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:
direct or adjoint
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 (Iterable[str]) – The functions to differentiate.
dres_dx (dok_matrix | LinearOperator) – The Jacobian of the residuals wrt the design variables.
dres_dy_t (dok_matrix | LinearOperator) – The Jacobian of the residuals wrt the coupling variables.
dfun_dx (Mapping[str, dok_matrix]) – The Jacobian of the functions wrt the design variables.
dfun_dy (Mapping[str, dok_matrix]) – The Jacobian of the functions wrt the coupling variables.
linear_solver (str) –
The name of the linear solver.
By default it is set to “DEFAULT”.
use_lu_fact (bool) –
Whether to factorize dres_dy_t once.
By default it is set to False.
**linear_solver_options (Any) – The optional parameters.
- Returns:
The Jacobian of total coupled derivatives.
- Return type:
- 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 (Iterable[str]) – The functions to differentiate.
n_variables (int) – The number of variables.
n_couplings (int) – The number of couplings.
dres_dx (dok_matrix | LinearOperator) – The Jacobian of the residuals wrt the design variables.
dres_dy (dok_matrix | LinearOperator) – The Jacobian of the residuals wrt the coupling variables.
dfun_dx (Mapping[str, dok_matrix]) – The Jacobian of the functions wrt the design variables.
dfun_dy (Mapping[str, dok_matrix]) – The Jacobian of the functions wrt the coupling variables.
linear_solver (str) –
The name of the linear solver.
By default it is set to “DEFAULT”.
use_lu_fact (bool) –
Whether to factorize dres_dy once.
By default it is set to False.
**linear_solver_options (Any) – The optional parameters.
- Returns:
The Jacobian of the total coupled derivatives.
- Return type:
- linear_problem: LinearProblem | None¶
The considered linear problem.
- 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 (MDOCouplingStructure) – The MDOCouplingStructure associated disciplines that form the coupled system.
- compute_dimension(names)[source]¶
Compute the total number of functions/variables/couplings of the full 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 (Mapping[str, Any]) – The input data.
couplings (Iterable[str]) – The coupling variables.
linear_solver (str) –
The name of the linear solver.
By default it is set to “DEFAULT”.
matrix_type (str) –
The representation of the matrix dR/dy (sparse or linear operator).
By default it is set to “sparse”.
**linear_solver_options (Any) – The options passed to the linear solver factory.
- Returns:
The Newton step -[dR/dy]^-1 . R as a dict of steps per coupling variable.
- Return type:
- compute_sizes(functions, variables, couplings, residual_variables=None)[source]¶
Compute the number of scalar functions, variables and couplings.
- Parameters:
- Raises:
ValueError – When the size of some variables could not be determined.
- Return type:
None
- 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:
- Returns:
The full Jacobian matrix.
- Return type:
- 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 (Iterable[str]) – The residuals.
variables (Iterable[str]) – The differentiation variables.
n_residuals (int) – The number of residuals.
n_variables (int) – The number of variables.
matrix_type (str) –
The type of the matrix.
By default it is set to “sparse”.
transpose (bool) –
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.
- Return type:
dok_matrix | LinearOperator
- 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 (Iterable[str]) – The functions to plot.
variables (Iterable[str]) – The variables.
show (bool) –
Whether the plot is displayed.
By default it is set to False.
save (bool) –
Whether the plot is saved in a PDF file.
By default it is set to True.
filepath (str | None) – The file name to save to. If None,
coupled_jacobian.pdf
is used, otherwisecoupled_jacobian_ + filepath + .pdf
.markersize (float | None) – size of the markers
- Returns:
The file name.
- Return type:
- 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]
- 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 (Iterable[str]) – The functions to differentiate.
variables (Iterable[str]) – The differentiation variables.
couplings (Iterable[str]) – The coupling variables.
linear_solver (str) –
The name of the linear solver.
By default it is set to “DEFAULT”.
mode (str) –
The linearization mode (auto, direct or adjoint).
By default it is set to “auto”.
matrix_type (str) –
The representation of the matrix dR/dy (sparse or linear operator).
By default it is set to “sparse”.
use_lu_fact (bool) –
Whether to factorize dres_dy once, unsupported for linear operator mode.
By default it is set to False.
exec_cache_tol (float | None) – The discipline cache tolerance to when calling the linearize method. If None, no tolerance is set (equivalent to tol=0.0).
force_no_exec (bool) –
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 (Mapping[str, str] | None) – a mapping of residuals of disciplines to their respective state variables.
**linear_solver_options (Any) – The options passed to the linear solver factory.
- Returns:
The total coupled derivatives.
- Raises:
ValueError – When the linearization_mode is incorrect.
- Return type:
- AVAILABLE_MAT_TYPES: ClassVar[tuple[str]] = ('sparse', 'linear_operator')¶
The enumeration of the available matrix types.
- AVAILABLE_MODES: ClassVar[tuple[str]] = ('direct', 'adjoint', 'auto', 'reverse')¶
The enumeration of the available modes.
- coupled_system: CoupledSystem¶
The coupled derivative system of residuals.
- coupling_structure: MDOCouplingStructure¶
The considered coupling structure.
- disciplines: dict[str, MDODiscipline]¶
The MDODisciplines, stored using their name.