gemseo / core / derivatives

# jacobian_assembly module¶

Coupled derivatives calculations.

class gemseo.core.derivatives.jacobian_assembly.CoupledSystem[source]

Bases: object

Compute coupled (total) derivatives of a system of residuals.

Use several methods:

• factorized for multiple RHS

adjoint_mode(functions, dres_dx, dres_dy_t, dfun_dx, dfun_dy, linear_solver='DEFAULT', use_lu_fact=False, **linear_solver_options)[source]

Compute the total derivative Jacobian in adjoint mode.

Parameters:
• functions – The functions to differentiate.

• dres_dx – The Jacobian of the residuals wrt the design variables.

• dres_dy_t – The Jacobian of the residuals wrt the coupling variables.

• dfun_dx – The Jacobian of the functions wrt the design variables.

• dfun_dy – The Jacobian of the functions wrt the coupling variables.

• linear_solver

The name of the linear solver.

By default it is set to “DEFAULT”.

• use_lu_fact

Whether to factorize dres_dy_t once.

By default it is set to False.

• **linear_solver_options – The optional parameters.

Returns:

The Jacobian of total coupled derivatives.

direct_mode(functions, n_variables, n_couplings, dres_dx, dres_dy, dfun_dx, dfun_dy, linear_solver='DEFAULT', use_lu_fact=False, **linear_solver_options)[source]

Compute the total derivative Jacobian in direct mode.

Parameters:
• functions – The functions to differentiate.

• n_variables – The number of variables.

• n_couplings – The number of couplings.

• dres_dx – The Jacobian of the residuals wrt the design variables.

• dres_dy – The Jacobian of the residuals wrt the coupling variables.

• dfun_dx – The Jacobian of the functions wrt the design variables.

• dfun_dy – The Jacobian of the functions wrt the coupling variables.

• linear_solver

The name of the linear solver.

By default it is set to “DEFAULT”.

• use_lu_fact

Whether to factorize dres_dy once.

By default it is set to False.

• **linear_solver_options – The optional parameters.

Returns:

The Jacobian of the total coupled derivatives.

class gemseo.core.derivatives.jacobian_assembly.JacobianAssembly(coupling_structure)[source]

Bases: object

Assembly of Jacobians.

Typically, assemble discipline’s Jacobians into a system Jacobian.

Parameters:

coupling_structure – The CouplingStructure associated disciplines that form the coupled system.

compute_dimension(names)[source]

Compute the total number of functions/variables/couplings of the full system.

Parameters:

names – The names of the inputs or the outputs.

Returns:

The dimension if the system.

compute_newton_step(in_data, couplings, relax_factor, linear_solver='DEFAULT', matrix_type='sparse', **linear_solver_options)[source]

Compute the Newton step for the coupled system of disciplines residuals.

Parameters:
• in_data – The input data.

• couplings – The coupling variables.

• relax_factor – The relaxation factor.

• linear_solver

The name of the linear solver.

By default it is set to “DEFAULT”.

• matrix_type

The representation of the matrix dR/dy (sparse or linear operator).

By default it is set to “sparse”.

• **linear_solver_options – The options passed to the linear solver factory.

Returns:

The Newton step -[dR/dy]^-1 . R as a dict of steps per coupling variable.

compute_sizes(functions, variables, couplings, residual_variables=None)[source]

Compute the number of scalar functions, variables and couplings.

Parameters:
• functions – The functions to differentiate.

• variables – The differentiation variables.

• couplings – The coupling variables.

• residual_variables – The mapping of residuals of disciplines to their respective state variables.

Raises:

ValueError – When the size of some variables could not be determined.

dfun_dvar(function, variables, n_variables)[source]

Forms the matrix of partial derivatives of a function.

Given disciplinary Jacobians dJi(v0…vn)/dvj, fill the sparse Jacobian: | | | dJi/dvj | | |

Parameters:
• function – The function to differentiate.

• variables – The differentiation variables.

• n_variables – The number of variables.

Returns:

The full Jacobian matrix.

dres_dvar(residuals, variables, n_residuals, n_variables, matrix_type='sparse', transpose=False)[source]

Form the matrix of partial derivatives of residuals.

Given disciplinary Jacobians dYi(Y0…Yn)/dvj, fill the sparse Jacobian: | | | dRi/dvj | | | (Default value = False)

Parameters:
• residuals – The residuals.

• variables – The differentiation variables.

• n_residuals – The number of residuals.

• n_variables – The number of variables.

• matrix_type

The type of the matrix.

By default it is set to “sparse”.

• transpose

Whether to transpose the matrix.

By default it is set to False.

Returns:

The jacobian of dres_dvar.

Raises:

TypeError – When the matrix type is unknown.

plot_dependency_jacobian(functions, variables, save=True, show=False, filepath=None, markersize=None)[source]

Plot the Jacobian matrix.

Nonzero elements of the sparse matrix are represented by blue squares.

Parameters:
• functions – The functions to plot.

• variables – The variables.

• show

WHether the plot is displayed.

By default it is set to False.

• save

WHether the plot is saved in a PDF file.

By default it is set to True.

• filepath – The file name to save to. If None, coupled_jacobian.pdf is used, otherwise coupled_jacobian_ + filepath + .pdf.

Returns:

The file name.

residuals(in_data, var_names)[source]

Form the matrix of residuals wrt coupling variables.

Given disciplinary explicit calculations Yi(Y0_t,…Yn_t), fill the residual matrix:

[Y0(Y0_t,...Yn_t) - Y0_t]
[                       ]
[Yn(Y0_t,...Yn_t) - Yn_t]

Parameters:
• in_data – The values prescribed for the calculation of the residuals (Y0_t,…Yn_t).

• var_names – The names of variables associated with the residuals (R).

Returns:

The residuals array.

split_jac(coupled_system, variables)[source]

Split a Jacobian dict into a dict of dict.

Parameters:
• coupled_system – The derivatives to split.

• variables – The variables wrt which the differentiation is performed.

Returns:

The Jacobian.

total_derivatives(in_data, functions, variables, couplings, linear_solver='DEFAULT', mode='auto', matrix_type='sparse', use_lu_fact=False, exec_cache_tol=None, force_no_exec=False, residual_variables=None, **linear_solver_options)[source]

Compute the Jacobian of total derivatives of the coupled system.

Parameters:
• in_data – The input data dict.

• functions – The functions to differentiate.

• variables – The differentiation variables.

• couplings – The coupling variables.

• linear_solver

The name of the linear solver.

By default it is set to “DEFAULT”.

• mode

The linearization mode (auto, direct or adjoint).

By default it is set to “auto”.

• matrix_type

The representation of the matrix dR/dy (sparse or linear operator).

By default it is set to “sparse”.

• use_lu_fact

Whether to factorize dres_dy once, unsupported for linear operator mode.

By default it is set to False.

• exec_cache_tol – The discipline cache tolerance to when calling the linearize method. If None, no tolerance is set (equivalent to tol=0.0).

• force_no_exec

Whether the discipline is not re-executed, the cache is loaded anyway.

By default it is set to False.

• linear_solver_options – The options passed to the linear solver factory.

• residual_variables – a mapping of residuals of disciplines to their respective state variables.

• **linear_solver_options – The options passed to the linear solver factory.

Returns:

The total coupled derivatives.

Raises:

ValueError – When the linearization_mode is incorrect.

AUTO_MODE = 'auto'
AVAILABLE_MAT_TYPES = ['sparse', 'linear_operator']
AVAILABLE_MODES = ('direct', 'adjoint', 'auto', 'reverse')
DIRECT_MODE = 'direct'
LINEAR_OPERATOR = 'linear_operator'
REVERSE_MODE = 'reverse'
SPARSE = 'sparse'
gemseo.core.derivatives.jacobian_assembly.default_dict_factory()[source]

Instantiates a defaultdict(None) object.

gemseo.core.derivatives.jacobian_assembly.none_factory()[source]

Returns None…

To be used for defaultdict