5. API documentation

torchimize.functions.lsq_gna(p: torch.Tensor, function: Callable, jac_function: Optional[Callable] = None, args: Union[Tuple, List] = (), ftol: float = 1e-08, ptol: float = 1e-08, gtol: float = 1e-08, l: float = 1.0, max_iter: int = 100) → List[torch.Tensor]

Gauss-Newton implementation for least-squares fitting of non-linear functions

Parameters:

• p – initial value(s)

• function – user-provided function which takes p (and additional arguments) as input

• jac_fun – user-provided Jacobian function which takes p (and additional arguments) as input

• args – optional arguments passed to function

• ftol – relative change in cost function as stop condition

• ptol – relative change in independant variables as stop condition

• gtol – maximum gradient tolerance as stop condition

• l – step size damping parameter

• max_iter – maximum number of iterations

Returns:

list of results

torchimize.functions.lsq_lma(p: torch.Tensor, function: Callable, jac_function: Optional[Callable] = None, args: Union[Tuple, List] = (), ftol: float = 1e-08, ptol: float = 1e-08, gtol: float = 1e-08, tau: float = 0.001, meth: str = 'lev', rho1: float = 0.25, rho2: float = 0.75, bet: float = 2, gam: float = 3, max_iter: int = 100) → List[torch.Tensor]

Levenberg-Marquardt implementation for least-squares fitting of non-linear functions

Parameters:

• p – initial value(s)

• function – user-provided function which takes p (and additional arguments) as input

• jac_fun – user-provided Jacobian function which takes p (and additional arguments) as input

• args – optional arguments passed to function

• ftol – relative change in cost function as stop condition

• ptol – relative change in independant variables as stop condition

• gtol – maximum gradient tolerance as stop condition

• tau – factor to initialize damping parameter

• meth – method which is default ‘lev’ for Levenberg and otherwise Marquardt

• rho1 – first gain factor threshold for damping parameter adjustment for Marquardt

• rho2 – second gain factor threshold for damping parameter adjustment for Marquardt

• bet – multiplier for damping parameter adjustment for Marquardt

• gam – divisor for damping parameter adjustment for Marquardt

• max_iter – maximum number of iterations

Returns:

list of results

torchimize.functions.lsq_gna_parallel(p: torch.Tensor, function: Callable, jac_function: Optional[Callable] = None, args: Union[Tuple, List] = (), wvec: Optional[torch.Tensor] = None, ftol: float = 1e-08, ptol: float = 1e-08, gtol: float = 1e-08, l: float = 1.0, max_iter: int = 100) → List[torch.Tensor]

Gauss-Newton implementation for parallel least-squares fitting of non-linear functions with conditions.

Parameters:

• p – initial value(s)

• function – user-provided function which takes p (and additional arguments) as input

• jac_fun – user-provided Jacobian function which takes p (and additional arguments) as input

• args – optional arguments passed to function

• wvec – weights vector used in reduction of multiple costs

• ftol – relative change in cost function as stop condition

• ptol – relative change in independant variables as stop condition

• gtol – maximum gradient tolerance as stop condition

• l – step size damping parameter

• max_iter – maximum number of iterations

Returns:

list of results

torchimize.functions.lsq_gna_parallel_plain(p: torch.Tensor, function: Callable, jac_function: Callable, wvec: torch.Tensor, l: float = 1.0, max_iter: int = 100) → torch.Tensor

Gauss-Newton implementation for parallel least-squares fitting of non-linear functions without conditions.

Parameters:

• p – initial value(s)

• function – user-provided function which takes p (and additional arguments) as input

• jac_fun – user-provided Jacobian function which takes p (and additional arguments) as input

• wvec – weights vector used in reduction of multiple costs

• l – step size damping parameter

• max_iter – maximum number of iterations

Returns:

result

torchimize.functions.lsq_lma_parallel(p: torch.Tensor, function: Callable, jac_function: Optional[Callable] = None, args: Union[Tuple, List] = (), wvec: Optional[torch.Tensor] = None, ftol: float = 1e-08, ptol: float = 1e-08, gtol: float = 1e-08, tau: float = 0.001, meth: str = 'lev', rho1: float = 0.25, rho2: float = 0.75, beta: float = 2, gama: float = 3, max_iter: int = 100) → List[torch.Tensor]

Levenberg-Marquardt implementation for parallel least-squares fitting of non-linear functions

Parameters:

• p – initial value(s)

• function – user-provided function which takes p (and additional arguments) as input

• jac_fun – user-provided Jacobian function which takes p (and additional arguments) as input

• args – optional arguments passed to function

• wvec – weights vector used in reduction of multiple costs

• ftol – relative change in cost function as stop condition

• ptol – relative change in independant variables as stop condition

• gtol – maximum gradient tolerance as stop condition

• tau – factor to initialize damping parameter

• meth – method which is default ‘lev’ for Levenberg and otherwise Marquardt

• rho1 – first gain factor threshold for damping parameter adjustment for Marquardt

• rho2 – second gain factor threshold for damping parameter adjustment for Marquardt

• beta – multiplier for damping parameter adjustment for Marquardt

• gama – divisor for damping parameter adjustment for Marquardt

• max_iter – maximum number of iterations

Returns:

list of results

torchimize.functions.newton_step_parallel(p: torch.Tensor, function: Callable, jac_function: Callable, wvec: torch.Tensor) → Tuple[torch.Tensor, torch.Tensor, torch.Tensor, torch.Tensor]

Newton second order step function for parallel least-squares fitting of non-linear functions

Parameters:

• p – current guess

• function – user-provided function which takes p (and additional arguments) as input

• jac_fun – user-provided Jacobian function which takes p (and additional arguments) as input

• wvec – weights vector used in reduction of multiple costs

Returns:

list of results

torchimize.functions.test_fun_dims_parallel(p: torch.Tensor, function: Callable, jac_function: Optional[Callable] = None, args: Union[Tuple, List] = (), wvec: Optional[torch.Tensor] = None) → bool

Helper function that tests whether dimensionality of output tensors suits the herein provided optimization functions.

Parameters:

• p – initial value(s)

• function – user-provided function which takes p (and additional arguments) as input

• jac_fun – user-provided Jacobian function which takes p (and additional arguments) as input

• args – optional arguments passed to function