Poisson1D#

class cuqi.testproblem.Poisson1D(dim=128, endpoint=1, source=<function Poisson1D.<lambda>>, field_type=None, field_params=None, map=None, imap=None, SNR=200, observation_grid_map=None, exactSolution=None)#

1D Poisson test problem. Discretized 1D Poisson equation (steady-state linear PDE).

Parameters:

  • dim (int) –

    size of the grid for the poisson problem

  • endpoint (float) –

    Location of end-point of grid.

  • source (lambda function) –

    Function for source term.

  • field_type (str or cuqi.geometry.Geometry) –

    Field type of domain. The accepted values are:
    a Geometry object.
    ”KL”: a cuqi.geometry.KLExpansion geometry object will be created and set as a domain geometry.
    ”KL_Full”: a cuqi.geometry.KLExpansion_Full geometry object will be created and set as a domain geometry.
    ”Step”: a cuqi.geometry.StepExpansion geometry object will be created and set as a domain geometry.
    ”CustomKL”: a cuqi.geometry.CustomKL geometry object will be created and set as a domain geometry.
    None: a cuqi.geometry.Continuous1D geometry object will be created and set as a domain geometry.

  • field_params (dict) –

    A dictionary of key word arguments that the underlying geometry accepts. (Passed to the underlying geometry when field type is KL, KL_Full, CustomKL, Step). For example, for Step field type, the dictionary can be {“n_steps”: 3}.

  • map (lambda function) –

    Mapping used to modify field.

  • imap (lambda function) –

    Inverse of KL map.

  • SNR (int) –

    Signal-to-noise ratio

observation_grid_maplambda function
Function that takes the grid as input and returns a sub-grid of the nodes where observations are available, e.g. observation_grid_map = lambda x: x[np.where(x>5.0)].
data#

Generated (noisy) data

Type:

ndarray

model#

Poisson 1D model

Type:

cuqi.model.PDEModel

prior#

Distribution of the prior

Type:

cuqi.distribution.Distribution

likelihood#

Likelihood function

Type:

cuqi.likelihood.Likelihood

exactSolution#

Exact solution (ground truth)

Type:

ndarray

exactData#

Noise free data

Type:

ndarray

MAP()#

Compute MAP estimate of posterior. NB: Requires prior to be defined.

sample_posterior(Ns)#

Sample Ns samples of the posterior. NB: Requires prior to be defined.

__init__(dim=128, endpoint=1, source=<function Poisson1D.<lambda>>, field_type=None, field_params=None, map=None, imap=None, SNR=200, observation_grid_map=None, exactSolution=None)#

Methods

MAP([disp, x0])

Compute the Maximum A Posteriori (MAP) estimate of the posterior.

ML([disp, x0])

Compute the Maximum Likelihood (ML) estimate of the posterior.

UQ([Ns, Nb, percent, exact, experimental])

Run an Uncertainty Quantification (UQ) analysis on the Bayesian problem and provide a summary of the results.

__init__([dim, endpoint, source, ...])

get_components()

Method that returns the model, the data and additional information to be used in formulating the Bayesian problem.

sample_posterior(Ns[, Nb, callback, ...])

Sample the posterior.

sample_prior(Ns[, callback])

Sample the prior distribution.

set_data(**kwargs)

Set the data of the problem.

Attributes

data

Extract the observed data from likelihood

likelihood

The likelihood function.

model

Extract the cuqi model from likelihood.

posterior

Create posterior distribution from likelihood and prior.

prior

The prior distribution