symforce.opt.optimizer module#

class Optimizer(factors, optimized_keys=None, params=None, debug_stats=None, include_jacobians=None)[source]#

Bases: object

A nonlinear least-squares optimizer

Typical usage is to construct an Optimizer from a set of factors and keys to optimize, and then call optimize() repeatedly with a Values.

Example creation with a single Factor:

factor = Factor(
    [my_key_0, my_key_1, my_key_2], my_residual_function
)
optimizer = Optimizer(
    factors=[factor],
    optimized_keys=[my_key_0, my_key_1],
)

And usage:

initial_guess = Values(...)
result = optimizer.optimize(initial_guess)
print(result.optimized_values)

Example creation with an optimization_problem.OptimizationProblem using make_numeric_factors(). The linearization functions are generated in make_numeric_factors() and are linearized with respect to problem.optimized_keys():

problem = OptimizationProblem(subproblems=[...], residual_blocks=...)
factors = problem.make_numeric_factors("my_problem")
optimizer = Optimizer(factors)

Example creation with an optimization_problem.OptimizationProblem using make_symbolic_factors(). The symbolic factors are converted into numeric factors when the optimizer is created, and are linearized with respect to the “optimized keys” passed to the optimizer. The linearization functions are generated when converting to numeric factors when the optimizer is created:

problem = OptimizationProblem(subproblems=[...], residual_blocks=...)
factors = problem.make_symbolic_factors("my_problem")
optimizer = Optimizer(factors, problem.optimized_keys())

Wraps the C++ sym::Optimizer class in opt/optimizer.h, so the API is mostly the same and optimization results will be identical.

Parameters:

factors (T.Iterable[T.Union[Factor, NumericFactor]]) – A sequence of either Factor or NumericFactor objects representing the residuals in the problem. If (symbolic) Factors are passed, they are convered to NumericFactors by generating linearization functions of the residual with respect to the keys in optimized_keys.
optimized_keys (T.Optional[T.Sequence[str]]) – A set of the keys to be optimized. Only required if symbolic factors are passed to the optimizer.
params (T.Optional[OptimizerParams]) – Params for the optimizer. Defaults are in OptimizerParams, except that verbose is True by default.
debug_stats (T.Optional[bool]) –
include_jacobians (T.Optional[bool]) –

Params#: alias of OptimizerParams

Status#: alias of optimization_status_t

FailureReason#: alias of levenberg_marquardt_solver_failure_reason_t

class Result(initial_values, optimized_values, _stats)[source]#

Bases: object

The result of an optimization, with additional stats and debug information

Parameters:

initial_values (Values) –
optimized_values (Values) –
_stats (OptimizationStats) –

initial_values#

The initial guess used for this optimization

Type:: symforce.values.values.Values

optimized_values#

The best Values achieved during the optimization (Values with the smallest error)

Type:: symforce.values.values.Values

iterations#: Per-iteration stats, if requested, like the error per iteration. If debug stats are turned on, also the Values and linearization per iteration.

best_index#: The index into iterations for the iteration that produced the smallest error. I.e. result.iterations[best_index].values == optimized_values. This is not guaranteed to be the last iteration, if the optimizer tried additional steps which did not reduce the error

status#: What was the result of the optimization? (did it converge, fail, etc.)

failure_reason#: If status == FAILED, why?

best_linearization#: The linearization at best_index (at optimized_values), filled out if populate_best_linearization=True

jacobian_sparsity#: The sparsity pattern of the jacobian, filled out if debug_stats=True and include_jacobians=True

linear_solver_ordering#: The ordering used for the linear solver, filled out if debug_stats=True

cholesky_factor_sparsity#: The sparsity pattern of the cholesky factor L, filled out if debug_stats=True

initial_values: Values#

optimized_values: Values#

property iterations: List[optimization_iteration_t]#

property best_index: int#

property status: optimization_status_t#

property failure_reason: levenberg_marquardt_solver_failure_reason_t#

property best_linearization: Linearization | None#

property jacobian_sparsity: sparse_matrix_structure_t#

property linear_solver_ordering: ndarray#

property cholesky_factor_sparsity: sparse_matrix_structure_t#

error()[source]#

The lowest error achieved by the optimization (the error at optimized_values)

Return type:: float

compute_all_covariances(optimized_value)[source]#

Compute the covariance matrix (J^T@J)^-1 for all optimized keys about a given linearization point

Parameters:: optimized_value (Values) – A value containing the linearization point to compute the covariance matrix about
Returns:: A dict of {optimized_key – numerical covariance matrix}
Return type:: Dict[str, ndarray]

compute_covariances(optimized_value, keys)[source]#

Get covariances for the given subset of keys at the given linearization

This version is potentially much more efficient than computing the covariances for all keys in the problem.

Currently requires that keys corresponds to a set of keys at the start of the list of keys for the full problem, and in the same order. It uses the Schur complement trick, so will be most efficient if the hessian is of the following form, with C block diagonal:

A = ( B    E )
    ( E^T  C )

Parameters:

optimized_value (Values) – A value containing the linearization point to compute the covariance matrix about
keys (Sequence[str]) – The subset of keys to compute covariances for

Returns:

A dict of {optimized_key – numerical covariance matrix}

Return type:

Dict[str, ndarray]

compute_full_covariance(optimized_value)[source]#

Get the full problem covariance at the given linearization

Unlike compute_covariance and compute_all_covariances, this includes the off-diagonal blocks, i.e. the cross-covariances between different keys.

The ordering of entries here is the same as the ordering of the keys in the linearization, which can be accessed via linearization_index().

May not be called before either optimize or linearize has been called.

Parameters:: optimized_value (Values) –
Return type:: ndarray

optimize(initial_guess, **kwargs)[source]#

Optimize from the given initial guess, and return the optimized Values and stats

Parameters:

initial_guess (Values) – A Values containing the initial guess, should contain at least all the keys required by the factors passed to the constructor
num_iterations – If < 0 (the default), uses the number of iterations specified by the params at construction
populate_best_linearization – If true, the linearization at the best values will be filled out in the stats
kwargs (Any) –

Returns:

The optimization results, with additional stats and debug information. See the
:class:`Optimizer.Result` documentation for more information

Return type:

Result

linearize(values)[source]#

Compute and return the linearization at the given Values

Parameters:: values (Values) –
Return type:: Linearization

load_iteration_values(values_msg)[source]#

Load a values_t message into a Python Values by first creating a C++ Values, then converting back to the python key names.

Parameters:: values_msg (values_t) –
Return type:: Values

linearization_index()[source]#

Get the index mapping keys to their positions in the linearized state vector. Useful for extracting blocks from the problem jacobian, hessian, or RHS

Returns: The index for the Optimizer’s problem linearization

Return type:: Dict[str, index_entry_t]

linearization_index_entry(key)[source]#

Get the index entry for a given key in the linearized state vector. Useful for extracting blocks from the problem jacobian, hessian, or RHS

Parameters:: key (str) – The string key for a variable in the Python Values
Return type:: index_entry_t

Returns: The index entry for the variable in the Optimizer’s problem linearization