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findopOptions

Option set for findop

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Syntax

opt = findopOptions(model)
opt = findopOptions(model,Name,Value)

Description

opt = findopOptions(model) creates a default option set for computing the operating point of a specified nonlinear ARX or Hammerstein-Wiener model. Use dot notation to modify this option set for your specific application. Options that you do not modify retain their default values.

example

opt = findopOptions(model,Name,Value) creates an option set with options specified by one or more Name,Value pair arguments.

example

Examples

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Open Live Script

Create a default option set for findop using an idnlarx model.

opt = findopOptions(idnlarx);
Open Live Script

Create a default option set for findop using an idnlhw model.

opt = findopOptions(idnlhw);

Use dot notation to specify a subspace Gauss-Newton least squares search with a maximum of 25 iterations.

opt.SearchMethod = 'gn';
opt.SearchOptions.MaxIterations = 25;
Open Live Script

Create an option set for findop using an idnlarx model. Specify a steepest descent least squares search with default search options.

opt = findopOptions(idnlarx,'SearchMethod','grad');

Input Arguments

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Estimated nonlinear model, specified as one of the following:

  • idnlarx model

  • idnlhw model

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: 'SearchMethod','grad' specifies a steepest descent least squares search method

Numerical search method used for iterative parameter estimation, specified as the one of the values in the following table.

SearchMethodDescription
'auto'

Automatic method selection

A combination of the line search algorithms, 'gn', 'lm', 'gna', and 'grad', is tried in sequence at each iteration. The first descent direction leading to a reduction in estimation cost is used.

'gn'

Subspace Gauss-Newton least-squares search

Singular values of the Jacobian matrix less than GnPinvConstant*eps*max(size(J))*norm(J) are discarded when computing the search direction. J is the Jacobian matrix. The Hessian matrix is approximated as JTJ. If this direction shows no improvement, the function tries the gradient direction.

'gna'

Adaptive subspace Gauss-Newton search

Eigenvalues less than gamma*max(sv) of the Hessian are ignored, where sv contains the singular values of the Hessian. The Gauss-Newton direction is computed in the remaining subspace. gamma has the initial value InitialGnaTolerance (see Advanced in 'SearchOptions' for more information). This value is increased by the factor LMStep each time the search fails to find a lower value of the criterion in fewer than five bisections. This value is decreased by the factor 2*LMStep each time a search is successful without any bisections.

'lm'

Levenberg-Marquardt least squares search

Each parameter value is -pinv(H+d*I)*grad from the previous value. H is the Hessian, I is the identity matrix, and grad is the gradient. d is a number that is increased until a lower value of the criterion is found.

'grad'

Steepest descent least-squares search

'lsqnonlin'

Trust-region-reflective algorithm of lsqnonlin (Optimization Toolbox)

This algorithm requires Optimization Toolbox™ software.

'fmincon'

Constrained nonlinear solvers

You can use the sequential quadratic programming (SQP) and trust-region-reflective algorithms of the fmincon (Optimization Toolbox) solver. If you have Optimization Toolbox software, you can also use the interior-point and active-set algorithms of the fmincon solver. Specify the algorithm in the SearchOptions.Algorithm option. The fmincon algorithms might result in improved estimation results in the following scenarios:

  • Constrained minimization problems when bounds are imposed on the model parameters.

  • Model structures where the loss function is a nonlinear or nonsmooth function of the parameters.

  • Multiple-output model estimation. A determinant loss function is minimized by default for multiple-output model estimation. fmincon algorithms are able to minimize such loss functions directly. The other search methods such as 'lm' and 'gn' minimize the determinant loss function by alternately estimating the noise variance and reducing the loss value for a given noise variance value. Hence, the fmincon algorithms can offer better efficiency and accuracy for multiple-output model estimations.

Option set for the search algorithm, specified as the comma-separated pair consisting of 'SearchOptions' and a search option set with fields that depend on the value of SearchMethod.

SearchOptions Structure When SearchMethod Is Specified as 'gn', 'gna', 'lm', 'grad', or 'auto'

Field NameDescriptionDefault
Tolerance

Minimum percentage difference between the current value of the loss function and its expected improvement after the next iteration, specified as a positive scalar. When the percentage of expected improvement is less than Tolerance, the iterations stop. The estimate of the expected loss-function improvement at the next iteration is based on the Gauss-Newton vector computed for the current parameter value.

0.01
MaxIterations

Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as Tolerance.

Setting MaxIterations = 0 returns the result of the start-up procedure.

Use sys.Report.Termination.Iterations to get the actual number of iterations during an estimation, where sys is an idtf model.

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Advanced

Advanced search settings, specified as a structure with the following fields.

Field NameDescriptionDefault
GnPinvConstant

Jacobian matrix singular value threshold, specified as a positive scalar. Singular values of the Jacobian matrix that are smaller than GnPinvConstant*max(size(J)*norm(J)*eps) are discarded when computing the search direction. Applicable when SearchMethod is 'gn'.

10000
InitialGnaTolerance

Initial value of gamma, specified as a positive scalar. Applicable when SearchMethod is 'gna'.

0.0001
LMStartValue

Starting value of search-direction length d in the Levenberg-Marquardt method, specified as a positive scalar. Applicable when SearchMethod is 'lm'.

0.001
LMStep

Size of the Levenberg-Marquardt step, specified as a positive integer. The next value of the search-direction length d in the Levenberg-Marquardt method is LMStep times the previous one. Applicable when SearchMethod is 'lm'.

2
MaxBisections

Maximum number of bisections used for line search along the search direction, specified as a positive integer.

25
MaxFunctionEvaluations

Maximum number of calls to the model file, specified as a positive integer. Iterations stop if the number of calls to the model file exceeds this value.

Inf
MinParameterChange

Smallest parameter update allowed per iteration, specified as a nonnegative scalar.

0
RelativeImprovement

Relative improvement threshold, specified as a nonnegative scalar. Iterations stop if the relative improvement of the criterion function is less than this value.

0
StepReduction

Step reduction factor, specified as a positive scalar that is greater than 1. The suggested parameter update is reduced by the factor StepReduction after each try. This reduction continues until MaxBisections tries are completed or a lower value of the criterion function is obtained.

StepReduction is not applicable for a SearchMethod of 'lm' (Levenberg-Marquardt method).

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SearchOptions Structure When SearchMethod Is Specified as 'lsqnonlin'

Field NameDescriptionDefault
FunctionTolerance

Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.

The value of FunctionTolerance is the same as that of opt.SearchOptions.Advanced.TolFun.

1e-5
StepTolerance

Termination tolerance on the estimated parameter values, specified as a positive scalar.

The value of StepTolerance is the same as that of opt.SearchOptions.Advanced.TolX.

1e-6
MaxIterations

Maximum number of iterations during loss-function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance.

The value of MaxIterations is the same as that of opt.SearchOptions.Advanced.MaxIter.

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SearchOptions Structure When SearchMethod Is Specified as 'fmincon'

Field NameDescriptionDefault
Algorithm

fmincon optimization algorithm, specified as one of the following:

  • 'sqp' — Sequential quadratic programming algorithm. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results. It is not a large-scale algorithm. For more information, see Large-Scale vs. Medium-Scale Algorithms (Optimization Toolbox).

  • 'trust-region-reflective' — Subspace trust-region method based on the interior-reflective Newton method. It is a large-scale algorithm.

  • 'interior-point' — Large-scale algorithm that requires Optimization Toolbox software. The algorithm satisfies bounds at all iterations, and it can recover from NaN or Inf results.

  • 'active-set' — Requires Optimization Toolbox software. The algorithm can take large steps, which adds speed. It is not a large-scale algorithm.

For more information about the algorithms, see Constrained Nonlinear Optimization Algorithms (Optimization Toolbox) and Choosing the Algorithm (Optimization Toolbox).

'sqp'
FunctionTolerance

Termination tolerance on the loss function that the software minimizes to determine the estimated parameter values, specified as a positive scalar.

1e-6
StepTolerance

Termination tolerance on the estimated parameter values, specified as a positive scalar.

1e-6
MaxIterations

Maximum number of iterations during loss function minimization, specified as a positive integer. The iterations stop when MaxIterations is reached or another stopping criterion is satisfied, such as FunctionTolerance.

100

To specify field values in SearchOptions, create a default findopOptions set and modify the fields using dot notation. Any fields that you do not modify retain their default values.

opt = findopOptions;
opt.SearchOptions.MaxIterations = 15;
opt.SearchOptions.Advanced.RelImprovement = 0.5;

Output Arguments

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Option set for findop command, returned as a findopOptions object.

Version History

Introduced in R2015a

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See Also

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