TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace

Module Contents

Classes

Coradia175Vehicle	param v: Longitudinal vehicle velocity (m/s)
ParametersPrior	Multivariate Gaussian distribution \(\mathcal{N}(\mu,\Sigma)\)
StateSpacePrior	Multivariate Gaussian distribution \(\pi({\bf x}\vert{\bf y}) \sim \mathcal{N}(\mu({\bf y}), \Sigma({\bf y}))\)
DynamicsMap	Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)
NoiseDynamicsMap	Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)
StateSpaceTransition	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 \(\pi \sim \mathcal{N}(\mu_k(\theta),Q_k(\theta))\).
ObservationSystemMap	Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)
StateSpaceLogLikelihood	Define the log-likelihood for the additive linear Gaussian model

Functions

generate_data(nsteps, vehicle[, par_name_list, ...])

Attributes

Yw1
Yw1dot
Pw1
Pw1dot
Yw2
Yw2dot
Pw2
Pw2dot
Yb
Ybdot
Pb
Pbdot
Yc
Ycdot
D1
D2
DEFAULTS

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw1

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw1dot

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw1

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw1dot

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw2

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yw2dot

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw2

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pw2dot

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yb

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Ybdot

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pb

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Pbdot

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Yc

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.Ycdot

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.D1

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.D2

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.DEFAULTS

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})

Bases: object

Parameters:

v (float) – Longitudinal vehicle velocity (m/s)

mw = 1000.0

Iw = 600.0

mb = 2000.0

Ib = 2300.0

mc = 8720.0

a = 1.05

l = 0.75

lmb = 0.15

r0 = 0.37

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'])

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'])

get_track_matrix()

get_grad_track_matrix(par_name_list)

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'])

get_grad_observation_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'])

get_matrices(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'])

class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.ParametersPrior(par_name_list)

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 or precision``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 \(\Sigma\). For square_root_type=='tri' or square_root_type=='chol', :maht:`L=C` where \(\Sigma=CC^T\) is the Cholesky decomposition of \(\Sigma\). For square_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 parameter square_root is provided, then the square_root_type attribute will be set user.

Note

The arguments covariance, precision and square_root are mutually exclusive.

class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.StateSpacePrior(vehicle, par_name_list=[], init_coeffs=None)

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 map

• sigma (Map) – covariance matrix map

• precision (Map) – precision matrix map

• coeffs (ndarray) – fix the coefficients \({\bf y}\)

class TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.DynamicsMap(vehicle, par_name_list=[])

Bases: TransportMaps.Maps.Map

Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)

Parameters:

• dim_in (int) – input dimension

• dim_out (int) – output dimension

evaluate(x, *args, **kwargs)

[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

(ndarray [\(m,d_y\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

grad_x(x, *args, **kwargs)

[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

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=[])

Bases: TransportMaps.Maps.Map

Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)

Parameters:

• dim_in (int) – input dimension

• dim_out (int) – output dimension

evaluate(x, *args, **kwargs)

[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

(ndarray [\(m,d_y\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

grad_x(x, *args, **kwargs)

[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

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)

Bases: TransportMaps.Distributions.Decomposable.LinearGaussianSequentialInferenceDistributions.ConditionallyLinearGaussianAR1TransitionDistribution

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 [\(d\)] or Map) – constant part or map returning the constant part given some parameters

• Fk (ndarray [\(d,d\)] or Map) – state transition matrix (dynamics) or map returning the linear part given some parametrs

• mu (ndarray [\(d\)] or Map) – mean \(\mu_k\) or parametric map for \(\mu_k(\theta)\)

• covariance (ndarray [\(d,d\)] or Map) – covariance \(Q_k\) or parametric map for \(Q_k(\theta)\)

• precision (ndarray [\(d,d\)] or Map) – 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=[])

Bases: TransportMaps.Maps.Map

Abstract map \(T:\mathbb{R}^{d_x}\rightarrow\mathbb{R}^{d_y}\)

Parameters:

• dim_in (int) – input dimension

• dim_out (int) – output dimension

evaluate(x, *args, **kwargs)

[Abstract] Evaluate the map \(T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

Returns:

(ndarray [\(m,d_y\)]) – transformed points

Raises:

NotImplementedError – to be implemented in sub-classes

grad_x(x, *args, **kwargs)

[Abstract] Evaluate the gradient \(\nabla_{\bf x}T\) at the points \({\bf x} \in \mathbb{R}^{m \times d_x}\).

Parameters:

• x (ndarray [\(m,d_x\)]) – evaluation points

• precomp (dict) – dictionary of precomputed values

• idxs_slice (slice) – if precomputed values are present, this parameter indicates at which of the points to evaluate. The number of indices represented by idxs_slice must match x.shape[0].

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))

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 [\(d_y\)]) – data

• c (ndarray [\(d_y\)] or Map) – system constant or parametric map returning the constant

• T (ndarray [\(d_y,d_x\)] or Map) – system matrix or parametric map returning the system matrix

• mu (ndarray [\(d_y\)] or Map) – noise mean or parametric map returning the mean

• covariance (ndarray [\(d_y,d_y\)] or Map) – noise covariance or parametric map returning the covariance

• precision (ndarray [\(d_y,d_y\)] or Map) – noise precision matrix or parametric map returning the precision matrix

• active_vars_system (list of int) – active variables identifying the parameters for for \(c(\theta), T(\theta)\).

• active_vars_distribution (list of int) – active variables identifying the parameters for for \(\mu(\theta), \Sigma(\theta)\).

• coeffs (ndarray) – initialization coefficients

TransportMaps.Distributions.Examples.RailwayVehicleDynamics.Coradia175.Coradia175VehicleStateSpace.generate_data(nsteps, vehicle, par_name_list=[], par_val_list=np.zeros(0))