java.lang.Object
- gov.nih.mipav.model.algorithms.LsqFit

```
public abstract class LsqFit
extends java.lang.Object
```
LsqFit.jl is licensed under the MIT License: Returns the argmin over x of `sum(f(x).^2)` using the Levenberg-Marquardt algorithm, and an estimate of the Jacobian of `f` at x. > Copyright (c) 2012: John Myles White and other contributors. > > Permission is hereby granted, free of charge, to any person obtaining > a copy of this software and associated documentation files (the > "Software"), to deal in the Software without restriction, including > without limitation the rights to use, copy, modify, merge, publish, > distribute, sublicense, and/or sell copies of the Software, and to > permit persons to whom the Software is furnished to do so, subject to > the following conditions: > > The above copyright notice and this permission notice shall be > included in all copies or substantial portions of the Software. > > THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, > EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF > MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND > NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE > LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION > OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION > WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

Field Summary

Fields
Modifier and Type	Field	Description
`private int`	`BARD`
`private int`	`BEALE`
`private int`	`BIGGS_EXP6`
`private int`	`BOX_3D`
`private int`	`BROWN_ALMOST_LINEAR`
`private int`	`BROWN_AND_DENNIS`
`private int`	`BROWN_BADLY_SCALED`
`private int`	`BROYDEN_BANDED`
`private int`	`BROYDEN_TRIDIAGONAL`
`private int`	`CHEBYQUAD`
`private boolean`	`converged`
`(package private) double`	`default_relstep`
`private int`	`DISCRETE_BOUNDARY_VALUE`
`private int`	`DISCRETE_INTEGRAL`
`private int`	`DRAPER24D`
`(package private) double`	`epsilon`
`private int`	`EQUILIBRIUM_COMBUSTION`
`private double`	`exp0p1`
`private double[]`	`expap1`
`private int`	`EXTENDED_POWELL_SINGULAR`
`private int`	`EXTENDED_ROSENBROCK`
`private int`	`FREUDENSTEIN_AND_ROTH`
`protected double`	`g_tol`
`private int`	`GAUSSIAN`
`protected boolean`	`geodesicAcceleration`
`protected double`	`good_step_quality`
`private int`	`GULF_RESEARCH_AND_DEVELOPMENT`
`private int`	`HATFLDB`
`private int`	`HATFLDC`
`private int`	`HELICAL_VALLEY`
`private int`	`HOCK1`
`private int`	`HOCK21_MODIFIED`
`private int`	`HOCK25`
`private int`	`HOCK3`
`private int`	`HOCK4`
`protected double`	`initial_lambda`
`protected double[]`	`initial_x`
`private int`	`iterCt`
`private double[][]`	`J`
`private int`	`JENNRICH_AND_SAMPSON`
`private int`	`KOWALIK_AND_OSBORNE`
`protected double`	`lambda_decrease`
`protected double`	`lambda_increase`
`private int`	`LEVMAR_ROSENBROCK`
`private int`	`LINEAR_FULL_RANK`
`private int`	`LINEAR_RANK1`
`private int`	`LINEAR_RANK1_WITH_ZERO_COLUMNS_AND_ROWS`
`protected double[]`	`lower`
`protected int`	`m`	integer scalar containing the number of data points.
`private int`	`MADSEN`
`protected int`	`maxIter`
`private int`	`MEYER`
`protected double`	`min_step_quality`
`private int`	`MODIFIED_ROSENBROCK`
`protected int`	`n`	variables integer scalar containing the number of unknowns.
`private int`	`OSBORNE1`
`private int`	`OSBORNE2`
`private double`	`p1sqrtem5`
`private int`	`PENALTY_FUNCTION_I`
`private int`	`PENALTY_FUNCTION_II`
`private int`	`POWELL_2_PARAMETER`
`private int`	`POWELL_BADLY_SCALED`
`private int`	`POWELL_SINGULAR`
`private double[]`	`residuals`
`private int`	`ROSENBROCK`
`protected boolean`	`show_trace`
`private double`	`sqrt10`
`private double`	`sqrt5`
`private double`	`sqrtem5`
`protected double`	`tau`
`private double[]`	`tdata`
`private int`	`testCase`
`private boolean`	`testMode`	module LsqFit export curve_fit, standard_error, margin_error, confidence_interval, estimate_covar, make_hessian, Avv, # StatsBase reexports dof, coef, nobs, mse, rss, stderror, weights, residuals using Distributions using OptimBase using LinearAlgebra using ForwardDiff import NLSolversBase: value, jacobian import StatsBase import StatsBase: coef, dof, nobs, rss, stderror, weights, residuals import Base.summary include("geodesic.jl") include("levenberg_marquardt.jl") include("curve_fit.jl") end
`private int`	`TRIGONOMETRIC`
`protected double[]`	`upper`
`protected boolean`	`useNumerical`
`private int`	`VARIABLY_DIMENSIONED_FUNCTION`
`private int`	`WATSON`
`private int`	`WOOD`
`private double[]`	`x`
`protected double`	`x_tol`
`private double[]`	`ydata`

Constructor Summary

Constructors
Constructor	Description
`LsqFit()`	To run LsqFit() use: boolean fullTest = true; if (fullTest) { FitAll fa = new FitAll(); return; } class FitAll extends LsqFit { public FitAll() { // nPoints data points, 3 coefficients, and exponential fitting super(); } public void fitToFunction(double[] x, double[] residuals) { return; } public void fitToJacobian(double[] x, double[][] jacobian) { return; } public void fitToHessian(double[] x, double[][][] hessian) { // n,n,m hessian return; } }
`LsqFit(int nPts, double[] initial_x)`

Method Summary

All Methods Instance Methods Abstract Methods Concrete Methods
Modifier and Type	Method	Description
`private void`	`driver()`
`private void`	`dumpTestResults()`
`abstract void`	`fitToFunction(double[] x, double[] residuals)`	fitToFunction communicates
`abstract void`	`fitToHessian(double[] x, double[][][] hessian)`
`abstract void`	`fitToJacobian(double[] x, double[][] jacobian)`	fitToJacobian communicates
`private void`	`fitToNumericalHessian(double[] xinit, double[][][] hessian)`
`private void`	`fitToNumericalJacobian(double[] xinit, double[][] jacobian)`
`void`	`fitToTestFunction(double[] x, double[] residuals)`
`private void`	`fitToTestHessian(double[] x, double[][][] hessian)`
`private void`	`fitToTestJacobian(double[] x, double[][] J)`
`boolean`	`getConverged()`
`double[][]`	`getCovariance()`
`int`	`getIterations()`
`double[]`	`getParameters()`	getParameters accessor to function parameters.
`double[]`	`getResiduals()`	DOCUMENT ME!
`private double`	`shiftedChebyshev(double x, int n)`
`private double`	`shiftedChebyshevDerivative(double x, int n)`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Field Detail
  - testMode
```
private boolean testMode
```
    module LsqFit export curve_fit, standard_error, margin_error, confidence_interval, estimate_covar, make_hessian, Avv, # StatsBase reexports dof, coef, nobs, mse, rss, stderror, weights, residuals using Distributions using OptimBase using LinearAlgebra using ForwardDiff import NLSolversBase: value, jacobian import StatsBase import StatsBase: coef, dof, nobs, rss, stderror, weights, residuals import Base.summary include("geodesic.jl") include("levenberg_marquardt.jl") include("curve_fit.jl") end
  - useNumerical
```
protected boolean useNumerical
```
  - x_tol
```
protected double x_tol
```
  - g_tol
```
protected double g_tol
```
  - maxIter
```
protected int maxIter
```
  - min_step_quality
```
protected double min_step_quality
```
  - good_step_quality
```
protected double good_step_quality
```
  - initial_lambda
```
protected double initial_lambda
```
  - tau
```
protected double tau
```
  - lambda_increase
```
protected double lambda_increase
```
  - lambda_decrease
```
protected double lambda_decrease
```
  - show_trace
```
protected boolean show_trace
```
  - lower
```
protected double[] lower
```
  - upper
```
protected double[] upper
```
  - geodesicAcceleration
```
protected boolean geodesicAcceleration
```
  - epsilon
```
double epsilon
```
  - default_relstep
```
double default_relstep
```
  - m
```
protected int m
```
    integer scalar containing the number of data points.
  - n
```
protected int n
```
    variables integer scalar containing the number of unknowns.
  - initial_x
```
protected double[] initial_x
```
  - iterCt
```
private int iterCt
```
  - x
```
private double[] x
```
  - residuals
```
private double[] residuals
```
  - J
```
private double[][] J
```
  - converged
```
private boolean converged
```
  - tdata
```
private double[] tdata
```
  - ydata
```
private double[] ydata
```
  - sqrtem5
```
private double sqrtem5
```
  - p1sqrtem5
```
private double p1sqrtem5
```
  - sqrt5
```
private double sqrt5
```
  - sqrt10
```
private double sqrt10
```
  - expap1
```
private double[] expap1
```
  - exp0p1
```
private double exp0p1
```
  - testCase
```
private int testCase
```
  - DRAPER24D
```
private final int DRAPER24D
```
    See Also:
    
    Constant Field Values
  - ROSENBROCK
```
private final int ROSENBROCK
```
    See Also:
    
    Constant Field Values
  - FREUDENSTEIN_AND_ROTH
```
private final int FREUDENSTEIN_AND_ROTH
```
    See Also:
    
    Constant Field Values
  - POWELL_BADLY_SCALED
```
private final int POWELL_BADLY_SCALED
```
    See Also:
    
    Constant Field Values
  - BROWN_BADLY_SCALED
```
private final int BROWN_BADLY_SCALED
```
    See Also:
    
    Constant Field Values
  - BEALE
```
private final int BEALE
```
    See Also:
    
    Constant Field Values
  - JENNRICH_AND_SAMPSON
```
private final int JENNRICH_AND_SAMPSON
```
    See Also:
    
    Constant Field Values
  - HELICAL_VALLEY
```
private final int HELICAL_VALLEY
```
    See Also:
    
    Constant Field Values
  - BARD
```
private final int BARD
```
    See Also:
    
    Constant Field Values
  - GAUSSIAN
```
private final int GAUSSIAN
```
    See Also:
    
    Constant Field Values
  - MEYER
```
private final int MEYER
```
    See Also:
    
    Constant Field Values
  - GULF_RESEARCH_AND_DEVELOPMENT
```
private final int GULF_RESEARCH_AND_DEVELOPMENT
```
    See Also:
    
    Constant Field Values
  - BOX_3D
```
private final int BOX_3D
```
    See Also:
    
    Constant Field Values
  - POWELL_SINGULAR
```
private final int POWELL_SINGULAR
```
    See Also:
    
    Constant Field Values
  - WOOD
```
private final int WOOD
```
    See Also:
    
    Constant Field Values
  - KOWALIK_AND_OSBORNE
```
private final int KOWALIK_AND_OSBORNE
```
    See Also:
    
    Constant Field Values
  - BROWN_AND_DENNIS
```
private final int BROWN_AND_DENNIS
```
    See Also:
    
    Constant Field Values
  - OSBORNE1
```
private final int OSBORNE1
```
    See Also:
    
    Constant Field Values
  - BIGGS_EXP6
```
private final int BIGGS_EXP6
```
    See Also:
    
    Constant Field Values
  - OSBORNE2
```
private final int OSBORNE2
```
    See Also:
    
    Constant Field Values
  - WATSON
```
private final int WATSON
```
    See Also:
    
    Constant Field Values
  - EXTENDED_ROSENBROCK
```
private final int EXTENDED_ROSENBROCK
```
    See Also:
    
    Constant Field Values
  - EXTENDED_POWELL_SINGULAR
```
private final int EXTENDED_POWELL_SINGULAR
```
    See Also:
    
    Constant Field Values
  - PENALTY_FUNCTION_I
```
private final int PENALTY_FUNCTION_I
```
    See Also:
    
    Constant Field Values
  - PENALTY_FUNCTION_II
```
private final int PENALTY_FUNCTION_II
```
    See Also:
    
    Constant Field Values
  - VARIABLY_DIMENSIONED_FUNCTION
```
private final int VARIABLY_DIMENSIONED_FUNCTION
```
    See Also:
    
    Constant Field Values
  - TRIGONOMETRIC
```
private final int TRIGONOMETRIC
```
    See Also:
    
    Constant Field Values
  - BROWN_ALMOST_LINEAR
```
private final int BROWN_ALMOST_LINEAR
```
    See Also:
    
    Constant Field Values
  - DISCRETE_BOUNDARY_VALUE
```
private final int DISCRETE_BOUNDARY_VALUE
```
    See Also:
    
    Constant Field Values
  - DISCRETE_INTEGRAL
```
private final int DISCRETE_INTEGRAL
```
    See Also:
    
    Constant Field Values
  - BROYDEN_TRIDIAGONAL
```
private final int BROYDEN_TRIDIAGONAL
```
    See Also:
    
    Constant Field Values
  - BROYDEN_BANDED
```
private final int BROYDEN_BANDED
```
    See Also:
    
    Constant Field Values
  - LINEAR_FULL_RANK
```
private final int LINEAR_FULL_RANK
```
    See Also:
    
    Constant Field Values
  - LINEAR_RANK1
```
private final int LINEAR_RANK1
```
    See Also:
    
    Constant Field Values
  - LINEAR_RANK1_WITH_ZERO_COLUMNS_AND_ROWS
```
private final int LINEAR_RANK1_WITH_ZERO_COLUMNS_AND_ROWS
```
    See Also:
    
    Constant Field Values
  - CHEBYQUAD
```
private final int CHEBYQUAD
```
    See Also:
    
    Constant Field Values
  - HOCK25
```
private final int HOCK25
```
    See Also:
    
    Constant Field Values
  - LEVMAR_ROSENBROCK
```
private final int LEVMAR_ROSENBROCK
```
    See Also:
    
    Constant Field Values
  - MODIFIED_ROSENBROCK
```
private final int MODIFIED_ROSENBROCK
```
    See Also:
    
    Constant Field Values
  - POWELL_2_PARAMETER
```
private final int POWELL_2_PARAMETER
```
    See Also:
    
    Constant Field Values
  - HOCK1
```
private final int HOCK1
```
    See Also:
    
    Constant Field Values
  - HOCK21_MODIFIED
```
private final int HOCK21_MODIFIED
```
    See Also:
    
    Constant Field Values
  - HATFLDB
```
private final int HATFLDB
```
    See Also:
    
    Constant Field Values
  - HATFLDC
```
private final int HATFLDC
```
    See Also:
    
    Constant Field Values
  - EQUILIBRIUM_COMBUSTION
```
private final int EQUILIBRIUM_COMBUSTION
```
    See Also:
    
    Constant Field Values
  - MADSEN
```
private final int MADSEN
```
    See Also:
    
    Constant Field Values
  - HOCK3
```
private final int HOCK3
```
    See Also:
    
    Constant Field Values
  - HOCK4
```
private final int HOCK4
```
    See Also:
    
    Constant Field Values
- Constructor Detail
  - LsqFit
```
public LsqFit(int nPts,
              double[] initial_x)
```
  - LsqFit
```
public LsqFit()
```
    To run LsqFit() use: boolean fullTest = true; if (fullTest) { FitAll fa = new FitAll(); return; } class FitAll extends LsqFit { public FitAll() { // nPoints data points, 3 coefficients, and exponential fitting super(); } public void fitToFunction(double[] x, double[] residuals) { return; } public void fitToJacobian(double[] x, double[][] jacobian) { return; } public void fitToHessian(double[] x, double[][][] hessian) { // n,n,m hessian return; } }
- Method Detail
  - dumpTestResults
```
private void dumpTestResults()
```
  - fitToTestFunction
```
public void fitToTestFunction(double[] x,
                              double[] residuals)
```
  - fitToTestJacobian
```
private void fitToTestJacobian(double[] x,
                               double[][] J)
```
  - fitToTestHessian
```
private void fitToTestHessian(double[] x,
                              double[][][] hessian)
```
  - shiftedChebyshev
```
private double shiftedChebyshev(double x,
                                int n)
```
  - shiftedChebyshevDerivative
```
private double shiftedChebyshevDerivative(double x,
                                          int n)
```
  - fitToNumericalJacobian
```
private void fitToNumericalJacobian(double[] xinit,
                                    double[][] jacobian)
```
  - fitToNumericalHessian
```
private void fitToNumericalHessian(double[] xinit,
                                   double[][][] hessian)
```
  - fitToFunction
```
public abstract void fitToFunction(double[] x,
                                   double[] residuals)
```
    fitToFunction communicates
    
    Parameters:
    
    x - DOCUMENT ME!
    
    residuals - DOCUMENT ME!
  - fitToJacobian
```
public abstract void fitToJacobian(double[] x,
                                   double[][] jacobian)
```
    fitToJacobian communicates
    
    Parameters:
    
    x - DOCUMENT ME!
    
    Jacobian - DOCUMENT ME!
  - fitToHessian
```
public abstract void fitToHessian(double[] x,
                                  double[][][] hessian)
```
  - driver
```
private void driver()
```
  - getIterations
```
public int getIterations()
```
  - getParameters
```
public double[] getParameters()
```
    getParameters accessor to function parameters.
    
    Returns:
    
    the function parameters determined by the algorithm
  - getResiduals
```
public double[] getResiduals()
```
    DOCUMENT ME!
    
    Returns:
    
    double[] residuals
  - getConverged
```
public boolean getConverged()
```
  - getCovariance
```
public double[][] getCovariance()
```

Class LsqFit

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

testMode

useNumerical

x_tol

g_tol

maxIter

min_step_quality

good_step_quality

initial_lambda

tau

lambda_increase

lambda_decrease

show_trace

lower

upper

geodesicAcceleration

epsilon

default_relstep

m

n

initial_x

iterCt

x

residuals

J

converged

tdata

ydata

sqrtem5

p1sqrtem5

sqrt5

sqrt10

expap1

exp0p1

testCase

DRAPER24D

ROSENBROCK

FREUDENSTEIN_AND_ROTH

POWELL_BADLY_SCALED

BROWN_BADLY_SCALED

BEALE

JENNRICH_AND_SAMPSON

HELICAL_VALLEY

BARD

GAUSSIAN

MEYER

GULF_RESEARCH_AND_DEVELOPMENT

BOX_3D

POWELL_SINGULAR

WOOD

KOWALIK_AND_OSBORNE

BROWN_AND_DENNIS

OSBORNE1

BIGGS_EXP6

OSBORNE2

WATSON

EXTENDED_ROSENBROCK

EXTENDED_POWELL_SINGULAR

PENALTY_FUNCTION_I

PENALTY_FUNCTION_II

VARIABLY_DIMENSIONED_FUNCTION

TRIGONOMETRIC

BROWN_ALMOST_LINEAR

DISCRETE_BOUNDARY_VALUE

DISCRETE_INTEGRAL

BROYDEN_TRIDIAGONAL

BROYDEN_BANDED

LINEAR_FULL_RANK

LINEAR_RANK1

LINEAR_RANK1_WITH_ZERO_COLUMNS_AND_ROWS

CHEBYQUAD

HOCK25

LEVMAR_ROSENBROCK

MODIFIED_ROSENBROCK

POWELL_2_PARAMETER