Stability	Experimental
Maintainer	Roel van Dijk <vandijk.roel@gmail.com> Bas van Dijk <v.dijk.bas@gmail.com>

Numeric.LevMar

Contents

Model & Jacobian.
Levenberg-Marquardt algorithm.
Minimization options.
Constraints
Output

Description

For additional documentation see the documentation of the levmar C library which this library is based on: http://www.ics.forth.gr/~lourakis/levmar/

Synopsis

Model & Jacobian.

type Model r = Vector r -> Vector rSource

A functional relation describing measurements represented as a function from a vector of parameters to a vector of expected measurements.

Ensure that the length of the parameters vector equals the length of the initial parameters vector in levmar.
Ensure that the length of the ouput vector equals the length of the samples vector in levmar.

type Jacobian r = Vector r -> Matrix rSource

The jacobian of the Model function. Expressed as a function from a vector of parameters to a matrix which for each expected measurement describes the partial derivatives of the parameters.

See: http://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant

Ensure that the length of the parameter vector equals the length of the initial parameter vector in levmar.
Ensure that the output matrix has the dimension n><m where n is the number of samples and m is the number of parameters.

Levenberg-Marquardt algorithm.

class LevMarable r whereSource

The Levenberg-Marquardt algorithm is overloaded to work on Double and Float.

Methods

levmar Source

Arguments

:: Model r	Model
-> Maybe (Jacobian r)	Optional jacobian
-> Vector r	Initial parameters
-> Vector r	Samples
-> Int	Maximum iterations
-> Options r	Minimization options
-> Constraints r	Constraints
-> Either LevMarError (Vector r, Info r, Matrix r)

The Levenberg-Marquardt algorithm.

Returns a tuple of the found parameters, a structure containing information about the minimization and the covariance matrix corresponding to LS solution.

Instances

LevMarable Double
LevMarable Float

Minimization options.

data Options r Source

Minimization options

Constructors

Opts

Fields

optScaleInitMu :: !r: Scale factor for initial mu.
optStopNormInfJacTe :: !r: Stopping thresholds for ||J^T e||_inf.
optStopNorm2Dp :: !r: Stopping thresholds for ||Dp||_2.
optStopNorm2E :: !r: Stopping thresholds for ||e||_2.
optDelta :: !r: Step used in the difference approximation to the Jacobian. If optDelta<0, the Jacobian is approximated with central differences which are more accurate (but slower!) compared to the forward differences employed by default.

Instances

Typeable1 Options
Read r => Read (Options r)
Show r => Show (Options r)

defaultOpts :: Fractional r => Options rSource

Default minimization options

Constraints

data Constraints r Source

Ensure that these vectors have the same length as the number of parameters.

Constructors

Constraints
Fields lowerBounds :: !(Maybe (Vector r)) Optional lower bounds upperBounds :: !(Maybe (Vector r)) Optional upper bounds weights :: !(Maybe (Vector r)) Optional weights linearConstraints :: !(Maybe (LinearConstraints r)) Optional linear constraints

Instances

Typeable1 Constraints
(Show r, Element r) => Show (Constraints r)
Monoid (Constraints r)	`mempty` is defined as a `Constraints` where all fields are `Nothing`. `mappend` merges two `Constraints` by taking the first non-`Nothing` value for each field.

type LinearConstraints r = (Matrix r, Vector r)Source

Linear constraints consisting of a constraints matrix, k><m and a right hand constraints vector, of length k where m is the number of parameters and k is the number of constraints.

Output

data Info r Source

Information regarding the minimization.

Constructors

Info

Fields

infNorm2initE :: !r: ||e||_2 at initial parameters.
infNorm2E :: !r: ||e||_2 at estimated parameters.
infNormInfJacTe :: !r: ||J^T e||_inf at estimated parameters.
infNorm2Dp :: !r: ||Dp||_2 at estimated parameters.
infMuDivMax :: !r: mu/max[J^T J]_ii ] at estimated parameters.
infNumIter :: !Int: Number of iterations.
infStopReason :: !StopReason: Reason for terminating.
infNumFuncEvals :: !Int: Number of function evaluations.
infNumJacobEvals :: !Int: Number of jacobian evaluations.
infNumLinSysSolved :: !Int: Number of linear systems solved, i.e. attempts for reducing error.

Instances

Typeable1 Info
Read r => Read (Info r)
Show r => Show (Info r)

data StopReason Source

Reason for terminating.

Constructors

SmallGradient	Stopped because of small gradient `J^T e`.
SmallDp	Stopped because of small Dp.
MaxIterations	Stopped because maximum iterations was reached.
SingularMatrix	Stopped because of singular matrix. Restart from current estimated parameters with increased `optScaleInitMu`.
SmallestError	Stopped because no further error reduction is possible. Restart with increased `optScaleInitMu`.
SmallNorm2E	Stopped because of small `\|\|e\|\|_2`.
InvalidValues	Stopped because model function returned invalid values (i.e. NaN or Inf). This is a user error.

Instances

Enum StopReason
Read StopReason
Show StopReason
Typeable StopReason

data LevMarError Source

Constructors

LevMarError	Generic error (not one of the others)
LapackError	A call to a lapack subroutine failed in the underlying C levmar library.
FailedBoxCheck	At least one lower bound exceeds the upper one.
MemoryAllocationFailure	A call to `malloc` failed in the underlying C levmar library.
ConstraintMatrixRowsGtCols	The matrix of constraints cannot have more rows than columns.
ConstraintMatrixNotFullRowRank	Constraints matrix is not of full row rank.
TooFewMeasurements	Cannot solve a problem with fewer measurements than unknowns. In case linear constraints are provided, this error is also returned when the number of measurements is smaller than the number of unknowns minus the number of equality constraints.

Instances

Read LevMarError
Show LevMarError
Typeable LevMarError
Exception LevMarError