tinyopt::Summary Struct Reference

Classes
struct	History

Public Types
using	Scalar = double

Public Member Functions
bool	Succeeded () const
	Returns true if the stop reason is not a failure to solve or NaNs or missing residuals.
bool	Converged () const
	Returns true if the optimization reached the specified minimal error, delta or gradient.
template<typename M = MatX>
std::optional< M >	Covariance (bool rescaled=false) const
	Computes an approximation of the covariance matrix.
bool	has_final_hessian () const
const auto &	final_hessian_dense () const
const auto &	final_hessian_sparse () const

Public Attributes
Cost	final_cost = Cost(std::numeric_limits<Scalar>::max(), 0)
	Last valid error.
Scalar	final_rerr_dec = std::numeric_limits<Scalar>::max()
StopReason	stop_reason = StopReason::kNone
	Stop reason.
Statistics
uint16_t	num_residuals = 0
	Final number of residuals.
uint16_t	num_iters = 0
	Final number of iterations.
uint8_t	num_failures = 0
	Final number of failures to decrease the error.
uint8_t	num_consec_failures
	Final number of the last consecutive failures to decrease the error.
TimePoint	start_time
float	duration_ms = 0
	Cumulated optimization duration.
std::variant< std::monostate, MatX, SparseMat >	final_hessian
	Final H, excluding any damping (only saved if options.hessian.save = true).
bool	num_diff_used = false
	True if numerical derivatives were used.
Per iteration results
struct tinyopt::Summary::History	hist

Member Function Documentation

Covariance()

template<typename M = MatX>

std::optional< M > tinyopt::Summary::Covariance ( bool rescaled = false ) const

inline

Computes an approximation of the covariance matrix.

This method calculates the covariance matrix, which is an approximation derived from the inverse of the Hessian matrix (H).

It is only meaningful at convergence, right Johan?

Parameters

rescaled

(optional) If true, the covariance matrix is rescaled by ε² / (#ε - dims), where ε² is the sum of squared residuals (final_cost²), #ε is the number of residuals (num_residuals), and dims is the number of parameters (H.cols()). This rescaling is useful when observations lack explicit noise modeling and provides a more accurate estimate of the covariance. Defaults to false.

Returns

std::optional<H_t> Returns the computed covariance matrix if H is invertible, wrapped in a std::optional. Returns std::nullopt if H is not invertible, indicating that the covariance cannot be estimated.

The covariance matrix is calculated as:

• If rescaled is false: (H)^-1
• If rescaled is true and num_residuals > H.cols(): (H)^-1 * (ε² / (#ε - dims))

Where:

• H is the approximated Hessian matrix.
• ε (final_cost) is the sum of residuals.
• #ε (num_residuals) is the number of residuals.
• dims (H.cols()) is the number of parameters.

The rescaling is applied only when the number of residuals exceeds the number of parameters, indicating an overdetermined system. This rescaling provides a more statistically sound estimate of the covariance in such scenarios, especially when noise modeling was not explicitly included in the observations.

Note

The function relies on the InvCov(H) method to compute the inverse of H. If InvCov returns std::nullopt, indicating that H is not invertible, this method also returns std::nullopt.

Template Parameters

H_t	The type of the covariance matrix.

Member Data Documentation

num_consec_failures

uint8_t tinyopt::Summary::num_consec_failures

Initial value:

                        =
0

Final number of the last consecutive failures to decrease the error.

start_time

TimePoint tinyopt::Summary::start_time

Initial value:

                 =
TimePoint::min()

Starting time of the optimization or std::chrono::system_clock::time_point::min() if not started

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The documentation for this struct was generated from the following file:

• include/tinyopt/summary.h