \mathcal{N}(\mu({\bf y}), \Sigma({\bf y}))\)
- Parameters:
mu (
Map
) – mean vector mapsigma (
Map
) – covariance matrix mapprecision (
Map
) – precision matrix mapcoeffs (
ndarray
) – fix the coefficients \({\bf y}\)
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.DynamicsMap(vehicle, par_name_list=[])[source]¶
Bases:
TransportMaps.Maps.Map
Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)
- evaluate(x, *args, **kwargs)[source]¶
[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- grad_x(x, *args, **kwargs)[source]¶
[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y,d_x\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.NoiseDynamicsMap(vehicle, par_name_list=[])[source]¶
Bases:
TransportMaps.Maps.Map
Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)
- evaluate(x, *args, **kwargs)[source]¶
[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- grad_x(x, *args, **kwargs)[source]¶
[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y,d_x\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.StateSpaceTransition(vehicle, par_name_list=[], init_coeffs=None)[source]¶
-
Transition probability distribution \(g(\theta,{\bf x}_{k-1},{\bf x}_k) = \pi_{{\bf X}_k \vert {\bf X}_{k-1}={\bf x}_{k-1}}({\bf x}_k, \Theta=\theta) = \pi({\bf x}_k - F_k(\theta) {\bf x}_{k-1} - {\bf c}_k(\theta))\) where \(\pi \sim \mathcal{N}(\mu_k(\theta),Q_k(\theta))\).
This represents the following Markov transition model:
\[\begin{split}{\bf x}_k = c_k + F_k {\bf x}_{k-1} + {\bf w}_k \\ {\bf w}_k \sim \mathcal{N}(\mu,Q_k)\end{split}\]where the control \({\bf c}_k := B_k {\bf u}_k\) can be used for control purposes
- Parameters:
ck (
ndarray
[\(d\)] orMap
) – constant part or map returning the constant part given some parametersFk (
ndarray
[\(d,d\)] orMap
) – state transition matrix (dynamics) or map returning the linear part given some parametrsmu (
ndarray
[\(d\)] orMap
) – mean \(\mu_k\) or parametric map for \(\mu_k(\theta)\)covariance (
ndarray
[\(d,d\)] orMap
) – covariance \(Q_k\) or parametric map for \(Q_k(\theta)\)precision (
ndarray
[\(d,d\)] orMap
) – precision \(Q_k^{-1}\) or parametric map for \(Q_k^{-1}(\theta)\)coeffs (
ndarray
) – fixing the coefficients \(\theta\)
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.ObservationSystemMap(vehicle, par_name_list=[])[source]¶
Bases:
TransportMaps.Maps.Map
Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)
- evaluate(x, *args, **kwargs)[source]¶
[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- grad_x(x, *args, **kwargs)[source]¶
[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).
- Parameters:
- Returns:
(
ndarray
[\(m,d_y,d_x\)]) – transformed points- Raises:
NotImplementedError – to be implemented in sub-classes
- class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.StateSpaceLogLikelihood(y, vehicle, par_name_list=[], init_coeffs=np.zeros(0))[source]¶
Bases:
TransportMaps.Likelihoods.AdditiveConditionallyLinearGaussianLogLikelihood
Define the log-likelihood for the additive linear Gaussian model
The model is
\[{\bf y} = {\bf c}(\theta) + {\bf T}(\theta){\bf x} + \varepsilon \;, \quad \varepsilon \sim \mathcal{N}(\mu(\theta), \Sigma(\theta))\]where \(T \in \mathbb{R}^{d_y \times d_x}\), \(\mu \in \mathbb{R}^{d_y}\) and \(\Sigma \in \mathbb{R}^{d_y \times d_y}\) is symmetric positve definite
- Parameters:
y (
ndarray
[\(d_y\)]) – datac (
ndarray
[\(d_y\)] orMap
) – system constant or parametric map returning the constantT (
ndarray
[\(d_y,d_x\)] orMap
) – system matrix or parametric map returning the system matrixmu (
ndarray
[\(d_y\)] orMap
) – noise mean or parametric map returning the meancovariance (
ndarray
[\(d_y,d_y\)] orMap
) – noise covariance or parametric map returning the covarianceprecision (
ndarray
[\(d_y,d_y\)] orMap
) – noise precision matrix or parametric map returning the precision matrixactive_vars_system (
list
ofint
) – active variables identifying the parameters for for \(c(\theta), T(\theta)\).active_vars_distribution (
list
ofint
) – active variables identifying the parameters for for \(\mu(\theta), \Sigma(\theta)\).coeffs (
ndarray
) – initialization coefficients