analyticsimdatagenerator.py

Generic tools for creating SimData objects based on analytic functions for the underlying physical fields. Useful for testing pyvale.

class AnalyticData2D(length_x=10.0, length_y=7.5, num_elem_x=4, num_elem_y=3, time_steps=None, field_keys=('scalar',), funcs_x=None, funcs_y=None, funcs_t=None, symbols=(y, x, t), offsets_space=(0.0,), offsets_time=(0.0,), nodes_per_elem=4)

Bases: object

Dataclass for describing a 2D analytic test case for pyvale sensor simulation. Includes information about the geometry, the mesh and the analytic functions used to generate the field data.

length_x

Length of the test case geometry in the X direction in length units. Defaults to 10.0.

length_y

Length of the test case geometry in the Y direction in length units. Defaults to 7.5.

num_elem_x

Number of elements in the mesh in the X direction. Defaults to 4.

num_elem_y

Number of elements in the mesh in the Y direction. Defaults to 3.

time_steps

1D array of time steps for the analytic test case. Defaults to None which is for a test case that only has spatially varying functions.

field_keys

Keys used to describe the field of interest. For a scalar field there is only a single key. For a vector field 2 keys are required in 2D (xx,yy). For a tensor field 3 keys are required for 2D (xx,yy,xy). Defaults to a single key for a scalar field: (“scalar”,).

funcs_x

Analytic functions describing the field variation as a function of the x coordinate. This tuple should have the same number of functions as the number of field keys. Analytic functions in x, y and t are multiplied together so setting a function to a constant of 1 will have no effect.

funcs_y

Analytic functions describing the field variation as a function of the y coordinate. This tuple should have the same number of functions as the number of field keys. Analytic functions in x, y and t are multiplied together so setting a function to a constant of 1 will have no effect.

funcs_t

Analytic functions describing the field variation as a function of time This tuple should have the same number of functions as the number of field keys. Analytic functions in x, y and t are multiplied together so setting a function to a constant of 1 will have no effect.

symbols

Sympy symbols describing the relevant dimensions of the problem. For 2D spatial dimensions default to x and y and time is denoted t. Note that these are the symbols used to describe the analytic field functions.

offsets_space

Constants which are added to the physical field functions in each spatial dimensions.

offsets_time

Constant which is added to the physical field function in time.

nodes_per_elem

Number of nodes per element. Currently only rectangular meshes and with 4 nodes per element are supported. Defaults to 4.

__init__(length_x=10.0, length_y=7.5, num_elem_x=4, num_elem_y=3, time_steps=None, field_keys=('scalar',), funcs_x=None, funcs_y=None, funcs_t=None, symbols=(y, x, t), offsets_space=(0.0,), offsets_time=(0.0,), nodes_per_elem=4)

class AnalyticSimDataGen(case_data)

Bases: object

Class for generating analytic field data as a SimData object to test the sensor simulation functionality of pyvale. Provides tools to evaluate the analytic field functions at a given spatial coordinate/time to check against pyvale interpolation functions. Currently only support 2D cases.

__init__(case_data)

Parameters:

case_data (AnalyticCaseData2D) – Data class containing the parameters required to create the analytic mesh and the underlying physical field functions.

case_data

coords

connect

field_sym_funcs

field_lam_funcs

field_eval

evaluate_field_truth(field_key, coords, time_steps=None)

Calculates the ‘truth’ from the analytical functions describing the physical fields at the specified coordinates and time steps.

Parameters:

• field_key (str) – Key for the underlying physical field.

• coords (np.ndarray) – Coordinates at which to evaluate the analytic physical field. shape =(n_coords,coord[x,y,z])

• time_steps (np.ndarray | None, optional) – Time steps at which to evaluate the physical field, by default None. If this is none the evaluation time steps are assumed to match the nominal time steps.

Returns:

np.ndarray – Array of analytic field evaluations with shape = (n_coords, n_time_steps)

evaluate_all_fields_truth(coords, time_steps=None)

Evaluates all analytic physical fields at the specified coordinates and time steps.

Parameters:

• coords (np.ndarray) – Coordinates at which to evaluate the analytic physical field. shape =(n_coords,coord[x,y,z])

• time_steps (np.ndarray | None, optional) – Time steps at which to evaluate the physical field, by default None. If this is none the evaluation time steps are assumed to match the nominal time steps.

Returns:

dict[str,np.ndarray] – Dictionary keyed by the field name giving a numpy array with shape = (n_coords,n_timesteps)

evaluate_field_at_nodes(field_key)

Evaluates the underlying physical field at the node locations and nominal time steps.

Parameters:

field_key (str) – String key for the field to be evaluated.

Returns:

np.ndarray – Array of field evaluations with shape=(n_nodes,n_timesteps)

evaluate_all_fields_at_nodes()

Evaluates all physical fields at the node locations and nominal time steps.

Returns:

dict[str,np.ndarray] – Dictionary keyed by the field name giving a numpy array with shape = (n_coords,n_timesteps)

generate_sim_data()

Creates a SimData object using the analytic case geometry, mesh parameters and the underlying physical fields.

Returns:

mh.SimData – SimData object built from the analytic case data.

get_visualisation_grid(field_key=None, time_step=-1)

Creates a visualisation grid for plotting heatmaps of the specified analytic field using matplotlib.

Parameters:

• field_key (str | None, optional) – String key for the field to be visualised, by default None. If None then the first field key is used.

• time_step (int, optional) – Time step at which to extract the field to be plotted, by default -1

Returns:

tuple[np.ndarray,np.ndarray,np.ndarray] – Tuple containing the 2D grid of x coordinates, grid of y coordinates and a grid of field evaluations.