Struct LevenbergMarquardt

pub struct LevenbergMarquardt<F> { /* private fields */ }

Levenberg-Marquardt optimization algorithm.

See the module documentation for a usage example.

The runtime and termination behavior can be controlled by various hyperparameters.

Implementations

impl<F: RealField + Float> LevenbergMarquardt<F>

pub fn new() -> Self

pub fn with_ftol(self, ftol: F) -> Self

Set the relative error desired in the objective function $f$.

Termination occurs when both the actual and predicted relative reductions for $f$ are at most ftol.

Panics

Panics if $\mathtt{ftol} < 0$.

pub fn with_xtol(self, xtol: F) -> Self

Set relative error between last two approximations.

Termination occurs when the relative error between two consecutive iterates is at most xtol.

Panics

Panics if $\mathtt{xtol} < 0$.

pub fn with_gtol(self, gtol: F) -> Self

Set orthogonality desired between the residual vector and its derivative.

Termination occurs when the cosine of the angle between the residual vector $\vec{r}$ and any column of the Jacobian $\mathbf{J}$ is at most gtol in absolute value.

With other words, the algorithm will terminate if

  \cos\bigl(\sphericalangle (\mathbf{J}\vec{e}_i, \vec{r})\bigr) =
  \frac{|(\mathbf{J}^\top \vec{r})_i|}{\|\mathbf{J}\vec{e}_i\|\|\vec{r}\|} \leq \texttt{gtol}
  \quad\text{for all }i=1,\ldots,n.

This is based on the fact that those vectors are orthogonal near the optimum (gradient is zero). The angle check is scale invariant, whereas checking that $\nabla f(\vec{x})\approx \vec{0}$ is not.

Panics

Panics if $\mathtt{gtol} < 0$.

pub fn with_tol(self, tol: F) -> Self

Shortcut to set tol as in MINPACK LMDER1.

Sets ftol = xtol = tol and gtol = 0.

Panics

Panics if $\mathtt{tol} \leq 0$.

pub fn with_stepbound(self, stepbound: F) -> Self

Set factor for the initial step bound.

This bound is set to $\mathtt{stepbound}\cdot\|\mathbf{D}\vec{x}\|$ if nonzero, or else to stepbound itself. In most cases stepbound should lie in the interval $[0.1,100]$.

Panics

Panics if $\mathtt{stepbound} \leq 0$.

pub fn with_patience(self, patience: usize) -> Self

Set factor for the maximal number of function evaluations.

The maximal number of function evaluations is set to $\texttt{patience}\cdot(n + 1)$.

Panics

Panics if $\mathtt{patience} \leq 0$.

pub fn with_scale_diag(self, scale_diag: bool) -> Self

Enable or disable whether the variables will be rescaled internally.

pub fn minimize<N, M, O>(&self, target: O) -> (O, MinimizationReport<F>)

where N: Dim, M: DimMin<N> + DimMax<N>, O: LeastSquaresProblem<F, M, N>, DefaultAllocator: Allocator<N> + Reallocator<F, M, N, DimMaximum<M, N>, N>,

Try to solve the given least squares problem.

The parameters of the problem which are set when this function is called are used as the initial guess for $\vec{x}$.

Trait Implementations

impl<F: Clone> Clone for LevenbergMarquardt<F>

fn clone(&self) -> LevenbergMarquardt<F>

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<F: Debug> Debug for LevenbergMarquardt<F>

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<F: RealField + Float> Default for LevenbergMarquardt<F>

fn default() -> Self

Returns the “default value” for a type.

impl<F: PartialEq> PartialEq for LevenbergMarquardt<F>

fn eq(&self, other: &LevenbergMarquardt<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F: Copy> Copy for LevenbergMarquardt<F>

impl<F: Eq> Eq for LevenbergMarquardt<F>

impl<F> StructuralPartialEq for LevenbergMarquardt<F>