meslas package

Subpackages

• meslas.covariance package
  • Submodules
  • meslas.covariance.cross_covariances module
    • LinearTrendCrossCov
    • ParabolicTrendCrossCov
    • UniformMixing
  • meslas.covariance.heterotopic module
    • Conventions
    • FactorCovariance
      • FactorCovariance.K()
    • FactorStationaryCovariance
    • StationaryCovariance
      • StationaryCovariance.K()
  • meslas.covariance.old module
    • K_isotopic()
    • k()
    • mu()
    • sample()
    • sample_isotopic()
  • meslas.covariance.spatial_covariance_functions module
    • Matern32()
  • Module contents
• meslas.external_dependencies package
  • Submodules
  • meslas.external_dependencies.numpytorch module
    • WrapTorch
      • WrapTorch.abs()
      • WrapTorch.arange()
      • WrapTorch.argmax()
      • WrapTorch.argmin()
      • WrapTorch.array()
      • WrapTorch.backend
      • WrapTorch.cat()
      • WrapTorch.exp()
      • WrapTorch.log()
      • WrapTorch.max()
      • WrapTorch.min()
      • WrapTorch.newaxis
      • WrapTorch.ones()
      • WrapTorch.sum()
      • WrapTorch.sumto1()
      • WrapTorch.zeros()
    • aggregate()
    • append_dim()
    • append_to_ndim()
    • attach_dim()
    • block_diag()
    • block_diag_irregular()
    • bootstrap()
    • categrnd()
    • circdiff()
    • conv_t()
    • crossvalincl()
    • deg2rad()
    • delta()
    • enforce_tensor()
    • entropy()
    • expand_all()
    • expand_batch()
    • expand_upto_dim()
    • float()
    • freeze()
    • get_jacobian()
    • interp1d()
    • inv_gaussian_cdf()
    • inv_gaussian_mean_std2params()
    • inv_gaussian_pdf()
    • inv_gaussian_pmf_mean_stdev()
    • inv_gaussian_variance()
    • inv_gaussian_variance2lam()
    • isnan()
    • kron()
    • kw_np2torch()
    • log_normpdf()
    • logistic()
    • logit()
    • lognorm_params_given_mean_stdev()
    • lognorm_pmf()
    • lognormal_params2mean_stdev()
    • m2v()
    • m2v0()
    • mat2vec0()
    • matmul0()
    • matmul2vec()
    • matsum()
    • matvecmul0()
    • max_distrib()
    • max_shape()
    • mean_distrib()
    • min_distrib()
    • mm0()
    • mvm0()
    • mvnpdf_log()
    • mvnrnd()
    • nan2v()
    • nanmean()
    • nansum()
    • normrnd()
    • npy()
    • npys()
    • numpy()
    • onehotrnd()
    • p2en()
    • p2st()
    • pconc2conc()
    • permute2en()
    • permute2st()
    • prad2unitvec()
    • prepend_dim()
    • prepend_to_ndim()
    • rad2deg()
    • rand()
    • ravel_multi_index()
    • repeat_all()
    • repeat_batch()
    • repeat_dim()
    • repeat_to_shape()
    • scatter_add()
    • sem()
    • sem_distrib()
    • shiftdim()
    • softmax_bias()
    • softmax_mask()
    • std_distrib()
    • sumto1()
    • t()
    • tensor()
    • test_kron()
    • test_softmax_bias()
    • unblock_diag()
    • unravel_index()
    • v2m()
    • v2m0()
    • var_distrib()
    • vec2mat0()
    • vec2matmul()
    • vec_on()
    • vec_on_dim()
    • vmpdf()
    • vmpdf_a_given_b()
    • vmpdf_prad_pconc()
  • Module contents
• meslas.geometry package
  • Submodules
  • meslas.geometry.grid module
  • meslas.geometry.tilings module
    • draw_tiling()
    • generate_hexagons()
    • generate_squares()
    • generate_triangles()
    • generate_unit_hexagons()
    • generate_unit_squares()
    • generate_unit_triangles()
  • Module contents

Submodules

meslas.excursion module

Compute coverage function, excursion sets and related quantities.

meslas.excursion.coverage_fct_fixed_location(mean_vec, cov_mat, lower, upper=None)

Computes coverage function at a fixed set of location.

Ths function should be used when a mean vector and covariance matrix for a set of locations have been precomputed.

Uses the torch implementation of the multivariate CDF by Sebastien Marmin, see torch-mvn.

Parameters:

mean_vec: (M, p) Tensor

Mean vector at each of the M locations. mean_vec[i, :] should give the mean vector at location nr i.

cov_mat: (M, p, p) Tensor

Covariance matrix at each of the M locations. cov_mat[i, :, :] should give the covariance matrix at location nr i.

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported. WARNING: wrong shapes can cause unexpected results.

upper: (p) Tensor

List of upper threshold for each response. The excursion set is the set where responses are above the specified threshold. If not provided, defaults to + infinity.

Returns:

excursion_prob: (M) Tensor

Probability to be in excursion at each location.

meslas.inverse_random_fields module

meslas.means module

Mean functions for GRFs.

class meslas.means.ConstantMean(means)

Bases: object

Constant mean function.

Parameters:

means: (p) array-like.

Constant mean of each of the p-components.

Methods

__call__(S, L)

Parameters:

class meslas.means.LinearMean(beta0s, beta1s)

Bases: object

Linear trend mean function. The mean at location x will be given by beta0 + beta1 x

Parameters:

betas0: (p) array-like.

Constant mean mean term for of each of the p-components.

betas1: (p, d) array-like.

Linear trend matrix for each of the p-components.

Methods

__call__(S, L)

Parameters:

meslas.plotting module

meslas.plotting_physical module

meslas.random_fields module

meslas.sensor module

TODO: Maybe add grid, grf, n_ouptuts to the sensor class.

class meslas.sensor.DiscreteSensor(discrete_grf)

Bases: Sensor

Sensor on a fixed discretization.

Methods

choose_next_point_myopic(noise_std, lower[, ...])	Choose the next observation location (given the current one) using the myopic strategy.
compute_exursion_prob(lower[, upper])	Compute the excursion probability on the whole grid, given the currently available data.
get_neighbors_isotopic_eibv(noise_std, lower)	For each neighbouring node of the current sensor location, compute the eibv if we were to measure every response (isotopic) at that node.
run_lookahead_stragegy(n_steps, data_feed, ...)	Run the myopic strategy for n_steps, starting from the current location.
run_myopic_stragegy(n_steps, data_feed, ...)	Run the myopic strategy for n_steps, starting from the current location.
update_design(S_y_inds, L_y, y[, noise_std])	Updates the full design grid by computing current conditional mean and covariance.

choose_next_point_myopic(noise_std, lower, upper=None)

Choose the next observation location (given the current one) using the myopic strategy.

Parameters:

noise_std: float

Standar deviation of measurement noise.

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

If not provided, defaults to +infty (excursion set above threshold).

Returns:

next_point_ind: (1) Tensor

Grid index of next observation location chosen according to the myopic strategy.

next_point_eibv: (1) Tensor

EIBV corresponding to the next chosen point.

compute_exursion_prob(lower, upper=None)

Compute the excursion probability on the whole grid, given the currently available data.

Parameters:

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

List of upper threshold for each response. The excursion set is the set where responses are above the specified threshold. If not provided, defaults to + infinity.

Returns:

excursion_proba: (self.grid.n_points) Tensor

Excursion probability at each point.

get_neighbors_isotopic_eibv(noise_std, lower, upper=None)

For each neighbouring node of the current sensor location, compute the eibv if we were to measure every response (isotopic) at that node. Returns a list containing the EIBV for each neighbor.

Parameters:

noise_std: float

Standar deviation of measurement noise.

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

If not provided, defaults to +infty (excursion set above threshold).

Returns:

neighbors_eibv: (n_neighbors) Tensor

EIBV for each neighbouring cell.

neighbors_inds: (n_neighbors) Tensor

Grid indices of the neighbouring cells.

run_lookahead_stragegy(n_steps, data_feed, noise_std, lower, upper=None, n_prune=3)

Run the myopic strategy for n_steps, starting from the current location. That is, at each point, pick the neighbors with the smallest EIBV, move there, observe, update model, repeat.

Parameters:

n_steps: int

Number of steps (observations) to run the strategy for.

data_feed: function(int)

Function that, given a node index, returns the measured data (isotopic) at that node.

noise_std

lower

upper

n_prune: int

Number of paths to consider at the first step. From the starting node, we will only consider the best n_prune nodes, ranked using the myopic strategy.

run_myopic_stragegy(n_steps, data_feed, noise_std, lower, upper=None)

Run the myopic strategy for n_steps, starting from the current location. That is, at each point, pick the neighbors with the smallest EIBV, move there, observe, update model, repeat.

Parameters:

n_steps: int

Number of steps (observations) to run the strategy for.

data_feed: function(int)

Function that, given a node index, returns the measured data (isotopic) at that node.

update_design(S_y_inds, L_y, y, noise_std=None)

Updates the full design grid by computing current conditional mean and covariance. Note that this updates the internal of the discrete GRF.

Returns:

mu_cond_iso: (self.grid.n_points, self.grf.n_out)

Conditional mean.

K_cond_iso: (self.grid.n_points, self.grid.n_points, self.grf.n_out, self.grf.n_out) Tensor

Conditional covariance matrix in isotopic ordered form. It means that the covariance matrix at cell i can be otained by subsetting K_cond_iso[i, i, :, :].

class meslas.sensor.Sensor(grid, grf)

Bases: object

Implements the data collection process. Will be responsible for querying the GP for mean and variances conditional on the already collected data.

Attributes:

S_y_tot: (N, d) Tensor

Spatial locations of the already collected data.

L_y_tot: (N) Tensor

Corresponding response indices.

location: (d) Tensor

Current position of the sensor.

grid: IrregularGrid

A discretization of space that defines the locations the sensor can move to.

grf: GRF

Gaussian Random Field used to model the unknown phenomenon of interest.

current_node_ind: int

Index of the point in the grid that is closest to the sensor location.

visited_nodes_inds: Tensor

Grid indices of the visited locations.

noise_std: float

Standard deviation of the sensor noise. TODO: allow different noises for each component.

Methods

add_data(S_y_inds, L_y, y)	Add new data to the already collected one.
compute_exursion_prob(points, lower[, upper])	Compute the excursion probability at a set of points given the currently available data.
compute_neighbors_exursion_prob(lower[, upper])	Compute the excursion probability of the neighbors of the current location.
get_current_neighbors()	Get the neighbouring grid nodes of the current sensor location.
set_location(location)	Setter for the location.

add_data(S_y_inds, L_y, y)

Add new data to the already collected one. Can also handle batches. This will just concatenate the new data vectors with the current ones.

Parameters:

S_y_inds: (n) Tensor

Grind index of spatial locations of the new measurements.

L_y :(n) Tensor

Corresponding response indices.

y :(n, p) Tensor

Measured data.

compute_exursion_prob(points, lower, upper=None)

Compute the excursion probability at a set of points given the currently available data.

Note this is a helper function that take an index in the grid as input.

Parameters:

points: (N, d) Tensor

List of points (coordinates) at which to compute the excursion probability.

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

List of upper threshold for each response. The excursion set is the set where responses are above the specified threshold. If not provided, defaults to + infinity.

Returns:

excursion_proba: (N) Tensor

Excursion probability at each point.

compute_neighbors_exursion_prob(lower, upper=None)

Compute the excursion probability of the neighbors of the current location.

Parameters:

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

List of upper threshold for each response. The excursion set is the set where responses are above the specified threshold. If not provided, defaults to + infinity.

get_current_neighbors()

Get the neighbouring grid nodes of the current sensor location.

This is done by first finding the node closes to the sensor location, and then returning its neighbors.

Returns:

neighbors_inds: (n_neighbors)

Grid indices of the neighbors.

set_location(location)

Setter for the location.

Parameters:

location: (d) array_like

meslas.sensor_plotting module

REPORTING VERSION OF THE SENSOR MODULE.

The problem is that at stage n, we havent yet computed the ebiv of the neighbors and if we want a sensible plot, we have to provide the eibvs with the CURRENT status of the model. This doesn’t agree with the natural flow of the myopic search, so we choose to have a dedicated version of the module to produce the plots.

class meslas.sensor_plotting.DiscreteSensor(discrete_grf)

Bases: Sensor

Sensor on a fixed discretization.

Methods

choose_next_point_myopic(noise_std, lower[, ...])	Choose the next observation location (given the current one) using the myopic strategy.
compute_exursion_prob(lower[, upper])	Compute the excursion probability on the whole grid, given the currently available data.
get_neighbors_isotopic_eibv(noise_std, lower)	For each neighbouring node of the current sensor location, compute the eibv if we were to measure every response (isotopic) at that node.
run_myopic_stragegy(n_steps, data_feed, ...)	Run the myopic strategy for n_steps, starting from the current location.
update_design(S_y_inds, L_y, y[, noise_std])	Updates the full design grid by computing current conditional mean and covariance.

choose_next_point_myopic(noise_std, lower, upper=None)

Choose the next observation location (given the current one) using the myopic strategy.

Parameters:

noise_std: float

Standar deviation of measurement noise.

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

If not provided, defaults to +infty (excursion set above threshold).

Returns:

next_point_ind: (1) Tensor

Grid index of next observation location chosen according to the myopic strategy.

next_point_eibv: (1) Tensor

EIBV corresponding to the next chosen point.

compute_exursion_prob(lower, upper=None)

Compute the excursion probability on the whole grid, given the currently available data.

Parameters:

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

List of upper threshold for each response. The excursion set is the set where responses are above the specified threshold. If not provided, defaults to + infinity.

Returns:

excursion_proba: (self.grid.n_points) Tensor

Excursion probability at each point.

get_neighbors_isotopic_eibv(noise_std, lower, upper=None)

For each neighbouring node of the current sensor location, compute the eibv if we were to measure every response (isotopic) at that node. Returns a list containing the EIBV for each neighbor.

Parameters:

noise_std: float

Standar deviation of measurement noise.

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

If not provided, defaults to +infty (excursion set above threshold).

Returns:

neighbors_eibv: (n_neighbors) Tensor

EIBV for each neighbouring cell.

neighbors_inds: (n_neighbors) Tensor

Grid indices of the neighbouring cells.

run_myopic_stragegy(n_steps, data_feed, noise_std, lower, upper=None)

Run the myopic strategy for n_steps, starting from the current location. That is, at each point, pick the neighbors with the smallest EIBV, move there, observe, update model, repeat.

Parameters:

n_steps: int

Number of steps (observations) to run the strategy for.

data_feed: function(int)

Function that, given a node index, returns the measured data (isotopic) at that node.

update_design(S_y_inds, L_y, y, noise_std=None)

Updates the full design grid by computing current conditional mean and covariance. Note that this updates the internal of the discrete GRF.

Returns:

mu_cond_iso: (self.grid.n_points, self.grf.n_out)

Conditional mean.

K_cond_iso: (self.grid.n_points, self.grid.n_points, self.grf.n_out, self.grf.n_out) Tensor

Conditional covariance matrix in isotopic ordered form. It means that the covariance matrix at cell i can be otained by subsetting K_cond_iso[i, i, :, :].

class meslas.sensor_plotting.Sensor(grid, grf)

Bases: object

Implements the data collection process. Will be responsible for querying the GP for mean and variances conditional on the already collected data.

Attributes:

S_y_tot: (N, d) Tensor

Spatial locations of the already collected data.

L_y_tot: (N) Tensor

Corresponding response indices.

location: (d) Tensor

Current position of the sensor.

grid: IrregularGrid

A discretization of space that defines the locations the sensor can move to.

grf: GRF

Gaussian Random Field used to model the unknown phenomenon of interest.

current_node_ind: int

Index of the point in the grid that is closest to the sensor location.

visited_nodes_inds: Tensor

Grid indices of the visited locations.

noise_std: float

Standard deviation of the sensor noise. TODO: allow different noises for each component.

Methods

add_data(S_y_inds, L_y, y)	Add new data to the already collected one.
compute_exursion_prob(points, lower[, upper])	Compute the excursion probability at a set of points given the currently available data.
compute_neighbors_exursion_prob(lower[, upper])	Compute the excursion probability of the neighbors of the current location.
get_current_neighbors()	Get the neighbouring grid nodes of the current sensor location.
set_location(location)	Setter for the location.

add_data(S_y_inds, L_y, y)

Add new data to the already collected one. Can also handle batches. This will just concatenate the new data vectors with the current ones.

Parameters:

S_y_inds: (n) Tensor

Grind index of spatial locations of the new measurements.

L_y :(n) Tensor

Corresponding response indices.

y :(n, p) Tensor

Measured data.

compute_exursion_prob(points, lower, upper=None)

Compute the excursion probability at a set of points given the currently available data.

Note this is a helper function that take an index in the grid as input.

Parameters:

points: (N, d) Tensor

List of points (coordinates) at which to compute the excursion probability.

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

List of upper threshold for each response. The excursion set is the set where responses are above the specified threshold. If not provided, defaults to + infinity.

Returns:

excursion_proba: (N) Tensor

Excursion probability at each point.

compute_neighbors_exursion_prob(lower, upper=None)

Compute the excursion probability of the neighbors of the current location.

Parameters:

lower: (p) Tensor

List of lower threshold for each response. The excursion set is the set where responses are above the specified threshold. Note that np.inf is supported.

upper: (p) Tensor

List of upper threshold for each response. The excursion set is the set where responses are above the specified threshold. If not provided, defaults to + infinity.

get_current_neighbors()

Get the neighbouring grid nodes of the current sensor location.

This is done by first finding the node closes to the sensor location, and then returning its neighbors.

Returns:

neighbors_inds: (n_neighbors)

Grid indices of the neighbors.

set_location(location)

Setter for the location.

Parameters:

location: (d) array_like

meslas.vectors module

Encapsulation of the reshaping between isotopic and non-isotopic form.

class meslas.vectors.GeneralizedMatrix(vals, n_points1, n_out1, n_points2, n_out2)

Bases: object

Same as GeneralizedVector, but for matrices.

Attributes:

isotopic

Returns the 2D isotopic form of the generalized vector.

list

Returns the 1D list form of the generalized vector.

shape

Methods

numpy()

Returns a numpy array containing the isotopic form of the matrix.

from_isotopic
from_list
set_vals

classmethod from_isotopic(vals_iso)

classmethod from_list(vals, n_points1, n_out1, n_points2, n_out2)

property isotopic

Returns the 2D isotopic form of the generalized vector.

Returns:

vals_isotopic: (self.n_points, self.n_out) Tensor

property list

Returns the 1D list form of the generalized vector.

Returns:

vals_list: (self.n_points * self.n_out) Tensor

numpy()

Returns a numpy array containing the isotopic form of the matrix. Used for interfacing with others libraries and for saving.

set_vals(vals)

property shape

class meslas.vectors.GeneralizedVector(vals, n_points, n_out)

Bases: object

A generalized vector is used to implement the types of vectors that appear when working with multivariate random fields. Given n_points points in space, the value of a n_out dimensional random process at those points may be represented as a (n_points, n_out) vector. But for some operations (like sampling) it makes sense to expand this as a one dimensional vector of lenght (n_points, n_out). This is what this class is used for.

The two dimensional form is called the isotopic form, by analogy with the process of measuring all components of a random field, whereas the one-dimensional form is called the list form.

The underlying data structure is always a one-dimensional list of values. The class is indexable as GeneralizedVector[…], and the indexing will be performed on the isotopic from. What will be returned is a subset of the isotopic tensor.

Attributes:

isotopic

Returns the 2D isotopic form of the generalized vector.

list

Returns the 1D list form of the generalized vector.

shape

Methods

numpy()

Returns a numpy array containing the isotopic form of the vector.

from_isotopic
from_list
set_vals

classmethod from_isotopic(vals_iso)

classmethod from_list(vals, n_points, n_out)

property isotopic

Returns the 2D isotopic form of the generalized vector.

Returns:

vals_isotopic: (self.n_points, self.n_out) Tensor

property list

Returns the 1D list form of the generalized vector.

Returns:

vals_list: (self.n_points * self.n_out) Tensor

numpy()

Returns a numpy array containing the isotopic form of the vector. Used for interfacing with others libraries and for saving.

set_vals(vals)

property shape

Module contents