gemseo / problems / scalable / data_driven

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diagonal module

Scalable diagonal model.

This module implements the concept of scalable diagonal model, which is a particular scalable model built from an input-output dataset relying on a diagonal design of experiments (DOE) where inputs vary proportionally from their lower bounds to their upper bounds, following the diagonal of the input space.

So for every output, the dataset catches its evolution with respect to this proportion, which makes it a mono dimensional behavior. Then, for a new user-defined problem dimension, the scalable model extrapolates this mono dimensional behavior to the different input directions.

The concept of scalable diagonal model is implemented through the ScalableDiagonalModel class which is composed of a ScalableDiagonalApproximation. With regard to the diagonal DOE, GEMSEO proposes the DiagonalDOE class.

class gemseo.problems.scalable.data_driven.diagonal.ScalableDiagonalApproximation(sizes, output_dependency, io_dependency, seed=0)[source]

Bases: object

Methodology that captures the trends of a physical problem, and extends it into a problem that has scalable input and outputs dimensions The original and the resulting scalable problem have the same interface:

all inputs and outputs have the same names; only their dimensions vary.

Constructor:

Parameters:

  • sizes (dict) – sizes of both input and output variables.

  • output_dependency (dict) – dependency between old and new outputs.

  • io_dependency (dict) – dependency between new inputs and new outputs.

  • seed (int) –

    By default it is set to 0.

build_scalable_function(function_name, dataset, input_names, degree=3)[source]

Build interpolation from a 1D input and output function. Add the model to the local dictionary.

Parameters:

  • function_name (str) – name of the output function

  • dataset (Dataset) – the input-output dataset

  • input_names (list(str)) – names of the input variables

  • degree (int) –

    degree of interpolation (Default value = 3)

    By default it is set to 3.

get_scalable_derivative(output_function)[source]

Retrieve the (scalable) gradient of the scalable function generated from the original discipline.

Parameters:

output_function (str) – name of the output function

get_scalable_function(output_function)[source]

Retrieve the scalable function generated from the original discipline.

Parameters:

output_function (str) – name of the output function

static scale_samples(samples)[source]

Scale samples of array into [0, 1].

Parameters:

samples (list(ndarray)) – samples of multivariate array

Returns:

samples of multivariate array

Return type:

ndarray

class gemseo.problems.scalable.data_driven.diagonal.ScalableDiagonalModel(data, sizes=None, fill_factor=-1, comp_dep=None, inpt_dep=None, force_input_dependency=False, allow_unused_inputs=True, seed=0, group_dep=None)[source]

Bases: ScalableModel

Scalable diagonal model.

Constructor.

Parameters:

  • data (Dataset) – learning dataset.

  • sizes (dict) – sizes of input and output variables. If None, use the original sizes. Default: None.

  • fill_factor –

    degree of sparsity of the dependency matrix. Default: -1.

    By default it is set to -1.

  • comp_dep – matrix that establishes the selection of a single original component for each scalable component

  • inpt_dep – dependency matrix that establishes the dependency of outputs wrt inputs

  • force_input_dependency (bool) –

    for any output, force dependency with at least on input.

    By default it is set to False.

  • allow_unused_inputs (bool) –

    possibility to have an input with no dependence with any output

    By default it is set to True.

  • seed (int) –

    seed

    By default it is set to 0.

  • group_dep (dict(list(str))) – dependency between inputs and outputs

build_model()[source]

Build model with original sizes for input and output variables.

Returns:

scalable approximation.

Return type:

ScalableDiagonalApproximation

compute_bounds()

Compute lower and upper bounds of both input and output variables.

Returns:

The lower and upper bounds.

Return type:

tuple[dict[str, int], dict[str, int]]

generate_random_dependency()[source]

Generates a random dependency structure for use in scalable discipline.

Returns:

output component dependency and input-output dependency

Return type:

dict(int), dict(dict(ndarray))

normalize_data()

Normalize the dataset from lower and upper bounds.

Return type:

None

plot_1d_interpolations(save=False, show=False, step=0.01, varnames=None, directory='.', png=False)[source]

Plot the scaled 1D interpolations, a.k.a. the basis functions.

A basis function is a mono dimensional function interpolating the samples of a given output component over the input sampling line \(t\in[0,1]\mapsto \\underline{x}+t(\overline{x}-\\underline{x})\).

There are as many basis functions as there are output components from the discipline. Thus, for a discipline with a single output in dimension 1, there is 1 basis function. For a discipline with a single output in dimension 2, there are 2 basis functions. For a discipline with an output in dimension 2 and an output in dimension 13, there are 15 basis functions. And so on. This method allows to plot the basis functions associated with all outputs or only part of them, either on screen (show=True), in a file (save=True) or both. We can also specify the discretization step whose default value is 0.01.

Parameters:

  • save (bool) –

    if True, export the plot as a PDF file (Default value = False)

    By default it is set to False.

  • show (bool) –

    if True, display the plot (Default value = False)

    By default it is set to False.

  • step (bool) –

    Step to evaluate the 1d interpolation function (Default value = 0.01)

    By default it is set to 0.01.

  • varnames (list(str)) – names of the variable to plot; if None, all variables are plotted (Default value = None)

  • directory (str) –

    directory path. Default: ‘.’.

    By default it is set to “.”.

  • png (bool) –

    if True, the file format is PNG. Otherwise, use PDF. Default: False.

    By default it is set to False.

Return type:

list[str]

plot_dependency(add_levels=True, save=True, show=False, directory='.', png=False)[source]

This method plots the dependency matrix of a discipline in the form of a chessboard, where rows represent inputs, columns represent output and gray scale represent the dependency level between inputs and outputs.

Parameters:

  • add_levels (bool) –

    add values of dependency levels in percentage. Default: True.

    By default it is set to True.

  • save (bool) –

    if True, export the plot into a file. Default: True.

    By default it is set to True.

  • show (bool) –

    if True, display the plot. Default: False.

    By default it is set to False.

  • directory (str) –

    directory path. Default: ‘.’.

    By default it is set to “.”.

  • png (bool) –

    if True, the file format is PNG. Otherwise, use PDF. Default: False.

    By default it is set to False.

Return type:

str

scalable_derivatives(input_value=None)[source]

Evaluate the scalable derivatives.

Parameters:

input_value (dict) – input values. If None, use default inputs.

Returns:

evaluation of the scalable derivatives.

Return type:

dict

scalable_function(input_value=None)[source]

Evaluate the scalable functions.

Parameters:

input_value (dict) – input values. If None, use default inputs.

Returns:

evaluation of the scalable functions.

Return type:

dict

ABBR = 'sdm'
data: IODataset

The learning dataset.

property input_names: list[str]

The input names.

property original_sizes: Mapping[str, int]

The original sizes of variables.

property output_names: list[str]

The output names.