Package gov.nih.mipav.model.algorithms

Class NLConstrainedEngine

java.lang.Object
gov.nih.mipav.model.algorithms.NLConstrainedEngine
Direct Known Subclasses:
AlgorithmAutoCorrelation.FitCorrelationModel, AlgorithmAutoCovariance.FitCovarianceModel, AlgorithmConstELSUNCOpt3D.FitOAR3DConstrainedModel, AlgorithmContrastEnhancementUsingExposureFusion.kFitting, AlgorithmDEMRI3.Fit24DModel, AlgorithmDEMRI3.Fit25HModel, AlgorithmDEMRI3.FitDEMRI3ConstrainedModel, AlgorithmELSUNCOpt2D.FitOAR2DELSUNCModel, AlgorithmELSUNCOpt3D.FitOAR3DELSUNCModel, AlgorithmFRAP.Fit24DModel, AlgorithmFRAP.FitDoubleExponentialModel, AlgorithmFRAP.FitDoubleExponentialNoWholeConstrainedModel, AlgorithmFRAP.FitDoubleExponentialNoWholeModel, AlgorithmFRAP.FitIntensityProfile, AlgorithmFRAP.FitPure1DModel, AlgorithmFRAP.FitSingleExponentialModel, AlgorithmFRAP.FitWholeNLConInt2, AlgorithmFRAP.FitWholeNLConModel, AlgorithmFRAP.FitWholeNLConModel2, AlgorithmFRAP.FitWholeNLConModel3, AlgorithmFRAP.FitWholeNLConModelqd, AlgorithmSM2.FitAll, AlgorithmSM2.FitSM2ConstrainedModel, AlgorithmSM2.FitSM2ConstrainedModelC, AlgorithmTimeFitting.FitExponential, AlgorithmTimeFitting.FitGaussian, AlgorithmTimeFitting.FitLaplace, AlgorithmTimeFitting.FitLine, AlgorithmTimeFitting.FitLorentz, AlgorithmTimeFitting.FitMultiExponential, AlgorithmTimeFitting.FitRayleigh, DSC_MRI_toolbox.gauss1Fitting, DSC_MRI_toolbox.gauss2Fitting, DSC_MRI_toolbox.gaussStandardDeviationFitting, DSC_MRI_toolbox.GVFitting, DSC_MRI_toolbox.GVRecirculation, NLFittedFunction, SchwarzChristoffelMapping.crpfun, SchwarzChristoffelMapping.depfun, SchwarzChristoffelMapping.dpfun, SchwarzChristoffelMapping.rpfun, SchwarzChristoffelMapping2.hppfun, SchwarzChristoffelMapping2.stpfun, SIFT.FitMosaicModel, WeibullDistribution.WeibullCostFunction2param, WeibullDistribution.WeibullCostFunction3param
public abstract class NLConstrainedEngine extends Object
Display results of displaying exponential fitting parameters.

  • Field Summary

    Fields
    Modifier and Type
    Field
    Description
    protected double[]
    a
    On completion if exitStatus >= 0 a[] contains the latest (best) estimate of the solution point.
    private double
    a1div3
    DOCUMENT ME!
    protected double
    absoluteConvergence
    absolute convergence constant Used to test for convergence by the sum of squares being less than the absoluteConvergence squared.
    private double
    aDiff
    DOCUMENT ME!
    private double
    alfkm1
    DOCUMENT ME!
    private double
    alfkm2
    DOCUMENT ME!
    private double
    alfnoi
    DOCUMENT ME!
    private double
    alpha
    DOCUMENT ME!
    private double
    alphup
    DOCUMENT ME!
    protected boolean
    analyticalJacobian
     
    private int[]
    aset
    1D integer array of length param containing a code which indicates whether an unknown is active or not aset[i] = 0 when a[i] is free = +1 when a[i] == bl[i] = -1 when a[i] == bu[i].
    private double
    aupkm1
    DOCUMENT ME!
    private final int
    BARD
     
    private final int
    BEALE
     
    private double
    bestpg
    DOCUMENT ME!
    private double
    beta
    scalar containing the norm of the orthogonal projection of residuals onto the space spanned by the columns of the Jacobian.
    private double
    betkm1
    DOCUMENT ME!
    private double
    betkm2
    DOCUMENT ME!
    private static final double
    big
    DOCUMENT ME!
    private final int
    BIGGS_EXP6
     
    protected double[]
    bl
    DOCUMENT ME!
    private double
    bl0
    DOCUMENT ME!
    private double
    bn
    DOCUMENT ME!
    protected int
    bounds
    integer scalar code for assessing the bounds bounds = 0 means an unconstrained problem bounds = 1 means the same lower bounds for all unknowns and the same upper bounds for all unknowns.
    private final int
    BOX_3D
     
    private final int
    BROWN_ALMOST_LINEAR
     
    private final int
    BROWN_AND_DENNIS
     
    private final int
    BROWN_BADLY_SCALED
     
    private final int
    BROYDEN_BANDED
     
    private final int
    BROYDEN_TRIDIAGONAL
     
    protected double[]
    bu
    DOCUMENT ME!
    private double
    bu0
    DOCUMENT ME!
    private final int
    CERES_CURVE_FITTING
     
    private final int
    CHEBYQUAD
     
    private double
    cnorm
    DOCUMENT ME!
    private int
    constraintAct
    Number of active constraints.
    private int
    ctrl
    ctrl can have 3 different values on entry.
    protected int[]
    ctrlMat
    Wrapper for ctrl or lctrl communication with driver.
    private double
    d1km1
    DOCUMENT ME!
    private double
    d1sqs
    scalar containing the predicted reduction in the objective function if gn-direction is used.
    private double
    deltaMinrm
    DOCUMENT ME!
    private double[]
    diag
    1D double array of length param conatiaing the diagonal elements of the diagonal matrix D if internalScaling is true.
    private final int
    DISCRETE_BOUNDARY_VALUE
     
    private final int
    DISCRETE_INTEGRAL
     
    private final int
    DRAPER24D
     
    private double[]
    dx
    double working areas 1D array of length param containing the solution of J * dx = -residuals.
    private double
    dxnkm1
    DOCUMENT ME!
    private double
    dxnorm
    DOCUMENT ME!
    protected double[]
    dyda
    DOCUMENT ME!
    private double
    eps
    DOCUMENT ME!
    private double
    epsl
    DOCUMENT ME!
    private final int
    EQUILIBRIUM_COMBUSTION
     
    private int
    errorStatus
    DOCUMENT ME!
    private int
    eval
    DOCUMENT ME!
    private int
    exitStatus
    integer scalar that indicates why the return was taken.
    private double
    exp0p1
     
    private double[]
    expap1
     
    private final int
    EXTENDED_POWELL_SINGULAR
     
    private final int
    EXTENDED_ROSENBROCK
     
    private final int
    FREUDENSTEIN_AND_ROTH
     
    private double
    fsqkm1
    DOCUMENT ME!
    private double
    fsum
    DOCUMENT ME!
    private int
    funcEval
    integer scalar containing the total number of function evaluations done inside this routine.
    private double[]
    g
    1D array of length param containing the gradient of the objective at the current point.
    private final int
    GAUSSIAN
     
    private double[][]
    gmat
    param by param array If secondAllowed if false, gmat can be used as a singly subscripted array of dimension param by setting all second indices to 0.
    private boolean
    gndok
    DOCUMENT ME!
    private double
    gnorm
    scalar containing norm of the gradient divided by norm of Jacobian.
    protected double[]
    gues
    DOCUMENT ME!
    private final int
    GULF_RESEARCH_AND_DEVELOPMENT
     
    private final int
    HATFLDB
     
    private final int
    HATFLDC
     
    private final int
    HELICAL_VALLEY
     
    private final int
    HOCK1
     
    private final int
    HOCK21_MODIFIED
     
    private final int
    HOCK25
     
    private final int
    HOCK3
     
    private final int
    HOCK4
     
    private int
    icount
    Variables used for restart information.
    private int
    iev
    DOCUMENT ME!
    private int
    ifree
    DOCUMENT ME!
    private int
    imax
    Variables used for restart information.
    private int
    indic
    DOCUMENT ME!
    private int
    info
    Consistently use 1 base indexing rather than 0 based indexing
    protected boolean
    internalScaling
    If true, the columns of the Jacobian are scaled to have unit length.
    private int
    irank
    Variables used for restart information.
    protected int
    iters
    integer scalar containing the number of iterations until termination.
    private int
    itotal
    Variables used for restart information.
    private int
    ival
    Variables used for restart information.
    protected double[][]
    jacobian
    2D array of doubles of dimension nPts by max(4,param) containing the main part of the covariance matrix (Jtranspose * J)inverse, where J is the Jacobian matrix computed at a.
    private int
    jacobianEval
    integer scalar containing the number of function evaluations caused by computing Jacobians with difference methods.
    private final int
    JENNRICH_AND_SAMPSON
     
    private int
    kod
    DOCUMENT ME!
    private int
    kodkm1
    The suffices km2 and km1 in the names of the variables represent time step k-2 and k-1 respectively.
    private int
    kodkm2
    The suffices km2 and km1 in the names of the variables represent time step k-2 and k-1 respectively.
    private final int
    KOWALIK_AND_OSBORNE
     
    private int
    lattry
    Variables used for restart information.
    private final int
    LEVMAR_ROSENBROCK
     
    private final int
    LINEAR_FULL_RANK
     
    private final int
    LINEAR_RANK1
     
    private final int
    LINEAR_RANK1_WITH_ZERO_COLUMNS_AND_ROWS
     
    private int
    lineEval
    integer scalar containing the number of function evaluations caused by the linesearch algorithm.
    private final int
    MADSEN
     
    protected int
    maxIterations
    DOCUMENT ME!
    private int
    mdg
    Leading dimension of array gmat mdg must be >= param if secondAllowed is true.
    private final int
    MEYER
     
    private final int
    MODIFIED_ROSENBROCK
     
    private double
    noise
    DOCUMENT ME!
    protected int
    nPts
    integer scalar containing the number of data points.
    private final int
    OSBORNE1
     
    private final int
    OSBORNE2
     
    protected boolean
    outputMes
     
    private double
    p1sqrtem5
     
    protected int
    param
    variables integer scalar containing the number of unknowns.
    protected double
    parameterConvergence
    parameter convergence constant Used to test for convergence by the relative change in a[] being less than the parameterConvergence.
    private final int
    PENALTY_FUNCTION_I
     
    private final int
    PENALTY_FUNCTION_II
     
    private double
    pgb1
    DOCUMENT ME!
    private double
    pgb2
    DOCUMENT ME!
    private double
    phi
    double scalar containging the value of the objective function = (0.5 * chisquare) at the termination point a.
    private double
    phikp1
    DOCUMENT ME!
    private double
    philat
    DOCUMENT ME!
    private int[]
    pivit
    array of integers of dimension param containing the permutation matrix E in the decomposition QTranspose * J * D E = (R) (0) pivit[i] contains the index of the column that was moved into column i.
    private double
    pMinrm
    DOCUMENT ME!
    private final int
    POWELL_2_PARAMETER
     
    private final int
    POWELL_BADLY_SCALED
     
    private final int
    POWELL_SINGULAR
     
    private double
    predb
    DOCUMENT ME!
    private double
    prekm1
    scalar containing the predicted reduction in the objective if pseudoRank from previous step is used.
    private double
    qMinrm
    DOCUMENT ME!
    private double
    rabs
    DOCUMENT ME!
    protected double
    relativeConvergence
    relative convergence constant Used to test for convergence by reduction in objective function being less than relativeConvergence squared.
    protected double[]
    residuals
    1D array of doubles of dimension nPts containing the value of the residuals at the termination point a;.
    private boolean
    restart
    DOCUMENT ME!
    private double
    rlenb
    DOCUMENT ME!
    private double
    rmin
    DOCUMENT ME!
    private int
    rngkm1
    The suffices km2 and km1 in the names of the variables represent time step k-2 and k-1 respectively.
    private double
    rootsp
    DOCUMENT ME!
    private final int
    ROSENBROCK
     
    private double
    scv0v1
    DOCUMENT ME!
    private double
    scv0v2
    DOCUMENT ME!
    private double
    scv1v2
    DOCUMENT ME!
    private int
    secind
    DOCUMENT ME!
    protected boolean
    secondAllowed
    The method of Newton is allowed at the end of the iteration in some situations (large residuals).
    private int
    secondEval
    integer scalar containing the number of function evaluations caused by using second derivatives in the method of Newton.
    private double
    smax
    DOCUMENT ME!
    private double
    sn
    DOCUMENT ME!
    private double
    speed
    double scalar containing an estimate of the linear convergence factor.
    private double
    sqrt10
     
    private double
    sqrt5
     
    private double
    sqrtem5
     
    private double
    srelpr
    single relative precision.
    protected double
    stdv
    DOCUMENT ME!
    private double
    stepb
    DOCUMENT ME!
    private int
    testCase
     
    private boolean
    testMode
     
    protected double
    tolerance
    pseudo rank tolerance constant used to determine the pseudo rank of the Jacobian J.
    private final int
    TRIGONOMETRIC
     
    private double[]
    v
    1D array of length nPts containing the orthogonal projection of residuals onto space spanned by the first pseudoRank linear independent columns of the Jacobian.
    private double
    v0norm
    DOCUMENT ME!
    private double
    v1norm
    DOCUMENT ME!
    private double
    v2norm
    DOCUMENT ME!
    private final int
    VARIABLY_DIMENSIONED_FUNCTION
     
    private double[]
    w0
    DOCUMENT ME!
    private double[]
    w1
    DOCUMENT ME!
    private double[]
    w2
    DOCUMENT ME!
    private double[]
    w3
    DOCUMENT ME!
    private final int
    WATSON
     
    private final int
    WOOD
     
    private double
    x1Minrm
    DOCUMENT ME!
    private double
    x2Minrm
    DOCUMENT ME!
    private double
    x3Minrm
    DOCUMENT ME!
    private double[]
    xSeries
    DOCUMENT ME!
    private double[]
    ySeries
    DOCUMENT ME!

  • Constructor Summary

    Constructors
    Constructor
    Description
    NLConstrainedEngine()
     
    NLConstrainedEngine(int nPts, int param)
    NLConstrainedEngine - non-linear fit to a function.

  • Method Summary

    Modifier and Type
    Method
    Description
    private void
    analuc(int[] prank)
    DOCUMENT ME!
    private void
    btrunc(int[] prank, boolean internalScaling, double[] work)
    DOCUMENT ME!
    private void
    chder(double dphize, int[] k, double[] alfk, double[] phik)
    DOCUMENT ME!
    private void
    choose(double xmin, double[] v2, double[] root1, double[] root2, double[] proot2)
    DOCUMENT ME!
    private void
    covar()
    DOCUMENT ME!
    private void
    dimsub(int[] prank, int[] rank)
    DOCUMENT ME!
    private double
    dnrm2(int n, double[] x, int incx)
    DOCUMENT ME!
    void
    driver()
    driver.
    private void
    driverCalls()
     
    void
    dumpTestResults()
     
    private void
    evreuc(int[] prank)
    DOCUMENT ME!
    private void
    fitTestModel()
    Creates a new Fit24DModel object.
    abstract void
    fitToFunction(double[] a, double[] residuals, double[][] jacobian)
    fitToFunction communicates with 3 protected variables param, nPts, and ctrlMat ctrlMat is used as a wrapper for ctrl or lctrl.
    void
    fitToTestFunction(double[] a, double[] residuals, double[][] jacobian)
     
    private void
    fsumsq(double alfk, double[] xnew, double[] fnew, double[] fn_val, int[] ctrl)
    DOCUMENT ME!
    private void
    gauc(int[] k, double alfmin, double[] gmod, double dphize, double[] u, double[] phiu, double tau, double pmax)
    DOCUMENT ME!
    double
    getChiSquared()
    getChiSquared - accessor to chi-squared value (goodness-of-fit measure).
    int
    getExitStatus()
     
    int
    getIterations()
     
    double[]
    getParameters()
    getParameters accessor to function parameters.
    double[]
    getResiduals()
    DOCUMENT ME!
    private void
    gnavuc()
    DOCUMENT ME!
    private double
    gndunc(boolean internalScaling, int[] prank, double[] work)
    DOCUMENT ME!
    private void
    hess()
    DOCUMENT ME!
    private void
    jacdif(int[] ctrl)
    DOCUMENT ME!
    private void
    jtrj(int nn)
    DOCUMENT ME!
    private void
    lineuc(double[] gmod, double dphize, double alplow)
    DOCUMENT ME!
    private void
    linuc2(double[] fnew, double alfk, double[] v2)
    DOCUMENT ME!
    private void
    lsunc()
    DOCUMENT ME!
    private void
    minrm(double[] v2, double alfmin, double alfmax, double xmin, double[] x, double[] px, double[] y, double[] py)
    DOCUMENT ME!
    private void
    minrm1(double[] v2)
    DOCUMENT ME!
    private void
    minrm2()
    DOCUMENT ME!
    private void
    minrn(double x, double fx, double w, double fw, double v, double fv, double alfmin, double alfmax, double pmax, double[] u, double[] pu)
    DOCUMENT ME!
    private void
    newunc()
    DOCUMENT ME!
    private void
    oner(double[] x)
    DOCUMENT ME!
    private void
    outuc()
    DOCUMENT ME!
    private void
    pivec(double[] work)
    DOCUMENT ME!
    private double
    pol3(double x)
    DOCUMENT ME!
    private double
    pol4(double[] v2, double x)
    DOCUMENT ME!
    private void
    pregn(double[] work, int mindim, int[] prank, int[] dim)
    DOCUMENT ME!
    private void
    presub(double[] work, int[] prank, int[] rank)
    DOCUMENT ME!
    private void
    quamin(double x, double fx, double w, double fw, double v, double fv, double[] u)
    DOCUMENT ME!
    private void
    reavuc()
    DOCUMENT ME!
    private void
    reduc(double[] alf, double[] phialf, double alfk, double pk, double diff, double eta, double[] gmod, double[] fnew, int[] k, double[] phik, boolean[] reduce)
    DOCUMENT ME!
    private void
    releps()
    DOCUMENT ME!
    private void
    rtrw1(int nn)
    DOCUMENT ME!
    private void
    scalv(double[] v, double factor, int n)
    DOCUMENT ME!
    private void
    scaunc()
    DOCUMENT ME!
    private void
    schdc(int nn, int[] jpvt, int job)
    DOCUMENT ME!
    private void
    secuc()
    DOCUMENT ME!
    private double
    shiftedChebyshev(double x, int n)
     
    private double
    shiftedChebyshevDerivative(double x, int n)
     
    private void
    soliuc(double tau, int[] prank)
    DOCUMENT ME!
    private void
    sposl(int nn)
    DOCUMENT ME!
    private void
    sqrdc(double[][] x, int n, int p, double[] qraux, int[] jpvt, int job)
    DOCUMENT ME!
    private void
    sqrsl(double[][] x, int n, int k, double[] qraux, double[] y, double[] qy, double[] qty, double[] b, double[] rsd, double[] xb, int job)
    DOCUMENT ME!
    void
    statusMessage(int status)
     
    private void
    stepuc(int[] prank)
    DOCUMENT ME!
    private void
    strsl(int[] prank, double[] b)
    DOCUMENT ME!
    private void
    subuc(int[] prank, int[] rank)
    DOCUMENT ME!
    private void
    termuc(int[] prank, double aNorm)
    DOCUMENT ME!
    private void
    triunc(double tol, int constraintAct, int[] prank)
    DOCUMENT ME!
    private void
    twor()
    DOCUMENT ME!

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Field Details

    • big

      private static final double big
      DOCUMENT ME!
      See Also:

    • a

      protected double[] a
      On completion if exitStatus >= 0 a[] contains the latest (best) estimate of the solution point.

    • absoluteConvergence

      protected double absoluteConvergence
      absolute convergence constant Used to test for convergence by the sum of squares being less than the absoluteConvergence squared.

    • bl

      protected double[] bl
      DOCUMENT ME!

    • bounds

      protected int bounds
      integer scalar code for assessing the bounds bounds = 0 means an unconstrained problem bounds = 1 means the same lower bounds for all unknowns and the same upper bounds for all unknowns. The lower and upper bound must be stored in bl[0] and bu[0] respectively. bounds = 2 means that the bounds must be supplied by the user in bl[i] and bu[i] for i = 0,1, param - 1.

    • bu

      protected double[] bu
      DOCUMENT ME!

    • jacobian

      protected double[][] jacobian
      2D array of doubles of dimension nPts by max(4,param) containing the main part of the covariance matrix (Jtranspose * J)inverse, where J is the Jacobian matrix computed at a.

    • ctrlMat

      protected int[] ctrlMat
      Wrapper for ctrl or lctrl communication with driver.

    • dyda

      protected double[] dyda
      DOCUMENT ME!

    • stdv

      protected double stdv
      DOCUMENT ME!

    • gues

      protected double[] gues
      DOCUMENT ME!

    • internalScaling

      protected boolean internalScaling
      If true, the columns of the Jacobian are scaled to have unit length. If false, internal scaling is not used to compute the Gauss-Newton search direction.

    • iters

      protected int iters
      integer scalar containing the number of iterations until termination.

    • maxIterations

      protected int maxIterations
      DOCUMENT ME!

    • nPts

      protected int nPts
      integer scalar containing the number of data points.

    • param

      protected int param
      variables integer scalar containing the number of unknowns.

    • parameterConvergence

      protected double parameterConvergence
      parameter convergence constant Used to test for convergence by the relative change in a[] being less than the parameterConvergence.

    • relativeConvergence

      protected double relativeConvergence
      relative convergence constant Used to test for convergence by reduction in objective function being less than relativeConvergence squared.

    • residuals

      protected double[] residuals
      1D array of doubles of dimension nPts containing the value of the residuals at the termination point a;.

    • secondAllowed

      protected boolean secondAllowed
      The method of Newton is allowed at the end of the iteration in some situations (large residuals). If true, the use of second derivatives is permitted

    • tolerance

      protected double tolerance
      pseudo rank tolerance constant used to determine the pseudo rank of the Jacobian J.

    • xSeries

      private double[] xSeries
      DOCUMENT ME!

    • ySeries

      private double[] ySeries
      DOCUMENT ME!

    • aDiff

      private double aDiff
      DOCUMENT ME!

    • alfnoi

      private double alfnoi
      DOCUMENT ME!

    • alpha

      private double alpha
      DOCUMENT ME!

    • alphup

      private double alphup
      DOCUMENT ME!

    • aset

      private int[] aset
      1D integer array of length param containing a code which indicates whether an unknown is active or not aset[i] = 0 when a[i] is free = +1 when a[i] == bl[i] = -1 when a[i] == bu[i].

    • beta

      private double beta
      scalar containing the norm of the orthogonal projection of residuals onto the space spanned by the columns of the Jacobian.

    • betkm2

      private double betkm2
      DOCUMENT ME!

    • alfkm2

      private double alfkm2
      DOCUMENT ME!

    • betkm1

      private double betkm1
      DOCUMENT ME!

    • d1km1

      private double d1km1
      DOCUMENT ME!

    • fsqkm1

      private double fsqkm1
      DOCUMENT ME!

    • dxnkm1

      private double dxnkm1
      DOCUMENT ME!

    • alfkm1

      private double alfkm1
      DOCUMENT ME!

    • aupkm1

      private double aupkm1
      DOCUMENT ME!

    • bn

      private double bn
      DOCUMENT ME!

    • cnorm

      private double cnorm
      DOCUMENT ME!

    • ctrl

      private int ctrl
      ctrl can have 3 different values on entry. If ctrl = 1 or ctrl = -1, compute the residuals for all nPts at a certain point a and return the residuals = yfit - yseries in the array residuals if the functions are computable. If not successful and ctrl was set to 1, set ctrl = -1. If not successful and ctrl was set to -1, set ctrl invalid input: '<' -10. If ctrl = 2 and the Jacobian is supplied analytically, calculate the Jacobian = Jij = dymodi/daj. The Jacobian is placed in matrix jacobian. If the Jacobian cannot be calculated, set ctrl invalid input: '<' -10. If you wish to compute the Jacobian numerically on return, set ctrl = 0.

    • d1sqs

      private double d1sqs
      scalar containing the predicted reduction in the objective function if gn-direction is used.

    • diag

      private double[] diag
      1D double array of length param conatiaing the diagonal elements of the diagonal matrix D if internalScaling is true. Otherwise, undefined.

    • dx

      private double[] dx
      double working areas 1D array of length param containing the solution of J * dx = -residuals.

    • dxnorm

      private double dxnorm
      DOCUMENT ME!

    • eps

      private double eps
      DOCUMENT ME!

    • epsl

      private double epsl
      DOCUMENT ME!

    • errorStatus

      private int errorStatus
      DOCUMENT ME!

    • eval

      private int eval
      DOCUMENT ME!

    • exitStatus

      private int exitStatus
      integer scalar that indicates why the return was taken. If exitStatus != -1 and exitStatus >= -10, then a[] contains the latest (best) estimate of the solution point. = 1000X convergence because relative predicted reduction in the objective function = (0.5 * chisquare) is less than (relativeConvergence)**2 = 200X convergence because sum of squares is less than (absoluteConvergence)**2 = 30X convergence because the relative change in a is less than parameterConvergence = 4X convergence because we are computing at noise level X, the last digit in the convergence code, indicates how the last steps were computed X = 0 no trouble (Gauss-Newton the last 3 steps) = 1 pseudoRank invalid input: '<'> param at termination point = 2 The method of Newton was used (at least) in the last step = 3 The (last - 2) step was subspace minimization, but the last 2 steps were Gauss-Newton steps = 4 The steplength was not unit in both the last 2 steps invalid input: '<' 0 indicates that no convergence criterion is fulfilled, but some abnormal termination criterion is satisfied = -1 Invalid starting condition: nPts invalid input: '<' param or param invalid input: '<'= 0 or nPts invalid input: '<'= 0 or maxIterations invalid input: '<'= 0 or relativeConvergence invalid input: '<' 0 or relativeConvergence invalid input: '<' 0 or absoluteConvergence invalid input: '<' 0 or tolerance invalid input: '<'= 0 or parameterConvergence invalid input: '<' 0 or invalid starting point on entry = -2 Number of iterations has exceeded maximum allowed iterations = -3 The Hessian emanating from the second order method is not positive definite = -4 The algorithm would like to use second derivatives but is not allowed to do that = -5 An undamped step with Newton's method is a failure = -6 The latest search direction computed using subspace minimization was not a descent direction (probably caused by wrongly computed Jacobian) = -7 There is only one feasible point, name a[i] = bl[i] = bu[i]; i = 0,1,...,param-1 invalid input: '<' -10 Termination due to user stop indicator

    • fsum

      private double fsum
      DOCUMENT ME!

    • funcEval

      private int funcEval
      integer scalar containing the total number of function evaluations done inside this routine.

    • g

      private double[] g
      1D array of length param containing the gradient of the objective at the current point.

    • gmat

      private double[][] gmat
      param by param array If secondAllowed if false, gmat can be used as a singly subscripted array of dimension param by setting all second indices to 0.

    • gndok

      private boolean gndok
      DOCUMENT ME!

    • gnorm

      private double gnorm
      scalar containing norm of the gradient divided by norm of Jacobian.

    • icount

      private int icount
      Variables used for restart information.

    • lattry

      private int lattry
      Variables used for restart information.

    • itotal

      private int itotal
      Variables used for restart information.

    • irank

      private int irank
      Variables used for restart information.

    • imax

      private int imax
      Variables used for restart information.

    • ival

      private int ival
      Variables used for restart information.

    • iev

      private int iev
      DOCUMENT ME!

    • ifree

      private int ifree
      DOCUMENT ME!

    • indic

      private int indic
      DOCUMENT ME!

    • info

      private int info
      Consistently use 1 base indexing rather than 0 based indexing

    • jacobianEval

      private int jacobianEval
      integer scalar containing the number of function evaluations caused by computing Jacobians with difference methods.

    • kod

      private int kod
      DOCUMENT ME!

    • lineEval

      private int lineEval
      integer scalar containing the number of function evaluations caused by the linesearch algorithm.

    • mdg

      private int mdg
      Leading dimension of array gmat mdg must be >= param if secondAllowed is true.

    • noise

      private double noise
      DOCUMENT ME!

    • constraintAct

      private int constraintAct
      Number of active constraints.

    • pgb1

      private double pgb1
      DOCUMENT ME!

    • pgb2

      private double pgb2
      DOCUMENT ME!

    • phi

      private double phi
      double scalar containging the value of the objective function = (0.5 * chisquare) at the termination point a.

    • phikp1

      private double phikp1
      DOCUMENT ME!

    • philat

      private double philat
      DOCUMENT ME!

    • bestpg

      private double bestpg
      DOCUMENT ME!

    • pivit

      private int[] pivit
      array of integers of dimension param containing the permutation matrix E in the decomposition QTranspose * J * D E = (R) (0) pivit[i] contains the index of the column that was moved into column i.

    • pMinrm

      private double pMinrm
      DOCUMENT ME!

    • qMinrm

      private double qMinrm
      DOCUMENT ME!

    • deltaMinrm

      private double deltaMinrm
      DOCUMENT ME!

    • a1div3

      private double a1div3
      DOCUMENT ME!

    • predb

      private double predb
      DOCUMENT ME!

    • prekm1

      private double prekm1
      scalar containing the predicted reduction in the objective if pseudoRank from previous step is used.

    • rabs

      private double rabs
      DOCUMENT ME!

    • restart

      private boolean restart
      DOCUMENT ME!

    • rlenb

      private double rlenb
      DOCUMENT ME!

    • rmin

      private double rmin
      DOCUMENT ME!

    • kodkm2

      private int kodkm2
      The suffices km2 and km1 in the names of the variables represent time step k-2 and k-1 respectively. These variables are updated only inside the routine evreuc.

    • rngkm1

      private int rngkm1
      The suffices km2 and km1 in the names of the variables represent time step k-2 and k-1 respectively. These variables are updated only inside the routine evreuc.

    • kodkm1

      private int kodkm1
      The suffices km2 and km1 in the names of the variables represent time step k-2 and k-1 respectively. These variables are updated only inside the routine evreuc.

    • rootsp

      private double rootsp
      DOCUMENT ME!

    • bl0

      private double bl0
      DOCUMENT ME!

    • bu0

      private double bu0
      DOCUMENT ME!

    • secind

      private int secind
      DOCUMENT ME!

    • secondEval

      private int secondEval
      integer scalar containing the number of function evaluations caused by using second derivatives in the method of Newton.

    • smax

      private double smax
      DOCUMENT ME!

    • sn

      private double sn
      DOCUMENT ME!

    • speed

      private double speed
      double scalar containing an estimate of the linear convergence factor.

    • srelpr

      private double srelpr
      single relative precision.

    • stepb

      private double stepb
      DOCUMENT ME!

    • v

      private double[] v
      1D array of length nPts containing the orthogonal projection of residuals onto space spanned by the first pseudoRank linear independent columns of the Jacobian.

    • v0norm

      private double v0norm
      DOCUMENT ME!

    • v1norm

      private double v1norm
      DOCUMENT ME!

    • v2norm

      private double v2norm
      DOCUMENT ME!

    • scv0v1

      private double scv0v1
      DOCUMENT ME!

    • scv0v2

      private double scv0v2
      DOCUMENT ME!

    • scv1v2

      private double scv1v2
      DOCUMENT ME!

    • w0

      private double[] w0
      DOCUMENT ME!

    • w1

      private double[] w1
      DOCUMENT ME!

    • w2

      private double[] w2
      DOCUMENT ME!

    • w3

      private double[] w3
      DOCUMENT ME!

    • x1Minrm

      private double x1Minrm
      DOCUMENT ME!

    • x2Minrm

      private double x2Minrm
      DOCUMENT ME!

    • x3Minrm

      private double x3Minrm
      DOCUMENT ME!

    • sqrtem5

      private double sqrtem5

    • p1sqrtem5

      private double p1sqrtem5

    • exp0p1

      private double exp0p1

    • sqrt5

      private double sqrt5

    • sqrt10

      private double sqrt10

    • expap1

      private double[] expap1

    • outputMes

      protected boolean outputMes

    • testMode

      private boolean testMode

    • analyticalJacobian

      protected boolean analyticalJacobian

    • testCase

      private int testCase

    • DRAPER24D

      private final int DRAPER24D
      See Also:

    • ROSENBROCK

      private final int ROSENBROCK
      See Also:

    • FREUDENSTEIN_AND_ROTH

      private final int FREUDENSTEIN_AND_ROTH
      See Also:

    • POWELL_BADLY_SCALED

      private final int POWELL_BADLY_SCALED
      See Also:

    • BROWN_BADLY_SCALED

      private final int BROWN_BADLY_SCALED
      See Also:

    • BEALE

      private final int BEALE
      See Also:

    • JENNRICH_AND_SAMPSON

      private final int JENNRICH_AND_SAMPSON
      See Also:

    • HELICAL_VALLEY

      private final int HELICAL_VALLEY
      See Also:

    • GAUSSIAN

      private final int GAUSSIAN
      See Also:

    • BARD

      private final int BARD
      See Also:

    • MEYER

      private final int MEYER
      See Also:

    • GULF_RESEARCH_AND_DEVELOPMENT

      private final int GULF_RESEARCH_AND_DEVELOPMENT
      See Also:

    • BOX_3D

      private final int BOX_3D
      See Also:

    • POWELL_SINGULAR

      private final int POWELL_SINGULAR
      See Also:

    • WOOD

      private final int WOOD
      See Also:

    • KOWALIK_AND_OSBORNE

      private final int KOWALIK_AND_OSBORNE
      See Also:

    • BROWN_AND_DENNIS

      private final int BROWN_AND_DENNIS
      See Also:

    • OSBORNE1

      private final int OSBORNE1
      See Also:

    • BIGGS_EXP6

      private final int BIGGS_EXP6
      See Also:

    • OSBORNE2

      private final int OSBORNE2
      See Also:

    • WATSON

      private final int WATSON
      See Also:

    • EXTENDED_ROSENBROCK

      private final int EXTENDED_ROSENBROCK
      See Also:

    • EXTENDED_POWELL_SINGULAR

      private final int EXTENDED_POWELL_SINGULAR
      See Also:

    • PENALTY_FUNCTION_I

      private final int PENALTY_FUNCTION_I
      See Also:

    • PENALTY_FUNCTION_II

      private final int PENALTY_FUNCTION_II
      See Also:

    • VARIABLY_DIMENSIONED_FUNCTION

      private final int VARIABLY_DIMENSIONED_FUNCTION
      See Also:

    • TRIGONOMETRIC

      private final int TRIGONOMETRIC
      See Also:

    • BROWN_ALMOST_LINEAR

      private final int BROWN_ALMOST_LINEAR
      See Also:

    • DISCRETE_BOUNDARY_VALUE

      private final int DISCRETE_BOUNDARY_VALUE
      See Also:

    • DISCRETE_INTEGRAL

      private final int DISCRETE_INTEGRAL
      See Also:

    • BROYDEN_TRIDIAGONAL

      private final int BROYDEN_TRIDIAGONAL
      See Also:

    • BROYDEN_BANDED

      private final int BROYDEN_BANDED
      See Also:

    • LINEAR_FULL_RANK

      private final int LINEAR_FULL_RANK
      See Also:

    • LINEAR_RANK1

      private final int LINEAR_RANK1
      See Also:

    • LINEAR_RANK1_WITH_ZERO_COLUMNS_AND_ROWS

      private final int LINEAR_RANK1_WITH_ZERO_COLUMNS_AND_ROWS
      See Also:

    • CHEBYQUAD

      private final int CHEBYQUAD
      See Also:

    • HOCK25

      private final int HOCK25
      See Also:

    • LEVMAR_ROSENBROCK

      private final int LEVMAR_ROSENBROCK
      See Also:

    • MODIFIED_ROSENBROCK

      private final int MODIFIED_ROSENBROCK
      See Also:

    • POWELL_2_PARAMETER

      private final int POWELL_2_PARAMETER
      See Also:

    • HOCK1

      private final int HOCK1
      See Also:

    • HOCK21_MODIFIED

      private final int HOCK21_MODIFIED
      See Also:

    • HATFLDB

      private final int HATFLDB
      See Also:

    • HATFLDC

      private final int HATFLDC
      See Also:

    • EQUILIBRIUM_COMBUSTION

      private final int EQUILIBRIUM_COMBUSTION
      See Also:

    • MADSEN

      private final int MADSEN
      See Also:

    • HOCK3

      private final int HOCK3
      See Also:

    • HOCK4

      private final int HOCK4
      See Also:

    • CERES_CURVE_FITTING

      private final int CERES_CURVE_FITTING
      See Also:

  • Constructor Details

    • NLConstrainedEngine

      public NLConstrainedEngine()

    • NLConstrainedEngine

      public NLConstrainedEngine(int nPts, int param)
      NLConstrainedEngine - non-linear fit to a function.
      Parameters:
      nPts - number of points to fit to the function to
      param - number of parameters of function
      xSeries - DOCUMENT ME!
      yData - DOCUMENT ME!

  • Method Details

    • fitTestModel

      private void fitTestModel()
      Creates a new Fit24DModel object.
      Parameters:
      nPoints - DOCUMENT ME!
      xData - DOCUMENT ME!
      yData - DOCUMENT ME!
      initial - DOCUMENT ME!

    • fitToTestFunction

      public void fitToTestFunction(double[] a, double[] residuals, double[][] jacobian)

    • shiftedChebyshev

      private double shiftedChebyshev(double x, int n)

    • shiftedChebyshevDerivative

      private double shiftedChebyshevDerivative(double x, int n)

    • dumpTestResults

      public void dumpTestResults()

    • driverCalls

      private void driverCalls()

    • fitToFunction

      public abstract void fitToFunction(double[] a, double[] residuals, double[][] jacobian)
      fitToFunction communicates with 3 protected variables param, nPts, and ctrlMat ctrlMat is used as a wrapper for ctrl or lctrl. Evaluates the residuals or the Jacobian at a certain a[]
      Parameters:
      a - DOCUMENT ME!
      residuals - DOCUMENT ME!
      jacobian - DOCUMENT ME!

    • driver

      public void driver()
      driver.

    • getChiSquared

      public double getChiSquared()
      getChiSquared - accessor to chi-squared value (goodness-of-fit measure).
      Returns:
      the value of chi squared

    • 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

    • getExitStatus

      public int getExitStatus()

    • statusMessage

      public void statusMessage(int status)

    • analuc

      private void analuc(int[] prank)
      DOCUMENT ME!

    • btrunc

      private void btrunc(int[] prank, boolean internalScaling, double[] work)
      DOCUMENT ME!
      Parameters:
      internalScaling - DOCUMENT ME!
      work - DOCUMENT ME!

    • chder

      private void chder(double dphize, int[] k, double[] alfk, double[] phik)
      DOCUMENT ME!
      Parameters:
      dphize - DOCUMENT ME!

    • choose

      private void choose(double xmin, double[] v2, double[] root1, double[] root2, double[] proot2)
      DOCUMENT ME!
      Parameters:
      xmin - DOCUMENT ME!
      v2 - DOCUMENT ME!

    • covar

      private void covar()
      DOCUMENT ME!

    • dimsub

      private void dimsub(int[] prank, int[] rank)
      DOCUMENT ME!

    • dnrm2

      private double dnrm2(int n, double[] x, int incx)
      DOCUMENT ME!
      Parameters:
      n - DOCUMENT ME!
      x - DOCUMENT ME!
      incx - DOCUMENT ME!
      Returns:
      DOCUMENT ME!

    • evreuc

      private void evreuc(int[] prank)
      DOCUMENT ME!

    • fsumsq

      private void fsumsq(double alfk, double[] xnew, double[] fnew, double[] fn_val, int[] ctrl)
      DOCUMENT ME!
      Parameters:
      alfk - DOCUMENT ME!
      xnew - DOCUMENT ME!
      fnew - DOCUMENT ME!
      phiMat - DOCUMENT ME!

    • gauc

      private void gauc(int[] k, double alfmin, double[] gmod, double dphize, double[] u, double[] phiu, double tau, double pmax)
      DOCUMENT ME!
      Parameters:
      gmod - DOCUMENT ME!
      dphize - DOCUMENT ME!
      tau - DOCUMENT ME!
      pmax - DOCUMENT ME!

    • gnavuc

      private void gnavuc()
      DOCUMENT ME!

    • gndunc

      private double gndunc(boolean internalScaling, int[] prank, double[] work)
      DOCUMENT ME!
      Parameters:
      internalScaling - DOCUMENT ME!
      work - DOCUMENT ME!
      pseudoRankMat - DOCUMENT ME!
      Returns:
      DOCUMENT ME!

    • hess

      private void hess()
      DOCUMENT ME!

    • jacdif

      private void jacdif(int[] ctrl)
      DOCUMENT ME!

    • jtrj

      private void jtrj(int nn)
      DOCUMENT ME!
      Parameters:
      nn - DOCUMENT ME!

    • lineuc

      private void lineuc(double[] gmod, double dphize, double alplow)
      DOCUMENT ME!
      Parameters:
      gmod - DOCUMENT ME!
      dphize - DOCUMENT ME!
      alplow - DOCUMENT ME!

    • linuc2

      private void linuc2(double[] fnew, double alfk, double[] v2)
      DOCUMENT ME!
      Parameters:
      fnew - DOCUMENT ME!
      v2 - DOCUMENT ME!

    • lsunc

      private void lsunc()
      DOCUMENT ME!

    • minrm

      private void minrm(double[] v2, double alfmin, double alfmax, double xmin, double[] x, double[] px, double[] y, double[] py)
      DOCUMENT ME!
      Parameters:
      v2 - DOCUMENT ME!
      xmin - DOCUMENT ME!

    • minrm1

      private void minrm1(double[] v2)
      DOCUMENT ME!
      Parameters:
      v2 - DOCUMENT ME!

    • minrm2

      private void minrm2()
      DOCUMENT ME!

    • minrn

      private void minrn(double x, double fx, double w, double fw, double v, double fv, double alfmin, double alfmax, double pmax, double[] u, double[] pu)
      DOCUMENT ME!
      Parameters:
      pmax - DOCUMENT ME!
      phikm2 - DOCUMENT ME!

    • newunc

      private void newunc()
      DOCUMENT ME!

    • oner

      private void oner(double[] x)
      DOCUMENT ME!

    • outuc

      private void outuc()
      DOCUMENT ME!

    • pivec

      private void pivec(double[] work)
      DOCUMENT ME!
      Parameters:
      work - DOCUMENT ME!

    • pol3

      private double pol3(double x)
      DOCUMENT ME!
      Parameters:
      x - DOCUMENT ME!
      Returns:
      DOCUMENT ME!

    • pol4

      private double pol4(double[] v2, double x)
      DOCUMENT ME!
      Parameters:
      v2 - DOCUMENT ME!
      x - DOCUMENT ME!
      Returns:
      DOCUMENT ME!

    • pregn

      private void pregn(double[] work, int mindim, int[] prank, int[] dim)
      DOCUMENT ME!
      Parameters:
      work - DOCUMENT ME!
      mindim - DOCUMENT ME!

    • presub

      private void presub(double[] work, int[] prank, int[] rank)
      DOCUMENT ME!
      Parameters:
      work - DOCUMENT ME!

    • quamin

      private void quamin(double x, double fx, double w, double fw, double v, double fv, double[] u)
      DOCUMENT ME!
      Parameters:
      phikm2 - DOCUMENT ME!

    • reavuc

      private void reavuc()
      DOCUMENT ME!

    • reduc

      private void reduc(double[] alf, double[] phialf, double alfk, double pk, double diff, double eta, double[] gmod, double[] fnew, int[] k, double[] phik, boolean[] reduce)
      DOCUMENT ME!
      Parameters:
      pk - DOCUMENT ME!
      eta - DOCUMENT ME!
      gmod - DOCUMENT ME!
      fnew - DOCUMENT ME!

    • releps

      private void releps()
      DOCUMENT ME!

    • rtrw1

      private void rtrw1(int nn)
      DOCUMENT ME!
      Parameters:
      nn - DOCUMENT ME!

    • scalv

      private void scalv(double[] v, double factor, int n)
      DOCUMENT ME!
      Parameters:
      v - DOCUMENT ME!
      factor - DOCUMENT ME!
      n - DOCUMENT ME!

    • scaunc

      private void scaunc()
      DOCUMENT ME!

    • schdc

      private void schdc(int nn, int[] jpvt, int job)
      DOCUMENT ME!
      Parameters:
      nn - DOCUMENT ME!
      jpvt - DOCUMENT ME!
      job - DOCUMENT ME!

    • secuc

      private void secuc()
      DOCUMENT ME!

    • soliuc

      private void soliuc(double tau, int[] prank)
      DOCUMENT ME!
      Parameters:
      tau - DOCUMENT ME!

    • sposl

      private void sposl(int nn)
      DOCUMENT ME!
      Parameters:
      nn - DOCUMENT ME!

    • sqrdc

      private void sqrdc(double[][] x, int n, int p, double[] qraux, int[] jpvt, int job)
      DOCUMENT ME!
      Parameters:
      x - DOCUMENT ME!
      n - DOCUMENT ME!
      p - DOCUMENT ME!
      qraux - DOCUMENT ME!
      jpvt - DOCUMENT ME!
      job - DOCUMENT ME!

    • sqrsl

      private void sqrsl(double[][] x, int n, int k, double[] qraux, double[] y, double[] qy, double[] qty, double[] b, double[] rsd, double[] xb, int job)
      DOCUMENT ME!
      Parameters:
      x - DOCUMENT ME!
      n - DOCUMENT ME!
      k - DOCUMENT ME!
      qraux - DOCUMENT ME!
      y - DOCUMENT ME!
      qy - DOCUMENT ME!
      qty - DOCUMENT ME!
      b - DOCUMENT ME!
      rsd - DOCUMENT ME!
      xb - DOCUMENT ME!
      job - DOCUMENT ME!

    • stepuc

      private void stepuc(int[] prank)
      DOCUMENT ME!

    • strsl

      private void strsl(int[] prank, double[] b)
      DOCUMENT ME!
      Parameters:
      b - DOCUMENT ME!

    • subuc

      private void subuc(int[] prank, int[] rank)
      DOCUMENT ME!

    • termuc

      private void termuc(int[] prank, double aNorm)
      DOCUMENT ME!
      Parameters:
      aNorm - DOCUMENT ME!

    • triunc

      private void triunc(double tol, int constraintAct, int[] prank)
      DOCUMENT ME!
      Parameters:
      tol - DOCUMENT ME!
      constraintAct - DOCUMENT ME!

    • twor

      private void twor()
      DOCUMENT ME!