Inverse Problem¶

This module provides a class encapsulating all data needed to define an inverse problem.

The goal is to allow the user to ignore the underlying details of the input data.

Indeed, if one want to work on Niklas’s data, and directly load all data from the raw .mat file, one just has to run:

InverseProblem.from_matfile(path)

Module implementation Details¶

class volcapy.inverse.inverse_problem.InverseProblem(cells_coords, forward, data_points, data_values)[source]¶

Numerical implementation of an inverse problem. Needs a forward and an inversion grid as input. Then can perform several inversions.

Attributes

cells_coords: 2D array: Coordinates of the inversion cells. Element i,j should contain j-th coordinate of inversion cell nr i. Note the order of the cells should reflect the order of the columns of the forward.
forward: 2D array: Forward operator.
data_points
data_values

Methods

`build_partial_covariance`(row_begin, row_end, …)	(DEPRECATED) Prepare a function for returning partial rows of the covariance matrix.
`compute_covariance_pushforward`(G, sigma0, …)	(DEPRECATED) Compute the matrix product C_m * G^T, which we call the covariance pushforward.
`compute_post_covariance`()	(DEPRECATED) Compute the full posterior covariance matrix.
`from_matfile`(path)	Read forward, inversion grid and data from a matlab file.
`inverse`(out_folder, prior_mean, sigma_d, …)	(DEPRECATED) Perform inversion.
`save_squared_distance_mesh`(path)	(DEPRECATED) Computes the matrix of squared euclidean distances betwen all couples and saves to disk.
`subset`(n_cells)	Subset an inverse problem by only keeping n_cells inversion cells selected at random.
`subset_data`(n_keep[, seed])	Subset an inverse problem by only keeping n_keep data points selected at random.

build_partial_covariance(row_begin, row_end, sigma0, lambda0)[source]¶

(DEPRECATED) Prepare a function for returning partial rows of the covariance matrix.

Warning: should cast, since returns MemoryView.

compute_covariance_pushforward(G, sigma0, lambda0)[source]¶

(DEPRECATED) Compute the matrix product C_m * G^T, which we call the covariance pushforward.

Parameters

G: 2-D array: The forward operator.

compute_post_covariance()[source]¶: (DEPRECATED) Compute the full posterior covariance matrix.

classmethod from_matfile(path)[source]¶

Read forward, inversion grid and data from a matlab file.

Parameters

path: string: Path to a matlab file containing the data. The file should have the same format as the original file from Niklas (see documentation).

inverse(out_folder, prior_mean, sigma_d, sigma0, lambda0, preload_covariance_pushforward=False, cov_pushforward=None, compute_post_covariance=False)[source]¶

(DEPRECATED) Perform inversion.

Parameters

out_folder: string: Path to a folder where we will save the resutls.
compute_post_covariance: Boolean: If set to True, then will compute and store the full posterior covariance matrix (huge).

save_squared_distance_mesh(path)[source]¶: (DEPRECATED) Computes the matrix of squared euclidean distances betwen all couples and saves to disk.

subset(n_cells)[source]¶

Subset an inverse problem by only keeping n_cells inversion cells selected at random. This is used to make the problem more tractable and allow prototyping calculations on a small computer.

The effect of this method is to directly modify the attributes of the class to adapt them to the smaller problem.

Parameters

n_cells: int: Only keep the first n_cells.

subset_data(n_keep, seed=None)[source]¶

Subset an inverse problem by only keeping n_keep data points selected at random.

The effect of this method is to directly modify the attributes of the class to adapt them to the smaller problem.

Parameters

n_keep: int: Only keep n_keep data points.
seed: int: Can be used to make choice of test data predictable.

Returns

(rest_forward, rest_data)