EspressoProblem
EspressoProblem#
- class cofi_espresso.EspressoProblem(example_number=1)[source]#
Base class for all Espresso problems. All Espresso problems shoud be a subclass of this class.
- Parameters
example_number (int, optional) – The index of example you want to access. A typical Espresso problem will have several examples that have indices starting from 1. By default 1.
- Raises
InvalidExampleError – when you’ve passed in an example number that isn’t included in current problem
Metadata
Problem-sepecific metadata include the following keys:
problem_title
problem_short_description
author_names
contact_name
contact_email
citations
linked_sites
And they can be accessed through the
metadata
dictionary:>>> from cofi_espresso import <ProblemClass> >>> <ProblemClass>.metadata["problem_title"] This is a problem about... >>> <ProblemClass>.metadata.keys() dict_keys(['problem_title', 'problem_short_description', 'author_names', 'contact_name', 'contact_email', 'citations', 'linked_sites'])
Required attributes
Required methods and properties are guaranteed to be written by problem contributors and available for user to access.
Returns the number of model parameters
Returns the number of data points
Returns a model vector that the contributor regards as a sensible explanation of the dataset
Returns a model vector representing a typical starting point for inversion
Returns a data vector in the same format as output by
forward
EspressoProblem.forward
(model[, with_jacobian])Perform forward simulation with a model to produce synthetic data
Optional attributes
Optional methods and properties have standards but are not always implemented for each Espresso problem. Try using them or check the documentation page for each problem to figure out whether they are available.
Returns a brief description of current example
Returns the covariance matrix for the data
Returns the inverse data covariance matrix for the data
EspressoProblem.jacobian
(model)Returns the Jacobian matrix
EspressoProblem.plot_model
(model)Returns a figure containing a basic visualisation of the model
EspressoProblem.plot_data
(data[, data2])Returns a figure containing a basic visualisation of a dataset and (optionally) comparing it to a second dataset
EspressoProblem.misfit
(data, pred)Returns a measure of the extent to which a predicted data vector agrees with observed data
EspressoProblem.log_likelihood
(data, pred)Returns the log likelihood density value
EspressoProblem.log_prior
(model)Returns the log prior density value
Reference Details
- abstract EspressoProblem.forward(model, with_jacobian=False)[source]#
Perform forward simulation with a model to produce synthetic data
If with_jacobian == True, returns (d, G); else, returns d, where:
d : numpy.ndarray, shape(
data_size
,), a simulated data vector corresponding to the given modelG : numpy.ndarray, shape(
data_size
,model_size
), the Jacobian such that \(G[i,j] = \partial d[i]/\partial model[j]\)
If an example does not permit calculation of the Jacobian then calling with with_jacobian=True should result in a NotImplementedError being raised.
- Parameters
model (numpy.ndarray) – a model vector, in the same shape of
model_size
with_jacobian (bool) – a switch governing the output required
- Returns
(d, G) or d, depending on the value of with_jacobian. Details above.
- Return type
- EspressoProblem.jacobian(model)[source]#
Returns the Jacobian matrix
- Parameters
model (numpy.ndarray) – a model vector, in the same shape of
model_size
- Returns
the Jacobian such that \(G[i,j] = \partial d[i]/\partial model[j]\), in the shape of (
data_size
,model_size
)- Return type
- EspressoProblem.log_likelihood(data, pred)[source]#
Returns the log likelihood density value
- Parameters
data (numpy.ndarray) – An observed data vector to base on
pred (numpy.ndarray) – A predicted data vector to evaluate
- Returns
The log likelihood that
data
is an imperfect observation of a system generating datapred
.- Return type
Number
- EspressoProblem.log_prior(model)[source]#
Returns the log prior density value
- Parameters
model (numpy.ndarray) – A model vector to evaluate, shape(
model_size
)- Returns
The log probability that a system is described by
model
prior to seeing any data.- Return type
Number
- EspressoProblem.misfit(data, pred)[source]#
Returns a measure of the extent to which a predicted data vector agrees with observed data
- Parameters
data (numpy.ndarray) – An observed data vector to base on
pred (numpy.ndarray) – A predicted data vector to evaluate
- Returns
A measure of the extent to which a predicted data vector,
pred
, agrees with observed data,data
. Smaller numbers imply better agreement; 0 -> perfect match.- Return type
Number
- EspressoProblem.plot_data(data, data2=None)[source]#
Returns a figure containing a basic visualisation of a dataset and (optionally) comparing it to a second dataset
- Parameters
data (numpy.ndarray) – A data vector for visualisation
data2 (numpy.ndarray, optional) – A second data vector, for comparison with the first, by default None
- Returns
A figure handle containing a basic visualisation of a dataset and (optionally) comparing it to a second dataset.
- Return type
- EspressoProblem.plot_model(model)[source]#
Returns a figure containing a basic visualisation of the model
- Parameters
model (numpy.ndarray) – a model vector for visualisatioin, in the same shape of
model_size
- Returns
A figure handle containing a basic visualisation of the model.
- Return type
- EspressoProblem.author_names = NotImplemented#
- EspressoProblem.citations = NotImplemented#
- EspressoProblem.contact_email = NotImplemented#
- EspressoProblem.contact_name = NotImplemented#
- EspressoProblem.covariance_matrix#
Returns the covariance matrix for the data
- EspressoProblem.data#
Returns a data vector in the same format as output by
forward
- EspressoProblem.data_size#
Returns the number of data points
- Returns
The number of data points (i.e. the dimension of a data vector).
- Return type
- EspressoProblem.description#
Returns a brief description of current example
- Returns
A string containing a brief (1-3 sentence) description of the example.
- Return type
- EspressoProblem.good_model#
Returns a model vector that the contributor regards as a sensible explanation of the dataset
- Returns
A model vector that the contributor regards as being a ‘correct’ or ‘sensible’ explanation of the dataset. (In some problems it may be the case that there are many ‘equally good’ models. The contributor should select just one of these.) It has the same shape as
model_size
.- Return type
- EspressoProblem.inverse_covariance_matrix#
Returns the inverse data covariance matrix for the data
- EspressoProblem.linked_sites = NotImplemented#
- EspressoProblem.model_size#
Returns the number of model parameters
- Returns
The number of model parameters (i.e. the dimension of a model vector).
- Return type
- EspressoProblem.problem_short_description = NotImplemented#
- EspressoProblem.problem_title = NotImplemented#
- EspressoProblem.starting_model#
Returns a model vector representing a typical starting point for inversion
- Returns
A model vector, possibly just np.zeros(model_size), representing a typical starting point or ‘null model’ for an inversion. It has the same shape as
model_size
.- Return type