API

class pydiffsol.AdjointCheckpoint: Bases: object

class pydiffsol.InitialConditionSolverOptions

Bases: object

armijo_constant

max_linear_solver_setups

max_linesearch_iterations

max_newton_iterations

step_reduction_factor

use_linesearch

class pydiffsol.JitBackendType

Bases: object

classmethod all()

classmethod from_str(value)

llvm = JitBackendType.llvm

class pydiffsol.LinearSolverType

Bases: object

Enumerates the possible linear solver types for diffsol

Attr default:: use the solver’s default linear solver choice, typically LU
Attr lu:: use LU decomposition linear solver (dense or sparse as appropriate)
Attr klu:: use KLU sparse linear solver

classmethod all()

classmethod from_str(value)

default = LinearSolverType.default

klu = LinearSolverType.klu

lu = LinearSolverType.lu

class pydiffsol.MatrixType

Bases: object

Enumerates the possible matrix types for diffsol

Attr nalgebra_dense:: dense matrix using nalgebra crate (https://nalgebra.rs/)
Attr faer_dense:: dense matrix using faer crate (https://faer.veganb.tw/)
Attr faer_sparse:: sparse matrix using faer crate (https://faer.veganb.tw/)

classmethod all(): Get all available matrix types :return: list of MatrixType

classmethod from_str(value): Create MatrixType from string name :param name: string representation of matrix type :return: valid MatrixType or exception if name is invalid

faer_dense = MatrixType.faer_dense

faer_sparse = MatrixType.faer_sparse

nalgebra_dense = MatrixType.nalgebra_dense

class pydiffsol.Ode(code, jit_backend=None, scalar_type=Ellipsis, matrix_type=Ellipsis, linear_solver=Ellipsis, ode_solver=Ellipsis)

Bases: object

has_stop(): Check if the diffsl code has a stop event defined.

rhs(params, t, y): Evaluate the right-hand side function at time t and state y.

rhs_jac_mul(params, t, y, v): Evaluate the right-hand side Jacobian-vector product Jv at time t and state y.

solve(params, final_time)

Solve the problem up to time final_time. Stop/reset events defined in the DiffSL code are handled automatically.

The number of params must match the expected params in the diffsl code.

Parameters:

params (numpy.ndarray) – 1D array of solver parameters
final_time (float) – end time of solver

Returns:

Solution object with fields ys and ts

Return type:

Solution

Example

>>> print(ode.solve(np.array([]), 0.5))

solve_adjoint_bkwd(solution, checkpoint, dgdu_eval)

Solve the discrete adjoint backward pass using a prior forward adjoint checkpoint and the gradient of a scalar objective with respect to model outputs at each saved evaluation time.

Parameters:: dgdu_eval (numpy.ndarray) – 2D array, shape (nout, len(solution.ts)); float32 or float64
Returns:: parameter gradient matrix
Return type:: numpy.ndarray

solve_adjoint_fwd(params, t_eval)

Solve the forward problem at t_eval and retain checkpoint data for a later discrete adjoint backward pass.

Returns:: tuple of (solution, checkpoint)
Return type:: tuple[Solution, AdjointCheckpoint]

solve_continuous_adjoint(params, final_time)

Solve the continuous adjoint problem for the integral of the model output from the initial time to final_time.

Returns:: tuple of (integral, gradient)
Return type:: tuple[numpy.ndarray, numpy.ndarray]

solve_dense(params, t_eval)

Solve the problem up to time t_eval[t_eval.len()-1]. Returns a Solution object with values at timepoints given by t_eval. Stop/reset events defined in the DiffSL code are handled automatically.

The number of params must match the expected params in the diffsl code.

Parameters:

params (numpy.ndarray) – 1D array of solver parameters
t_eval (numpy.ndarray) – 1D array of solver times

Returns:

Solution object with fields ys and ts

Return type:

Solution

solve_fwd_sens(params, t_eval)

Solve the problem up to time t_eval[t_eval.len()-1]. Returns a Solution object with values at t_eval and sensitivity arrays at the same timepoints. Stop/reset events defined in the DiffSL code are handled automatically.

The number of params must match the expected params in the diffsl code.

Parameters:

params (numpy.ndarray) – 1D array of solver parameters
t_eval (numpy.ndarray) – 1D array of solver times

Returns:

Solution object with fields ys, ts, and sens

Return type:

Solution

y0(params): Get the initial condition vector y0 as a 1D numpy array.

atol: Absolute tolerance for the solver, default 1e-6. Governs the error as the solution goes to zero.

code: Get the DiffSl code used to generate this ODE.

h0: Initial step size for the solver, default 1.0.

ic_options

integrate_out: Whether to integrate output equations alongside state equations.

jit_backend: JIT backend used for compilation. This is fixed after construction.

linear_solver: Linear solver type used in the ODE solver. Set to default to use the solver’s default choice, which is typically an LU solver.

matrix_type: Matrix type used in the ODE solver. This is fixed after construction.

nout: Get the number of outputs in the ODE system. If there is no out tensor, this is the number of states.

nparams: Get the number of parameters expected by the diffsl code.

nstates: Get the number of states in the ODE system.

ode_solver: ODE solver method, default Bdf (backward differentiation formula).

options

out_atol: Absolute tolerance for integrated output equations.

out_rtol: Relative tolerance for integrated output equations.

param_atol: Absolute tolerance for adjoint parameter gradient equations.

param_rtol: Relative tolerance for adjoint parameter gradient equations.

rtol: Relative tolerance for the solver, default 1e-6. Governs the error relative to the solution size.

scalar_type: Scalar type used in the ODE solver. This is fixed after construction.

sens_atol: Absolute tolerance for forward sensitivity or adjoint equations.

sens_rtol: Relative tolerance for forward sensitivity or adjoint equations.

t0: Initial time for the solver, default 0.0.

class pydiffsol.OdeSolverOptions

Bases: object

max_error_test_failures

max_nonlinear_solver_iterations

min_timestep

threshold_to_update_jacobian

threshold_to_update_rhs_jacobian

update_jacobian_after_steps

update_rhs_jacobian_after_steps

class pydiffsol.OdeSolverType

Bases: object

classmethod all()

classmethod from_str(value)

bdf = OdeSolverType.bdf

esdirk34 = OdeSolverType.esdirk34

tr_bdf2 = OdeSolverType.tr_bdf2

tsit45 = OdeSolverType.tsit45

class pydiffsol.ScalarType

Bases: object

classmethod all()

classmethod from_str(value)

f32 = ScalarType.f32

f64 = ScalarType.f64

class pydiffsol.Solution

Bases: object

sens

ts

ys

pydiffsol.default_enabled_jit_backend()

pydiffsol.diffsl_version()

pydiffsol.diffsol_c_version()

pydiffsol.diffsol_version()

pydiffsol.is_klu_available(): Indicate whether KLU functions are available.

pydiffsol.is_sens_available(): Indicate whether sensitivity analysis is available.

pydiffsol.version(): Get version of this pydiffsol module