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Posted to commits@commons.apache.org by er...@apache.org on 2021/05/15 04:02:08 UTC
[commons-math] branch modularized_master created (now 9d1741b)
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at 9d1741b Modularization.
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new 9d1741b Modularization.
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[commons-math] 01/01: Modularization.
Posted by er...@apache.org.
This is an automated email from the ASF dual-hosted git repository.
erans pushed a commit to branch modularized_master
in repository https://gitbox.apache.org/repos/asf/commons-math.git
commit 9d1741bfe4a7808cfa0c313891a717adf98a3087
Author: Gilles Sadowski <gi...@gmail.com>
AuthorDate: Fri May 14 17:18:27 2021 +0200
Modularization.
For now, all codes were placed in module "commons-math-legacy".
Selected parts should gradually be moved out of that module into their own.
---
RELEASE-NOTES.txt | 25 -
build.xml | 376 --
commons-math-legacy/LICENCE | 457 ++
commons-math-legacy/NOTICE | 9 +
commons-math-legacy/pom.xml | 131 +
.../org/apache/commons/math4/legacy/Field.java | 58 +
.../apache/commons/math4/legacy/FieldElement.java | 87 +
.../commons/math4/legacy/RealFieldElement.java | 402 ++
.../math4/legacy/analysis/BivariateFunction.java | 35 +
.../math4/legacy/analysis/FunctionUtils.java | 544 ++
.../legacy/analysis/MultivariateFunction.java | 42 +
.../analysis/MultivariateMatrixFunction.java | 35 +
.../analysis/MultivariateVectorFunction.java | 35 +
.../analysis/ParametricUnivariateFunction.java | 44 +
.../analysis/RealFieldUnivariateFunction.java | 86 +
.../math4/legacy/analysis/TrivariateFunction.java | 35 +
.../math4/legacy/analysis/UnivariateFunction.java | 81 +
.../legacy/analysis/UnivariateMatrixFunction.java | 33 +
.../legacy/analysis/UnivariateVectorFunction.java | 33 +
.../analysis/differentiation/DSCompiler.java | 1834 ++++++
.../differentiation/DerivativeStructure.java | 1256 ++++
.../FiniteDifferencesDifferentiator.java | 393 ++
.../analysis/differentiation/GradientFunction.java | 66 +
.../analysis/differentiation/JacobianFunction.java | 70 +
.../MultivariateDifferentiableFunction.java | 42 +
.../MultivariateDifferentiableVectorFunction.java | 43 +
.../analysis/differentiation/SparseGradient.java | 937 +++
.../UnivariateDifferentiableFunction.java | 43 +
.../UnivariateDifferentiableMatrixFunction.java | 40 +
.../UnivariateDifferentiableVectorFunction.java | 40 +
.../UnivariateFunctionDifferentiator.java | 33 +
.../UnivariateMatrixFunctionDifferentiator.java | 33 +
.../UnivariateVectorFunctionDifferentiator.java | 33 +
.../analysis/differentiation/package-info.java | 42 +
.../math4/legacy/analysis/function/Abs.java | 34 +
.../math4/legacy/analysis/function/Acos.java | 44 +
.../math4/legacy/analysis/function/Acosh.java | 44 +
.../math4/legacy/analysis/function/Add.java | 33 +
.../math4/legacy/analysis/function/Asin.java | 44 +
.../math4/legacy/analysis/function/Asinh.java | 44 +
.../math4/legacy/analysis/function/Atan.java | 44 +
.../math4/legacy/analysis/function/Atan2.java | 34 +
.../math4/legacy/analysis/function/Atanh.java | 44 +
.../math4/legacy/analysis/function/Cbrt.java | 44 +
.../math4/legacy/analysis/function/Ceil.java | 34 +
.../math4/legacy/analysis/function/Constant.java | 53 +
.../math4/legacy/analysis/function/Cos.java | 44 +
.../math4/legacy/analysis/function/Cosh.java | 44 +
.../math4/legacy/analysis/function/Divide.java | 33 +
.../math4/legacy/analysis/function/Exp.java | 44 +
.../math4/legacy/analysis/function/Expm1.java | 44 +
.../math4/legacy/analysis/function/Floor.java | 34 +
.../math4/legacy/analysis/function/Gaussian.java | 252 +
.../analysis/function/HarmonicOscillator.java | 176 +
.../math4/legacy/analysis/function/Identity.java | 43 +
.../math4/legacy/analysis/function/Inverse.java | 43 +
.../math4/legacy/analysis/function/Log.java | 44 +
.../math4/legacy/analysis/function/Log10.java | 45 +
.../math4/legacy/analysis/function/Log1p.java | 44 +
.../math4/legacy/analysis/function/Logistic.java | 221 +
.../math4/legacy/analysis/function/Logit.java | 205 +
.../math4/legacy/analysis/function/Max.java | 34 +
.../math4/legacy/analysis/function/Min.java | 34 +
.../math4/legacy/analysis/function/Minus.java | 43 +
.../math4/legacy/analysis/function/Multiply.java | 33 +
.../math4/legacy/analysis/function/Pow.java | 34 +
.../math4/legacy/analysis/function/Power.java | 54 +
.../math4/legacy/analysis/function/Rint.java | 34 +
.../math4/legacy/analysis/function/Sigmoid.java | 211 +
.../math4/legacy/analysis/function/Signum.java | 34 +
.../math4/legacy/analysis/function/Sin.java | 44 +
.../math4/legacy/analysis/function/Sinc.java | 196 +
.../math4/legacy/analysis/function/Sinh.java | 44 +
.../math4/legacy/analysis/function/Sqrt.java | 44 +
.../legacy/analysis/function/StepFunction.java | 102 +
.../math4/legacy/analysis/function/Subtract.java | 33 +
.../math4/legacy/analysis/function/Tan.java | 44 +
.../math4/legacy/analysis/function/Tanh.java | 44 +
.../math4/legacy/analysis/function/Ulp.java | 34 +
.../legacy/analysis/function/package-info.java | 26 +
.../BaseAbstractUnivariateIntegrator.java | 273 +
.../IterativeLegendreGaussIntegrator.java | 178 +
.../analysis/integration/MidPointIntegrator.java | 166 +
.../analysis/integration/RombergIntegrator.java | 134 +
.../analysis/integration/SimpsonIntegrator.java | 120 +
.../analysis/integration/TrapezoidIntegrator.java | 154 +
.../analysis/integration/UnivariateIntegrator.java | 88 +
.../integration/gauss/BaseRuleFactory.java | 151 +
.../integration/gauss/GaussIntegrator.java | 126 +
.../integration/gauss/GaussIntegratorFactory.java | 181 +
.../integration/gauss/HermiteRuleFactory.java | 174 +
.../integration/gauss/LaguerreRuleFactory.java | 81 +
.../gauss/LegendreHighPrecisionRuleFactory.java | 212 +
.../integration/gauss/LegendreRuleFactory.java | 137 +
.../gauss/SymmetricGaussIntegrator.java | 99 +
.../analysis/integration/gauss/package-info.java | 22 +
.../legacy/analysis/integration/package-info.java | 22 +
.../interpolation/AkimaSplineInterpolator.java | 248 +
.../BicubicInterpolatingFunction.java | 329 ++
.../interpolation/BicubicInterpolator.java | 114 +
.../interpolation/BivariateGridInterpolator.java | 51 +
.../DividedDifferenceInterpolator.java | 122 +
.../interpolation/FieldHermiteInterpolator.java | 210 +
.../interpolation/HermiteInterpolator.java | 242 +
.../interpolation/InterpolatingMicrosphere.java | 387 ++
.../interpolation/InterpolatingMicrosphere2D.java | 87 +
.../analysis/interpolation/LinearInterpolator.java | 80 +
.../analysis/interpolation/LoessInterpolator.java | 474 ++
.../MicrosphereProjectionInterpolator.java | 168 +
.../interpolation/MultivariateInterpolator.java | 51 +
.../interpolation/NevilleInterpolator.java | 61 +
...iecewiseBicubicSplineInterpolatingFunction.java | 212 +
.../PiecewiseBicubicSplineInterpolator.java | 62 +
.../analysis/interpolation/SplineInterpolator.java | 137 +
.../TricubicInterpolatingFunction.java | 509 ++
.../interpolation/TricubicInterpolator.java | 144 +
.../interpolation/TrivariateGridInterpolator.java | 54 +
.../interpolation/UnivariateInterpolator.java | 41 +
.../UnivariatePeriodicInterpolator.java | 126 +
.../analysis/interpolation/package-info.java | 22 +
.../math4/legacy/analysis/package-info.java | 32 +
.../analysis/polynomials/PolynomialFunction.java | 406 ++
.../PolynomialFunctionLagrangeForm.java | 327 ++
.../polynomials/PolynomialFunctionNewtonForm.java | 247 +
.../polynomials/PolynomialSplineFunction.java | 237 +
.../analysis/polynomials/PolynomialsUtils.java | 454 ++
.../legacy/analysis/polynomials/package-info.java | 23 +
.../analysis/solvers/AbstractPolynomialSolver.java | 80 +
.../AbstractUnivariateDifferentiableSolver.java | 82 +
.../analysis/solvers/AbstractUnivariateSolver.java | 60 +
.../legacy/analysis/solvers/AllowedSolution.java | 75 +
.../solvers/BaseAbstractUnivariateSolver.java | 315 +
.../legacy/analysis/solvers/BaseSecantSolver.java | 280 +
.../analysis/solvers/BaseUnivariateSolver.java | 142 +
.../legacy/analysis/solvers/BisectionSolver.java | 91 +
.../BracketedRealFieldUnivariateSolver.java | 142 +
.../solvers/BracketedUnivariateSolver.java | 92 +
.../solvers/BracketingNthOrderBrentSolver.java | 413 ++
.../math4/legacy/analysis/solvers/BrentSolver.java | 109 +
.../FieldBracketingNthOrderBrentSolver.java | 453 ++
.../legacy/analysis/solvers/IllinoisSolver.java | 82 +
.../legacy/analysis/solvers/LaguerreSolver.java | 384 ++
.../legacy/analysis/solvers/MullerSolver.java | 202 +
.../legacy/analysis/solvers/MullerSolver2.java | 168 +
.../analysis/solvers/NewtonRaphsonSolver.java | 92 +
.../legacy/analysis/solvers/PegasusSolver.java | 84 +
.../legacy/analysis/solvers/PolynomialSolver.java | 28 +
.../legacy/analysis/solvers/RegulaFalsiSolver.java | 94 +
.../legacy/analysis/solvers/RiddersSolver.java | 142 +
.../legacy/analysis/solvers/SecantSolver.java | 135 +
.../solvers/UnivariateDifferentiableSolver.java | 29 +
.../legacy/analysis/solvers/UnivariateSolver.java | 28 +
.../analysis/solvers/UnivariateSolverUtils.java | 467 ++
.../legacy/analysis/solvers/package-info.java | 22 +
.../math4/legacy/complex/ComplexFormat.java | 428 ++
.../commons/math4/legacy/complex/package-info.java | 23 +
.../org/apache/commons/math4/legacy/dfp/Dfp.java | 2928 ++++++++++
.../apache/commons/math4/legacy/dfp/DfpDec.java | 368 ++
.../apache/commons/math4/legacy/dfp/DfpField.java | 762 +++
.../apache/commons/math4/legacy/dfp/DfpMath.java | 965 +++
.../commons/math4/legacy/dfp/package-info.java | 88 +
.../distribution/AbstractIntegerDistribution.java | 228 +
.../AbstractMultivariateRealDistribution.java | 72 +
.../distribution/AbstractRealDistribution.java | 278 +
.../legacy/distribution/EmpiricalDistribution.java | 753 +++
.../distribution/EnumeratedDistribution.java | 254 +
.../EnumeratedIntegerDistribution.java | 247 +
.../distribution/EnumeratedRealDistribution.java | 294 +
.../MixtureMultivariateNormalDistribution.java | 91 +
.../MixtureMultivariateRealDistribution.java | 166 +
.../MultivariateNormalDistribution.java | 225 +
.../distribution/MultivariateRealDistribution.java | 77 +
...ariateNormalMixtureExpectationMaximization.java | 455 ++
.../legacy/distribution/fitting/package-info.java | 20 +
.../math4/legacy/distribution/package-info.java | 21 +
.../legacy/exception/ConvergenceException.java | 49 +
.../exception/DimensionMismatchException.java | 64 +
.../exception/InsufficientDataException.java | 49 +
.../legacy/exception/MathArithmeticException.java | 52 +
.../exception/MathIllegalArgumentException.java | 41 +
.../exception/MathIllegalNumberException.java | 60 +
.../exception/MathIllegalStateException.java | 63 +
.../math4/legacy/exception/MathInternalError.java | 57 +
.../math4/legacy/exception/MathParseException.java | 51 +
.../legacy/exception/MathRuntimeException.java | 80 +
.../MathUnsupportedOperationException.java | 49 +
.../exception/MaxCountExceededException.java | 63 +
.../exception/MultiDimensionMismatchException.java | 90 +
.../legacy/exception/NoBracketingException.java | 106 +
.../math4/legacy/exception/NoDataException.java | 46 +
.../exception/NonMonotonicSequenceException.java | 120 +
.../legacy/exception/NotANumberException.java | 37 +
.../legacy/exception/NotFiniteNumberException.java | 54 +
.../legacy/exception/NotPositiveException.java | 48 +
.../exception/NotStrictlyPositiveException.java | 49 +
.../legacy/exception/NullArgumentException.java | 84 +
.../exception/NumberIsTooLargeException.java | 85 +
.../exception/NumberIsTooSmallException.java | 86 +
.../legacy/exception/OutOfRangeException.java | 79 +
.../exception/TooManyEvaluationsException.java | 39 +
.../exception/TooManyIterationsException.java | 39 +
.../math4/legacy/exception/ZeroException.java | 48 +
.../math4/legacy/exception/package-info.java | 23 +
.../math4/legacy/exception/util/ArgUtils.java | 54 +
.../legacy/exception/util/DummyLocalizable.java | 59 +
.../legacy/exception/util/ExceptionContext.java | 334 ++
.../exception/util/ExceptionContextProvider.java | 33 +
.../math4/legacy/exception/util/Localizable.java | 43 +
.../legacy/exception/util/LocalizedFormats.java | 417 ++
.../math4/legacy/exception/util/package-info.java | 22 +
.../field/linalg/FieldDecompositionSolver.java | 57 +
.../legacy/field/linalg/FieldDenseMatrix.java | 354 ++
.../legacy/field/linalg/FieldLUDecomposition.java | 359 ++
.../math4/legacy/field/linalg/package-info.java | 21 +
.../commons/math4/legacy/field/package-info.java | 22 +
.../legacy/filter/DefaultMeasurementModel.java | 86 +
.../math4/legacy/filter/DefaultProcessModel.java | 170 +
.../commons/math4/legacy/filter/KalmanFilter.java | 388 ++
.../math4/legacy/filter/MeasurementModel.java | 44 +
.../commons/math4/legacy/filter/ProcessModel.java | 73 +
.../commons/math4/legacy/filter/package-info.java | 20 +
.../math4/legacy/fitting/AbstractCurveFitter.java | 139 +
.../math4/legacy/fitting/GaussianCurveFitter.java | 427 ++
.../math4/legacy/fitting/HarmonicCurveFitter.java | 445 ++
.../legacy/fitting/PolynomialCurveFitter.java | 131 +
.../math4/legacy/fitting/SimpleCurveFitter.java | 125 +
.../legacy/fitting/WeightedObservedPoint.java | 78 +
.../legacy/fitting/WeightedObservedPoints.java | 112 +
.../fitting/leastsquares/AbstractEvaluation.java | 101 +
.../leastsquares/DenseWeightedEvaluation.java | 71 +
...entiatorVectorMultivariateJacobianFunction.java | 95 +
.../fitting/leastsquares/EvaluationRmsChecker.java | 76 +
.../fitting/leastsquares/GaussNewtonOptimizer.java | 300 +
.../fitting/leastsquares/LeastSquaresAdapter.java | 84 +
.../fitting/leastsquares/LeastSquaresBuilder.java | 226 +
.../fitting/leastsquares/LeastSquaresFactory.java | 541 ++
.../leastsquares/LeastSquaresOptimizer.java | 62 +
.../fitting/leastsquares/LeastSquaresProblem.java | 174 +
.../leastsquares/LevenbergMarquardtOptimizer.java | 1043 ++++
.../leastsquares/MultivariateJacobianFunction.java | 39 +
.../legacy/fitting/leastsquares/OptimumImpl.java | 118 +
.../fitting/leastsquares/ParameterValidator.java | 34 +
.../leastsquares/ValueAndJacobianFunction.java | 44 +
.../legacy/fitting/leastsquares/package-info.java | 39 +
.../commons/math4/legacy/fitting/package-info.java | 26 +
.../legacy/genetics/AbstractListChromosome.java | 106 +
.../math4/legacy/genetics/BinaryChromosome.java | 98 +
.../math4/legacy/genetics/BinaryMutation.java | 57 +
.../commons/math4/legacy/genetics/Chromosome.java | 105 +
.../math4/legacy/genetics/ChromosomePair.java | 66 +
.../math4/legacy/genetics/CrossoverPolicy.java | 38 +
.../math4/legacy/genetics/CycleCrossover.java | 182 +
.../legacy/genetics/ElitisticListPopulation.java | 118 +
.../commons/math4/legacy/genetics/Fitness.java | 32 +
.../math4/legacy/genetics/FixedElapsedTime.java | 79 +
.../legacy/genetics/FixedGenerationCount.java | 74 +
.../math4/legacy/genetics/GeneticAlgorithm.java | 232 +
.../genetics/InvalidRepresentationException.java | 42 +
.../math4/legacy/genetics/ListPopulation.java | 201 +
.../math4/legacy/genetics/MutationPolicy.java | 35 +
.../math4/legacy/genetics/NPointCrossover.java | 179 +
.../math4/legacy/genetics/OnePointCrossover.java | 129 +
.../math4/legacy/genetics/OrderedCrossover.java | 151 +
.../legacy/genetics/PermutationChromosome.java | 40 +
.../commons/math4/legacy/genetics/Population.java | 59 +
.../commons/math4/legacy/genetics/RandomKey.java | 300 +
.../math4/legacy/genetics/RandomKeyMutation.java | 55 +
.../math4/legacy/genetics/SelectionPolicy.java | 34 +
.../math4/legacy/genetics/StoppingCondition.java | 33 +
.../math4/legacy/genetics/TournamentSelection.java | 117 +
.../math4/legacy/genetics/UniformCrossover.java | 135 +
.../math4/legacy/genetics/package-info.java | 20 +
.../math4/legacy/linear/AbstractFieldMatrix.java | 1114 ++++
.../math4/legacy/linear/AbstractRealMatrix.java | 1026 ++++
.../commons/math4/legacy/linear/AnyMatrix.java | 97 +
.../math4/legacy/linear/Array2DRowFieldMatrix.java | 612 ++
.../math4/legacy/linear/Array2DRowRealMatrix.java | 589 ++
.../math4/legacy/linear/ArrayFieldVector.java | 1123 ++++
.../math4/legacy/linear/ArrayRealVector.java | 953 +++
.../math4/legacy/linear/BiDiagonalTransformer.java | 380 ++
.../math4/legacy/linear/BlockFieldMatrix.java | 1588 +++++
.../math4/legacy/linear/BlockRealMatrix.java | 1580 +++++
.../math4/legacy/linear/CholeskyDecomposition.java | 314 +
.../math4/legacy/linear/ConjugateGradient.java | 234 +
.../math4/legacy/linear/DecompositionSolver.java | 97 +
.../linear/DefaultFieldMatrixChangingVisitor.java | 61 +
.../DefaultFieldMatrixPreservingVisitor.java | 59 +
.../linear/DefaultIterativeLinearSolverEvent.java | 143 +
.../linear/DefaultRealMatrixChangingVisitor.java | 47 +
.../linear/DefaultRealMatrixPreservingVisitor.java | 45 +
.../math4/legacy/linear/DiagonalMatrix.java | 370 ++
.../math4/legacy/linear/EigenDecomposition.java | 942 +++
.../legacy/linear/EigenDecomposition.java_PRINT | 945 +++
.../legacy/linear/FieldDecompositionSolver.java | 75 +
.../math4/legacy/linear/FieldLUDecomposition.java | 448 ++
.../commons/math4/legacy/linear/FieldMatrix.java | 814 +++
.../legacy/linear/FieldMatrixChangingVisitor.java | 57 +
.../linear/FieldMatrixPreservingVisitor.java | 56 +
.../commons/math4/legacy/linear/FieldVector.java | 290 +
.../legacy/linear/FieldVectorChangingVisitor.java | 56 +
.../linear/FieldVectorPreservingVisitor.java | 55 +
.../math4/legacy/linear/HessenbergTransformer.java | 232 +
.../linear/IllConditionedOperatorException.java | 42 +
.../math4/legacy/linear/IterativeLinearSolver.java | 173 +
.../legacy/linear/IterativeLinearSolverEvent.java | 115 +
.../math4/legacy/linear/JacobiPreconditioner.java | 135 +
.../math4/legacy/linear/LUDecomposition.java | 394 ++
.../linear/MatrixDimensionMismatchException.java | 73 +
.../commons/math4/legacy/linear/MatrixUtils.java | 1026 ++++
.../linear/NonPositiveDefiniteMatrixException.java | 73 +
.../NonPositiveDefiniteOperatorException.java | 43 +
.../linear/NonSelfAdjointOperatorException.java | 46 +
.../legacy/linear/NonSquareMatrixException.java | 41 +
.../legacy/linear/NonSquareOperatorException.java | 40 +
.../legacy/linear/NonSymmetricMatrixException.java | 71 +
.../math4/legacy/linear/OpenMapRealMatrix.java | 308 +
.../math4/legacy/linear/OpenMapRealVector.java | 812 +++
.../PreconditionedIterativeLinearSolver.java | 214 +
.../math4/legacy/linear/QRDecomposition.java | 507 ++
.../math4/legacy/linear/RRQRDecomposition.java | 247 +
.../math4/legacy/linear/RealLinearOperator.java | 109 +
.../commons/math4/legacy/linear/RealMatrix.java | 828 +++
.../legacy/linear/RealMatrixChangingVisitor.java | 55 +
.../math4/legacy/linear/RealMatrixFormat.java | 392 ++
.../legacy/linear/RealMatrixPreservingVisitor.java | 54 +
.../commons/math4/legacy/linear/RealVector.java | 1629 ++++++
.../legacy/linear/RealVectorChangingVisitor.java | 58 +
.../math4/legacy/linear/RealVectorFormat.java | 288 +
.../legacy/linear/RealVectorPreservingVisitor.java | 57 +
.../linear/RectangularCholeskyDecomposition.java | 195 +
.../math4/legacy/linear/SchurTransformer.java | 453 ++
.../legacy/linear/SingularMatrixException.java | 37 +
.../legacy/linear/SingularOperatorException.java | 38 +
.../legacy/linear/SingularValueDecomposition.java | 744 +++
.../math4/legacy/linear/SparseFieldMatrix.java | 187 +
.../math4/legacy/linear/SparseFieldVector.java | 811 +++
.../math4/legacy/linear/SparseRealMatrix.java | 34 +
.../math4/legacy/linear/SparseRealVector.java | 31 +
.../apache/commons/math4/legacy/linear/SymmLQ.java | 1221 ++++
.../legacy/linear/TriDiagonalTransformer.java | 253 +
.../commons/math4/legacy/linear/package-info.java | 20 +
.../legacy/ml/clustering/CentroidCluster.java | 53 +
.../math4/legacy/ml/clustering/Cluster.java | 84 +
.../legacy/ml/clustering/ClusterEvaluator.java | 55 +
.../math4/legacy/ml/clustering/ClusterRanking.java | 39 +
.../math4/legacy/ml/clustering/Clusterable.java | 32 +
.../math4/legacy/ml/clustering/Clusterer.java | 80 +
.../legacy/ml/clustering/DBSCANClusterer.java | 220 +
.../math4/legacy/ml/clustering/DoublePoint.java | 87 +
.../legacy/ml/clustering/FuzzyKMeansClusterer.java | 421 ++
.../ml/clustering/KMeansPlusPlusClusterer.java | 543 ++
.../ml/clustering/MiniBatchKMeansClusterer.java | 301 +
.../clustering/MultiKMeansPlusPlusClusterer.java | 105 +
.../ml/clustering/evaluation/CalinskiHarabasz.java | 171 +
.../evaluation/SumOfClusterVariances.java | 88 +
.../ml/clustering/evaluation/package-info.java | 24 +
.../math4/legacy/ml/clustering/package-info.java | 20 +
.../math4/legacy/ml/distance/CanberraDistance.java | 47 +
.../legacy/ml/distance/ChebyshevDistance.java | 39 +
.../math4/legacy/ml/distance/DistanceMeasure.java | 41 +
.../legacy/ml/distance/EarthMoversDistance.java | 49 +
.../legacy/ml/distance/EuclideanDistance.java | 39 +
.../legacy/ml/distance/ManhattanDistance.java | 39 +
.../math4/legacy/ml/distance/package-info.java | 20 +
.../legacy/ml/neuralnet/FeatureInitializer.java | 32 +
.../ml/neuralnet/FeatureInitializerFactory.java | 116 +
.../math4/legacy/ml/neuralnet/MapRanking.java | 156 +
.../math4/legacy/ml/neuralnet/MapUtils.java | 99 +
.../commons/math4/legacy/ml/neuralnet/Network.java | 489 ++
.../commons/math4/legacy/ml/neuralnet/Neuron.java | 272 +
.../legacy/ml/neuralnet/SquareNeighbourhood.java | 38 +
.../math4/legacy/ml/neuralnet/UpdateAction.java | 34 +
.../legacy/ml/neuralnet/oned/NeuronString.java | 239 +
.../legacy/ml/neuralnet/oned/package-info.java | 22 +
.../math4/legacy/ml/neuralnet/package-info.java | 22 +
.../ml/neuralnet/sofm/KohonenTrainingTask.java | 61 +
.../ml/neuralnet/sofm/KohonenUpdateAction.java | 228 +
.../ml/neuralnet/sofm/LearningFactorFunction.java | 34 +
.../sofm/LearningFactorFunctionFactory.java | 119 +
.../neuralnet/sofm/NeighbourhoodSizeFunction.java | 37 +
.../sofm/NeighbourhoodSizeFunctionFactory.java | 109 +
.../legacy/ml/neuralnet/sofm/package-info.java | 22 +
.../sofm/util/ExponentialDecayFunction.java | 83 +
.../sofm/util/QuasiSigmoidDecayFunction.java | 87 +
.../ml/neuralnet/sofm/util/package-info.java | 22 +
.../ml/neuralnet/twod/NeuronSquareMesh2D.java | 868 +++
.../legacy/ml/neuralnet/twod/package-info.java | 22 +
.../ml/neuralnet/twod/util/LocationFinder.java | 105 +
.../neuralnet/twod/util/MapDataVisualization.java | 38 +
.../ml/neuralnet/twod/util/MapVisualization.java | 34 +
.../neuralnet/twod/util/SmoothedDataHistogram.java | 98 +
.../neuralnet/twod/util/UnifiedDistanceMatrix.java | 155 +
.../ml/neuralnet/twod/util/package-info.java | 22 +
.../commons/math4/legacy/ml/package-info.java | 20 +
.../math4/legacy/ode/AbstractFieldIntegrator.java | 467 ++
.../math4/legacy/ode/AbstractIntegrator.java | 471 ++
.../math4/legacy/ode/AbstractParameterizable.java | 76 +
.../legacy/ode/ContinuousOutputFieldModel.java | 345 ++
.../math4/legacy/ode/ContinuousOutputModel.java | 445 ++
.../commons/math4/legacy/ode/EquationsMapper.java | 97 +
.../math4/legacy/ode/ExpandableStatefulODE.java | 330 ++
.../math4/legacy/ode/FieldEquationsMapper.java | 203 +
.../math4/legacy/ode/FieldExpandableODE.java | 147 +
.../commons/math4/legacy/ode/FieldODEState.java | 139 +
.../legacy/ode/FieldODEStateAndDerivative.java | 82 +
.../math4/legacy/ode/FieldSecondaryEquations.java | 75 +
.../math4/legacy/ode/FirstOrderConverter.java | 116 +
.../ode/FirstOrderDifferentialEquations.java | 68 +
.../ode/FirstOrderFieldDifferentialEquations.java | 73 +
.../legacy/ode/FirstOrderFieldIntegrator.java | 188 +
.../math4/legacy/ode/FirstOrderIntegrator.java | 66 +
.../commons/math4/legacy/ode/JacobianMatrices.java | 496 ++
.../legacy/ode/MainStateJacobianProvider.java | 41 +
.../math4/legacy/ode/MultistepFieldIntegrator.java | 456 ++
.../math4/legacy/ode/MultistepIntegrator.java | 465 ++
.../commons/math4/legacy/ode/ODEIntegrator.java | 158 +
.../math4/legacy/ode/ParameterConfiguration.java | 67 +
.../legacy/ode/ParameterJacobianProvider.java | 48 +
.../math4/legacy/ode/ParameterJacobianWrapper.java | 102 +
.../commons/math4/legacy/ode/Parameterizable.java | 42 +
.../commons/math4/legacy/ode/ParameterizedODE.java | 42 +
.../math4/legacy/ode/ParameterizedWrapper.java | 88 +
.../ode/SecondOrderDifferentialEquations.java | 64 +
.../math4/legacy/ode/SecondOrderIntegrator.java | 60 +
.../math4/legacy/ode/SecondaryEquations.java | 61 +
.../legacy/ode/UnknownParameterException.java | 52 +
.../commons/math4/legacy/ode/events/Action.java | 56 +
.../math4/legacy/ode/events/EventFilter.java | 208 +
.../math4/legacy/ode/events/EventHandler.java | 219 +
.../math4/legacy/ode/events/EventState.java | 432 ++
.../math4/legacy/ode/events/FieldEventHandler.java | 180 +
.../math4/legacy/ode/events/FieldEventState.java | 345 ++
.../math4/legacy/ode/events/FilterType.java | 400 ++
.../math4/legacy/ode/events/Transformer.java | 107 +
.../math4/legacy/ode/events/package-info.java | 94 +
.../nonstiff/AdamsBashforthFieldIntegrator.java | 353 ++
.../ode/nonstiff/AdamsBashforthIntegrator.java | 361 ++
.../legacy/ode/nonstiff/AdamsFieldIntegrator.java | 146 +
.../ode/nonstiff/AdamsFieldStepInterpolator.java | 189 +
.../math4/legacy/ode/nonstiff/AdamsIntegrator.java | 136 +
.../ode/nonstiff/AdamsMoultonFieldIntegrator.java | 418 ++
.../ode/nonstiff/AdamsMoultonIntegrator.java | 423 ++
.../nonstiff/AdamsNordsieckFieldTransformer.java | 359 ++
.../ode/nonstiff/AdamsNordsieckTransformer.java | 364 ++
.../nonstiff/AdaptiveStepsizeFieldIntegrator.java | 366 ++
.../ode/nonstiff/AdaptiveStepsizeIntegrator.java | 375 ++
.../ClassicalRungeKuttaFieldIntegrator.java | 113 +
.../ClassicalRungeKuttaFieldStepInterpolator.java | 135 +
.../nonstiff/ClassicalRungeKuttaIntegrator.java | 74 +
.../ClassicalRungeKuttaStepInterpolator.java | 135 +
.../nonstiff/DormandPrince54FieldIntegrator.java | 235 +
.../DormandPrince54FieldStepInterpolator.java | 249 +
.../ode/nonstiff/DormandPrince54Integrator.java | 161 +
.../nonstiff/DormandPrince54StepInterpolator.java | 225 +
.../nonstiff/DormandPrince853FieldIntegrator.java | 457 ++
.../DormandPrince853FieldStepInterpolator.java | 302 +
.../ode/nonstiff/DormandPrince853Integrator.java | 286 +
.../nonstiff/DormandPrince853StepInterpolator.java | 501 ++
.../EmbeddedRungeKuttaFieldIntegrator.java | 385 ++
.../ode/nonstiff/EmbeddedRungeKuttaIntegrator.java | 379 ++
.../legacy/ode/nonstiff/EulerFieldIntegrator.java | 99 +
.../ode/nonstiff/EulerFieldStepInterpolator.java | 107 +
.../math4/legacy/ode/nonstiff/EulerIntegrator.java | 72 +
.../legacy/ode/nonstiff/EulerStepInterpolator.java | 101 +
.../ode/nonstiff/FieldButcherArrayProvider.java | 46 +
.../legacy/ode/nonstiff/GillFieldIntegrator.java | 124 +
.../ode/nonstiff/GillFieldStepInterpolator.java | 147 +
.../math4/legacy/ode/nonstiff/GillIntegrator.java | 74 +
.../legacy/ode/nonstiff/GillStepInterpolator.java | 150 +
.../ode/nonstiff/GraggBulirschStoerIntegrator.java | 948 +++
.../GraggBulirschStoerStepInterpolator.java | 406 ++
.../ode/nonstiff/HighamHall54FieldIntegrator.java | 208 +
.../HighamHall54FieldStepInterpolator.java | 116 +
.../ode/nonstiff/HighamHall54Integrator.java | 135 +
.../ode/nonstiff/HighamHall54StepInterpolator.java | 122 +
.../legacy/ode/nonstiff/LutherFieldIntegrator.java | 149 +
.../ode/nonstiff/LutherFieldStepInterpolator.java | 224 +
.../legacy/ode/nonstiff/LutherIntegrator.java | 89 +
.../ode/nonstiff/LutherStepInterpolator.java | 182 +
.../ode/nonstiff/MidpointFieldIntegrator.java | 98 +
.../nonstiff/MidpointFieldStepInterpolator.java | 117 +
.../legacy/ode/nonstiff/MidpointIntegrator.java | 68 +
.../ode/nonstiff/MidpointStepInterpolator.java | 115 +
.../ode/nonstiff/RungeKuttaFieldIntegrator.java | 273 +
.../nonstiff/RungeKuttaFieldStepInterpolator.java | 147 +
.../legacy/ode/nonstiff/RungeKuttaIntegrator.java | 268 +
.../ode/nonstiff/RungeKuttaStepInterpolator.java | 211 +
.../ode/nonstiff/ThreeEighthesFieldIntegrator.java | 112 +
.../ThreeEighthesFieldStepInterpolator.java | 138 +
.../ode/nonstiff/ThreeEighthesIntegrator.java | 71 +
.../nonstiff/ThreeEighthesStepInterpolator.java | 145 +
.../math4/legacy/ode/nonstiff/package-info.java | 25 +
.../commons/math4/legacy/ode/package-info.java | 161 +
.../sampling/AbstractFieldStepInterpolator.java | 175 +
.../ode/sampling/AbstractStepInterpolator.java | 617 ++
.../legacy/ode/sampling/DummyStepHandler.java | 91 +
.../legacy/ode/sampling/FieldFixedStepHandler.java | 69 +
.../legacy/ode/sampling/FieldStepHandler.java | 75 +
.../legacy/ode/sampling/FieldStepInterpolator.java | 76 +
.../legacy/ode/sampling/FieldStepNormalizer.java | 273 +
.../legacy/ode/sampling/FixedStepHandler.java | 71 +
.../ode/sampling/NordsieckStepInterpolator.java | 293 +
.../math4/legacy/ode/sampling/StepHandler.java | 75 +
.../legacy/ode/sampling/StepInterpolator.java | 181 +
.../math4/legacy/ode/sampling/StepNormalizer.java | 300 +
.../legacy/ode/sampling/StepNormalizerBounds.java | 84 +
.../legacy/ode/sampling/StepNormalizerMode.java | 70 +
.../math4/legacy/ode/sampling/package-info.java | 60 +
.../legacy/optim/AbstractConvergenceChecker.java | 70 +
.../legacy/optim/AbstractOptimizationProblem.java | 111 +
.../optim/BaseMultiStartMultivariateOptimizer.java | 230 +
.../legacy/optim/BaseMultivariateOptimizer.java | 155 +
.../commons/math4/legacy/optim/BaseOptimizer.java | 277 +
.../math4/legacy/optim/ConvergenceChecker.java | 55 +
.../commons/math4/legacy/optim/InitialGuess.java | 46 +
.../apache/commons/math4/legacy/optim/MaxEval.java | 61 +
.../apache/commons/math4/legacy/optim/MaxIter.java | 61 +
.../math4/legacy/optim/OptimizationData.java | 28 +
.../math4/legacy/optim/OptimizationProblem.java | 53 +
.../commons/math4/legacy/optim/PointValuePair.java | 122 +
.../math4/legacy/optim/PointVectorValuePair.java | 147 +
.../commons/math4/legacy/optim/SimpleBounds.java | 79 +
.../math4/legacy/optim/SimplePointChecker.java | 133 +
.../math4/legacy/optim/SimpleValueChecker.java | 125 +
.../legacy/optim/SimpleVectorValueChecker.java | 134 +
.../legacy/optim/linear/LinearConstraint.java | 230 +
.../legacy/optim/linear/LinearConstraintSet.java | 62 +
.../optim/linear/LinearObjectiveFunction.java | 151 +
.../math4/legacy/optim/linear/LinearOptimizer.java | 132 +
.../optim/linear/NoFeasibleSolutionException.java | 37 +
.../legacy/optim/linear/NonNegativeConstraint.java | 47 +
.../legacy/optim/linear/PivotSelectionRule.java | 38 +
.../math4/legacy/optim/linear/Relationship.java | 65 +
.../math4/legacy/optim/linear/SimplexSolver.java | 409 ++
.../math4/legacy/optim/linear/SimplexTableau.java | 915 +++
.../legacy/optim/linear/SolutionCallback.java | 62 +
.../optim/linear/UnboundedSolutionException.java | 37 +
.../math4/legacy/optim/linear/package-info.java | 21 +
.../legacy/optim/nonlinear/scalar/GoalType.java | 32 +
.../scalar/GradientMultivariateOptimizer.java | 102 +
.../nonlinear/scalar/LeastSquaresConverter.java | 187 +
.../legacy/optim/nonlinear/scalar/LineSearch.java | 139 +
.../scalar/MultiStartMultivariateOptimizer.java | 113 +
.../scalar/MultivariateFunctionMappingAdapter.java | 303 +
.../scalar/MultivariateFunctionPenaltyAdapter.java | 187 +
.../nonlinear/scalar/MultivariateOptimizer.java | 117 +
.../optim/nonlinear/scalar/ObjectiveFunction.java | 46 +
.../scalar/ObjectiveFunctionGradient.java | 46 +
.../optim/nonlinear/scalar/PopulationSize.java | 50 +
.../math4/legacy/optim/nonlinear/scalar/Sigma.java | 51 +
.../NonLinearConjugateGradientOptimizer.java | 337 ++
.../nonlinear/scalar/gradient/Preconditioner.java | 44 +
.../nonlinear/scalar/gradient/package-info.java | 21 +
.../nonlinear/scalar/noderiv/AbstractSimplex.java | 345 ++
.../nonlinear/scalar/noderiv/BOBYQAOptimizer.java | 2475 ++++++++
.../nonlinear/scalar/noderiv/CMAESOptimizer.java | 1358 +++++
.../scalar/noderiv/MultiDirectionalSimplex.java | 215 +
.../scalar/noderiv/NelderMeadSimplex.java | 280 +
.../nonlinear/scalar/noderiv/PowellOptimizer.java | 299 +
.../nonlinear/scalar/noderiv/SimplexOptimizer.java | 231 +
.../scalar/noderiv/SimplexOptimizer.java.DEBUG | 339 ++
.../nonlinear/scalar/noderiv/package-info.java | 21 +
.../optim/nonlinear/scalar/package-info.java | 21 +
.../commons/math4/legacy/optim/package-info.java | 59 +
.../legacy/optim/univariate/BracketFinder.java | 314 +
.../legacy/optim/univariate/BrentOptimizer.java | 314 +
.../univariate/MultiStartUnivariateOptimizer.java | 230 +
.../legacy/optim/univariate/SearchInterval.java | 95 +
.../univariate/SimpleUnivariateValueChecker.java | 127 +
.../univariate/UnivariateObjectiveFunction.java | 46 +
.../optim/univariate/UnivariateOptimizer.java | 151 +
.../optim/univariate/UnivariatePointValuePair.java | 66 +
.../legacy/optim/univariate/package-info.java | 21 +
.../apache/commons/math4/legacy/package-info.java | 20 +
.../random/CorrelatedRandomVectorGenerator.java | 185 +
.../legacy/random/GaussianRandomGenerator.java | 51 +
.../legacy/random/HaltonSequenceGenerator.java | 184 +
.../legacy/random/NormalizedRandomGenerator.java | 37 +
.../math4/legacy/random/RandomGenerator.java | 148 +
.../commons/math4/legacy/random/RandomUtils.java | 403 ++
.../math4/legacy/random/RandomVectorGenerator.java | 32 +
.../commons/math4/legacy/random/RngAdaptor.java | 231 +
.../legacy/random/SobolSequenceGenerator.java | 326 ++
.../math4/legacy/random/StableRandomGenerator.java | 133 +
.../legacy/random/SynchronizedRandomGenerator.java | 134 +
.../random/UncorrelatedRandomVectorGenerator.java | 92 +
.../legacy/random/UniformRandomGenerator.java | 58 +
.../commons/math4/legacy/random/package-info.java | 33 +
.../commons/math4/legacy/special/BesselJ.java | 649 ++
.../commons/math4/legacy/special/package-info.java | 20 +
.../commons/math4/legacy/stat/Frequency.java | 390 ++
.../commons/math4/legacy/stat/StatUtils.java | 856 +++
.../math4/legacy/stat/correlation/Covariance.java | 290 +
.../stat/correlation/KendallsCorrelation.java | 273 +
.../stat/correlation/PearsonsCorrelation.java | 330 ++
.../stat/correlation/SpearmansCorrelation.java | 203 +
.../correlation/StorelessBivariateCovariance.java | 138 +
.../stat/correlation/StorelessCovariance.java | 229 +
.../legacy/stat/correlation/package-info.java | 22 +
.../AbstractStorelessUnivariateStatistic.java | 192 +
.../descriptive/AbstractUnivariateStatistic.java | 132 +
.../descriptive/AggregateSummaryStatistics.java | 429 ++
.../stat/descriptive/DescriptiveStatistics.java | 802 +++
.../descriptive/MultivariateSummaryStatistics.java | 646 ++
.../StatisticalMultivariateSummary.java | 119 +
.../stat/descriptive/StatisticalSummary.java | 64 +
.../stat/descriptive/StatisticalSummaryValues.java | 193 +
.../descriptive/StorelessUnivariateStatistic.java | 91 +
.../legacy/stat/descriptive/SummaryStatistics.java | 772 +++
.../SynchronizedDescriptiveStatistics.java | 192 +
.../SynchronizedMultivariateSummaryStatistics.java | 297 +
.../descriptive/SynchronizedSummaryStatistics.java | 366 ++
.../stat/descriptive/UnivariateStatistic.java | 56 +
.../stat/descriptive/WeightedEvaluation.java | 57 +
.../stat/descriptive/moment/FirstMoment.java | 166 +
.../stat/descriptive/moment/FourthMoment.java | 150 +
.../stat/descriptive/moment/GeometricMean.java | 209 +
.../legacy/stat/descriptive/moment/Kurtosis.java | 226 +
.../math4/legacy/stat/descriptive/moment/Mean.java | 288 +
.../stat/descriptive/moment/SecondMoment.java | 132 +
.../stat/descriptive/moment/SemiVariance.java | 363 ++
.../legacy/stat/descriptive/moment/Skewness.java | 227 +
.../stat/descriptive/moment/StandardDeviation.java | 277 +
.../stat/descriptive/moment/ThirdMoment.java | 148 +
.../legacy/stat/descriptive/moment/Variance.java | 627 ++
.../descriptive/moment/VectorialCovariance.java | 157 +
.../stat/descriptive/moment/VectorialMean.java | 105 +
.../stat/descriptive/moment/package-info.java | 20 +
.../legacy/stat/descriptive/package-info.java | 44 +
.../math4/legacy/stat/descriptive/rank/Max.java | 170 +
.../math4/legacy/stat/descriptive/rank/Median.java | 96 +
.../math4/legacy/stat/descriptive/rank/Min.java | 170 +
.../stat/descriptive/rank/PSquarePercentile.java | 990 ++++
.../legacy/stat/descriptive/rank/Percentile.java | 1382 +++++
.../legacy/stat/descriptive/rank/package-info.java | 20 +
.../legacy/stat/descriptive/summary/Product.java | 231 +
.../math4/legacy/stat/descriptive/summary/Sum.java | 225 +
.../legacy/stat/descriptive/summary/SumOfLogs.java | 171 +
.../stat/descriptive/summary/SumOfSquares.java | 160 +
.../stat/descriptive/summary/package-info.java | 20 +
.../stat/inference/AlternativeHypothesis.java | 40 +
.../math4/legacy/stat/inference/BinomialTest.java | 163 +
.../math4/legacy/stat/inference/ChiSquareTest.java | 602 ++
.../commons/math4/legacy/stat/inference/GTest.java | 538 ++
.../legacy/stat/inference/InferenceTestUtils.java | 745 +++
.../stat/inference/KolmogorovSmirnovTest.java | 1228 ++++
.../legacy/stat/inference/MannWhitneyUTest.java | 236 +
.../math4/legacy/stat/inference/OneWayAnova.java | 355 ++
.../commons/math4/legacy/stat/inference/TTest.java | 1183 ++++
.../stat/inference/WilcoxonSignedRankTest.java | 323 +
.../math4/legacy/stat/inference/package-info.java | 22 +
.../legacy/stat/interval/AgrestiCoullInterval.java | 49 +
.../stat/interval/BinomialConfidenceInterval.java | 61 +
.../stat/interval/ClopperPearsonInterval.java | 60 +
.../legacy/stat/interval/ConfidenceInterval.java | 108 +
.../math4/legacy/stat/interval/IntervalUtils.java | 173 +
.../stat/interval/NormalApproximationInterval.java | 45 +
.../legacy/stat/interval/WilsonScoreInterval.java | 51 +
.../math4/legacy/stat/interval/package-info.java | 22 +
.../commons/math4/legacy/stat/package-info.java | 20 +
.../math4/legacy/stat/ranking/NaNStrategy.java | 55 +
.../math4/legacy/stat/ranking/NaturalRanking.java | 478 ++
.../legacy/stat/ranking/RankingAlgorithm.java | 40 +
.../math4/legacy/stat/ranking/TiesStrategy.java | 54 +
.../math4/legacy/stat/ranking/package-info.java | 22 +
.../AbstractMultipleLinearRegression.java | 386 ++
.../regression/GLSMultipleLinearRegression.java | 135 +
.../stat/regression/MillerUpdatingRegression.java | 1108 ++++
.../regression/ModelSpecificationException.java | 39 +
.../stat/regression/MultipleLinearRegression.java | 69 +
.../regression/OLSMultipleLinearRegression.java | 285 +
.../legacy/stat/regression/RegressionResults.java | 421 ++
.../legacy/stat/regression/SimpleRegression.java | 889 +++
.../UpdatingMultipleLinearRegression.java | 93 +
.../math4/legacy/stat/regression/package-info.java | 22 +
.../math4/legacy/transform/DctNormalization.java | 66 +
.../math4/legacy/transform/DftNormalization.java | 56 +
.../math4/legacy/transform/DstNormalization.java | 56 +
.../legacy/transform/FastCosineTransformer.java | 183 +
.../legacy/transform/FastFourierTransformer.java | 416 ++
.../legacy/transform/FastHadamardTransformer.java | 325 ++
.../legacy/transform/FastSineTransformer.java | 182 +
.../math4/legacy/transform/RealTransformer.java | 67 +
.../math4/legacy/transform/TransformType.java | 30 +
.../math4/legacy/transform/TransformUtils.java | 163 +
.../math4/legacy/transform/package-info.java | 22 +
.../apache/commons/math4/legacy/util/BigReal.java | 334 ++
.../commons/math4/legacy/util/BigRealField.java | 86 +
.../math4/legacy/util/CentralPivotingStrategy.java | 47 +
.../math4/legacy/util/CombinatoricsUtils.java | 125 +
.../commons/math4/legacy/util/CompositeFormat.java | 218 +
.../commons/math4/legacy/util/Decimal64.java | 754 +++
.../commons/math4/legacy/util/Decimal64Field.java | 64 +
.../math4/legacy/util/DefaultTransformer.java | 81 +
.../commons/math4/legacy/util/DoubleArray.java | 110 +
.../apache/commons/math4/legacy/util/FastMath.java | 4351 ++++++++++++++
.../commons/math4/legacy/util/FastMathCalc.java | 658 +++
.../math4/legacy/util/FastMathLiteralArrays.java | 6175 ++++++++++++++++++++
.../commons/math4/legacy/util/IntegerSequence.java | 376 ++
.../commons/math4/legacy/util/IterationEvent.java | 55 +
.../math4/legacy/util/IterationListener.java | 57 +
.../math4/legacy/util/IterationManager.java | 185 +
.../commons/math4/legacy/util/KthSelector.java | 157 +
.../commons/math4/legacy/util/MathArrays.java | 1284 ++++
.../commons/math4/legacy/util/MathUtils.java | 284 +
.../legacy/util/MedianOf3PivotingStrategy.java | 64 +
.../math4/legacy/util/NumberTransformer.java | 38 +
.../math4/legacy/util/OpenIntToDoubleHashMap.java | 596 ++
.../math4/legacy/util/OpenIntToFieldHashMap.java | 617 ++
.../org/apache/commons/math4/legacy/util/Pair.java | 156 +
.../legacy/util/PivotingStrategyInterface.java | 44 +
.../math4/legacy/util/RandomPivotingStrategy.java | 101 +
.../math4/legacy/util/ResizableDoubleArray.java | 849 +++
.../commons/math4/legacy/util/TransformerMap.java | 190 +
.../commons/math4/legacy/util/package-info.java | 20 +
.../exception/util/LocalizedFormats_en.properties | 0
.../exception/util/LocalizedFormats_fr.properties | 343 ++
.../math4/legacy}/random/new-joe-kuo-6.21201 | 0
.../src}/test/R/ChiSquareDistributionTestCases.R | 0
.../src}/test/R/FDistributionTestCases.R | 0
.../src}/test/R/GammaDistributionTestCases.R | 0
.../R/KolmogorovSmirnovDistributionTestCases.R | 0
.../src}/test/R/KolmogorovSmirnovTestCases.R | 0
.../src}/test/R/LevyDistributionTestCases.R | 0
{src => commons-math-legacy/src}/test/R/README.txt | 0
.../src}/test/R/TDistributionTestCases.R | 0
{src => commons-math-legacy/src}/test/R/TTestCases | 0
.../src}/test/R/WeibullDistributionTestCases.R | 0
.../src}/test/R/anovaTestCases | 0
.../src}/test/R/binomialTestCases | 0
.../src}/test/R/cauchyTestCases.R | 0
.../src}/test/R/chiSquareTestCases | 0
.../src}/test/R/correlationTestCases | 0
.../src}/test/R/covarianceTestCases | 0
.../src}/test/R/descriptiveTestCases | 0
.../src}/test/R/exponentialTestCases | 0
.../src}/test/R/geometricTestCases | 0
.../src}/test/R/gumbelTestCases.R | 0
.../src}/test/R/hypergeometricTestCases | 0
.../src}/test/R/laplaceTestCases.R | 0
.../src}/test/R/logNormalTestCases | 0
.../src}/test/R/logisticsTestCases.R | 0
.../src}/test/R/multipleOLSRegressionTestCases | 0
.../src}/test/R/nakagamiTestCases.R | 0
.../src}/test/R/normalTestCases | 0
.../src}/test/R/paretoTestCases | 0
.../src}/test/R/pascalTestCases | 0
.../src}/test/R/poissonTestCases | 0
.../src}/test/R/regressionTestCases | 0
{src => commons-math-legacy/src}/test/R/testAll | 0
.../src}/test/R/testFunctions | 0
.../src}/test/R/zipfTestCases | 0
.../legacy/ExtendedFieldElementAbstractTest.java | 540 ++
.../apache/commons/math4/legacy/PerfTestUtils.java | 384 ++
.../org/apache/commons/math4/legacy/Retry.java | 29 +
.../apache/commons/math4/legacy/RetryRunner.java | 81 +
.../commons/math4/legacy/RetryRunnerTest.java | 54 +
.../org/apache/commons/math4/legacy/TestUtils.java | 586 ++
.../math4/legacy/analysis/FunctionUtilsTest.java | 431 ++
.../math4/legacy/analysis/MonitoredFunction.java | 48 +
.../math4/legacy/analysis/QuinticFunction.java | 41 +
.../math4/legacy/analysis/SumSincFunction.java | 55 +
.../math4/legacy/analysis/XMinus5Function.java | 41 +
.../analysis/differentiation/DSCompilerTest.java | 477 ++
.../differentiation/DerivativeStructureTest.java | 1632 ++++++
.../FiniteDifferencesDifferentiatorTest.java | 413 ++
.../differentiation/GradientFunctionTest.java | 90 +
.../differentiation/JacobianFunctionTest.java | 97 +
.../differentiation/SparseGradientTest.java | 1131 ++++
.../analysis/function/BivariateFunctionTest.java | 44 +
.../legacy/analysis/function/GaussianTest.java | 161 +
.../analysis/function/HarmonicOscillatorTest.java | 139 +
.../legacy/analysis/function/LogisticTest.java | 199 +
.../math4/legacy/analysis/function/LogitTest.java | 227 +
.../legacy/analysis/function/SigmoidTest.java | 110 +
.../math4/legacy/analysis/function/SincTest.java | 122 +
.../math4/legacy/analysis/function/SqrtTest.java | 72 +
.../legacy/analysis/function/StepFunctionTest.java | 115 +
.../UnivariateDifferentiableFunctionTest.java | 227 +
.../analysis/function/UnivariateFunctionTest.java | 124 +
.../IterativeLegendreGaussIntegratorTest.java | 171 +
.../integration/MidPointIntegratorTest.java | 175 +
.../integration/RombergIntegratorTest.java | 123 +
.../integration/SimpsonIntegratorTest.java | 385 ++
.../integration/TrapezoidIntegratorTest.java | 123 +
.../integration/gauss/BaseRuleFactoryTest.java | 113 +
.../integration/gauss/GaussIntegratorTest.java | 74 +
.../gauss/GaussianQuadratureAbstractTest.java | 116 +
.../integration/gauss/HermiteParametricTest.java | 96 +
.../analysis/integration/gauss/HermiteTest.java | 112 +
.../analysis/integration/gauss/LaguerreTest.java | 50 +
.../gauss/LegendreHighPrecisionParametricTest.java | 85 +
.../gauss/LegendreHighPrecisionTest.java | 58 +
.../integration/gauss/LegendreParametricTest.java | 85 +
.../analysis/integration/gauss/LegendreTest.java | 58 +
.../interpolation/AkimaSplineInterpolatorTest.java | 267 +
.../BicubicInterpolatingFunctionTest.java | 391 ++
.../interpolation/BicubicInterpolatorTest.java | 178 +
.../DividedDifferenceInterpolatorTest.java | 146 +
.../FieldHermiteInterpolatorTest.java | 276 +
.../interpolation/HermiteInterpolatorTest.java | 257 +
.../interpolation/LinearInterpolatorTest.java | 147 +
.../interpolation/LoessInterpolatorTest.java | 259 +
.../MicrosphereProjectionInterpolatorTest.java | 149 +
.../interpolation/NevilleInterpolatorTest.java | 146 +
...wiseBicubicSplineInterpolatingFunctionTest.java | 271 +
.../PiecewiseBicubicSplineInterpolatorTest.java | 229 +
.../interpolation/SplineInterpolatorTest.java | 223 +
.../TricubicInterpolatingFunctionTest.java | 653 +++
.../interpolation/TricubicInterpolatorTest.java | 227 +
.../UnivariatePeriodicInterpolatorTest.java | 163 +
.../PolynomialFunctionLagrangeFormTest.java | 153 +
.../PolynomialFunctionNewtonFormTest.java | 178 +
.../polynomials/PolynomialFunctionTest.java | 263 +
.../polynomials/PolynomialSplineFunctionTest.java | 187 +
.../analysis/polynomials/PolynomialsUtilsTest.java | 394 ++
.../solvers/BaseSecantSolverAbstractTest.java | 259 +
.../analysis/solvers/BisectionSolverTest.java | 90 +
.../solvers/BracketingNthOrderBrentSolverTest.java | 214 +
.../legacy/analysis/solvers/BrentSolverTest.java | 268 +
.../FieldBracketingNthOrderBrentSolverTest.java | 180 +
.../analysis/solvers/IllinoisSolverTest.java | 36 +
.../analysis/solvers/LaguerreSolverTest.java | 159 +
.../legacy/analysis/solvers/MullerSolver2Test.java | 145 +
.../legacy/analysis/solvers/MullerSolverTest.java | 148 +
.../analysis/solvers/NewtonRaphsonSolverTest.java | 90 +
.../legacy/analysis/solvers/PegasusSolverTest.java | 36 +
.../analysis/solvers/RegulaFalsiSolverTest.java | 60 +
.../legacy/analysis/solvers/RiddersSolverTest.java | 141 +
.../legacy/analysis/solvers/SecantSolverTest.java | 39 +
.../solvers/UnivariateSolverUtilsTest.java | 217 +
.../legacy/complex/ComplexFormatAbstractTest.java | 416 ++
.../math4/legacy/complex/ComplexFormatTest.java | 33 +
.../legacy/complex/FrenchComplexFormatTest.java | 34 +
.../apache/commons/math4/legacy/dfp/Decimal10.java | 99 +
.../commons/math4/legacy/dfp/DfpDecTest.java | 566 ++
.../commons/math4/legacy/dfp/DfpMathTest.java | 588 ++
.../apache/commons/math4/legacy/dfp/DfpTest.java | 1674 ++++++
.../AbstractIntegerDistributionTest.java | 130 +
.../distribution/AbstractRealDistributionTest.java | 211 +
.../distribution/EmpiricalDistributionTest.java | 689 +++
.../EnumeratedIntegerDistributionTest.java | 198 +
.../EnumeratedRealDistributionTest.java | 254 +
.../IntegerDistributionAbstractTest.java | 426 ++
.../MixtureMultivariateNormalDistributionTest.java | 265 +
.../MultivariateNormalDistributionTest.java | 156 +
.../distribution/RealDistributionAbstractTest.java | 515 ++
...teNormalMixtureExpectationMaximizationTest.java | 349 ++
.../exception/DimensionMismatchExceptionTest.java | 33 +
.../exception/MaxCountExceededExceptionTest.java | 32 +
.../NonMonotonicSequenceExceptionTest.java | 45 +
.../legacy/exception/NotPositiveExceptionTest.java | 34 +
.../NotStrictlyPositiveExceptionTest.java | 34 +
.../exception/NumberIsTooLargeExceptionTest.java | 34 +
.../exception/NumberIsTooSmallExceptionTest.java | 34 +
.../legacy/exception/OutOfRangeExceptionTest.java | 34 +
.../exception/TooManyEvaluationsExceptionTest.java | 39 +
.../math4/legacy/exception/util/ArgUtilsTest.java | 75 +
.../exception/util/ExceptionContextTest.java | 130 +
.../exception/util/LocalizedFormatsTest.java | 104 +
.../field/linalg/FP64FieldDenseMatrixTest.java | 285 +
.../field/linalg/FieldLUDecompositionTest.java | 314 +
.../math4/legacy/filter/KalmanFilterTest.java | 442 ++
.../legacy/fitting/GaussianCurveFitterTest.java | 424 ++
.../legacy/fitting/HarmonicCurveFitterTest.java | 182 +
.../legacy/fitting/PolynomialCurveFitterTest.java | 167 +
.../legacy/fitting/SimpleCurveFitterTest.java | 59 +
.../legacy/fitting/WeightedObservedPointsTest.java | 126 +
.../AbstractLeastSquaresOptimizerAbstractTest.java | 607 ++
.../fitting/leastsquares/BevingtonProblem.java | 79 +
.../legacy/fitting/leastsquares/CircleProblem.java | 178 +
.../fitting/leastsquares/CircleVectorial.java | 97 +
...atorVectorMultivariateJacobianFunctionTest.java | 154 +
.../leastsquares/EvaluationRmsCheckerTest.java | 103 +
.../fitting/leastsquares/EvaluationTest.java | 335 ++
.../leastsquares/EvaluationTestValidation.java | 304 +
.../GaussNewtonOptimizerWithCholeskyTest.java | 133 +
.../GaussNewtonOptimizerWithLUTest.java | 133 +
.../GaussNewtonOptimizerWithQRTest.java | 119 +
.../GaussNewtonOptimizerWithSVDTest.java | 151 +
.../LevenbergMarquardtOptimizerTest.java | 350 ++
.../legacy/fitting/leastsquares/MinpackTest.java | 1484 +++++
.../leastsquares/RandomCirclePointGenerator.java | 88 +
.../RandomStraightLinePointGenerator.java | 97 +
.../leastsquares/StatisticalReferenceDataset.java | 373 ++
.../StatisticalReferenceDatasetFactory.java | 202 +
.../fitting/leastsquares/StraightLineProblem.java | 169 +
.../legacy/genetics/BinaryChromosomeTest.java | 66 +
.../math4/legacy/genetics/BinaryMutationTest.java | 45 +
.../math4/legacy/genetics/ChromosomeTest.java | 120 +
.../math4/legacy/genetics/CycleCrossoverTest.java | 151 +
.../legacy/genetics/DummyBinaryChromosome.java | 45 +
.../math4/legacy/genetics/DummyListChromosome.java | 79 +
.../math4/legacy/genetics/DummyRandomKey.java | 45 +
.../genetics/ElitisticListPopulationTest.java | 106 +
.../math4/legacy/genetics/FitnessCachingTest.java | 95 +
.../legacy/genetics/FixedElapsedTimeTest.java | 80 +
.../legacy/genetics/FixedGenerationCountTest.java | 70 +
.../genetics/GeneticAlgorithmTestBinary.java | 125 +
.../genetics/GeneticAlgorithmTestPermutations.java | 133 +
.../math4/legacy/genetics/ListPopulationTest.java | 220 +
.../math4/legacy/genetics/NPointCrossoverTest.java | 131 +
.../legacy/genetics/OnePointCrossoverTest.java | 61 +
.../legacy/genetics/OrderedCrossoverTest.java | 104 +
.../legacy/genetics/RandomKeyMutationTest.java | 44 +
.../math4/legacy/genetics/RandomKeyTest.java | 173 +
.../legacy/genetics/TournamentSelectionTest.java | 57 +
.../legacy/genetics/UniformCrossoverTest.java | 153 +
.../legacy/linear/Array2DRowRealMatrixTest.java | 1171 ++++
.../math4/legacy/linear/ArrayFieldVectorTest.java | 1265 ++++
.../math4/legacy/linear/ArrayRealVectorTest.java | 172 +
.../legacy/linear/BiDiagonalTransformerTest.java | 201 +
.../math4/legacy/linear/BlockFieldMatrixTest.java | 1391 +++++
.../math4/legacy/linear/BlockRealMatrixTest.java | 1280 ++++
.../legacy/linear/CholeskyDecompositionTest.java | 138 +
.../math4/legacy/linear/CholeskySolverTest.java | 112 +
.../math4/legacy/linear/ConjugateGradientTest.java | 622 ++
.../apache/commons/math4/legacy/linear/Dfp25.java | 41 +
.../math4/legacy/linear/DiagonalMatrixTest.java | 368 ++
.../legacy/linear/EigenComplexSolverTest.java_NEW | 322 +
.../legacy/linear/EigenDecompositionTest.java | 785 +++
.../math4/legacy/linear/EigenSolverTest.java | 199 +
.../legacy/linear/FieldLUDecompositionTest.java | 301 +
.../math4/legacy/linear/FieldLUSolverTest.java | 176 +
.../math4/legacy/linear/FieldMatrixImplTest.java | 1158 ++++
.../legacy/linear/FrenchRealVectorFormatTest.java | 34 +
.../legacy/linear/HessenbergTransformerTest.java | 225 +
.../commons/math4/legacy/linear/HilbertMatrix.java | 75 +
.../math4/legacy/linear/InverseHilbertMatrix.java | 100 +
.../math4/legacy/linear/LUDecompositionTest.java | 291 +
.../commons/math4/legacy/linear/LUSolverTest.java | 168 +
.../MatrixDimensionMismatchExceptionTest.java | 36 +
.../math4/legacy/linear/MatrixUtilsTest.java | 488 ++
.../math4/legacy/linear/OpenMapRealMatrixTest.java | 49 +
.../math4/legacy/linear/QRDecompositionTest.java | 285 +
.../commons/math4/legacy/linear/QRSolverTest.java | 195 +
.../math4/legacy/linear/RRQRDecompositionTest.java | 257 +
.../math4/legacy/linear/RRQRSolverTest.java | 201 +
.../linear/RealMatrixFormatAbstractTest.java | 362 ++
.../math4/legacy/linear/RealMatrixFormatTest.java | 34 +
.../legacy/linear/RealVectorAbstractTest.java | 2008 +++++++
.../linear/RealVectorFormatAbstractTest.java | 354 ++
.../math4/legacy/linear/RealVectorFormatTest.java | 34 +
.../math4/legacy/linear/RealVectorTest.java | 233 +
.../RectangularCholeskyDecompositionTest.java | 114 +
.../math4/legacy/linear/SchurTransformerTest.java | 206 +
.../linear/SingularValueDecompositionTest.java | 331 ++
.../legacy/linear/SingularValueSolverTest.java | 158 +
.../math4/legacy/linear/SparseFieldMatrixTest.java | 700 +++
.../math4/legacy/linear/SparseFieldVectorTest.java | 816 +++
.../math4/legacy/linear/SparseRealMatrixTest.java | 697 +++
.../math4/legacy/linear/SparseRealVectorTest.java | 150 +
.../commons/math4/legacy/linear/SymmLQTest.java | 700 +++
.../legacy/linear/TriDiagonalTransformerTest.java | 177 +
.../linear/UnmodifiableArrayRealVectorTest.java | 39 +
.../linear/UnmodifiableOpenMapRealVectorTest.java | 45 +
.../linear/UnmodifiableRealVectorAbstractTest.java | 455 ++
.../legacy/ml/clustering/DBSCANClustererTest.java | 190 +
.../ml/clustering/FuzzyKMeansClustererTest.java | 135 +
.../ml/clustering/KMeansPlusPlusClustererTest.java | 188 +
.../clustering/MiniBatchKMeansClustererTest.java | 181 +
.../MultiKMeansPlusPlusClustererTest.java | 98 +
.../evaluation/CalinskiHarabaszTest.java | 165 +
.../evaluation/SumOfClusterVariancesTest.java | 81 +
.../legacy/ml/distance/CanberraDistanceTest.java | 48 +
.../legacy/ml/distance/ChebyshevDistanceTest.java | 42 +
.../ml/distance/EarthMoversDistanceTest.java | 48 +
.../legacy/ml/distance/EuclideanDistanceTest.java | 43 +
.../legacy/ml/distance/ManhattanDistanceTest.java | 42 +
.../math4/legacy/ml/neuralnet/MapRankingTest.java | 119 +
.../math4/legacy/ml/neuralnet/NetworkTest.java | 209 +
.../math4/legacy/ml/neuralnet/NeuronTest.java | 139 +
.../ml/neuralnet/OffsetFeatureInitializer.java | 48 +
.../legacy/ml/neuralnet/oned/NeuronStringTest.java | 184 +
.../ml/neuralnet/sofm/KohonenTrainingTaskTest.java | 221 +
.../ml/neuralnet/sofm/KohonenUpdateActionTest.java | 93 +
.../sofm/LearningFactorFunctionFactoryTest.java | 94 +
.../sofm/NeighbourhoodSizeFunctionFactoryTest.java | 83 +
.../neuralnet/sofm/TravellingSalesmanSolver.java | 427 ++
.../sofm/util/ExponentialDecayFunctionTest.java | 57 +
.../sofm/util/QuasiSigmoidDecayFunctionTest.java | 54 +
.../ml/neuralnet/twod/NeuronSquareMesh2DTest.java | 914 +++
.../ml/neuralnet/twod/util/LocationFinderTest.java | 69 +
.../legacy/ode/ContinuousOutputFieldModelTest.java | 229 +
.../legacy/ode/ContinuousOutputModelTest.java | 206 +
.../math4/legacy/ode/FieldExpandableODETest.java | 345 ++
.../math4/legacy/ode/FirstOrderConverterTest.java | 114 +
.../math4/legacy/ode/JacobianMatricesTest.java | 619 ++
.../math4/legacy/ode/TestFieldProblem1.java | 79 +
.../math4/legacy/ode/TestFieldProblem2.java | 78 +
.../math4/legacy/ode/TestFieldProblem3.java | 124 +
.../math4/legacy/ode/TestFieldProblem4.java | 168 +
.../math4/legacy/ode/TestFieldProblem5.java | 41 +
.../math4/legacy/ode/TestFieldProblem6.java | 84 +
.../math4/legacy/ode/TestFieldProblemAbstract.java | 204 +
.../math4/legacy/ode/TestFieldProblemHandler.java | 156 +
.../commons/math4/legacy/ode/TestProblem1.java | 74 +
.../commons/math4/legacy/ode/TestProblem2.java | 76 +
.../commons/math4/legacy/ode/TestProblem3.java | 113 +
.../commons/math4/legacy/ode/TestProblem4.java | 151 +
.../commons/math4/legacy/ode/TestProblem5.java | 34 +
.../commons/math4/legacy/ode/TestProblem6.java | 75 +
.../math4/legacy/ode/TestProblemAbstract.java | 162 +
.../math4/legacy/ode/TestProblemHandler.java | 161 +
.../math4/legacy/ode/events/CloseEventsTest.java | 133 +
.../math4/legacy/ode/events/EventFilterTest.java | 275 +
.../math4/legacy/ode/events/EventStateTest.java | 297 +
.../legacy/ode/events/OverlappingEventsTest.java | 174 +
.../legacy/ode/events/ReappearingEventTest.java | 101 +
...tractEmbeddedRungeKuttaFieldIntegratorTest.java | 616 ++
.../AbstractRungeKuttaFieldIntegratorTest.java | 682 +++
.../AdamsBashforthFieldIntegratorTest.java | 86 +
.../ode/nonstiff/AdamsBashforthIntegratorTest.java | 302 +
.../nonstiff/AdamsFieldIntegratorAbstractTest.java | 265 +
.../nonstiff/AdamsMoultonFieldIntegratorTest.java | 86 +
.../ode/nonstiff/AdamsMoultonIntegratorTest.java | 289 +
.../nonstiff/AdamsNordsieckTransformerTest.java | 120 +
...lassicalRungKuttaFieldStepInterpolatorTest.java | 68 +
.../ClassicalRungeKuttaFieldIntegratorTest.java | 104 +
.../ClassicalRungeKuttaIntegratorTest.java | 354 ++
.../ClassicalRungeKuttaStepInterpolatorTest.java | 98 +
.../DormandPrince54FieldIntegratorTest.java | 99 +
.../DormandPrince54FieldStepInterpolatorTest.java | 68 +
.../nonstiff/DormandPrince54IntegratorTest.java | 360 ++
.../DormandPrince54StepInterpolatorTest.java | 155 +
.../DormandPrince853FieldIntegratorTest.java | 99 +
.../DormandPrince853FieldStepInterpolatorTest.java | 68 +
.../nonstiff/DormandPrince853IntegratorTest.java | 499 ++
.../DormandPrince853StepInterpolatorTest.java | 155 +
...eddedRungeKuttaFieldIntegratorAbstractTest.java | 616 ++
.../ode/nonstiff/EulerFieldIntegratorTest.java | 105 +
.../nonstiff/EulerFieldStepInterpolatorTest.java | 67 +
.../legacy/ode/nonstiff/EulerIntegratorTest.java | 197 +
.../ode/nonstiff/EulerStepInterpolatorTest.java | 194 +
.../ode/nonstiff/GillFieldIntegratorTest.java | 104 +
.../nonstiff/GillFieldStepInterpolatorTest.java | 68 +
.../legacy/ode/nonstiff/GillIntegratorTest.java | 253 +
.../ode/nonstiff/GillStepInterpolatorTest.java | 98 +
.../nonstiff/GraggBulirschStoerIntegratorTest.java | 436 ++
.../GraggBulirschStoerStepInterpolatorTest.java | 157 +
.../nonstiff/HighamHall54FieldIntegratorTest.java | 99 +
.../HighamHall54FieldStepInterpolatorTest.java | 68 +
.../ode/nonstiff/HighamHall54IntegratorTest.java | 377 ++
.../nonstiff/HighamHall54StepInterpolatorTest.java | 155 +
.../ode/nonstiff/LutherFieldIntegratorTest.java | 123 +
.../nonstiff/LutherFieldStepInterpolatorTest.java | 68 +
.../legacy/ode/nonstiff/LutherIntegratorTest.java | 344 ++
.../ode/nonstiff/LutherStepInterpolatorTest.java | 98 +
.../ode/nonstiff/MidpointFieldIntegratorTest.java | 104 +
.../MidpointFieldStepInterpolatorTest.java | 68 +
.../ode/nonstiff/MidpointIntegratorTest.java | 197 +
.../ode/nonstiff/MidpointStepInterpolatorTest.java | 99 +
.../RungeKuttaFieldIntegratorAbstractTest.java | 682 +++
...ungeKuttaFieldStepInterpolatorAbstractTest.java | 308 +
.../legacy/ode/nonstiff/StepFieldProblem.java | 85 +
.../math4/legacy/ode/nonstiff/StepProblem.java | 71 +
.../nonstiff/ThreeEighthesFieldIntegratorTest.java | 104 +
.../ThreeEighthesFieldStepInterpolatorTest.java | 68 +
.../ode/nonstiff/ThreeEighthesIntegratorTest.java | 247 +
.../ThreeEighthesStepInterpolatorTest.java | 98 +
.../ode/sampling/DummyFieldStepInterpolator.java | 55 +
.../legacy/ode/sampling/DummyStepInterpolator.java | 153 +
.../ode/sampling/DummyStepInterpolatorTest.java | 136 +
.../sampling/NordsieckStepInterpolatorTest.java | 96 +
.../ode/sampling/StepInterpolatorTestUtils.java | 146 +
.../sampling/StepNormalizerOutputOverlapTest.java | 69 +
.../ode/sampling/StepNormalizerOutputTest.java | 69 +
.../ode/sampling/StepNormalizerOutputTestBase.java | 286 +
.../legacy/ode/sampling/StepNormalizerTest.java | 130 +
.../math4/legacy/optim/PointValuePairTest.java | 35 +
.../legacy/optim/PointVectorValuePairTest.java | 39 +
.../math4/legacy/optim/SimplePointCheckerTest.java | 53 +
.../math4/legacy/optim/SimpleValueCheckerTest.java | 52 +
.../legacy/optim/SimpleVectorValueCheckerTest.java | 53 +
.../legacy/optim/linear/SimplexSolverTest.java | 905 +++
.../legacy/optim/linear/SimplexTableauTest.java | 109 +
.../MultiStartMultivariateOptimizerTest.java | 134 +
.../MultivariateFunctionMappingAdapterTest.java | 193 +
.../MultivariateFunctionPenaltyAdapterTest.java | 203 +
.../nonlinear/scalar/gradient/CircleScalar.java | 87 +
.../NonLinearConjugateGradientOptimizerTest.java | 480 ++
.../scalar/noderiv/BOBYQAOptimizerTest.java | 355 ++
.../scalar/noderiv/CMAESOptimizerTest.java | 852 +++
.../nonlinear/scalar/noderiv/OptimTestUtils.java | 397 ++
.../scalar/noderiv/PowellOptimizerTest.java | 272 +
.../SimplexOptimizerMultiDirectionalTest.java | 337 ++
.../SimplexOptimizerMultiDirectionalTest.java.NEW | 409 ++
.../noderiv/SimplexOptimizerNelderMeadTest.java | 423 ++
.../legacy/optim/univariate/BracketFinderTest.java | 121 +
.../optim/univariate/BrentOptimizerTest.java | 303 +
.../MultiStartUnivariateOptimizerTest.java | 127 +
.../SimpleUnivariateValueCheckerTest.java | 52 +
.../CorrelatedRandomVectorGeneratorTest.java | 192 +
.../legacy/random/GaussianRandomGeneratorTest.java | 38 +
.../legacy/random/HaltonSequenceGeneratorTest.java | 134 +
.../RandomUtilsDataGeneratorAbstractTest.java | 303 +
.../RandomUtilsDataGeneratorJDKRandomTest.java | 31 +
.../legacy/random/SobolSequenceGeneratorTest.java | 107 +
.../legacy/random/StableRandomGeneratorTest.java | 130 +
.../random/SynchronizedRandomGeneratorTest.java | 120 +
.../UncorrelatedRandomVectorGeneratorTest.java | 65 +
.../legacy/random/UniformRandomGeneratorTest.java | 40 +
.../commons/math4/legacy/special/BesselJTest.java | 775 +++
.../math4/legacy/stat/CertifiedDataTest.java | 149 +
.../commons/math4/legacy/stat/FrequencyTest.java | 354 ++
.../commons/math4/legacy/stat/StatUtilsTest.java | 556 ++
.../math4/legacy/stat/StatUtilsTest.java.orig | 0
.../legacy/stat/correlation/CovarianceTest.java | 253 +
.../stat/correlation/KendallsCorrelationTest.java | 280 +
.../stat/correlation/PearsonsCorrelationTest.java | 318 +
.../correlation/SpearmansRankCorrelationTest.java | 163 +
.../stat/correlation/StorelessCovarianceTest.java | 264 +
.../stat/data/CertifiedDataAbstractTest.java | 158 +
.../commons/math4/legacy/stat/data/LewTest.java | 28 +
.../math4/legacy/stat/data/LotteryTest.java | 28 +
.../AggregateSummaryStatisticsTest.java | 341 ++
.../descriptive/DescriptiveStatisticsTest.java | 485 ++
.../stat/descriptive/ListUnivariateImpl.java | 197 +
.../stat/descriptive/ListUnivariateImplTest.java | 157 +
.../descriptive/MixedListUnivariateImplTest.java | 204 +
.../MultivariateSummaryStatisticsTest.java | 321 +
.../descriptive/StatisticalSummaryValuesTest.java | 82 +
.../StorelessUnivariateStatisticAbstractTest.java | 239 +
.../stat/descriptive/SummaryStatisticsTest.java | 372 ++
.../SynchronizedDescriptiveStatisticsTest.java | 27 +
...chronizedMultivariateSummaryStatisticsTest.java | 27 +
.../SynchronizedSummaryStatisticsTest.java | 26 +
.../UnivariateStatisticAbstractTest.java | 223 +
.../stat/descriptive/moment/FirstMomentTest.java | 111 +
.../stat/descriptive/moment/FourthMomentTest.java | 46 +
.../stat/descriptive/moment/GeometricMeanTest.java | 78 +
.../stat/descriptive/moment/InteractionTest.java | 79 +
.../stat/descriptive/moment/KurtosisTest.java | 64 +
.../legacy/stat/descriptive/moment/MeanTest.java | 67 +
.../stat/descriptive/moment/SecondMomentTest.java | 46 +
.../stat/descriptive/moment/SemiVarianceTest.java | 153 +
.../stat/descriptive/moment/SkewnessTest.java | 63 +
.../descriptive/moment/StandardDeviationTest.java | 95 +
.../stat/descriptive/moment/ThirdMomentTest.java | 46 +
.../stat/descriptive/moment/VarianceTest.java | 117 +
.../moment/VectorialCovarianceTest.java | 91 +
.../stat/descriptive/moment/VectorialMeanTest.java | 86 +
.../legacy/stat/descriptive/rank/MaxTest.java | 73 +
.../legacy/stat/descriptive/rank/MedianTest.java | 115 +
.../legacy/stat/descriptive/rank/MinTest.java | 73 +
.../descriptive/rank/PSquarePercentileTest.java | 763 +++
.../stat/descriptive/rank/PercentileTest.java | 1046 ++++
.../stat/descriptive/summary/ProductTest.java | 91 +
.../stat/descriptive/summary/SumLogTest.java | 84 +
.../legacy/stat/descriptive/summary/SumSqTest.java | 69 +
.../legacy/stat/descriptive/summary/SumTest.java | 81 +
.../legacy/stat/inference/BinomialTestTest.java | 129 +
.../legacy/stat/inference/ChiSquareTestTest.java | 260 +
.../math4/legacy/stat/inference/GTestTest.java | 291 +
.../stat/inference/InferenceTestUtilsTest.java | 554 ++
.../stat/inference/KolmogorovSmirnovTestTest.java | 956 +++
.../stat/inference/MannWhitneyUTestTest.java | 127 +
.../legacy/stat/inference/OneWayAnovaTest.java | 154 +
.../math4/legacy/stat/inference/TTestTest.java | 297 +
.../stat/inference/WilcoxonSignedRankTestTest.java | 183 +
.../stat/interval/AgrestiCoullIntervalTest.java | 40 +
.../BinomialConfidenceIntervalAbstractTest.java | 80 +
.../stat/interval/ClopperPearsonIntervalTest.java | 110 +
.../legacy/stat/interval/IntervalUtilsTest.java | 64 +
.../interval/NormalApproximationIntervalTest.java | 40 +
.../stat/interval/WilsonScoreIntervalTest.java | 45 +
.../legacy/stat/ranking/NaturalRankingTest.java | 271 +
.../GLSMultipleLinearRegressionTest.java | 300 +
.../regression/MillerUpdatingRegressionTest.java | 1110 ++++
.../MultipleLinearRegressionAbstractTest.java | 136 +
.../OLSMultipleLinearRegressionTest.java | 822 +++
.../stat/regression/SimpleRegressionTest.java | 693 +++
.../transform/FastCosineTransformerTest.java | 276 +
.../transform/FastFourierTransformerTest.java | 482 ++
.../transform/FastHadamardTransformerTest.java | 127 +
.../legacy/transform/FastSineTransformerTest.java | 300 +
.../transform/RealTransformerAbstractTest.java | 344 ++
.../math4/legacy/util/BigRealFieldTest.java | 43 +
.../commons/math4/legacy/util/BigRealTest.java | 189 +
.../math4/legacy/util/CombinatoricsUtilsTest.java | 95 +
.../commons/math4/legacy/util/Decimal64Test.java | 426 ++
.../math4/legacy/util/DefaultTransformerTest.java | 104 +
.../math4/legacy/util/DoubleArrayAbstractTest.java | 132 +
.../legacy/util/FastMathStrictComparisonTest.java | 262 +
.../commons/math4/legacy/util/FastMathTest.java | 1965 +++++++
.../math4/legacy/util/IntegerSequenceTest.java | 327 ++
.../commons/math4/legacy/util/KthSelectorTest.java | 56 +
.../commons/math4/legacy/util/MathArraysTest.java | 848 +++
.../commons/math4/legacy/util/MathUtilsTest.java | 348 ++
.../legacy/util/OpenIntToDoubleHashMapTest.java | 332 ++
.../math4/legacy/util/OpenIntToFieldTest.java | 335 ++
.../apache/commons/math4/legacy/util/PairTest.java | 118 +
.../legacy/util/ResizableDoubleArrayTest.java | 581 ++
.../apache/commons/math4/legacy/util/TestBean.java | 71 +
.../math4/legacy/util/TransformerMapTest.java | 122 +
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.../commons/math4/linear/LUDecompositionTest.java | 291 -
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.../math4/linear/RealVectorAbstractTest.java | 2008 -------
.../math4/linear/RealVectorFormatAbstractTest.java | 354 --
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.../linear/SingularValueDecompositionTest.java | 331 --
.../math4/linear/SingularValueSolverTest.java | 158 -
.../math4/linear/SparseFieldMatrixTest.java | 700 ---
.../math4/linear/SparseFieldVectorTest.java | 816 ---
.../commons/math4/linear/SparseRealMatrixTest.java | 697 ---
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.../math4/ml/neuralnet/oned/NeuronStringTest.java | 184 -
.../ml/neuralnet/sofm/KohonenTrainingTaskTest.java | 221 -
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.../neuralnet/sofm/TravellingSalesmanSolver.java | 427 --
.../sofm/util/ExponentialDecayFunctionTest.java | 57 -
.../sofm/util/QuasiSigmoidDecayFunctionTest.java | 54 -
.../ml/neuralnet/twod/NeuronSquareMesh2DTest.java | 914 ---
.../ml/neuralnet/twod/util/LocationFinderTest.java | 69 -
.../math4/ode/ContinuousOutputFieldModelTest.java | 229 -
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.../commons/math4/ode/FieldExpandableODETest.java | 345 --
.../commons/math4/ode/FirstOrderConverterTest.java | 114 -
.../commons/math4/ode/JacobianMatricesTest.java | 619 --
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.../org/apache/commons/math4/ode/TestProblem1.java | 74 -
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.../org/apache/commons/math4/ode/TestProblem4.java | 151 -
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.../commons/math4/ode/TestProblemAbstract.java | 162 -
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.../commons/math4/ode/events/CloseEventsTest.java | 133 -
.../commons/math4/ode/events/EventFilterTest.java | 275 -
.../commons/math4/ode/events/EventStateTest.java | 297 -
.../math4/ode/events/OverlappingEventsTest.java | 174 -
.../math4/ode/events/ReappearingEventTest.java | 101 -
...tractEmbeddedRungeKuttaFieldIntegratorTest.java | 616 --
.../AbstractRungeKuttaFieldIntegratorTest.java | 682 ---
.../AdamsBashforthFieldIntegratorTest.java | 86 -
.../ode/nonstiff/AdamsBashforthIntegratorTest.java | 302 -
.../nonstiff/AdamsFieldIntegratorAbstractTest.java | 265 -
.../nonstiff/AdamsMoultonFieldIntegratorTest.java | 86 -
.../ode/nonstiff/AdamsMoultonIntegratorTest.java | 289 -
.../nonstiff/AdamsNordsieckTransformerTest.java | 120 -
...lassicalRungKuttaFieldStepInterpolatorTest.java | 68 -
.../ClassicalRungeKuttaFieldIntegratorTest.java | 104 -
.../ClassicalRungeKuttaIntegratorTest.java | 354 --
.../ClassicalRungeKuttaStepInterpolatorTest.java | 98 -
.../DormandPrince54FieldIntegratorTest.java | 99 -
.../DormandPrince54FieldStepInterpolatorTest.java | 68 -
.../nonstiff/DormandPrince54IntegratorTest.java | 360 --
.../DormandPrince54StepInterpolatorTest.java | 155 -
.../DormandPrince853FieldIntegratorTest.java | 99 -
.../DormandPrince853FieldStepInterpolatorTest.java | 68 -
.../nonstiff/DormandPrince853IntegratorTest.java | 499 --
.../DormandPrince853StepInterpolatorTest.java | 155 -
...eddedRungeKuttaFieldIntegratorAbstractTest.java | 616 --
.../ode/nonstiff/EulerFieldIntegratorTest.java | 105 -
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.../math4/ode/nonstiff/EulerIntegratorTest.java | 197 -
.../ode/nonstiff/EulerStepInterpolatorTest.java | 194 -
.../ode/nonstiff/GillFieldIntegratorTest.java | 104 -
.../nonstiff/GillFieldStepInterpolatorTest.java | 68 -
.../math4/ode/nonstiff/GillIntegratorTest.java | 253 -
.../ode/nonstiff/GillStepInterpolatorTest.java | 98 -
.../nonstiff/GraggBulirschStoerIntegratorTest.java | 436 --
.../GraggBulirschStoerStepInterpolatorTest.java | 157 -
.../nonstiff/HighamHall54FieldIntegratorTest.java | 99 -
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.../ode/nonstiff/HighamHall54IntegratorTest.java | 377 --
.../nonstiff/HighamHall54StepInterpolatorTest.java | 155 -
.../ode/nonstiff/LutherFieldIntegratorTest.java | 123 -
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.../math4/ode/nonstiff/LutherIntegratorTest.java | 344 --
.../ode/nonstiff/LutherStepInterpolatorTest.java | 98 -
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.../ode/nonstiff/MidpointStepInterpolatorTest.java | 99 -
.../RungeKuttaFieldIntegratorAbstractTest.java | 682 ---
...ungeKuttaFieldStepInterpolatorAbstractTest.java | 308 -
.../math4/ode/nonstiff/StepFieldProblem.java | 85 -
.../commons/math4/ode/nonstiff/StepProblem.java | 71 -
.../nonstiff/ThreeEighthesFieldIntegratorTest.java | 104 -
.../ThreeEighthesFieldStepInterpolatorTest.java | 68 -
.../ode/nonstiff/ThreeEighthesIntegratorTest.java | 247 -
.../ThreeEighthesStepInterpolatorTest.java | 98 -
.../ode/sampling/DummyFieldStepInterpolator.java | 55 -
.../math4/ode/sampling/DummyStepInterpolator.java | 153 -
.../ode/sampling/DummyStepInterpolatorTest.java | 136 -
.../sampling/NordsieckStepInterpolatorTest.java | 96 -
.../ode/sampling/StepInterpolatorTestUtils.java | 146 -
.../sampling/StepNormalizerOutputOverlapTest.java | 69 -
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.../commons/math4/optim/PointValuePairTest.java | 35 -
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.../math4/optim/SimpleVectorValueCheckerTest.java | 53 -
.../math4/optim/linear/SimplexSolverTest.java | 905 ---
.../math4/optim/linear/SimplexTableauTest.java | 109 -
.../MultiStartMultivariateOptimizerTest.java | 134 -
.../MultivariateFunctionMappingAdapterTest.java | 193 -
.../MultivariateFunctionPenaltyAdapterTest.java | 203 -
.../nonlinear/scalar/gradient/CircleScalar.java | 87 -
.../NonLinearConjugateGradientOptimizerTest.java | 480 --
.../scalar/noderiv/BOBYQAOptimizerTest.java | 355 --
.../scalar/noderiv/CMAESOptimizerTest.java | 852 ---
.../nonlinear/scalar/noderiv/OptimTestUtils.java | 397 --
.../scalar/noderiv/PowellOptimizerTest.java | 272 -
.../SimplexOptimizerMultiDirectionalTest.java | 337 --
.../noderiv/SimplexOptimizerNelderMeadTest.java | 423 --
.../math4/optim/univariate/BracketFinderTest.java | 121 -
.../math4/optim/univariate/BrentOptimizerTest.java | 303 -
.../MultiStartUnivariateOptimizerTest.java | 127 -
.../SimpleUnivariateValueCheckerTest.java | 52 -
.../CorrelatedRandomVectorGeneratorTest.java | 192 -
.../math4/random/GaussianRandomGeneratorTest.java | 38 -
.../math4/random/HaltonSequenceGeneratorTest.java | 134 -
.../RandomUtilsDataGeneratorAbstractTest.java | 303 -
.../RandomUtilsDataGeneratorJDKRandomTest.java | 31 -
.../math4/random/SobolSequenceGeneratorTest.java | 107 -
.../math4/random/StableRandomGeneratorTest.java | 130 -
.../random/SynchronizedRandomGeneratorTest.java | 120 -
.../UncorrelatedRandomVectorGeneratorTest.java | 65 -
.../math4/random/UniformRandomGeneratorTest.java | 40 -
.../apache/commons/math4/special/BesselJTest.java | 775 ---
.../commons/math4/stat/CertifiedDataTest.java | 149 -
.../apache/commons/math4/stat/FrequencyTest.java | 354 --
.../math4/stat/correlation/CovarianceTest.java | 253 -
.../stat/correlation/KendallsCorrelationTest.java | 280 -
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.../correlation/SpearmansRankCorrelationTest.java | 163 -
.../stat/correlation/StorelessCovarianceTest.java | 264 -
.../math4/stat/data/CertifiedDataAbstractTest.java | 158 -
.../apache/commons/math4/stat/data/LewTest.java | 28 -
.../commons/math4/stat/data/LotteryTest.java | 28 -
.../AggregateSummaryStatisticsTest.java | 341 --
.../descriptive/DescriptiveStatisticsTest.java | 485 --
.../math4/stat/descriptive/ListUnivariateImpl.java | 197 -
.../stat/descriptive/ListUnivariateImplTest.java | 157 -
.../descriptive/MixedListUnivariateImplTest.java | 204 -
.../MultivariateSummaryStatisticsTest.java | 321 -
.../descriptive/StatisticalSummaryValuesTest.java | 82 -
.../StorelessUnivariateStatisticAbstractTest.java | 239 -
.../stat/descriptive/SummaryStatisticsTest.java | 372 --
.../SynchronizedDescriptiveStatisticsTest.java | 27 -
...chronizedMultivariateSummaryStatisticsTest.java | 27 -
.../SynchronizedSummaryStatisticsTest.java | 26 -
.../UnivariateStatisticAbstractTest.java | 223 -
.../stat/descriptive/moment/FirstMomentTest.java | 111 -
.../stat/descriptive/moment/FourthMomentTest.java | 46 -
.../stat/descriptive/moment/GeometricMeanTest.java | 78 -
.../stat/descriptive/moment/InteractionTest.java | 79 -
.../stat/descriptive/moment/KurtosisTest.java | 64 -
.../math4/stat/descriptive/moment/MeanTest.java | 67 -
.../stat/descriptive/moment/SecondMomentTest.java | 46 -
.../stat/descriptive/moment/SemiVarianceTest.java | 153 -
.../stat/descriptive/moment/SkewnessTest.java | 63 -
.../descriptive/moment/StandardDeviationTest.java | 95 -
.../stat/descriptive/moment/ThirdMomentTest.java | 46 -
.../stat/descriptive/moment/VarianceTest.java | 117 -
.../moment/VectorialCovarianceTest.java | 91 -
.../stat/descriptive/moment/VectorialMeanTest.java | 86 -
.../math4/stat/descriptive/rank/MaxTest.java | 73 -
.../math4/stat/descriptive/rank/MedianTest.java | 115 -
.../math4/stat/descriptive/rank/MinTest.java | 73 -
.../descriptive/rank/PSquarePercentileTest.java | 763 ---
.../stat/descriptive/rank/PercentileTest.java | 1046 ----
.../stat/descriptive/summary/ProductTest.java | 91 -
.../math4/stat/descriptive/summary/SumLogTest.java | 84 -
.../math4/stat/descriptive/summary/SumSqTest.java | 69 -
.../math4/stat/descriptive/summary/SumTest.java | 81 -
.../math4/stat/inference/BinomialTestTest.java | 129 -
.../math4/stat/inference/ChiSquareTestTest.java | 260 -
.../commons/math4/stat/inference/GTestTest.java | 291 -
.../stat/inference/InferenceTestUtilsTest.java | 554 --
.../stat/inference/KolmogorovSmirnovTestTest.java | 956 ---
.../math4/stat/inference/MannWhitneyUTestTest.java | 127 -
.../math4/stat/inference/OneWayAnovaTest.java | 154 -
.../commons/math4/stat/inference/TTestTest.java | 297 -
.../stat/inference/WilcoxonSignedRankTestTest.java | 183 -
.../stat/interval/AgrestiCoullIntervalTest.java | 40 -
.../BinomialConfidenceIntervalAbstractTest.java | 80 -
.../stat/interval/ClopperPearsonIntervalTest.java | 110 -
.../math4/stat/interval/IntervalUtilsTest.java | 64 -
.../interval/NormalApproximationIntervalTest.java | 40 -
.../stat/interval/WilsonScoreIntervalTest.java | 45 -
.../math4/stat/ranking/NaturalRankingTest.java | 271 -
.../GLSMultipleLinearRegressionTest.java | 300 -
.../regression/MillerUpdatingRegressionTest.java | 1110 ----
.../MultipleLinearRegressionAbstractTest.java | 136 -
.../OLSMultipleLinearRegressionTest.java | 822 ---
.../stat/regression/SimpleRegressionTest.java | 693 ---
.../math4/transform/FastCosineTransformerTest.java | 276 -
.../transform/FastFourierTransformerTest.java | 482 --
.../transform/FastHadamardTransformerTest.java | 127 -
.../math4/transform/FastSineTransformerTest.java | 300 -
.../transform/RealTransformerAbstractTest.java | 344 --
.../commons/math4/util/BigRealFieldTest.java | 43 -
.../org/apache/commons/math4/util/BigRealTest.java | 189 -
.../commons/math4/util/CombinatoricsUtilsTest.java | 95 -
.../apache/commons/math4/util/Decimal64Test.java | 426 --
.../commons/math4/util/DefaultTransformerTest.java | 104 -
.../math4/util/DoubleArrayAbstractTest.java | 132 -
.../math4/util/FastMathStrictComparisonTest.java | 262 -
.../apache/commons/math4/util/FastMathTest.java | 1965 -------
.../commons/math4/util/IntegerSequenceTest.java | 327 --
.../apache/commons/math4/util/KthSelectorTest.java | 56 -
.../apache/commons/math4/util/MathArraysTest.java | 848 ---
.../apache/commons/math4/util/MathUtilsTest.java | 348 --
.../math4/util/OpenIntToDoubleHashMapTest.java | 332 --
.../commons/math4/util/OpenIntToFieldTest.java | 335 --
.../org/apache/commons/math4/util/PairTest.java | 118 -
.../math4/util/ResizableDoubleArrayTest.java | 581 --
.../org/apache/commons/math4/util/TestBean.java | 71 -
.../commons/math4/util/TransformerMapTest.java | 122 -
.../RealFunctionValidation.java | 361 --
.../math4/geometry/euclidean/threed/issue-1211.bsp | 15 -
.../threed/pentomino-N-bad-orientation.ply | 40 -
.../geometry/euclidean/threed/pentomino-N-hole.ply | 39 -
.../euclidean/threed/pentomino-N-out-of-plane.ply | 40 -
.../euclidean/threed/pentomino-N-too-close.ply | 86 -
.../geometry/euclidean/threed/pentomino-N.ply | 39 -
src/userguide/resources/references.txt | 4 -
2404 files changed, 262681 insertions(+), 260153 deletions(-)
diff --git a/RELEASE-NOTES.txt b/RELEASE-NOTES.txt
deleted file mode 100644
index 94e476f..0000000
--- a/RELEASE-NOTES.txt
+++ /dev/null
@@ -1,25 +0,0 @@
-
- Apache Commons Math 3.4.1 RELEASE NOTES
-
-The Apache Commons Math team is pleased to announce the release of commons-math3-3.4.1
-
-The Apache Commons Math project is a library of lightweight, self-contained mathematics
-and statistics components addressing the most common practical problems not immediately
-available in the Java programming language or commons-lang.
-
-This is a maintenance release: It fixes issue MATH-1188.
-
-Changes in this version include:
-
-
-Fixed Bugs:
-o MATH-1188: Fixed non-Java1.5 code in BesselJ.
-
-
-
-For complete information on Apache Commons Math, including instructions on how to submit bug reports,
-patches, or suggestions for improvement, see the Apache Commons Math website:
-
-http://commons.apache.org/proper/commons-math/
-
-
diff --git a/build.xml b/build.xml
deleted file mode 100644
index 747f243..0000000
--- a/build.xml
+++ /dev/null
@@ -1,376 +0,0 @@
-<!--
- Licensed to the Apache Software Foundation (ASF) under one or more
- contributor license agreements. See the NOTICE file distributed with
- this work for additional information regarding copyright ownership.
- The ASF licenses this file to You under the Apache License, Version 2.0
- (the "License"); you may not use this file except in compliance with
- the License. You may obtain a copy of the License at
-
- http://www.apache.org/licenses/LICENSE-2.0
-
- Unless required by applicable law or agreed to in writing, software
- distributed under the License is distributed on an "AS IS" BASIS,
- WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- See the License for the specific language governing permissions and
- limitations under the License.
--->
-<project name="Commons Math" default="jar" basedir=".">
-
-
-<!--
- "Math" component of the Apache Commons Project
--->
-
-
-<!-- ========== Initialize Properties ===================================== -->
-
- <property file="build.properties"/> <!-- Component local -->
- <property file="${user.home}/build.properties"/> <!-- User local -->
-
-
-<!-- ========== External Dependencies ===================================== -->
-
- <property name="repository" value = "${user.home}/.m2/repository"/>
-
- <!-- Junit -->
- <property name="junit.version" value="4.11"/>
- <property name="junit.jar" value="$junit-{junit.version}.jar"/>
- <property name="hamcrest.jar" value="hamcrest-core-1.3.jar"/>
-
-<!-- ========== Component Declarations ==================================== -->
-
-
- <!-- The name of this component -->
- <property name="component.name" value="commons-math"/>
-
- <!-- The primary package name of this component -->
- <property name="component.package" value="org.apache.commons.math4"/>
-
- <!-- The title of this component -->
- <property name="component.title" value="Commons MATH"/>
-
- <!-- The current version number of this component -->
- <property name="component.version" value="4.0-SNAPSHOT"/>
-
- <!-- The base directory for component sources -->
- <property name="source.home" value="src/main/java"/>
-
- <!-- The base directory for component resources -->
- <property name="source.resources" value="src/main/resources"/>
-
- <!-- The base directory for unit test sources -->
- <property name="test.home" value="src/test/java"/>
-
- <!-- The base directory for unit test resources -->
- <property name="test.resources" value="src/test/resources"/>
-
- <!-- Download lib dir -->
- <property name="download.lib.dir" value="lib"/>
-
- <!-- The base directory for compilation targets -->
- <property name="build.home" value="target"/>
-
- <!-- The base directory for distribution targets -->
- <property name="dist.home" value="${build.home}/dist"/>
-
- <!-- The base directory for test reports -->
- <property name="test.reports" value="${build.home}/test-reports"/>
-
- <!-- Base file name for dist files -->
- <property name="final.name" value="${component.name}-${component.version}"/>
-
- <!-- Directory where binary release files are staged -->
- <property name="stage.bin.dir" value="${dist.home}/stage-bin"/>
-
- <!-- Directory where source release files are staged -->
- <property name="stage.src.dir" value="${dist.home}/stage-src"/>
-
-<!-- ========== Compiler Defaults ========================================= -->
-
- <!-- Should Java compilations set the 'debug' compiler option? -->
- <property name="compile.debug" value="true"/>
-
- <!-- Should Java compilations set the 'deprecation' compiler option? -->
- <property name="compile.deprecation" value="false"/>
-
- <!-- Should Java compilations set the 'optimize' compiler option? -->
- <property name="compile.optimize" value="true"/>
-
- <!-- File encoding -->
- <property name="source.encoding" value="UTF-8"/>
-
- <!-- JDK level -->
- <property name="compile.source" value="1.5"/>
- <property name="compile.target" value="1.5"/>
-
- <!-- Base compile classpath -->
- <path id="compile.classpath">
- <pathelement location="${build.home}/classes"/>
- </path>
-
- <!-- External dependency classpath -->
- <path id="downloaded.lib.classpath">
- <pathelement location="${download.lib.dir}/junit-${junit.version}.jar"/>
- <pathelement location="${download.lib.dir}/${hamcrest.jar}"/>
- </path>
-
-<!-- ========== Test Execution Defaults =================================== -->
-
-
- <!-- Construct unit test classpath -->
- <path id="test.classpath">
- <pathelement location="${build.home}/classes"/>
- <pathelement location="${build.home}/test-classes"/>
- <pathelement location="${junit.jar}"/>
- <pathelement location="${hamcrest.jar}"/>
- <path refid="downloaded.lib.classpath"/>
- </path>
-
- <!-- Should the build fail if there are test failures? -->
- <property name="test.failonerror" value="true"/>
-
-<!-- ========== Executable Targets ======================================== -->
-
- <target name="clean" description="Clean build and distribution directories">
- <delete dir="${build.home}"/>
- </target>
-
-
- <target name="init"
- description="Initialize and evaluate conditionals">
- <echo message="-------- ${component.title} ${component.version} --------"/>
- <filter token="name" value="${component.name}"/>
- <filter token="package" value="${component.package}"/>
- <filter token="version" value="${component.version}"/>
- <filter token="compilesource" value="${compile.source}"/>
- <filter token="compiletarget" value="${compile.target}"/>
- <tstamp/>
- <mkdir dir="${build.home}"/>
- <mkdir dir="${build.home}/classes"/>
- <mkdir dir="${build.home}/test-classes"/>
- <copy todir="${build.home}/classes/">
- <fileset dir="${source.resources}" />
- </copy>
-
- </target>
-
-<!-- ========== Compile Targets =========================================== -->
-
- <target name="compile" depends="init" description="Compile">
-
- <javac srcdir="${source.home}"
- destdir="${build.home}/classes"
- source="${compile.source}"
- target="${compile.target}"
- debug="${compile.debug}"
- deprecation="${compile.deprecation}"
- includeantruntime="false"
- encoding="${source.encoding}"
- optimize="${compile.optimize}">
- <classpath refid="compile.classpath"/>
- </javac>
- </target>
-
-
-<!-- ========== Unit Test Targets ========================================= -->
-
- <target name="compile.tests" depends="compile, download-dependencies" description="Compile unit tests.">
-
- <javac srcdir="${test.home}"
- destdir="${build.home}/test-classes"
- debug="${compile.debug}"
- deprecation="${compile.deprecation}"
- encoding="${source.encoding}"
- includeantruntime="false"
- optimize="${compile.optimize}">
- <classpath refid="test.classpath"/>
- </javac>
-
- <copy todir="${build.home}/test-classes">
- <fileset dir="${test.resources}">
- </fileset>
- </copy>
-
- </target>
-
- <target name="test" depends="compile.tests"
- description="Run unit tests">
- <mkdir dir="${test.reports}"/>
- <junit printsummary="true"
- errorProperty="test.failed"
- failureProperty="test.failed"
- fork="true"
- showOutput="true">
- <formatter type="brief"/>
- <classpath refid="test.classpath"/>
- <!-- If test.entry is defined, run a single test, otherwise run all valid tests -->
- <!-- N.B. test.entry must be the full path to the test class, for example:
- ant test -Dtest.entry=org.apache.commons.math4.util.FastMathTestPerformance
- -->
- <test name="${test.entry}" todir="${test.reports}" if="test.entry"/>
- <batchtest todir="${test.reports}" unless="test.entry">
- <fileset dir="${test.home}">
- <include name="**/*Test.java"/>
- <include name="**/*TestBinary.java"/>
- <include name="**/*TestPermutations.java"/>
- <exclude name="**/*AbstractTest.java"/>
- </fileset>
- </batchtest>
- </junit>
- <fail message="There were test failures.">
- <condition>
- <and>
- <istrue value="${test.failonerror}"/>
- <isset property="test.failed"/>
- </and>
- </condition>
- </fail>
- </target>
-
-
-<!-- ========== Produce Javadocs ========================================== -->
-
- <target name="javadoc" depends="compile" description="Create component Javadoc documentation">
- <mkdir dir="${build.home}/apidocs"/>
- <tstamp>
- <format property="current.year" pattern="yyyy"/>
- </tstamp>
- <javadoc sourcepath="${source.home}"
- destdir="${build.home}/apidocs"
- packagenames="org.apache.commons.*"
- author="true"
- private="true"
- version="true"
- encoding="${source.encoding}"
- charset="${source.encoding}"
- docencoding="${source.encoding}"
- doctitle="<h1>${component.title} ${component.version}</h1>"
- windowtitle="${component.title} ${component.version}"
- bottom="Copyright (c) 2003-${current.year} Apache Software Foundation"
- additionalparam="-header '<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>'"
- classpathref="compile.classpath">
- <link href="http://java.sun.com/j2se/1.5.0/docs/api/"/>
- </javadoc>
- </target>
-
-
-<!-- ========== Create Jar ================================================ -->
-
- <target name="jar" depends="test" description="Create jar file">
-
- <copy file="LICENSE.txt" tofile="${build.home}/classes/META-INF/LICENSE.txt"/>
- <copy file="NOTICE.txt" tofile="${build.home}/classes/META-INF/NOTICE.txt"/>
-
- <manifest file="${build.home}/MANIFEST.MF">
- <attribute name="Specification-Title" value="${component.title}"/>
- <attribute name="Specification-Version" value="${component.version}"/>
- <attribute name="Specification-Vendor" value="Apache Software Foundation"/>
- <attribute name="Implementation-Title" value="${component.title}"/>
- <attribute name="Implementation-Version" value="${component.version}"/>
- <attribute name="Implementation-Vendor" value="Apache Software Foundation"/>
- <attribute name="Implementation-Vendor-Id" value="org.apache"/>
- <attribute name="X-Compile-Source-JDK" value="${compile.source}"/>
- <attribute name="X-Compile-Target-JDK" value="${compile.target}"/>
- </manifest>
-
- <jar jarfile="${build.home}/${final.name}.jar"
- basedir="${build.home}/classes"
- manifest="${build.home}/MANIFEST.MF"/>
- </target>
-
-
-<!-- ========== Distribution Target =========================================== -->
-
- <target name="dist" depends="clean,jar,javadoc" description="Create distribution artifacts">
-
- <mkdir dir="${dist.home}"/>
-
- <!-- jar(s) -->
- <copy todir="${dist.home}">
- <fileset dir=".">
- <include name="RELEASE-NOTES.txt"/>
- </fileset>
- <fileset dir="${build.home}">
- <include name="*.jar"/>
- </fileset>
- </copy>
-
- <!-- Binary Distro -->
- <mkdir dir="${stage.bin.dir}/${final.name}"/>
- <copy todir="${stage.bin.dir}/${final.name}">
- <fileset dir=".">
- <include name="LICENSE.txt"/>
- <include name="NOTICE.txt"/>
- <include name="RELEASE-NOTES.txt"/>
- </fileset>
- <fileset dir="${build.home}">
- <include name="*.jar"/>
- </fileset>
- </copy>
- <copy todir="${stage.bin.dir}/${final.name}/apidocs">
- <fileset dir="${build.home}/apidocs" />
- </copy>
-
- <!-- Source Distro -->
- <mkdir dir="${stage.src.dir}/${final.name}-src"/>
- <copy todir="${stage.src.dir}/${final.name}-src">
- <fileset dir=".">
- <include name="*.xml"/>
- <include name="*.txt"/>
- <include name="*.html"/>
- </fileset>
- </copy>
- <copy todir="${stage.src.dir}/${final.name}-src/src">
- <fileset dir="src" excludes="mantissa/**,experimental/**" />
- </copy>
- <zip zipfile="${dist.home}/${final.name}.zip" basedir="${stage.bin.dir}"/>
- <zip zipfile="${dist.home}/${final.name}-src.zip" basedir="${stage.src.dir}"/>
- <tar tarfile="${dist.home}/${final.name}.tar" basedir="${stage.bin.dir}" longfile="gnu"/>
- <tar tarfile="${dist.home}/${final.name}-src.tar" basedir="${stage.src.dir}" longfile="gnu"/>
- <gzip src="${dist.home}/${final.name}.tar" zipfile="${dist.home}/${final.name}.tar.gz"/>
- <gzip src="${dist.home}/${final.name}-src.tar" zipfile="${dist.home}/${final.name}-src.tar.gz"/>
-
- <!-- clean up staging directories -->
- <delete dir="${stage.bin.dir}"/>
- <delete dir="${stage.src.dir}"/>
-
- </target>
-
-
-<!-- ========== Gump Target ===================================================== -->
-
- <target name="gump" depends="clean,test,javadoc,jar" description="Gump Target - clean,test,javadoc,jar"/>
-
-
-<!-- ========== Download Dependencies =========================================== -->
-
- <target name="download-dependencies"
- depends="check-availability" unless="skip.download">
- <echo message="doing download-dependencies..." />
- <antcall target="download-junit" />
- <antcall target="download-hamcrest" />
- </target>
-
- <target name="check-availability">
- <echo message="doing check-availability..." />
- <available file="${junit.jar}" property="junit.found"/>
- </target>
-
- <target name="download-junit" unless="junit.found">
- <echo message="Downloading junit..."/>
- <mkdir dir="${download.lib.dir}" />
- <get dest="${download.lib.dir}/junit-${junit.version}.jar"
- usetimestamp="true" ignoreerrors="true"
- src="http://repo1.maven.org/maven2/junit/junit/${junit.version}/junit-${junit.version}.jar"/>
- </target>
-
- <target name="download-hamcrest" unless="hamcrest.found">
- <echo message="Downloading hamcrest..."/>
- <mkdir dir="${download.lib.dir}" />
- <get dest="${download.lib.dir}/${hamcrest.jar}"
- usetimestamp="true" ignoreerrors="true"
- src="http://repo1.maven.org/maven2/org/hamcrest/hamcrest-core/1.3/hamcrest-core-1.3.jar"/>
- </target>
-
-</project>
-
diff --git a/commons-math-legacy/LICENCE b/commons-math-legacy/LICENCE
new file mode 100644
index 0000000..d97b49a
--- /dev/null
+++ b/commons-math-legacy/LICENCE
@@ -0,0 +1,457 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
+
+ 1. Definitions.
+
+ "License" shall mean the terms and conditions for use, reproduction,
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+ APPENDIX: How to apply the Apache License to your work.
+
+ To apply the Apache License to your work, attach the following
+ boilerplate notice, with the fields enclosed by brackets "[]"
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+
+
+Apache Commons Math includes the following code provided to the ASF under the
+Apache License 2.0:
+
+ - The inverse error function implementation in the Erf class is based on CUDA
+ code developed by Mike Giles, Oxford-Man Institute of Quantitative Finance,
+ and published in GPU Computing Gems, volume 2, 2010 (grant received on
+ March 23th 2013)
+ - The LinearConstraint, LinearObjectiveFunction, LinearOptimizer,
+ RelationShip, SimplexSolver and SimplexTableau classes in package
+ org.apache.commons.math3.optimization.linear include software developed by
+ Benjamin McCann (http://www.benmccann.com) and distributed with
+ the following copyright: Copyright 2009 Google Inc. (grant received on
+ March 16th 2009)
+ - The class "org.apache.commons.math3.exception.util.LocalizedFormatsTest" which
+ is an adapted version of "OrekitMessagesTest" test class for the Orekit library
+ - The "org.apache.commons.math3.analysis.interpolation.HermiteInterpolator"
+ has been imported from the Orekit space flight dynamics library.
+
+===============================================================================
+
+
+
+APACHE COMMONS MATH DERIVATIVE WORKS:
+
+The Apache commons-math library includes a number of subcomponents
+whose implementation is derived from original sources written
+in C or Fortran. License terms of the original sources
+are reproduced below.
+
+===============================================================================
+For the lmder, lmpar and qrsolv Fortran routine from minpack and translated in
+the LevenbergMarquardtOptimizer class in package
+org.apache.commons.math3.optimization.general
+Original source copyright and license statement:
+
+Minpack Copyright Notice (1999) University of Chicago. All rights reserved
+
+Redistribution and use in source and binary forms, with or
+without modification, are permitted provided that the
+following conditions are met:
+
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+
+2. Redistributions in binary form must reproduce the above
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+redistribution, if any, must include the following
+acknowledgment:
+
+ "This product includes software developed by the
+ University of Chicago, as Operator of Argonne National
+ Laboratory.
+
+Alternately, this acknowledgment may appear in the software
+itself, if and wherever such third-party acknowledgments
+normally appear.
+
+4. WARRANTY DISCLAIMER. THE SOFTWARE IS SUPPLIED "AS IS"
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+PROFITS OR LOSS OF DATA, FOR ANY REASON WHATSOEVER, WHETHER
+SUCH LIABILITY IS ASSERTED ON THE BASIS OF CONTRACT, TORT
+(INCLUDING NEGLIGENCE OR STRICT LIABILITY), OR OTHERWISE,
+EVEN IF ANY OF SAID PARTIES HAS BEEN WARNED OF THE
+POSSIBILITY OF SUCH LOSS OR DAMAGES.
+===============================================================================
+
+Copyright and license statement for the odex Fortran routine developed by
+E. Hairer and G. Wanner and translated in GraggBulirschStoerIntegrator class
+in package org.apache.commons.math3.ode.nonstiff:
+
+
+Copyright (c) 2004, Ernst Hairer
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+- Redistributions of source code must retain the above copyright
+notice, this list of conditions and the following disclaimer.
+
+- Redistributions in binary form must reproduce the above copyright
+notice, this list of conditions and the following disclaimer in the
+documentation and/or other materials provided with the distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR
+CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+===============================================================================
+
+Copyright and license statement for the original Mersenne twister C
+routines translated in MersenneTwister class in package
+org.apache.commons.math3.random:
+
+ Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
+ All rights reserved.
+
+ Redistribution and use in source and binary forms, with or without
+ modification, are permitted provided that the following conditions
+ are met:
+
+ 1. Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ 2. Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ 3. The names of its contributors may not be used to endorse or promote
+ products derived from this software without specific prior written
+ permission.
+
+ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+ "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+ LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+ A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
+ CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+ EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+ PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+ PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+ LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+ NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+ SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+
+===============================================================================
+
+The initial code for shuffling an array (originally in class
+"org.apache.commons.math3.random.RandomDataGenerator", now replaced by
+a method in class "org.apache.commons.math3.util.MathArrays") was
+inspired from the algorithm description provided in
+"Algorithms", by Ian Craw and John Pulham (University of Aberdeen 1999).
+The textbook (containing a proof that the shuffle is uniformly random) is
+available here:
+ http://citeseerx.ist.psu.edu/viewdoc/download;?doi=10.1.1.173.1898&rep=rep1&type=pdf
+
+===============================================================================
+License statement for the direction numbers in the resource files for Sobol sequences.
+
+-----------------------------------------------------------------------------
+Licence pertaining to sobol.cc and the accompanying sets of direction numbers
+
+-----------------------------------------------------------------------------
+Copyright (c) 2008, Frances Y. Kuo and Stephen Joe
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ * Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ * Neither the names of the copyright holders nor the names of the
+ University of New South Wales and the University of Waikato
+ and its contributors may be used to endorse or promote products derived
+ from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS ``AS IS'' AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDERS BE LIABLE FOR ANY
+DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+===============================================================================
+
+The initial commit of package "org.apache.commons.math3.ml.neuralnet" is
+an adapted version of code developed in the context of the Data Processing
+and Analysis Consortium (DPAC) of the "Gaia" project of the European Space
+Agency (ESA).
+===============================================================================
+
+The initial commit of the class "org.apache.commons.math3.special.BesselJ" is
+an adapted version of code translated from the netlib Fortran program, rjbesl
+http://www.netlib.org/specfun/rjbesl by R.J. Cody at Argonne National
+Laboratory (USA). There is no license or copyright statement included with the
+original Fortran sources.
+===============================================================================
+
+
+The BracketFinder (package org.apache.commons.math3.optimization.univariate)
+and PowellOptimizer (package org.apache.commons.math3.optimization.general)
+classes are based on the Python code in module "optimize.py" (version 0.5)
+developed by Travis E. Oliphant for the SciPy library (http://www.scipy.org/)
+Copyright © 2003-2009 SciPy Developers.
+
+SciPy license
+Copyright © 2001, 2002 Enthought, Inc.
+All rights reserved.
+
+Copyright © 2003-2013 SciPy Developers.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+ * Redistributions of source code must retain the above copyright
+ notice, this list of conditions and the following disclaimer.
+
+ * Redistributions in binary form must reproduce the above copyright
+ notice, this list of conditions and the following disclaimer in the
+ documentation and/or other materials provided with the distribution.
+
+ * Neither the name of Enthought nor the names of the SciPy Developers may
+ be used to endorse or promote products derived from this software without
+ specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY
+EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
+WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
+DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
+DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
+(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
+LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
+ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+===============================================================================
+
diff --git a/commons-math-legacy/NOTICE b/commons-math-legacy/NOTICE
new file mode 100644
index 0000000..587cd7f
--- /dev/null
+++ b/commons-math-legacy/NOTICE
@@ -0,0 +1,9 @@
+Apache Commons Math
+Copyright 2001-2020 The Apache Software Foundation
+
+This product includes software developed at
+The Apache Software Foundation (http://www.apache.org/).
+
+This product includes software developed for Orekit by
+CS Systèmes d'Information (http://www.c-s.fr/)
+Copyright 2010-2012 CS Systèmes d'Information
diff --git a/commons-math-legacy/pom.xml b/commons-math-legacy/pom.xml
new file mode 100644
index 0000000..8795be8
--- /dev/null
+++ b/commons-math-legacy/pom.xml
@@ -0,0 +1,131 @@
+<?xml version="1.0"?>
+<!--
+ Licensed to the Apache Software Foundation (ASF) under one or more
+ contributor license agreements. See the NOTICE file distributed with
+ this work for additional information regarding copyright ownership.
+ The ASF licenses this file to You under the Apache License, Version 2.0
+ (the "License"); you may not use this file except in compliance with
+ the License. You may obtain a copy of the License at
+
+ http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+-->
+<project xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd"
+ xmlns="http://maven.apache.org/POM/4.0.0"
+ xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
+ <modelVersion>4.0.0</modelVersion>
+
+ <parent>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-math-parent</artifactId>
+ <version>4.0-SNAPSHOT</version>
+ </parent>
+
+ <artifactId>commons-math-legacy</artifactId>
+ <name>Apache Commons Math (Legacy)</name>
+
+ <description>Legacy codes that are either currently unsupported or not yet modularized.</description>
+
+ <properties>
+ <!-- The Java Module System Name -->
+ <commons.module.name>org.apache.commons.math4.legacy</commons.module.name>
+ <!-- This value must reflect the current name of the base package. -->
+ <commons.osgi.symbolicName>org.apache.commons.math4.legacy</commons.osgi.symbolicName>
+ <!-- OSGi -->
+ <commons.osgi.export>org.apache.commons.math4.legacy</commons.osgi.export>
+ <!-- Workaround to avoid duplicating config files. -->
+ <math.parent.dir>${basedir}/..</math.parent.dir>
+ </properties>
+
+ <dependencies>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-math3</artifactId>
+ <scope>test</scope>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-statistics-distribution</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-core</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-complex</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-complex-streams</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-gamma</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-combinatorics</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-arrays</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-angle</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-rootfinder</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-field</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-numbers-quaternion</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-rng-client-api</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-rng-simple</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-rng-sampling</artifactId>
+ </dependency>
+
+ <dependency>
+ <groupId>org.apache.commons</groupId>
+ <artifactId>commons-geometry-euclidean</artifactId>
+ <scope>test</scope>
+ </dependency>
+
+ </dependencies>
+
+</project>
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/Field.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/Field.java
new file mode 100644
index 0000000..f6168c4
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/Field.java
@@ -0,0 +1,58 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy;
+
+/**
+ * Interface representing a <a href="http://mathworld.wolfram.com/Field.html">field</a>.
+ * <p>
+ * Classes implementing this interface will often be singletons.
+ * </p>
+ * @param <T> the type of the field elements
+ * @see FieldElement
+ * @since 2.0
+ */
+public interface Field<T> {
+
+ /** Get the additive identity of the field.
+ * <p>
+ * The additive identity is the element e<sub>0</sub> of the field such that
+ * for all elements a of the field, the equalities a + e<sub>0</sub> =
+ * e<sub>0</sub> + a = a hold.
+ * </p>
+ * @return additive identity of the field
+ */
+ T getZero();
+
+ /** Get the multiplicative identity of the field.
+ * <p>
+ * The multiplicative identity is the element e<sub>1</sub> of the field such that
+ * for all elements a of the field, the equalities a × e<sub>1</sub> =
+ * e<sub>1</sub> × a = a hold.
+ * </p>
+ * @return multiplicative identity of the field
+ */
+ T getOne();
+
+ /**
+ * Returns the runtime class of the FieldElement.
+ *
+ * @return The {@code Class} object that represents the runtime
+ * class of this object.
+ */
+ Class<? extends FieldElement<T>> getRuntimeClass();
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/FieldElement.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/FieldElement.java
new file mode 100644
index 0000000..bcd1dae
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/FieldElement.java
@@ -0,0 +1,87 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy;
+
+import org.apache.commons.math4.legacy.exception.MathArithmeticException;
+import org.apache.commons.math4.legacy.exception.NullArgumentException;
+
+
+/**
+ * Interface representing <a href="http://mathworld.wolfram.com/Field.html">field</a> elements.
+ * @param <T> the type of the field elements
+ * @see Field
+ * @since 2.0
+ */
+public interface FieldElement<T> {
+
+ /** Compute this + a.
+ * @param a element to add
+ * @return a new element representing this + a
+ * @throws NullArgumentException if {@code a} is {@code null}.
+ */
+ T add(T a) throws NullArgumentException;
+
+ /** Compute this - a.
+ * @param a element to subtract
+ * @return a new element representing this - a
+ * @throws NullArgumentException if {@code a} is {@code null}.
+ */
+ T subtract(T a) throws NullArgumentException;
+
+ /**
+ * Returns the additive inverse of {@code this} element.
+ * @return the opposite of {@code this}.
+ */
+ T negate();
+
+ /** Compute n × this. Multiplication by an integer number is defined
+ * as the following sum
+ * <center>
+ * n × this = ∑<sub>i=1</sub><sup>n</sup> this.
+ * </center>
+ * @param n Number of times {@code this} must be added to itself.
+ * @return A new element representing n × this.
+ */
+ T multiply(int n);
+
+ /** Compute this × a.
+ * @param a element to multiply
+ * @return a new element representing this × a
+ * @throws NullArgumentException if {@code a} is {@code null}.
+ */
+ T multiply(T a) throws NullArgumentException;
+
+ /** Compute this ÷ a.
+ * @param a element to divide by
+ * @return a new element representing this ÷ a
+ * @throws NullArgumentException if {@code a} is {@code null}.
+ * @throws MathArithmeticException if {@code a} is zero
+ */
+ T divide(T a) throws NullArgumentException, MathArithmeticException;
+
+ /**
+ * Returns the multiplicative inverse of {@code this} element.
+ * @return the inverse of {@code this}.
+ * @throws MathArithmeticException if {@code this} is zero
+ */
+ T reciprocal() throws MathArithmeticException;
+
+ /** Get the {@link Field} to which the instance belongs.
+ * @return {@link Field} to which the instance belongs
+ */
+ Field<T> getField();
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/RealFieldElement.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/RealFieldElement.java
new file mode 100644
index 0000000..3defca5
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/RealFieldElement.java
@@ -0,0 +1,402 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy;
+
+import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
+
+/**
+ * Interface representing a <a href="http://mathworld.wolfram.com/RealNumber.html">real</a>
+ * <a href="http://mathworld.wolfram.com/Field.html">field</a>.
+ * @param <T> the type of the field elements
+ * @see FieldElement
+ * @since 3.2
+ */
+public interface RealFieldElement<T> extends FieldElement<T> {
+
+ /** Get the real value of the number.
+ * @return real value
+ */
+ double getReal();
+
+ /** '+' operator.
+ * @param a right hand side parameter of the operator
+ * @return this+a
+ */
+ T add(double a);
+
+ /** '-' operator.
+ * @param a right hand side parameter of the operator
+ * @return this-a
+ */
+ T subtract(double a);
+
+ /** '×' operator.
+ * @param a right hand side parameter of the operator
+ * @return this×a
+ */
+ T multiply(double a);
+
+ /** '÷' operator.
+ * @param a right hand side parameter of the operator
+ * @return this÷a
+ */
+ T divide(double a);
+
+ /** IEEE remainder operator.
+ * @param a right hand side parameter of the operator
+ * @return this - n × a where n is the closest integer to this/a
+ * (the even integer is chosen for n if this/a is halfway between two integers)
+ */
+ T remainder(double a);
+
+ /** IEEE remainder operator.
+ * @param a right hand side parameter of the operator
+ * @return this - n × a where n is the closest integer to this/a
+ * (the even integer is chosen for n if this/a is halfway between two integers)
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ T remainder(T a)
+ throws DimensionMismatchException;
+
+ /** absolute value.
+ * @return abs(this)
+ */
+ T abs();
+
+ /** Get the smallest whole number larger than instance.
+ * @return ceil(this)
+ */
+ T ceil();
+
+ /** Get the largest whole number smaller than instance.
+ * @return floor(this)
+ */
+ T floor();
+
+ /** Get the whole number that is the nearest to the instance, or the even one if x is exactly half way between two integers.
+ * @return a double number r such that r is an integer r - 0.5 ≤ this ≤ r + 0.5
+ */
+ T rint();
+
+ /** Get the closest long to instance value.
+ * @return closest long to {@link #getReal()}
+ */
+ long round();
+
+ /** Compute the signum of the instance.
+ * The signum is -1 for negative numbers, +1 for positive numbers and 0 otherwise
+ * @return -1.0, -0.0, +0.0, +1.0 or NaN depending on sign of a
+ */
+ T signum();
+
+ /**
+ * Returns the instance with the sign of the argument.
+ * A NaN {@code sign} argument is treated as positive.
+ *
+ * @param sign the sign for the returned value
+ * @return the instance with the same sign as the {@code sign} argument
+ */
+ T copySign(T sign);
+
+ /**
+ * Returns the instance with the sign of the argument.
+ * A NaN {@code sign} argument is treated as positive.
+ *
+ * @param sign the sign for the returned value
+ * @return the instance with the same sign as the {@code sign} argument
+ */
+ T copySign(double sign);
+
+ /**
+ * Multiply the instance by a power of 2.
+ * @param n power of 2
+ * @return this × 2<sup>n</sup>
+ */
+ T scalb(int n);
+
+ /**
+ * Returns the hypotenuse of a triangle with sides {@code this} and {@code y}
+ * - sqrt(<i>this</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ * avoiding intermediate overflow or underflow.
+ *
+ * <ul>
+ * <li> If either argument is infinite, then the result is positive infinity.</li>
+ * <li> else, if either argument is NaN then the result is NaN.</li>
+ * </ul>
+ *
+ * @param y a value
+ * @return sqrt(<i>this</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ T hypot(T y)
+ throws DimensionMismatchException;
+
+ /** {@inheritDoc} */
+ @Override
+ T reciprocal();
+
+ /** Square root.
+ * @return square root of the instance
+ */
+ T sqrt();
+
+ /** Cubic root.
+ * @return cubic root of the instance
+ */
+ T cbrt();
+
+ /** N<sup>th</sup> root.
+ * @param n order of the root
+ * @return n<sup>th</sup> root of the instance
+ */
+ T rootN(int n);
+
+ /** Power operation.
+ * @param p power to apply
+ * @return this<sup>p</sup>
+ */
+ T pow(double p);
+
+ /** Integer power operation.
+ * @param n power to apply
+ * @return this<sup>n</sup>
+ */
+ T pow(int n);
+
+ /** Power operation.
+ * @param e exponent
+ * @return this<sup>e</sup>
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ T pow(T e)
+ throws DimensionMismatchException;
+
+ /** Exponential.
+ * @return exponential of the instance
+ */
+ T exp();
+
+ /** Exponential minus 1.
+ * @return exponential minus one of the instance
+ */
+ T expm1();
+
+ /** Natural logarithm.
+ * @return logarithm of the instance
+ */
+ T log();
+
+ /** Shifted natural logarithm.
+ * @return logarithm of one plus the instance
+ */
+ T log1p();
+
+ /** Base 10 logarithm.
+ * @return base 10 logarithm of the instance
+ * @since 4.0
+ */
+ T log10();
+
+ /** Cosine operation.
+ * @return cos(this)
+ */
+ T cos();
+
+ /** Sine operation.
+ * @return sin(this)
+ */
+ T sin();
+
+ /** Tangent operation.
+ * @return tan(this)
+ */
+ T tan();
+
+ /** Arc cosine operation.
+ * @return acos(this)
+ */
+ T acos();
+
+ /** Arc sine operation.
+ * @return asin(this)
+ */
+ T asin();
+
+ /** Arc tangent operation.
+ * @return atan(this)
+ */
+ T atan();
+
+ /** Two arguments arc tangent operation.
+ * @param x second argument of the arc tangent
+ * @return atan2(this, x)
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ T atan2(T x)
+ throws DimensionMismatchException;
+
+ /** Hyperbolic cosine operation.
+ * @return cosh(this)
+ */
+ T cosh();
+
+ /** Hyperbolic sine operation.
+ * @return sinh(this)
+ */
+ T sinh();
+
+ /** Hyperbolic tangent operation.
+ * @return tanh(this)
+ */
+ T tanh();
+
+ /** Inverse hyperbolic cosine operation.
+ * @return acosh(this)
+ */
+ T acosh();
+
+ /** Inverse hyperbolic sine operation.
+ * @return asin(this)
+ */
+ T asinh();
+
+ /** Inverse hyperbolic tangent operation.
+ * @return atanh(this)
+ */
+ T atanh();
+
+ /**
+ * Compute a linear combination.
+ * @param a Factors.
+ * @param b Factors.
+ * @return <code>Σ<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
+ * @throws DimensionMismatchException if arrays dimensions don't match
+ * @since 3.2
+ */
+ T linearCombination(T[] a, T[] b)
+ throws DimensionMismatchException;
+
+ /**
+ * Compute a linear combination.
+ * @param a Factors.
+ * @param b Factors.
+ * @return <code>Σ<sub>i</sub> a<sub>i</sub> b<sub>i</sub></code>.
+ * @throws DimensionMismatchException if arrays dimensions don't match
+ * @since 3.2
+ */
+ T linearCombination(double[] a, T[] b)
+ throws DimensionMismatchException;
+
+ /**
+ * Compute a linear combination.
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub>
+ * @see #linearCombination(Object, Object, Object, Object, Object, Object)
+ * @see #linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
+ * @since 3.2
+ */
+ T linearCombination(T a1, T b1, T a2, T b2);
+
+ /**
+ * Compute a linear combination.
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub>
+ * @see #linearCombination(double, Object, double, Object, double, Object)
+ * @see #linearCombination(double, Object, double, Object, double, Object, double, Object)
+ * @since 3.2
+ */
+ T linearCombination(double a1, T b1, double a2, T b2);
+
+ /**
+ * Compute a linear combination.
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @param a3 first factor of the third term
+ * @param b3 second factor of the third term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
+ * @see #linearCombination(Object, Object, Object, Object)
+ * @see #linearCombination(Object, Object, Object, Object, Object, Object, Object, Object)
+ * @since 3.2
+ */
+ T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3);
+
+ /**
+ * Compute a linear combination.
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @param a3 first factor of the third term
+ * @param b3 second factor of the third term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub>
+ * @see #linearCombination(double, Object, double, Object)
+ * @see #linearCombination(double, Object, double, Object, double, Object, double, Object)
+ * @since 3.2
+ */
+ T linearCombination(double a1, T b1, double a2, T b2, double a3, T b3);
+
+ /**
+ * Compute a linear combination.
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @param a3 first factor of the third term
+ * @param b3 second factor of the third term
+ * @param a4 first factor of the third term
+ * @param b4 second factor of the third term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
+ * a<sub>4</sub>×b<sub>4</sub>
+ * @see #linearCombination(Object, Object, Object, Object)
+ * @see #linearCombination(Object, Object, Object, Object, Object, Object)
+ * @since 3.2
+ */
+ T linearCombination(T a1, T b1, T a2, T b2, T a3, T b3, T a4, T b4);
+
+ /**
+ * Compute a linear combination.
+ * @param a1 first factor of the first term
+ * @param b1 second factor of the first term
+ * @param a2 first factor of the second term
+ * @param b2 second factor of the second term
+ * @param a3 first factor of the third term
+ * @param b3 second factor of the third term
+ * @param a4 first factor of the third term
+ * @param b4 second factor of the third term
+ * @return a<sub>1</sub>×b<sub>1</sub> +
+ * a<sub>2</sub>×b<sub>2</sub> + a<sub>3</sub>×b<sub>3</sub> +
+ * a<sub>4</sub>×b<sub>4</sub>
+ * @see #linearCombination(double, Object, double, Object)
+ * @see #linearCombination(double, Object, double, Object, double, Object)
+ * @since 3.2
+ */
+ T linearCombination(double a1, T b1, double a2, T b2, double a3, T b3, double a4, T b4);
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/BivariateFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/BivariateFunction.java
new file mode 100644
index 0000000..19b5383
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/BivariateFunction.java
@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a bivariate real function.
+ *
+ * @since 2.1
+ */
+public interface BivariateFunction {
+ /**
+ * Compute the value for the function.
+ *
+ * @param x Abscissa for which the function value should be computed.
+ * @param y Ordinate for which the function value should be computed.
+ * @return the value.
+ */
+ double value(double x, double y);
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/FunctionUtils.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/FunctionUtils.java
new file mode 100644
index 0000000..6f0e550
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/FunctionUtils.java
@@ -0,0 +1,544 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis;
+
+import org.apache.commons.numbers.arrays.LinearCombination;
+import org.apache.commons.math4.legacy.analysis.differentiation.DerivativeStructure;
+import org.apache.commons.math4.legacy.analysis.differentiation.MultivariateDifferentiableFunction;
+import org.apache.commons.math4.legacy.analysis.differentiation.UnivariateDifferentiableFunction;
+import org.apache.commons.math4.legacy.analysis.function.Identity;
+import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
+import org.apache.commons.math4.legacy.exception.NotStrictlyPositiveException;
+import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
+import org.apache.commons.math4.legacy.exception.util.LocalizedFormats;
+
+/**
+ * Utilities for manipulating function objects.
+ *
+ * @since 3.0
+ */
+public class FunctionUtils {
+ /**
+ * Class only contains static methods.
+ */
+ private FunctionUtils() {}
+
+ /**
+ * Composes functions.
+ * <p>
+ * The functions in the argument list are composed sequentially, in the
+ * given order. For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).</p>
+ *
+ * @param f List of functions.
+ * @return the composite function.
+ */
+ public static UnivariateFunction compose(final UnivariateFunction ... f) {
+ return new UnivariateFunction() {
+ /** {@inheritDoc} */
+ @Override
+ public double value(double x) {
+ double r = x;
+ for (int i = f.length - 1; i >= 0; i--) {
+ r = f[i].value(r);
+ }
+ return r;
+ }
+ };
+ }
+
+ /**
+ * Composes functions.
+ * <p>
+ * The functions in the argument list are composed sequentially, in the
+ * given order. For example, compose(f1,f2,f3) acts like f1(f2(f3(x))).</p>
+ *
+ * @param f List of functions.
+ * @return the composite function.
+ * @since 3.1
+ */
+ public static UnivariateDifferentiableFunction compose(final UnivariateDifferentiableFunction ... f) {
+ return new UnivariateDifferentiableFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double t) {
+ double r = t;
+ for (int i = f.length - 1; i >= 0; i--) {
+ r = f[i].value(r);
+ }
+ return r;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure value(final DerivativeStructure t) {
+ DerivativeStructure r = t;
+ for (int i = f.length - 1; i >= 0; i--) {
+ r = f[i].value(r);
+ }
+ return r;
+ }
+
+ };
+ }
+
+ /**
+ * Adds functions.
+ *
+ * @param f List of functions.
+ * @return a function that computes the sum of the functions.
+ */
+ public static UnivariateFunction add(final UnivariateFunction ... f) {
+ return new UnivariateFunction() {
+ /** {@inheritDoc} */
+ @Override
+ public double value(double x) {
+ double r = f[0].value(x);
+ for (int i = 1; i < f.length; i++) {
+ r += f[i].value(x);
+ }
+ return r;
+ }
+ };
+ }
+
+ /**
+ * Adds functions.
+ *
+ * @param f List of functions.
+ * @return a function that computes the sum of the functions.
+ * @since 3.1
+ */
+ public static UnivariateDifferentiableFunction add(final UnivariateDifferentiableFunction ... f) {
+ return new UnivariateDifferentiableFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double t) {
+ double r = f[0].value(t);
+ for (int i = 1; i < f.length; i++) {
+ r += f[i].value(t);
+ }
+ return r;
+ }
+
+ /** {@inheritDoc}
+ * @throws DimensionMismatchException if functions are not consistent with each other
+ */
+ @Override
+ public DerivativeStructure value(final DerivativeStructure t)
+ throws DimensionMismatchException {
+ DerivativeStructure r = f[0].value(t);
+ for (int i = 1; i < f.length; i++) {
+ r = r.add(f[i].value(t));
+ }
+ return r;
+ }
+
+ };
+ }
+
+ /**
+ * Multiplies functions.
+ *
+ * @param f List of functions.
+ * @return a function that computes the product of the functions.
+ */
+ public static UnivariateFunction multiply(final UnivariateFunction ... f) {
+ return new UnivariateFunction() {
+ /** {@inheritDoc} */
+ @Override
+ public double value(double x) {
+ double r = f[0].value(x);
+ for (int i = 1; i < f.length; i++) {
+ r *= f[i].value(x);
+ }
+ return r;
+ }
+ };
+ }
+
+ /**
+ * Multiplies functions.
+ *
+ * @param f List of functions.
+ * @return a function that computes the product of the functions.
+ * @since 3.1
+ */
+ public static UnivariateDifferentiableFunction multiply(final UnivariateDifferentiableFunction ... f) {
+ return new UnivariateDifferentiableFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double t) {
+ double r = f[0].value(t);
+ for (int i = 1; i < f.length; i++) {
+ r *= f[i].value(t);
+ }
+ return r;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure value(final DerivativeStructure t) {
+ DerivativeStructure r = f[0].value(t);
+ for (int i = 1; i < f.length; i++) {
+ r = r.multiply(f[i].value(t));
+ }
+ return r;
+ }
+
+ };
+ }
+
+ /**
+ * Returns the univariate function
+ * {@code h(x) = combiner(f(x), g(x)).}
+ *
+ * @param combiner Combiner function.
+ * @param f Function.
+ * @param g Function.
+ * @return the composite function.
+ */
+ public static UnivariateFunction combine(final BivariateFunction combiner,
+ final UnivariateFunction f,
+ final UnivariateFunction g) {
+ return new UnivariateFunction() {
+ /** {@inheritDoc} */
+ @Override
+ public double value(double x) {
+ return combiner.value(f.value(x), g.value(x));
+ }
+ };
+ }
+
+ /**
+ * Returns a MultivariateFunction h(x[]) defined by <pre> <code>
+ * h(x[]) = combiner(...combiner(combiner(initialValue,f(x[0])),f(x[1]))...),f(x[x.length-1]))
+ * </code></pre>
+ *
+ * @param combiner Combiner function.
+ * @param f Function.
+ * @param initialValue Initial value.
+ * @return a collector function.
+ */
+ public static MultivariateFunction collector(final BivariateFunction combiner,
+ final UnivariateFunction f,
+ final double initialValue) {
+ return new MultivariateFunction() {
+ /** {@inheritDoc} */
+ @Override
+ public double value(double[] point) {
+ double result = combiner.value(initialValue, f.value(point[0]));
+ for (int i = 1; i < point.length; i++) {
+ result = combiner.value(result, f.value(point[i]));
+ }
+ return result;
+ }
+ };
+ }
+
+ /**
+ * Returns a MultivariateFunction h(x[]) defined by <pre> <code>
+ * h(x[]) = combiner(...combiner(combiner(initialValue,x[0]),x[1])...),x[x.length-1])
+ * </code></pre>
+ *
+ * @param combiner Combiner function.
+ * @param initialValue Initial value.
+ * @return a collector function.
+ */
+ public static MultivariateFunction collector(final BivariateFunction combiner,
+ final double initialValue) {
+ return collector(combiner, new Identity(), initialValue);
+ }
+
+ /**
+ * Creates a unary function by fixing the first argument of a binary function.
+ *
+ * @param f Binary function.
+ * @param fixed value to which the first argument of {@code f} is set.
+ * @return the unary function h(x) = f(fixed, x)
+ */
+ public static UnivariateFunction fix1stArgument(final BivariateFunction f,
+ final double fixed) {
+ return new UnivariateFunction() {
+ /** {@inheritDoc} */
+ @Override
+ public double value(double x) {
+ return f.value(fixed, x);
+ }
+ };
+ }
+ /**
+ * Creates a unary function by fixing the second argument of a binary function.
+ *
+ * @param f Binary function.
+ * @param fixed value to which the second argument of {@code f} is set.
+ * @return the unary function h(x) = f(x, fixed)
+ */
+ public static UnivariateFunction fix2ndArgument(final BivariateFunction f,
+ final double fixed) {
+ return new UnivariateFunction() {
+ /** {@inheritDoc} */
+ @Override
+ public double value(double x) {
+ return f.value(x, fixed);
+ }
+ };
+ }
+
+ /**
+ * Samples the specified univariate real function on the specified interval.
+ * <p>
+ * The interval is divided equally into {@code n} sections and sample points
+ * are taken from {@code min} to {@code max - (max - min) / n}; therefore
+ * {@code f} is not sampled at the upper bound {@code max}.</p>
+ *
+ * @param f Function to be sampled
+ * @param min Lower bound of the interval (included).
+ * @param max Upper bound of the interval (excluded).
+ * @param n Number of sample points.
+ * @return the array of samples.
+ * @throws NumberIsTooLargeException if the lower bound {@code min} is
+ * greater than, or equal to the upper bound {@code max}.
+ * @throws NotStrictlyPositiveException if the number of sample points
+ * {@code n} is negative.
+ */
+ public static double[] sample(UnivariateFunction f, double min, double max, int n)
+ throws NumberIsTooLargeException, NotStrictlyPositiveException {
+
+ if (n <= 0) {
+ throw new NotStrictlyPositiveException(
+ LocalizedFormats.NOT_POSITIVE_NUMBER_OF_SAMPLES,
+ Integer.valueOf(n));
+ }
+ if (min >= max) {
+ throw new NumberIsTooLargeException(min, max, false);
+ }
+
+ final double[] s = new double[n];
+ final double h = (max - min) / n;
+ for (int i = 0; i < n; i++) {
+ s[i] = f.value(min + i * h);
+ }
+ return s;
+ }
+
+ /** Convert regular functions to {@link UnivariateDifferentiableFunction}.
+ * <p>
+ * This method handle the case with one free parameter and several derivatives.
+ * For the case with several free parameters and only first order derivatives,
+ * see {@link #toDifferentiable(MultivariateFunction, MultivariateVectorFunction)}.
+ * There are no direct support for intermediate cases, with several free parameters
+ * and order 2 or more derivatives, as is would be difficult to specify all the
+ * cross derivatives.
+ * </p>
+ * <p>
+ * Note that the derivatives are expected to be computed only with respect to the
+ * raw parameter x of the base function, i.e. they are df/dx, df<sup>2</sup>/dx<sup>2</sup>, ...
+ * Even if the built function is later used in a composition like f(sin(t)), the provided
+ * derivatives should <em>not</em> apply the composition with sine and its derivatives by
+ * themselves. The composition will be done automatically here and the result will properly
+ * contain f(sin(t)), df(sin(t))/dt, df<sup>2</sup>(sin(t))/dt<sup>2</sup> despite the
+ * provided derivatives functions know nothing about the sine function.
+ * </p>
+ * @param f base function f(x)
+ * @param derivatives derivatives of the base function, in increasing differentiation order
+ * @return a differentiable function with value and all specified derivatives
+ * @see #toDifferentiable(MultivariateFunction, MultivariateVectorFunction)
+ * @see #derivative(UnivariateDifferentiableFunction, int)
+ */
+ public static UnivariateDifferentiableFunction toDifferentiable(final UnivariateFunction f,
+ final UnivariateFunction ... derivatives) {
+
+ return new UnivariateDifferentiableFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double x) {
+ return f.value(x);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure value(final DerivativeStructure x) {
+ if (x.getOrder() > derivatives.length) {
+ throw new NumberIsTooLargeException(x.getOrder(), derivatives.length, true);
+ }
+ final double[] packed = new double[x.getOrder() + 1];
+ packed[0] = f.value(x.getValue());
+ for (int i = 0; i < x.getOrder(); ++i) {
+ packed[i + 1] = derivatives[i].value(x.getValue());
+ }
+ return x.compose(packed);
+ }
+
+ };
+
+ }
+
+ /** Convert regular functions to {@link MultivariateDifferentiableFunction}.
+ * <p>
+ * This method handle the case with several free parameters and only first order derivatives.
+ * For the case with one free parameter and several derivatives,
+ * see {@link #toDifferentiable(UnivariateFunction, UnivariateFunction...)}.
+ * There are no direct support for intermediate cases, with several free parameters
+ * and order 2 or more derivatives, as is would be difficult to specify all the
+ * cross derivatives.
+ * </p>
+ * <p>
+ * Note that the gradient is expected to be computed only with respect to the
+ * raw parameter x of the base function, i.e. it is df/dx<sub>1</sub>, df/dx<sub>2</sub>, ...
+ * Even if the built function is later used in a composition like f(sin(t), cos(t)), the provided
+ * gradient should <em>not</em> apply the composition with sine or cosine and their derivative by
+ * itself. The composition will be done automatically here and the result will properly
+ * contain f(sin(t), cos(t)), df(sin(t), cos(t))/dt despite the provided derivatives functions
+ * know nothing about the sine or cosine functions.
+ * </p>
+ * @param f base function f(x)
+ * @param gradient gradient of the base function
+ * @return a differentiable function with value and gradient
+ * @see #toDifferentiable(UnivariateFunction, UnivariateFunction...)
+ * @see #derivative(MultivariateDifferentiableFunction, int[])
+ */
+ public static MultivariateDifferentiableFunction toDifferentiable(final MultivariateFunction f,
+ final MultivariateVectorFunction gradient) {
+
+ return new MultivariateDifferentiableFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double[] point) {
+ return f.value(point);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure value(final DerivativeStructure[] point) {
+
+ // set up the input parameters
+ final double[] dPoint = new double[point.length];
+ for (int i = 0; i < point.length; ++i) {
+ dPoint[i] = point[i].getValue();
+ if (point[i].getOrder() > 1) {
+ throw new NumberIsTooLargeException(point[i].getOrder(), 1, true);
+ }
+ }
+
+ // evaluate regular functions
+ final double v = f.value(dPoint);
+ final double[] dv = gradient.value(dPoint);
+ if (dv.length != point.length) {
+ // the gradient function is inconsistent
+ throw new DimensionMismatchException(dv.length, point.length);
+ }
+
+ // build the combined derivative
+ final int parameters = point[0].getFreeParameters();
+ final double[] partials = new double[point.length];
+ final double[] packed = new double[parameters + 1];
+ packed[0] = v;
+ final int orders[] = new int[parameters];
+ for (int i = 0; i < parameters; ++i) {
+
+ // we differentiate once with respect to parameter i
+ orders[i] = 1;
+ for (int j = 0; j < point.length; ++j) {
+ partials[j] = point[j].getPartialDerivative(orders);
+ }
+ orders[i] = 0;
+
+ // compose partial derivatives
+ packed[i + 1] = LinearCombination.value(dv, partials);
+
+ }
+
+ return new DerivativeStructure(parameters, 1, packed);
+
+ }
+
+ };
+
+ }
+
+ /** Convert an {@link UnivariateDifferentiableFunction} to an
+ * {@link UnivariateFunction} computing n<sup>th</sup> order derivative.
+ * <p>
+ * This converter is only a convenience method. Beware computing only one derivative does
+ * not save any computation as the original function will really be called under the hood.
+ * The derivative will be extracted from the full {@link DerivativeStructure} result.
+ * </p>
+ * @param f original function, with value and all its derivatives
+ * @param order of the derivative to extract
+ * @return function computing the derivative at required order
+ * @see #derivative(MultivariateDifferentiableFunction, int[])
+ * @see #toDifferentiable(UnivariateFunction, UnivariateFunction...)
+ */
+ public static UnivariateFunction derivative(final UnivariateDifferentiableFunction f, final int order) {
+ return new UnivariateFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double x) {
+ final DerivativeStructure dsX = new DerivativeStructure(1, order, 0, x);
+ return f.value(dsX).getPartialDerivative(order);
+ }
+
+ };
+ }
+
+ /** Convert an {@link MultivariateDifferentiableFunction} to an
+ * {@link MultivariateFunction} computing n<sup>th</sup> order derivative.
+ * <p>
+ * This converter is only a convenience method. Beware computing only one derivative does
+ * not save any computation as the original function will really be called under the hood.
+ * The derivative will be extracted from the full {@link DerivativeStructure} result.
+ * </p>
+ * @param f original function, with value and all its derivatives
+ * @param orders of the derivative to extract, for each free parameters
+ * @return function computing the derivative at required order
+ * @see #derivative(UnivariateDifferentiableFunction, int)
+ * @see #toDifferentiable(MultivariateFunction, MultivariateVectorFunction)
+ */
+ public static MultivariateFunction derivative(final MultivariateDifferentiableFunction f, final int[] orders) {
+ return new MultivariateFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double[] point) {
+
+ // the maximum differentiation order is the sum of all orders
+ int sumOrders = 0;
+ for (final int order : orders) {
+ sumOrders += order;
+ }
+
+ // set up the input parameters
+ final DerivativeStructure[] dsPoint = new DerivativeStructure[point.length];
+ for (int i = 0; i < point.length; ++i) {
+ dsPoint[i] = new DerivativeStructure(point.length, sumOrders, i, point[i]);
+ }
+
+ return f.value(dsPoint).getPartialDerivative(orders);
+
+ }
+
+ };
+ }
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateFunction.java
new file mode 100644
index 0000000..9809217
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateFunction.java
@@ -0,0 +1,42 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a multivariate real function.
+ *
+ * @since 2.0
+ */
+public interface MultivariateFunction {
+
+ /**
+ * Compute the value for the function at the given point.
+ *
+ * @param point Point at which the function must be evaluated.
+ * @return the function value for the given point.
+ * @throws org.apache.commons.math4.legacy.exception.DimensionMismatchException
+ * if the parameter's dimension is wrong for the function being evaluated.
+ * @throws org.apache.commons.math4.legacy.exception.MathIllegalArgumentException
+ * when the activated method itself can ascertain that preconditions,
+ * specified in the API expressed at the level of the activated method,
+ * have been violated. In the vast majority of cases where Commons Math
+ * throws this exception, it is the result of argument checking of actual
+ * parameters immediately passed to a method.
+ */
+ double value(double[] point);
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateMatrixFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateMatrixFunction.java
new file mode 100644
index 0000000..1d1ba59
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateMatrixFunction.java
@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a multivariate matrix function.
+ * @since 2.0
+ */
+public interface MultivariateMatrixFunction {
+
+ /**
+ * Compute the value for the function at the given point.
+ * @param point point at which the function must be evaluated
+ * @return function value for the given point
+ * @exception IllegalArgumentException if point's dimension is wrong
+ */
+ double[][] value(double[] point)
+ throws IllegalArgumentException;
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateVectorFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateVectorFunction.java
new file mode 100644
index 0000000..2e2d41c
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/MultivariateVectorFunction.java
@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a multivariate vectorial function.
+ * @since 2.0
+ */
+public interface MultivariateVectorFunction {
+
+ /**
+ * Compute the value for the function at the given point.
+ * @param point point at which the function must be evaluated
+ * @return function value for the given point
+ * @exception IllegalArgumentException if point's dimension is wrong
+ */
+ double[] value(double[] point)
+ throws IllegalArgumentException;
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/ParametricUnivariateFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/ParametricUnivariateFunction.java
new file mode 100644
index 0000000..dca2be9
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/ParametricUnivariateFunction.java
@@ -0,0 +1,44 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a real function that depends on one independent
+ * variable plus some extra parameters.
+ *
+ * @since 3.0
+ */
+public interface ParametricUnivariateFunction {
+ /**
+ * Compute the value of the function.
+ *
+ * @param x Point for which the function value should be computed.
+ * @param parameters Function parameters.
+ * @return the value.
+ */
+ double value(double x, double ... parameters);
+
+ /**
+ * Compute the gradient of the function with respect to its parameters.
+ *
+ * @param x Point for which the function value should be computed.
+ * @param parameters Function parameters.
+ * @return the value.
+ */
+ double[] gradient(double x, double ... parameters);
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/RealFieldUnivariateFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/RealFieldUnivariateFunction.java
new file mode 100644
index 0000000..e08744c
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/RealFieldUnivariateFunction.java
@@ -0,0 +1,86 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis;
+
+import org.apache.commons.math4.legacy.RealFieldElement;
+
+/**
+ * An interface representing a univariate real function.
+ * <p>
+ * When a <em>user-defined</em> function encounters an error during
+ * evaluation, the {@link #value(RealFieldElement) value} method should throw a
+ * <em>user-defined</em> unchecked exception.</p>
+ * <p>
+ * The following code excerpt shows the recommended way to do that using
+ * a root solver as an example, but the same construct is applicable to
+ * ODE integrators or optimizers.
+ *
+ * <pre>
+ * private static class LocalException extends RuntimeException {
+ * // The x value that caused the problem.
+ * private final SomeFieldType x;
+ *
+ * public LocalException(SomeFieldType x) {
+ * this.x = x;
+ * }
+ *
+ * public double getX() {
+ * return x;
+ * }
+ * }
+ *
+ * private static class MyFunction implements FieldUnivariateFunction<SomeFieldType> {
+ * public SomeFieldType value(SomeFieldType x) {
+ * SomeFieldType y = hugeFormula(x);
+ * if (somethingBadHappens) {
+ * throw new LocalException(x);
+ * }
+ * return y;
+ * }
+ * }
+ *
+ * public void compute() {
+ * try {
+ * solver.solve(maxEval, new MyFunction(a, b, c), min, max);
+ * } catch (LocalException le) {
+ * // Retrieve the x value.
+ * }
+ * }
+ * </pre>
+ *<p>
+ * As shown, the exception is local to the user's code and it is guaranteed
+ * that Apache Commons Math will not catch it.</p>
+ *
+ * @param <T> the type of the field elements
+ * @since 3.6
+ * @see UnivariateFunction
+ */
+public interface RealFieldUnivariateFunction<T extends RealFieldElement<T>> {
+ /**
+ * Compute the value of the function.
+ *
+ * @param x Point at which the function value should be computed.
+ * @return the value of the function.
+ * @throws IllegalArgumentException when the activated method itself can
+ * ascertain that a precondition, specified in the API expressed at the
+ * level of the activated method, has been violated.
+ * When Commons Math throws an {@code IllegalArgumentException}, it is
+ * usually the consequence of checking the actual parameters passed to
+ * the method.
+ */
+ T value(T x);
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/TrivariateFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/TrivariateFunction.java
new file mode 100644
index 0000000..351018f
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/TrivariateFunction.java
@@ -0,0 +1,35 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a trivariate real function.
+ *
+ * @since 2.2
+ */
+public interface TrivariateFunction {
+ /**
+ * Compute the value for the function.
+ *
+ * @param x x-coordinate for which the function value should be computed.
+ * @param y y-coordinate for which the function value should be computed.
+ * @param z z-coordinate for which the function value should be computed.
+ * @return the value.
+ */
+ double value(double x, double y, double z);
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateFunction.java
new file mode 100644
index 0000000..ff66cbb
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateFunction.java
@@ -0,0 +1,81 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a univariate real function.
+ * <p>
+ * When a <em>user-defined</em> function encounters an error during
+ * evaluation, the {@link #value(double) value} method should throw a
+ * <em>user-defined</em> unchecked exception.</p>
+ * <p>
+ * The following code excerpt shows the recommended way to do that using
+ * a root solver as an example, but the same construct is applicable to
+ * ODE integrators or optimizers.</p>
+ *
+ * <pre>
+ * private static class LocalException extends RuntimeException {
+ * // The x value that caused the problem.
+ * private final double x;
+ *
+ * public LocalException(double x) {
+ * this.x = x;
+ * }
+ *
+ * public double getX() {
+ * return x;
+ * }
+ * }
+ *
+ * private static class MyFunction implements UnivariateFunction {
+ * public double value(double x) {
+ * double y = hugeFormula(x);
+ * if (somethingBadHappens) {
+ * throw new LocalException(x);
+ * }
+ * return y;
+ * }
+ * }
+ *
+ * public void compute() {
+ * try {
+ * solver.solve(maxEval, new MyFunction(a, b, c), min, max);
+ * } catch (LocalException le) {
+ * // Retrieve the x value.
+ * }
+ * }
+ * </pre>
+ *
+ * As shown, the exception is local to the user's code and it is guaranteed
+ * that Apache Commons Math will not catch it.
+ *
+ */
+public interface UnivariateFunction {
+ /**
+ * Compute the value of the function.
+ *
+ * @param x Point at which the function value should be computed.
+ * @return the value of the function.
+ * @throws IllegalArgumentException when the activated method itself can
+ * ascertain that a precondition, specified in the API expressed at the
+ * level of the activated method, has been violated.
+ * When Commons Math throws an {@code IllegalArgumentException}, it is
+ * usually the consequence of checking the actual parameters passed to
+ * the method.
+ */
+ double value(double x);
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateMatrixFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateMatrixFunction.java
new file mode 100644
index 0000000..ab5282e
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateMatrixFunction.java
@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a univariate matrix function.
+ *
+ * @since 2.0
+ */
+public interface UnivariateMatrixFunction {
+
+ /**
+ * Compute the value for the function.
+ * @param x the point for which the function value should be computed
+ * @return the value
+ */
+ double[][] value(double x);
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateVectorFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateVectorFunction.java
new file mode 100644
index 0000000..1688b1c
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/UnivariateVectorFunction.java
@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis;
+
+/**
+ * An interface representing a univariate vectorial function.
+ *
+ * @since 2.0
+ */
+public interface UnivariateVectorFunction {
+
+ /**
+ * Compute the value for the function.
+ * @param x the point for which the function value should be computed
+ * @return the value
+ */
+ double[] value(double x);
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DSCompiler.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DSCompiler.java
new file mode 100644
index 0000000..6310c1f
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DSCompiler.java
@@ -0,0 +1,1834 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+import java.util.concurrent.atomic.AtomicReference;
+
+import org.apache.commons.numbers.arrays.LinearCombination;
+import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
+import org.apache.commons.math4.legacy.exception.MathArithmeticException;
+import org.apache.commons.math4.legacy.exception.MathInternalError;
+import org.apache.commons.math4.legacy.exception.NotPositiveException;
+import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
+import org.apache.commons.numbers.combinatorics.FactorialDouble;
+import org.apache.commons.math4.legacy.util.FastMath;
+
+/** Class holding "compiled" computation rules for derivative structures.
+ * <p>This class implements the computation rules described in Dan Kalman's paper <a
+ * href="http://www1.american.edu/cas/mathstat/People/kalman/pdffiles/mmgautodiff.pdf">Doubly
+ * Recursive Multivariate Automatic Differentiation</a>, Mathematics Magazine, vol. 75,
+ * no. 3, June 2002. However, in order to avoid performances bottlenecks, the recursive
+ * rules are "compiled" once in an unfold form. This class does this recursion unrolling
+ * and stores the computation rules as simple loops with pre-computed indirection arrays.</p>
+ * <p>
+ * This class maps all derivative computation into single dimension arrays that hold the
+ * value and partial derivatives. The class does not hold these arrays, which remains under
+ * the responsibility of the caller. For each combination of number of free parameters and
+ * derivation order, only one compiler is necessary, and this compiler will be used to
+ * perform computations on all arrays provided to it, which can represent hundreds or
+ * thousands of different parameters kept together with all their partial derivatives.
+ * </p>
+ * <p>
+ * The arrays on which compilers operate contain only the partial derivatives together
+ * with the 0<sup>th</sup> derivative, i.e. the value. The partial derivatives are stored in
+ * a compiler-specific order, which can be retrieved using methods {@link
+ * #getPartialDerivativeIndex(int...) getPartialDerivativeIndex} and {@link
+ * #getPartialDerivativeOrders(int)}. The value is guaranteed to be stored as the first element
+ * (i.e. the {@link #getPartialDerivativeIndex(int...) getPartialDerivativeIndex} method returns
+ * 0 when called with 0 for all derivation orders and {@link #getPartialDerivativeOrders(int)
+ * getPartialDerivativeOrders} returns an array filled with 0 when called with 0 as the index).
+ * </p>
+ * <p>
+ * Note that the ordering changes with number of parameters and derivation order. For example
+ * given 2 parameters x and y, df/dy is stored at index 2 when derivation order is set to 1 (in
+ * this case the array has three elements: f, df/dx and df/dy). If derivation order is set to
+ * 2, then df/dy will be stored at index 3 (in this case the array has six elements: f, df/dx,
+ * df/dxdx, df/dy, df/dxdy and df/dydy).
+ * </p>
+ * <p>
+ * Given this structure, users can perform some simple operations like adding, subtracting
+ * or multiplying constants and negating the elements by themselves, knowing if they want to
+ * mutate their array or create a new array. These simple operations are not provided by
+ * the compiler. The compiler provides only the more complex operations between several arrays.
+ * </p>
+ * <p>This class is mainly used as the engine for scalar variable {@link DerivativeStructure}.
+ * It can also be used directly to hold several variables in arrays for more complex data
+ * structures. User can for example store a vector of n variables depending on three x, y
+ * and z free parameters in one array as follows:</p> <pre>
+ * // parameter 0 is x, parameter 1 is y, parameter 2 is z
+ * int parameters = 3;
+ * DSCompiler compiler = DSCompiler.getCompiler(parameters, order);
+ * int size = compiler.getSize();
+ *
+ * // pack all elements in a single array
+ * double[] array = new double[n * size];
+ * for (int i = 0; i < n; ++i) {
+ *
+ * // we know value is guaranteed to be the first element
+ * array[i * size] = v[i];
+ *
+ * // we don't know where first derivatives are stored, so we ask the compiler
+ * array[i * size + compiler.getPartialDerivativeIndex(1, 0, 0) = dvOnDx[i][0];
+ * array[i * size + compiler.getPartialDerivativeIndex(0, 1, 0) = dvOnDy[i][0];
+ * array[i * size + compiler.getPartialDerivativeIndex(0, 0, 1) = dvOnDz[i][0];
+ *
+ * // we let all higher order derivatives set to 0
+ *
+ * }
+ * </pre>
+ * <p>Then in another function, user can perform some operations on all elements stored
+ * in the single array, such as a simple product of all variables:</p> <pre>
+ * // compute the product of all elements
+ * double[] product = new double[size];
+ * prod[0] = 1.0;
+ * for (int i = 0; i < n; ++i) {
+ * double[] tmp = product.clone();
+ * compiler.multiply(tmp, 0, array, i * size, product, 0);
+ * }
+ *
+ * // value
+ * double p = product[0];
+ *
+ * // first derivatives
+ * double dPdX = product[compiler.getPartialDerivativeIndex(1, 0, 0)];
+ * double dPdY = product[compiler.getPartialDerivativeIndex(0, 1, 0)];
+ * double dPdZ = product[compiler.getPartialDerivativeIndex(0, 0, 1)];
+ *
+ * // cross derivatives (assuming order was at least 2)
+ * double dPdXdX = product[compiler.getPartialDerivativeIndex(2, 0, 0)];
+ * double dPdXdY = product[compiler.getPartialDerivativeIndex(1, 1, 0)];
+ * double dPdXdZ = product[compiler.getPartialDerivativeIndex(1, 0, 1)];
+ * double dPdYdY = product[compiler.getPartialDerivativeIndex(0, 2, 0)];
+ * double dPdYdZ = product[compiler.getPartialDerivativeIndex(0, 1, 1)];
+ * double dPdZdZ = product[compiler.getPartialDerivativeIndex(0, 0, 2)];
+ * </pre>
+ * @see DerivativeStructure
+ * @since 3.1
+ */
+public class DSCompiler {
+ /** Cache for factorials. */
+ private static FactorialDouble FACTORIAL = FactorialDouble.create().withCache(30);
+
+ /** Array of all compilers created so far. */
+ private static AtomicReference<DSCompiler[][]> compilers =
+ new AtomicReference<>(null);
+
+ /** Number of free parameters. */
+ private final int parameters;
+
+ /** Derivation order. */
+ private final int order;
+
+ /** Number of partial derivatives (including the single 0 order derivative element). */
+ private final int[][] sizes;
+
+ /** Indirection array for partial derivatives. */
+ private final int[][] derivativesIndirection;
+
+ /** Indirection array of the lower derivative elements. */
+ private final int[] lowerIndirection;
+
+ /** Indirection arrays for multiplication. */
+ private final int[][][] multIndirection;
+
+ /** Indirection arrays for function composition. */
+ private final int[][][] compIndirection;
+
+ /** Private constructor, reserved for the factory method {@link #getCompiler(int, int)}.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param valueCompiler compiler for the value part
+ * @param derivativeCompiler compiler for the derivative part
+ * @throws NumberIsTooLargeException if order is too large
+ */
+ private DSCompiler(final int parameters, final int order,
+ final DSCompiler valueCompiler, final DSCompiler derivativeCompiler)
+ throws NumberIsTooLargeException {
+
+ this.parameters = parameters;
+ this.order = order;
+ this.sizes = compileSizes(parameters, order, valueCompiler);
+ this.derivativesIndirection =
+ compileDerivativesIndirection(parameters, order,
+ valueCompiler, derivativeCompiler);
+ this.lowerIndirection =
+ compileLowerIndirection(parameters, order,
+ valueCompiler, derivativeCompiler);
+ this.multIndirection =
+ compileMultiplicationIndirection(parameters, order,
+ valueCompiler, derivativeCompiler, lowerIndirection);
+ this.compIndirection =
+ compileCompositionIndirection(parameters, order,
+ valueCompiler, derivativeCompiler,
+ sizes, derivativesIndirection);
+
+ }
+
+ /** Get the compiler for number of free parameters and order.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @return cached rules set
+ * @throws NumberIsTooLargeException if order is too large
+ */
+ public static DSCompiler getCompiler(int parameters, int order)
+ throws NumberIsTooLargeException {
+
+ // get the cached compilers
+ final DSCompiler[][] cache = compilers.get();
+ if (cache != null && cache.length > parameters &&
+ cache[parameters].length > order && cache[parameters][order] != null) {
+ // the compiler has already been created
+ return cache[parameters][order];
+ }
+
+ // we need to create more compilers
+ final int maxParameters = FastMath.max(parameters, cache == null ? 0 : cache.length);
+ final int maxOrder = FastMath.max(order, cache == null ? 0 : cache[0].length);
+ final DSCompiler[][] newCache = new DSCompiler[maxParameters + 1][maxOrder + 1];
+
+ if (cache != null) {
+ // preserve the already created compilers
+ for (int i = 0; i < cache.length; ++i) {
+ System.arraycopy(cache[i], 0, newCache[i], 0, cache[i].length);
+ }
+ }
+
+ // create the array in increasing diagonal order
+ for (int diag = 0; diag <= parameters + order; ++diag) {
+ for (int o = FastMath.max(0, diag - parameters); o <= FastMath.min(order, diag); ++o) {
+ final int p = diag - o;
+ if (newCache[p][o] == null) {
+ final DSCompiler valueCompiler = (p == 0) ? null : newCache[p - 1][o];
+ final DSCompiler derivativeCompiler = (o == 0) ? null : newCache[p][o - 1];
+ newCache[p][o] = new DSCompiler(p, o, valueCompiler, derivativeCompiler);
+ }
+ }
+ }
+
+ // atomically reset the cached compilers array
+ compilers.compareAndSet(cache, newCache);
+
+ return newCache[parameters][order];
+
+ }
+
+ /** Compile the sizes array.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param valueCompiler compiler for the value part
+ * @return sizes array
+ */
+ private static int[][] compileSizes(final int parameters, final int order,
+ final DSCompiler valueCompiler) {
+
+ final int[][] sizes = new int[parameters + 1][order + 1];
+ if (parameters == 0) {
+ Arrays.fill(sizes[0], 1);
+ } else {
+ System.arraycopy(valueCompiler.sizes, 0, sizes, 0, parameters);
+ sizes[parameters][0] = 1;
+ for (int i = 0; i < order; ++i) {
+ sizes[parameters][i + 1] = sizes[parameters][i] + sizes[parameters - 1][i + 1];
+ }
+ }
+
+ return sizes;
+
+ }
+
+ /** Compile the derivatives indirection array.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param valueCompiler compiler for the value part
+ * @param derivativeCompiler compiler for the derivative part
+ * @return derivatives indirection array
+ */
+ private static int[][] compileDerivativesIndirection(final int parameters, final int order,
+ final DSCompiler valueCompiler,
+ final DSCompiler derivativeCompiler) {
+
+ if (parameters == 0 || order == 0) {
+ return new int[1][parameters];
+ }
+
+ final int vSize = valueCompiler.derivativesIndirection.length;
+ final int dSize = derivativeCompiler.derivativesIndirection.length;
+ final int[][] derivativesIndirection = new int[vSize + dSize][parameters];
+
+ // set up the indices for the value part
+ for (int i = 0; i < vSize; ++i) {
+ // copy the first indices, the last one remaining set to 0
+ System.arraycopy(valueCompiler.derivativesIndirection[i], 0,
+ derivativesIndirection[i], 0,
+ parameters - 1);
+ }
+
+ // set up the indices for the derivative part
+ for (int i = 0; i < dSize; ++i) {
+
+ // copy the indices
+ System.arraycopy(derivativeCompiler.derivativesIndirection[i], 0,
+ derivativesIndirection[vSize + i], 0,
+ parameters);
+
+ // increment the derivation order for the last parameter
+ derivativesIndirection[vSize + i][parameters - 1]++;
+
+ }
+
+ return derivativesIndirection;
+
+ }
+
+ /** Compile the lower derivatives indirection array.
+ * <p>
+ * This indirection array contains the indices of all elements
+ * except derivatives for last derivation order.
+ * </p>
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param valueCompiler compiler for the value part
+ * @param derivativeCompiler compiler for the derivative part
+ * @return lower derivatives indirection array
+ */
+ private static int[] compileLowerIndirection(final int parameters, final int order,
+ final DSCompiler valueCompiler,
+ final DSCompiler derivativeCompiler) {
+
+ if (parameters == 0 || order <= 1) {
+ return new int[] { 0 };
+ }
+
+ // this is an implementation of definition 6 in Dan Kalman's paper.
+ final int vSize = valueCompiler.lowerIndirection.length;
+ final int dSize = derivativeCompiler.lowerIndirection.length;
+ final int[] lowerIndirection = new int[vSize + dSize];
+ System.arraycopy(valueCompiler.lowerIndirection, 0, lowerIndirection, 0, vSize);
+ for (int i = 0; i < dSize; ++i) {
+ lowerIndirection[vSize + i] = valueCompiler.getSize() + derivativeCompiler.lowerIndirection[i];
+ }
+
+ return lowerIndirection;
+
+ }
+
+ /** Compile the multiplication indirection array.
+ * <p>
+ * This indirection array contains the indices of all pairs of elements
+ * involved when computing a multiplication. This allows a straightforward
+ * loop-based multiplication (see {@link #multiply(double[], int, double[], int, double[], int)}).
+ * </p>
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param valueCompiler compiler for the value part
+ * @param derivativeCompiler compiler for the derivative part
+ * @param lowerIndirection lower derivatives indirection array
+ * @return multiplication indirection array
+ */
+ private static int[][][] compileMultiplicationIndirection(final int parameters, final int order,
+ final DSCompiler valueCompiler,
+ final DSCompiler derivativeCompiler,
+ final int[] lowerIndirection) {
+
+ if ((parameters == 0) || (order == 0)) {
+ return new int[][][] { { { 1, 0, 0 } } };
+ }
+
+ // this is an implementation of definition 3 in Dan Kalman's paper.
+ final int vSize = valueCompiler.multIndirection.length;
+ final int dSize = derivativeCompiler.multIndirection.length;
+ final int[][][] multIndirection = new int[vSize + dSize][][];
+
+ System.arraycopy(valueCompiler.multIndirection, 0, multIndirection, 0, vSize);
+
+ for (int i = 0; i < dSize; ++i) {
+ final int[][] dRow = derivativeCompiler.multIndirection[i];
+ List<int[]> row = new ArrayList<>(dRow.length * 2);
+ for (int j = 0; j < dRow.length; ++j) {
+ row.add(new int[] { dRow[j][0], lowerIndirection[dRow[j][1]], vSize + dRow[j][2] });
+ row.add(new int[] { dRow[j][0], vSize + dRow[j][1], lowerIndirection[dRow[j][2]] });
+ }
+
+ // combine terms with similar derivation orders
+ final List<int[]> combined = new ArrayList<>(row.size());
+ for (int j = 0; j < row.size(); ++j) {
+ final int[] termJ = row.get(j);
+ if (termJ[0] > 0) {
+ for (int k = j + 1; k < row.size(); ++k) {
+ final int[] termK = row.get(k);
+ if (termJ[1] == termK[1] && termJ[2] == termK[2]) {
+ // combine termJ and termK
+ termJ[0] += termK[0];
+ // make sure we will skip termK later on in the outer loop
+ termK[0] = 0;
+ }
+ }
+ combined.add(termJ);
+ }
+ }
+
+ multIndirection[vSize + i] = combined.toArray(new int[combined.size()][]);
+
+ }
+
+ return multIndirection;
+
+ }
+
+ /** Compile the function composition indirection array.
+ * <p>
+ * This indirection array contains the indices of all sets of elements
+ * involved when computing a composition. This allows a straightforward
+ * loop-based composition (see {@link #compose(double[], int, double[], double[], int)}).
+ * </p>
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param valueCompiler compiler for the value part
+ * @param derivativeCompiler compiler for the derivative part
+ * @param sizes sizes array
+ * @param derivativesIndirection derivatives indirection array
+ * @return multiplication indirection array
+ * @throws NumberIsTooLargeException if order is too large
+ */
+ private static int[][][] compileCompositionIndirection(final int parameters, final int order,
+ final DSCompiler valueCompiler,
+ final DSCompiler derivativeCompiler,
+ final int[][] sizes,
+ final int[][] derivativesIndirection)
+ throws NumberIsTooLargeException {
+
+ if ((parameters == 0) || (order == 0)) {
+ return new int[][][] { { { 1, 0 } } };
+ }
+
+ final int vSize = valueCompiler.compIndirection.length;
+ final int dSize = derivativeCompiler.compIndirection.length;
+ final int[][][] compIndirection = new int[vSize + dSize][][];
+
+ // the composition rules from the value part can be reused as is
+ System.arraycopy(valueCompiler.compIndirection, 0, compIndirection, 0, vSize);
+
+ // the composition rules for the derivative part are deduced by
+ // differentiation the rules from the underlying compiler once
+ // with respect to the parameter this compiler handles and the
+ // underlying one did not handle
+ for (int i = 0; i < dSize; ++i) {
+ List<int[]> row = new ArrayList<>();
+ for (int[] term : derivativeCompiler.compIndirection[i]) {
+
+ // handle term p * f_k(g(x)) * g_l1(x) * g_l2(x) * ... * g_lp(x)
+
+ // derive the first factor in the term: f_k with respect to new parameter
+ int[] derivedTermF = new int[term.length + 1];
+ derivedTermF[0] = term[0]; // p
+ derivedTermF[1] = term[1] + 1; // f_(k+1)
+ int[] orders = new int[parameters];
+ orders[parameters - 1] = 1;
+ derivedTermF[term.length] = getPartialDerivativeIndex(parameters, order, sizes, orders); // g_1
+ for (int j = 2; j < term.length; ++j) {
+ // convert the indices as the mapping for the current order
+ // is different from the mapping with one less order
+ derivedTermF[j] = convertIndex(term[j], parameters,
+ derivativeCompiler.derivativesIndirection,
+ parameters, order, sizes);
+ }
+ Arrays.sort(derivedTermF, 2, derivedTermF.length);
+ row.add(derivedTermF);
+
+ // derive the various g_l
+ for (int l = 2; l < term.length; ++l) {
+ int[] derivedTermG = new int[term.length];
+ derivedTermG[0] = term[0];
+ derivedTermG[1] = term[1];
+ for (int j = 2; j < term.length; ++j) {
+ // convert the indices as the mapping for the current order
+ // is different from the mapping with one less order
+ derivedTermG[j] = convertIndex(term[j], parameters,
+ derivativeCompiler.derivativesIndirection,
+ parameters, order, sizes);
+ if (j == l) {
+ // derive this term
+ System.arraycopy(derivativesIndirection[derivedTermG[j]], 0, orders, 0, parameters);
+ orders[parameters - 1]++;
+ derivedTermG[j] = getPartialDerivativeIndex(parameters, order, sizes, orders);
+ }
+ }
+ Arrays.sort(derivedTermG, 2, derivedTermG.length);
+ row.add(derivedTermG);
+ }
+
+ }
+
+ // combine terms with similar derivation orders
+ final List<int[]> combined = new ArrayList<>(row.size());
+ for (int j = 0; j < row.size(); ++j) {
+ final int[] termJ = row.get(j);
+ if (termJ[0] > 0) {
+ for (int k = j + 1; k < row.size(); ++k) {
+ final int[] termK = row.get(k);
+ boolean equals = termJ.length == termK.length;
+ for (int l = 1; equals && l < termJ.length; ++l) {
+ equals &= termJ[l] == termK[l];
+ }
+ if (equals) {
+ // combine termJ and termK
+ termJ[0] += termK[0];
+ // make sure we will skip termK later on in the outer loop
+ termK[0] = 0;
+ }
+ }
+ combined.add(termJ);
+ }
+ }
+
+ compIndirection[vSize + i] = combined.toArray(new int[combined.size()][]);
+
+ }
+
+ return compIndirection;
+
+ }
+
+ /** Get the index of a partial derivative in the array.
+ * <p>
+ * If all orders are set to 0, then the 0<sup>th</sup> order derivative
+ * is returned, which is the value of the function.
+ * </p>
+ * <p>The indices of derivatives are between 0 and {@link #getSize() getSize()} - 1.
+ * Their specific order is fixed for a given compiler, but otherwise not
+ * publicly specified. There are however some simple cases which have guaranteed
+ * indices:
+ * </p>
+ * <ul>
+ * <li>the index of 0<sup>th</sup> order derivative is always 0</li>
+ * <li>if there is only 1 {@link #getFreeParameters() free parameter}, then the
+ * derivatives are sorted in increasing derivation order (i.e. f at index 0, df/dp
+ * at index 1, d<sup>2</sup>f/dp<sup>2</sup> at index 2 ...
+ * d<sup>k</sup>f/dp<sup>k</sup> at index k),</li>
+ * <li>if the {@link #getOrder() derivation order} is 1, then the derivatives
+ * are sorted in increasing free parameter order (i.e. f at index 0, df/dx<sub>1</sub>
+ * at index 1, df/dx<sub>2</sub> at index 2 ... df/dx<sub>k</sub> at index k),</li>
+ * <li>all other cases are not publicly specified</li>
+ * </ul>
+ * <p>
+ * This method is the inverse of method {@link #getPartialDerivativeOrders(int)}
+ * </p>
+ * @param orders derivation orders with respect to each parameter
+ * @return index of the partial derivative
+ * @exception DimensionMismatchException if the numbers of parameters does not
+ * match the instance
+ * @exception NumberIsTooLargeException if sum of derivation orders is larger
+ * than the instance limits
+ * @see #getPartialDerivativeOrders(int)
+ */
+ public int getPartialDerivativeIndex(final int ... orders)
+ throws DimensionMismatchException, NumberIsTooLargeException {
+
+ // safety check
+ if (orders.length != getFreeParameters()) {
+ throw new DimensionMismatchException(orders.length, getFreeParameters());
+ }
+
+ return getPartialDerivativeIndex(parameters, order, sizes, orders);
+
+ }
+
+ /** Get the index of a partial derivative in an array.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param sizes sizes array
+ * @param orders derivation orders with respect to each parameter
+ * (the length of this array must match the number of parameters)
+ * @return index of the partial derivative
+ * @exception NumberIsTooLargeException if sum of derivation orders is larger
+ * than the instance limits
+ */
+ private static int getPartialDerivativeIndex(final int parameters, final int order,
+ final int[][] sizes, final int ... orders)
+ throws NumberIsTooLargeException {
+
+ // the value is obtained by diving into the recursive Dan Kalman's structure
+ // this is theorem 2 of his paper, with recursion replaced by iteration
+ int index = 0;
+ int m = order;
+ int ordersSum = 0;
+ for (int i = parameters - 1; i >= 0; --i) {
+
+ // derivative order for current free parameter
+ int derivativeOrder = orders[i];
+
+ // safety check
+ ordersSum += derivativeOrder;
+ if (ordersSum > order) {
+ throw new NumberIsTooLargeException(ordersSum, order, true);
+ }
+
+ while (derivativeOrder-- > 0) {
+ // as long as we differentiate according to current free parameter,
+ // we have to skip the value part and dive into the derivative part
+ // so we add the size of the value part to the base index
+ index += sizes[i][m--];
+ }
+
+ }
+
+ return index;
+
+ }
+
+ /** Convert an index from one (parameters, order) structure to another.
+ * @param index index of a partial derivative in source derivative structure
+ * @param srcP number of free parameters in source derivative structure
+ * @param srcDerivativesIndirection derivatives indirection array for the source
+ * derivative structure
+ * @param destP number of free parameters in destination derivative structure
+ * @param destO derivation order in destination derivative structure
+ * @param destSizes sizes array for the destination derivative structure
+ * @return index of the partial derivative with the <em>same</em> characteristics
+ * in destination derivative structure
+ * @throws NumberIsTooLargeException if order is too large
+ */
+ private static int convertIndex(final int index,
+ final int srcP, final int[][] srcDerivativesIndirection,
+ final int destP, final int destO, final int[][] destSizes)
+ throws NumberIsTooLargeException {
+ int[] orders = new int[destP];
+ System.arraycopy(srcDerivativesIndirection[index], 0, orders, 0, FastMath.min(srcP, destP));
+ return getPartialDerivativeIndex(destP, destO, destSizes, orders);
+ }
+
+ /** Get the derivation orders for a specific index in the array.
+ * <p>
+ * This method is the inverse of {@link #getPartialDerivativeIndex(int...)}.
+ * </p>
+ * @param index of the partial derivative
+ * @return orders derivation orders with respect to each parameter
+ * @see #getPartialDerivativeIndex(int...)
+ */
+ public int[] getPartialDerivativeOrders(final int index) {
+ return derivativesIndirection[index];
+ }
+
+ /** Get the number of free parameters.
+ * @return number of free parameters
+ */
+ public int getFreeParameters() {
+ return parameters;
+ }
+
+ /** Get the derivation order.
+ * @return derivation order
+ */
+ public int getOrder() {
+ return order;
+ }
+
+ /** Get the array size required for holding partial derivatives data.
+ * <p>
+ * This number includes the single 0 order derivative element, which is
+ * guaranteed to be stored in the first element of the array.
+ * </p>
+ * @return array size required for holding partial derivatives data
+ */
+ public int getSize() {
+ return sizes[parameters][order];
+ }
+
+ /** Compute linear combination.
+ * The derivative structure built will be a1 * ds1 + a2 * ds2
+ * @param a1 first scale factor
+ * @param c1 first base (unscaled) component
+ * @param offset1 offset of first operand in its array
+ * @param a2 second scale factor
+ * @param c2 second base (unscaled) component
+ * @param offset2 offset of second operand in its array
+ * @param result array where result must be stored (it may be
+ * one of the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void linearCombination(final double a1, final double[] c1, final int offset1,
+ final double a2, final double[] c2, final int offset2,
+ final double[] result, final int resultOffset) {
+ for (int i = 0; i < getSize(); ++i) {
+ result[resultOffset + i] =
+ LinearCombination.value(a1, c1[offset1 + i], a2, c2[offset2 + i]);
+ }
+ }
+
+ /** Compute linear combination.
+ * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
+ * @param a1 first scale factor
+ * @param c1 first base (unscaled) component
+ * @param offset1 offset of first operand in its array
+ * @param a2 second scale factor
+ * @param c2 second base (unscaled) component
+ * @param offset2 offset of second operand in its array
+ * @param a3 third scale factor
+ * @param c3 third base (unscaled) component
+ * @param offset3 offset of third operand in its array
+ * @param result array where result must be stored (it may be
+ * one of the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void linearCombination(final double a1, final double[] c1, final int offset1,
+ final double a2, final double[] c2, final int offset2,
+ final double a3, final double[] c3, final int offset3,
+ final double[] result, final int resultOffset) {
+ for (int i = 0; i < getSize(); ++i) {
+ result[resultOffset + i] =
+ LinearCombination.value(a1, c1[offset1 + i],
+ a2, c2[offset2 + i],
+ a3, c3[offset3 + i]);
+ }
+ }
+
+ /** Compute linear combination.
+ * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
+ * @param a1 first scale factor
+ * @param c1 first base (unscaled) component
+ * @param offset1 offset of first operand in its array
+ * @param a2 second scale factor
+ * @param c2 second base (unscaled) component
+ * @param offset2 offset of second operand in its array
+ * @param a3 third scale factor
+ * @param c3 third base (unscaled) component
+ * @param offset3 offset of third operand in its array
+ * @param a4 fourth scale factor
+ * @param c4 fourth base (unscaled) component
+ * @param offset4 offset of fourth operand in its array
+ * @param result array where result must be stored (it may be
+ * one of the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void linearCombination(final double a1, final double[] c1, final int offset1,
+ final double a2, final double[] c2, final int offset2,
+ final double a3, final double[] c3, final int offset3,
+ final double a4, final double[] c4, final int offset4,
+ final double[] result, final int resultOffset) {
+ for (int i = 0; i < getSize(); ++i) {
+ result[resultOffset + i] =
+ LinearCombination.value(a1, c1[offset1 + i],
+ a2, c2[offset2 + i],
+ a3, c3[offset3 + i],
+ a4, c4[offset4 + i]);
+ }
+ }
+
+ /** Perform addition of two derivative structures.
+ * @param lhs array holding left hand side of addition
+ * @param lhsOffset offset of the left hand side in its array
+ * @param rhs array right hand side of addition
+ * @param rhsOffset offset of the right hand side in its array
+ * @param result array where result must be stored (it may be
+ * one of the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void add(final double[] lhs, final int lhsOffset,
+ final double[] rhs, final int rhsOffset,
+ final double[] result, final int resultOffset) {
+ for (int i = 0; i < getSize(); ++i) {
+ result[resultOffset + i] = lhs[lhsOffset + i] + rhs[rhsOffset + i];
+ }
+ }
+ /** Perform subtraction of two derivative structures.
+ * @param lhs array holding left hand side of subtraction
+ * @param lhsOffset offset of the left hand side in its array
+ * @param rhs array right hand side of subtraction
+ * @param rhsOffset offset of the right hand side in its array
+ * @param result array where result must be stored (it may be
+ * one of the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void subtract(final double[] lhs, final int lhsOffset,
+ final double[] rhs, final int rhsOffset,
+ final double[] result, final int resultOffset) {
+ for (int i = 0; i < getSize(); ++i) {
+ result[resultOffset + i] = lhs[lhsOffset + i] - rhs[rhsOffset + i];
+ }
+ }
+
+ /** Perform multiplication of two derivative structures.
+ * @param lhs array holding left hand side of multiplication
+ * @param lhsOffset offset of the left hand side in its array
+ * @param rhs array right hand side of multiplication
+ * @param rhsOffset offset of the right hand side in its array
+ * @param result array where result must be stored (for
+ * multiplication the result array <em>cannot</em> be one of
+ * the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void multiply(final double[] lhs, final int lhsOffset,
+ final double[] rhs, final int rhsOffset,
+ final double[] result, final int resultOffset) {
+ for (int i = 0; i < multIndirection.length; ++i) {
+ final int[][] mappingI = multIndirection[i];
+ double r = 0;
+ for (int j = 0; j < mappingI.length; ++j) {
+ r += mappingI[j][0] *
+ lhs[lhsOffset + mappingI[j][1]] *
+ rhs[rhsOffset + mappingI[j][2]];
+ }
+ result[resultOffset + i] = r;
+ }
+ }
+
+ /** Perform division of two derivative structures.
+ * @param lhs array holding left hand side of division
+ * @param lhsOffset offset of the left hand side in its array
+ * @param rhs array right hand side of division
+ * @param rhsOffset offset of the right hand side in its array
+ * @param result array where result must be stored (for
+ * division the result array <em>cannot</em> be one of
+ * the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void divide(final double[] lhs, final int lhsOffset,
+ final double[] rhs, final int rhsOffset,
+ final double[] result, final int resultOffset) {
+ final double[] reciprocal = new double[getSize()];
+ pow(rhs, lhsOffset, -1, reciprocal, 0);
+ multiply(lhs, lhsOffset, reciprocal, 0, result, resultOffset);
+ }
+
+ /** Perform remainder of two derivative structures.
+ * @param lhs array holding left hand side of remainder
+ * @param lhsOffset offset of the left hand side in its array
+ * @param rhs array right hand side of remainder
+ * @param rhsOffset offset of the right hand side in its array
+ * @param result array where result must be stored (it may be
+ * one of the input arrays)
+ * @param resultOffset offset of the result in its array
+ */
+ public void remainder(final double[] lhs, final int lhsOffset,
+ final double[] rhs, final int rhsOffset,
+ final double[] result, final int resultOffset) {
+
+ // compute k such that lhs % rhs = lhs - k rhs
+ final double rem = FastMath.IEEEremainder(lhs[lhsOffset], rhs[rhsOffset]);
+ final double k = FastMath.rint((lhs[lhsOffset] - rem) / rhs[rhsOffset]);
+
+ // set up value
+ result[resultOffset] = rem;
+
+ // set up partial derivatives
+ for (int i = 1; i < getSize(); ++i) {
+ result[resultOffset + i] = lhs[lhsOffset + i] - k * rhs[rhsOffset + i];
+ }
+
+ }
+
+ /** Compute power of a double to a derivative structure.
+ * @param a number to exponentiate
+ * @param operand array holding the power
+ * @param operandOffset offset of the power in its array
+ * @param result array where result must be stored (for
+ * power the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ * @since 3.3
+ */
+ public void pow(final double a,
+ final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ // [a^x, ln(a) a^x, ln(a)^2 a^x,, ln(a)^3 a^x, ... ]
+ final double[] function = new double[1 + order];
+ if (a == 0) {
+ if (operand[operandOffset] == 0) {
+ function[0] = 1;
+ double infinity = Double.POSITIVE_INFINITY;
+ for (int i = 1; i < function.length; ++i) {
+ infinity = -infinity;
+ function[i] = infinity;
+ }
+ } else if (operand[operandOffset] < 0) {
+ Arrays.fill(function, Double.NaN);
+ }
+ } else {
+ function[0] = FastMath.pow(a, operand[operandOffset]);
+ final double lnA = FastMath.log(a);
+ for (int i = 1; i < function.length; ++i) {
+ function[i] = lnA * function[i - 1];
+ }
+ }
+
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute power of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param p power to apply
+ * @param result array where result must be stored (for
+ * power the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void pow(final double[] operand, final int operandOffset, final double p,
+ final double[] result, final int resultOffset) {
+
+ if (p == 0) {
+ // special case, x^0 = 1 for all x
+ result[resultOffset] = 1.0;
+ Arrays.fill(result, resultOffset + 1, resultOffset + getSize(), 0);
+ return;
+ }
+
+ if (operand[operandOffset] == 0) {
+ // special case, 0^p = 0 for all p
+ Arrays.fill(result, resultOffset, resultOffset + getSize(), 0);
+ return;
+ }
+
+ // create the function value and derivatives
+ // [x^p, px^(p-1), p(p-1)x^(p-2), ... ]
+ double[] function = new double[1 + order];
+ double xk = FastMath.pow(operand[operandOffset], p - order);
+ for (int i = order; i > 0; --i) {
+ function[i] = xk;
+ xk *= operand[operandOffset];
+ }
+ function[0] = xk;
+ double coefficient = p;
+ for (int i = 1; i <= order; ++i) {
+ function[i] *= coefficient;
+ coefficient *= p - i;
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute integer power of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param n power to apply
+ * @param result array where result must be stored (for
+ * power the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void pow(final double[] operand, final int operandOffset, final int n,
+ final double[] result, final int resultOffset) {
+
+ if (n == 0) {
+ // special case, x^0 = 1 for all x
+ result[resultOffset] = 1.0;
+ Arrays.fill(result, resultOffset + 1, resultOffset + getSize(), 0);
+ return;
+ }
+
+ // create the power function value and derivatives
+ // [x^n, nx^(n-1), n(n-1)x^(n-2), ... ]
+ double[] function = new double[1 + order];
+
+ if (n > 0) {
+ // strictly positive power
+ final int maxOrder = FastMath.min(order, n);
+ double xk = FastMath.pow(operand[operandOffset], n - maxOrder);
+ for (int i = maxOrder; i > 0; --i) {
+ function[i] = xk;
+ xk *= operand[operandOffset];
+ }
+ function[0] = xk;
+ } else {
+ // strictly negative power
+ final double inv = 1.0 / operand[operandOffset];
+ double xk = FastMath.pow(inv, -n);
+ for (int i = 0; i <= order; ++i) {
+ function[i] = xk;
+ xk *= inv;
+ }
+ }
+
+ double coefficient = n;
+ for (int i = 1; i <= order; ++i) {
+ function[i] *= coefficient;
+ coefficient *= n - i;
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute power of a derivative structure.
+ * @param x array holding the base
+ * @param xOffset offset of the base in its array
+ * @param y array holding the exponent
+ * @param yOffset offset of the exponent in its array
+ * @param result array where result must be stored (for
+ * power the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void pow(final double[] x, final int xOffset,
+ final double[] y, final int yOffset,
+ final double[] result, final int resultOffset) {
+ final double[] logX = new double[getSize()];
+ log(x, xOffset, logX, 0);
+ final double[] yLogX = new double[getSize()];
+ multiply(logX, 0, y, yOffset, yLogX, 0);
+ exp(yLogX, 0, result, resultOffset);
+ }
+
+ /** Compute n<sup>th</sup> root of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param n order of the root
+ * @param result array where result must be stored (for
+ * n<sup>th</sup> root the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void rootN(final double[] operand, final int operandOffset, final int n,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ // [x^(1/n), (1/n)x^((1/n)-1), (1-n)/n^2x^((1/n)-2), ... ]
+ double[] function = new double[1 + order];
+ double xk;
+ if (n == 2) {
+ function[0] = FastMath.sqrt(operand[operandOffset]);
+ xk = 0.5 / function[0];
+ } else if (n == 3) {
+ function[0] = FastMath.cbrt(operand[operandOffset]);
+ xk = 1.0 / (3.0 * function[0] * function[0]);
+ } else {
+ function[0] = FastMath.pow(operand[operandOffset], 1.0 / n);
+ xk = 1.0 / (n * FastMath.pow(function[0], n - 1));
+ }
+ final double nReciprocal = 1.0 / n;
+ final double xReciprocal = 1.0 / operand[operandOffset];
+ for (int i = 1; i <= order; ++i) {
+ function[i] = xk;
+ xk *= xReciprocal * (nReciprocal - i);
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute exponential of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * exponential the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void exp(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ Arrays.fill(function, FastMath.exp(operand[operandOffset]));
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute exp(x) - 1 of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * exponential the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void expm1(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.expm1(operand[operandOffset]);
+ Arrays.fill(function, 1, 1 + order, FastMath.exp(operand[operandOffset]));
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute natural logarithm of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * logarithm the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void log(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.log(operand[operandOffset]);
+ if (order > 0) {
+ double inv = 1.0 / operand[operandOffset];
+ double xk = inv;
+ for (int i = 1; i <= order; ++i) {
+ function[i] = xk;
+ xk *= -i * inv;
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Computes shifted logarithm of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * shifted logarithm the result array <em>cannot</em> be the input array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void log1p(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.log1p(operand[operandOffset]);
+ if (order > 0) {
+ double inv = 1.0 / (1.0 + operand[operandOffset]);
+ double xk = inv;
+ for (int i = 1; i <= order; ++i) {
+ function[i] = xk;
+ xk *= -i * inv;
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Computes base 10 logarithm of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * base 10 logarithm the result array <em>cannot</em> be the input array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void log10(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.log10(operand[operandOffset]);
+ if (order > 0) {
+ double inv = 1.0 / operand[operandOffset];
+ double xk = inv / FastMath.log(10.0);
+ for (int i = 1; i <= order; ++i) {
+ function[i] = xk;
+ xk *= -i * inv;
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute cosine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * cosine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void cos(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.cos(operand[operandOffset]);
+ if (order > 0) {
+ function[1] = -FastMath.sin(operand[operandOffset]);
+ for (int i = 2; i <= order; ++i) {
+ function[i] = -function[i - 2];
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute sine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * sine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void sin(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.sin(operand[operandOffset]);
+ if (order > 0) {
+ function[1] = FastMath.cos(operand[operandOffset]);
+ for (int i = 2; i <= order; ++i) {
+ function[i] = -function[i - 2];
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute tangent of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * tangent the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void tan(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ final double[] function = new double[1 + order];
+ final double t = FastMath.tan(operand[operandOffset]);
+ function[0] = t;
+
+ if (order > 0) {
+
+ // the nth order derivative of tan has the form:
+ // dn(tan(x)/dxn = P_n(tan(x))
+ // where P_n(t) is a degree n+1 polynomial with same parity as n+1
+ // P_0(t) = t, P_1(t) = 1 + t^2, P_2(t) = 2 t (1 + t^2) ...
+ // the general recurrence relation for P_n is:
+ // P_n(x) = (1+t^2) P_(n-1)'(t)
+ // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
+ final double[] p = new double[order + 2];
+ p[1] = 1;
+ final double t2 = t * t;
+ for (int n = 1; n <= order; ++n) {
+
+ // update and evaluate polynomial P_n(t)
+ double v = 0;
+ p[n + 1] = n * p[n];
+ for (int k = n + 1; k >= 0; k -= 2) {
+ v = v * t2 + p[k];
+ if (k > 2) {
+ p[k - 2] = (k - 1) * p[k - 1] + (k - 3) * p[k - 3];
+ } else if (k == 2) {
+ p[0] = p[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= t;
+ }
+
+ function[n] = v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute arc cosine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * arc cosine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void acos(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ final double x = operand[operandOffset];
+ function[0] = FastMath.acos(x);
+ if (order > 0) {
+ // the nth order derivative of acos has the form:
+ // dn(acos(x)/dxn = P_n(x) / [1 - x^2]^((2n-1)/2)
+ // where P_n(x) is a degree n-1 polynomial with same parity as n-1
+ // P_1(x) = -1, P_2(x) = -x, P_3(x) = -2x^2 - 1 ...
+ // the general recurrence relation for P_n is:
+ // P_n(x) = (1-x^2) P_(n-1)'(x) + (2n-3) x P_(n-1)(x)
+ // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
+ final double[] p = new double[order];
+ p[0] = -1;
+ final double x2 = x * x;
+ final double f = 1.0 / (1 - x2);
+ double coeff = FastMath.sqrt(f);
+ function[1] = coeff * p[0];
+ for (int n = 2; n <= order; ++n) {
+
+ // update and evaluate polynomial P_n(x)
+ double v = 0;
+ p[n - 1] = (n - 1) * p[n - 2];
+ for (int k = n - 1; k >= 0; k -= 2) {
+ v = v * x2 + p[k];
+ if (k > 2) {
+ p[k - 2] = (k - 1) * p[k - 1] + (2 * n - k) * p[k - 3];
+ } else if (k == 2) {
+ p[0] = p[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= x;
+ }
+
+ coeff *= f;
+ function[n] = coeff * v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute arc sine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * arc sine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void asin(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ final double x = operand[operandOffset];
+ function[0] = FastMath.asin(x);
+ if (order > 0) {
+ // the nth order derivative of asin has the form:
+ // dn(asin(x)/dxn = P_n(x) / [1 - x^2]^((2n-1)/2)
+ // where P_n(x) is a degree n-1 polynomial with same parity as n-1
+ // P_1(x) = 1, P_2(x) = x, P_3(x) = 2x^2 + 1 ...
+ // the general recurrence relation for P_n is:
+ // P_n(x) = (1-x^2) P_(n-1)'(x) + (2n-3) x P_(n-1)(x)
+ // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
+ final double[] p = new double[order];
+ p[0] = 1;
+ final double x2 = x * x;
+ final double f = 1.0 / (1 - x2);
+ double coeff = FastMath.sqrt(f);
+ function[1] = coeff * p[0];
+ for (int n = 2; n <= order; ++n) {
+
+ // update and evaluate polynomial P_n(x)
+ double v = 0;
+ p[n - 1] = (n - 1) * p[n - 2];
+ for (int k = n - 1; k >= 0; k -= 2) {
+ v = v * x2 + p[k];
+ if (k > 2) {
+ p[k - 2] = (k - 1) * p[k - 1] + (2 * n - k) * p[k - 3];
+ } else if (k == 2) {
+ p[0] = p[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= x;
+ }
+
+ coeff *= f;
+ function[n] = coeff * v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute arc tangent of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * arc tangent the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void atan(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ final double x = operand[operandOffset];
+ function[0] = FastMath.atan(x);
+ if (order > 0) {
+ // the nth order derivative of atan has the form:
+ // dn(atan(x)/dxn = Q_n(x) / (1 + x^2)^n
+ // where Q_n(x) is a degree n-1 polynomial with same parity as n-1
+ // Q_1(x) = 1, Q_2(x) = -2x, Q_3(x) = 6x^2 - 2 ...
+ // the general recurrence relation for Q_n is:
+ // Q_n(x) = (1+x^2) Q_(n-1)'(x) - 2(n-1) x Q_(n-1)(x)
+ // as per polynomial parity, we can store coefficients of both Q_(n-1) and Q_n in the same array
+ final double[] q = new double[order];
+ q[0] = 1;
+ final double x2 = x * x;
+ final double f = 1.0 / (1 + x2);
+ double coeff = f;
+ function[1] = coeff * q[0];
+ for (int n = 2; n <= order; ++n) {
+
+ // update and evaluate polynomial Q_n(x)
+ double v = 0;
+ q[n - 1] = -n * q[n - 2];
+ for (int k = n - 1; k >= 0; k -= 2) {
+ v = v * x2 + q[k];
+ if (k > 2) {
+ q[k - 2] = (k - 1) * q[k - 1] + (k - 1 - 2 * n) * q[k - 3];
+ } else if (k == 2) {
+ q[0] = q[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= x;
+ }
+
+ coeff *= f;
+ function[n] = coeff * v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute two arguments arc tangent of a derivative structure.
+ * @param y array holding the first operand
+ * @param yOffset offset of the first operand in its array
+ * @param x array holding the second operand
+ * @param xOffset offset of the second operand in its array
+ * @param result array where result must be stored (for
+ * two arguments arc tangent the result array <em>cannot</em>
+ * be the input array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void atan2(final double[] y, final int yOffset,
+ final double[] x, final int xOffset,
+ final double[] result, final int resultOffset) {
+
+ // compute r = sqrt(x^2+y^2)
+ double[] tmp1 = new double[getSize()];
+ multiply(x, xOffset, x, xOffset, tmp1, 0); // x^2
+ double[] tmp2 = new double[getSize()];
+ multiply(y, yOffset, y, yOffset, tmp2, 0); // y^2
+ add(tmp1, 0, tmp2, 0, tmp2, 0); // x^2 + y^2
+ rootN(tmp2, 0, 2, tmp1, 0); // r = sqrt(x^2 + y^2)
+
+ if (x[xOffset] >= 0) {
+
+ // compute atan2(y, x) = 2 atan(y / (r + x))
+ add(tmp1, 0, x, xOffset, tmp2, 0); // r + x
+ divide(y, yOffset, tmp2, 0, tmp1, 0); // y /(r + x)
+ atan(tmp1, 0, tmp2, 0); // atan(y / (r + x))
+ for (int i = 0; i < tmp2.length; ++i) {
+ result[resultOffset + i] = 2 * tmp2[i]; // 2 * atan(y / (r + x))
+ }
+
+ } else {
+
+ // compute atan2(y, x) = +/- pi - 2 atan(y / (r - x))
+ subtract(tmp1, 0, x, xOffset, tmp2, 0); // r - x
+ divide(y, yOffset, tmp2, 0, tmp1, 0); // y /(r - x)
+ atan(tmp1, 0, tmp2, 0); // atan(y / (r - x))
+ result[resultOffset] =
+ ((tmp2[0] <= 0) ? -FastMath.PI : FastMath.PI) - 2 * tmp2[0]; // +/-pi - 2 * atan(y / (r - x))
+ for (int i = 1; i < tmp2.length; ++i) {
+ result[resultOffset + i] = -2 * tmp2[i]; // +/-pi - 2 * atan(y / (r - x))
+ }
+
+ }
+
+ // fix value to take special cases (+0/+0, +0/-0, -0/+0, -0/-0, +/-infinity) correctly
+ result[resultOffset] = FastMath.atan2(y[yOffset], x[xOffset]);
+
+ }
+
+ /** Compute hyperbolic cosine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * hyperbolic cosine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void cosh(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.cosh(operand[operandOffset]);
+ if (order > 0) {
+ function[1] = FastMath.sinh(operand[operandOffset]);
+ for (int i = 2; i <= order; ++i) {
+ function[i] = function[i - 2];
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute hyperbolic sine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * hyperbolic sine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void sinh(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ function[0] = FastMath.sinh(operand[operandOffset]);
+ if (order > 0) {
+ function[1] = FastMath.cosh(operand[operandOffset]);
+ for (int i = 2; i <= order; ++i) {
+ function[i] = function[i - 2];
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute hyperbolic tangent of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * hyperbolic tangent the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void tanh(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ final double[] function = new double[1 + order];
+ final double t = FastMath.tanh(operand[operandOffset]);
+ function[0] = t;
+
+ if (order > 0) {
+
+ // the nth order derivative of tanh has the form:
+ // dn(tanh(x)/dxn = P_n(tanh(x))
+ // where P_n(t) is a degree n+1 polynomial with same parity as n+1
+ // P_0(t) = t, P_1(t) = 1 - t^2, P_2(t) = -2 t (1 - t^2) ...
+ // the general recurrence relation for P_n is:
+ // P_n(x) = (1-t^2) P_(n-1)'(t)
+ // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
+ final double[] p = new double[order + 2];
+ p[1] = 1;
+ final double t2 = t * t;
+ for (int n = 1; n <= order; ++n) {
+
+ // update and evaluate polynomial P_n(t)
+ double v = 0;
+ p[n + 1] = -n * p[n];
+ for (int k = n + 1; k >= 0; k -= 2) {
+ v = v * t2 + p[k];
+ if (k > 2) {
+ p[k - 2] = (k - 1) * p[k - 1] - (k - 3) * p[k - 3];
+ } else if (k == 2) {
+ p[0] = p[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= t;
+ }
+
+ function[n] = v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute inverse hyperbolic cosine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * inverse hyperbolic cosine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void acosh(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ final double x = operand[operandOffset];
+ function[0] = FastMath.acosh(x);
+ if (order > 0) {
+ // the nth order derivative of acosh has the form:
+ // dn(acosh(x)/dxn = P_n(x) / [x^2 - 1]^((2n-1)/2)
+ // where P_n(x) is a degree n-1 polynomial with same parity as n-1
+ // P_1(x) = 1, P_2(x) = -x, P_3(x) = 2x^2 + 1 ...
+ // the general recurrence relation for P_n is:
+ // P_n(x) = (x^2-1) P_(n-1)'(x) - (2n-3) x P_(n-1)(x)
+ // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
+ final double[] p = new double[order];
+ p[0] = 1;
+ final double x2 = x * x;
+ final double f = 1.0 / (x2 - 1);
+ double coeff = FastMath.sqrt(f);
+ function[1] = coeff * p[0];
+ for (int n = 2; n <= order; ++n) {
+
+ // update and evaluate polynomial P_n(x)
+ double v = 0;
+ p[n - 1] = (1 - n) * p[n - 2];
+ for (int k = n - 1; k >= 0; k -= 2) {
+ v = v * x2 + p[k];
+ if (k > 2) {
+ p[k - 2] = (1 - k) * p[k - 1] + (k - 2 * n) * p[k - 3];
+ } else if (k == 2) {
+ p[0] = -p[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= x;
+ }
+
+ coeff *= f;
+ function[n] = coeff * v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute inverse hyperbolic sine of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * inverse hyperbolic sine the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void asinh(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ final double x = operand[operandOffset];
+ function[0] = FastMath.asinh(x);
+ if (order > 0) {
+ // the nth order derivative of asinh has the form:
+ // dn(asinh(x)/dxn = P_n(x) / [x^2 + 1]^((2n-1)/2)
+ // where P_n(x) is a degree n-1 polynomial with same parity as n-1
+ // P_1(x) = 1, P_2(x) = -x, P_3(x) = 2x^2 - 1 ...
+ // the general recurrence relation for P_n is:
+ // P_n(x) = (x^2+1) P_(n-1)'(x) - (2n-3) x P_(n-1)(x)
+ // as per polynomial parity, we can store coefficients of both P_(n-1) and P_n in the same array
+ final double[] p = new double[order];
+ p[0] = 1;
+ final double x2 = x * x;
+ final double f = 1.0 / (1 + x2);
+ double coeff = FastMath.sqrt(f);
+ function[1] = coeff * p[0];
+ for (int n = 2; n <= order; ++n) {
+
+ // update and evaluate polynomial P_n(x)
+ double v = 0;
+ p[n - 1] = (1 - n) * p[n - 2];
+ for (int k = n - 1; k >= 0; k -= 2) {
+ v = v * x2 + p[k];
+ if (k > 2) {
+ p[k - 2] = (k - 1) * p[k - 1] + (k - 2 * n) * p[k - 3];
+ } else if (k == 2) {
+ p[0] = p[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= x;
+ }
+
+ coeff *= f;
+ function[n] = coeff * v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute inverse hyperbolic tangent of a derivative structure.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param result array where result must be stored (for
+ * inverse hyperbolic tangent the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void atanh(final double[] operand, final int operandOffset,
+ final double[] result, final int resultOffset) {
+
+ // create the function value and derivatives
+ double[] function = new double[1 + order];
+ final double x = operand[operandOffset];
+ function[0] = FastMath.atanh(x);
+ if (order > 0) {
+ // the nth order derivative of atanh has the form:
+ // dn(atanh(x)/dxn = Q_n(x) / (1 - x^2)^n
+ // where Q_n(x) is a degree n-1 polynomial with same parity as n-1
+ // Q_1(x) = 1, Q_2(x) = 2x, Q_3(x) = 6x^2 + 2 ...
+ // the general recurrence relation for Q_n is:
+ // Q_n(x) = (1-x^2) Q_(n-1)'(x) + 2(n-1) x Q_(n-1)(x)
+ // as per polynomial parity, we can store coefficients of both Q_(n-1) and Q_n in the same array
+ final double[] q = new double[order];
+ q[0] = 1;
+ final double x2 = x * x;
+ final double f = 1.0 / (1 - x2);
+ double coeff = f;
+ function[1] = coeff * q[0];
+ for (int n = 2; n <= order; ++n) {
+
+ // update and evaluate polynomial Q_n(x)
+ double v = 0;
+ q[n - 1] = n * q[n - 2];
+ for (int k = n - 1; k >= 0; k -= 2) {
+ v = v * x2 + q[k];
+ if (k > 2) {
+ q[k - 2] = (k - 1) * q[k - 1] + (2 * n - k + 1) * q[k - 3];
+ } else if (k == 2) {
+ q[0] = q[1];
+ }
+ }
+ if ((n & 0x1) == 0) {
+ v *= x;
+ }
+
+ coeff *= f;
+ function[n] = coeff * v;
+
+ }
+ }
+
+ // apply function composition
+ compose(operand, operandOffset, function, result, resultOffset);
+
+ }
+
+ /** Compute composition of a derivative structure by a function.
+ * @param operand array holding the operand
+ * @param operandOffset offset of the operand in its array
+ * @param f array of value and derivatives of the function at
+ * the current point (i.e. at {@code operand[operandOffset]}).
+ * @param result array where result must be stored (for
+ * composition the result array <em>cannot</em> be the input
+ * array)
+ * @param resultOffset offset of the result in its array
+ */
+ public void compose(final double[] operand, final int operandOffset, final double[] f,
+ final double[] result, final int resultOffset) {
+ for (int i = 0; i < compIndirection.length; ++i) {
+ final int[][] mappingI = compIndirection[i];
+ double r = 0;
+ for (int j = 0; j < mappingI.length; ++j) {
+ final int[] mappingIJ = mappingI[j];
+ double product = mappingIJ[0] * f[mappingIJ[1]];
+ for (int k = 2; k < mappingIJ.length; ++k) {
+ product *= operand[operandOffset + mappingIJ[k]];
+ }
+ r += product;
+ }
+ result[resultOffset + i] = r;
+ }
+ }
+
+ /** Evaluate Taylor expansion of a derivative structure.
+ * @param ds array holding the derivative structure
+ * @param dsOffset offset of the derivative structure in its array
+ * @param delta parameters offsets (Δx, Δy, ...)
+ * @return value of the Taylor expansion at x + Δx, y + Δy, ...
+ * @throws MathArithmeticException if factorials becomes too large
+ */
+ public double taylor(final double[] ds, final int dsOffset, final double ... delta)
+ throws MathArithmeticException {
+ double value = 0;
+ for (int i = getSize() - 1; i >= 0; --i) {
+ final int[] orders = getPartialDerivativeOrders(i);
+ double term = ds[dsOffset + i];
+ for (int k = 0; k < orders.length; ++k) {
+ if (orders[k] > 0) {
+ try {
+ term *= FastMath.pow(delta[k], orders[k]) / FACTORIAL.value(orders[k]);
+ } catch (NotPositiveException e) {
+ // this cannot happen
+ throw new MathInternalError(e);
+ }
+ }
+ }
+ value += term;
+ }
+ return value;
+ }
+
+ /** Check rules set compatibility.
+ * @param compiler other compiler to check against instance
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ public void checkCompatibility(final DSCompiler compiler)
+ throws DimensionMismatchException {
+ if (parameters != compiler.parameters) {
+ throw new DimensionMismatchException(parameters, compiler.parameters);
+ }
+ if (order != compiler.order) {
+ throw new DimensionMismatchException(order, compiler.order);
+ }
+ }
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java
new file mode 100644
index 0000000..56ea24c
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/DerivativeStructure.java
@@ -0,0 +1,1256 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import java.io.Serializable;
+
+import org.apache.commons.numbers.arrays.LinearCombination;
+import org.apache.commons.math4.legacy.Field;
+import org.apache.commons.math4.legacy.FieldElement;
+import org.apache.commons.math4.legacy.RealFieldElement;
+import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
+import org.apache.commons.math4.legacy.exception.MathArithmeticException;
+import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
+import org.apache.commons.math4.legacy.util.FastMath;
+import org.apache.commons.math4.legacy.util.MathArrays;
+import org.apache.commons.math4.legacy.util.MathUtils;
+
+/** Class representing both the value and the differentials of a function.
+ * <p>This class is the workhorse of the differentiation package.</p>
+ * <p>This class is an implementation of the extension to Rall's
+ * numbers described in Dan Kalman's paper <a
+ * href="http://www1.american.edu/cas/mathstat/People/kalman/pdffiles/mmgautodiff.pdf">Doubly
+ * Recursive Multivariate Automatic Differentiation</a>, Mathematics Magazine, vol. 75,
+ * no. 3, June 2002. Rall's numbers are an extension to the real numbers used
+ * throughout mathematical expressions; they hold the derivative together with the
+ * value of a function. Dan Kalman's derivative structures hold all partial derivatives
+ * up to any specified order, with respect to any number of free parameters. Rall's
+ * numbers therefore can be seen as derivative structures for order one derivative and
+ * one free parameter, and real numbers can be seen as derivative structures with zero
+ * order derivative and no free parameters.</p>
+ * <p>{@link DerivativeStructure} instances can be used directly thanks to
+ * the arithmetic operators to the mathematical functions provided as
+ * methods by this class (+, -, *, /, %, sin, cos ...).</p>
+ * <p>Implementing complex expressions by hand using these classes is
+ * a tedious and error-prone task but has the advantage of having no limitation
+ * on the derivation order despite not requiring users to compute the derivatives by
+ * themselves. Implementing complex expression can also be done by developing computation
+ * code using standard primitive double values and to use {@link
+ * UnivariateFunctionDifferentiator differentiators} to create the {@link
+ * DerivativeStructure}-based instances. This method is simpler but may be limited in
+ * the accuracy and derivation orders and may be computationally intensive (this is
+ * typically the case for {@link FiniteDifferencesDifferentiator finite differences
+ * differentiator}.</p>
+ * <p>Instances of this class are guaranteed to be immutable.</p>
+ * @see DSCompiler
+ * @since 3.1
+ */
+public class DerivativeStructure implements RealFieldElement<DerivativeStructure>, Serializable {
+
+ /** Serializable UID. */
+ private static final long serialVersionUID = 20120730L;
+
+ /** Compiler for the current dimensions. */
+ private transient DSCompiler compiler;
+
+ /** Combined array holding all values. */
+ private final double[] data;
+
+ /** Build an instance with all values and derivatives set to 0.
+ * @param compiler compiler to use for computation
+ */
+ private DerivativeStructure(final DSCompiler compiler) {
+ this.compiler = compiler;
+ this.data = new double[compiler.getSize()];
+ }
+
+ /** Build an instance with all values and derivatives set to 0.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @throws NumberIsTooLargeException if order is too large
+ */
+ public DerivativeStructure(final int parameters, final int order)
+ throws NumberIsTooLargeException {
+ this(DSCompiler.getCompiler(parameters, order));
+ }
+
+ /** Build an instance representing a constant value.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param value value of the constant
+ * @throws NumberIsTooLargeException if order is too large
+ * @see #DerivativeStructure(int, int, int, double)
+ */
+ public DerivativeStructure(final int parameters, final int order, final double value)
+ throws NumberIsTooLargeException {
+ this(parameters, order);
+ this.data[0] = value;
+ }
+
+ /** Build an instance representing a variable.
+ * <p>Instances built using this constructor are considered
+ * to be the free variables with respect to which differentials
+ * are computed. As such, their differential with respect to
+ * themselves is +1.</p>
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param index index of the variable (from 0 to {@code parameters - 1})
+ * @param value value of the variable
+ * @exception NumberIsTooLargeException if {@code index ≥ parameters}.
+ * @see #DerivativeStructure(int, int, double)
+ */
+ public DerivativeStructure(final int parameters, final int order,
+ final int index, final double value)
+ throws NumberIsTooLargeException {
+ this(parameters, order, value);
+
+ if (index >= parameters) {
+ throw new NumberIsTooLargeException(index, parameters, false);
+ }
+
+ if (order > 0) {
+ // the derivative of the variable with respect to itself is 1.
+ data[DSCompiler.getCompiler(index, order).getSize()] = 1.0;
+ }
+
+ }
+
+ /** Linear combination constructor.
+ * The derivative structure built will be a1 * ds1 + a2 * ds2
+ * @param a1 first scale factor
+ * @param ds1 first base (unscaled) derivative structure
+ * @param a2 second scale factor
+ * @param ds2 second base (unscaled) derivative structure
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ public DerivativeStructure(final double a1, final DerivativeStructure ds1,
+ final double a2, final DerivativeStructure ds2)
+ throws DimensionMismatchException {
+ this(ds1.compiler);
+ compiler.checkCompatibility(ds2.compiler);
+ compiler.linearCombination(a1, ds1.data, 0, a2, ds2.data, 0, data, 0);
+ }
+
+ /** Linear combination constructor.
+ * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3
+ * @param a1 first scale factor
+ * @param ds1 first base (unscaled) derivative structure
+ * @param a2 second scale factor
+ * @param ds2 second base (unscaled) derivative structure
+ * @param a3 third scale factor
+ * @param ds3 third base (unscaled) derivative structure
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ public DerivativeStructure(final double a1, final DerivativeStructure ds1,
+ final double a2, final DerivativeStructure ds2,
+ final double a3, final DerivativeStructure ds3)
+ throws DimensionMismatchException {
+ this(ds1.compiler);
+ compiler.checkCompatibility(ds2.compiler);
+ compiler.checkCompatibility(ds3.compiler);
+ compiler.linearCombination(a1, ds1.data, 0, a2, ds2.data, 0, a3, ds3.data, 0, data, 0);
+ }
+
+ /** Linear combination constructor.
+ * The derivative structure built will be a1 * ds1 + a2 * ds2 + a3 * ds3 + a4 * ds4
+ * @param a1 first scale factor
+ * @param ds1 first base (unscaled) derivative structure
+ * @param a2 second scale factor
+ * @param ds2 second base (unscaled) derivative structure
+ * @param a3 third scale factor
+ * @param ds3 third base (unscaled) derivative structure
+ * @param a4 fourth scale factor
+ * @param ds4 fourth base (unscaled) derivative structure
+ * @exception DimensionMismatchException if number of free parameters or orders are inconsistent
+ */
+ public DerivativeStructure(final double a1, final DerivativeStructure ds1,
+ final double a2, final DerivativeStructure ds2,
+ final double a3, final DerivativeStructure ds3,
+ final double a4, final DerivativeStructure ds4)
+ throws DimensionMismatchException {
+ this(ds1.compiler);
+ compiler.checkCompatibility(ds2.compiler);
+ compiler.checkCompatibility(ds3.compiler);
+ compiler.checkCompatibility(ds4.compiler);
+ compiler.linearCombination(a1, ds1.data, 0, a2, ds2.data, 0,
+ a3, ds3.data, 0, a4, ds4.data, 0,
+ data, 0);
+ }
+
+ /** Build an instance from all its derivatives.
+ * @param parameters number of free parameters
+ * @param order derivation order
+ * @param derivatives derivatives sorted according to
+ * {@link DSCompiler#getPartialDerivativeIndex(int...)}
+ * @exception DimensionMismatchException if derivatives array does not match the
+ * {@link DSCompiler#getSize() size} expected by the compiler
+ * @throws NumberIsTooLargeException if order is too large
+ * @see #getAllDerivatives()
+ */
+ public DerivativeStructure(final int parameters, final int order, final double ... derivatives)
+ throws DimensionMismatchException, NumberIsTooLargeException {
+ this(parameters, order);
+ if (derivatives.length != data.length) {
+ throw new DimensionMismatchException(derivatives.length, data.length);
+ }
+ System.arraycopy(derivatives, 0, data, 0, data.length);
+ }
+
+ /** Copy constructor.
+ * @param ds instance to copy
+ */
+ private DerivativeStructure(final DerivativeStructure ds) {
+ this.compiler = ds.compiler;
+ this.data = ds.data.clone();
+ }
+
+ /** Get the number of free parameters.
+ * @return number of free parameters
+ */
+ public int getFreeParameters() {
+ return compiler.getFreeParameters();
+ }
+
+ /** Get the derivation order.
+ * @return derivation order
+ */
+ public int getOrder() {
+ return compiler.getOrder();
+ }
+
+ /** Create a constant compatible with instance order and number of parameters.
+ * <p>
+ * This method is a convenience factory method, it simply calls
+ * {@code new DerivativeStructure(getFreeParameters(), getOrder(), c)}
+ * </p>
+ * @param c value of the constant
+ * @return a constant compatible with instance order and number of parameters
+ * @see #DerivativeStructure(int, int, double)
+ * @since 3.3
+ */
+ public DerivativeStructure createConstant(final double c) {
+ return new DerivativeStructure(getFreeParameters(), getOrder(), c);
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public double getReal() {
+ return data[0];
+ }
+
+ /** Get the value part of the derivative structure.
+ * @return value part of the derivative structure
+ * @see #getPartialDerivative(int...)
+ */
+ public double getValue() {
+ return data[0];
+ }
+
+ /** Get a partial derivative.
+ * @param orders derivation orders with respect to each variable (if all orders are 0,
+ * the value is returned)
+ * @return partial derivative
+ * @see #getValue()
+ * @exception DimensionMismatchException if the numbers of variables does not
+ * match the instance
+ * @exception NumberIsTooLargeException if sum of derivation orders is larger
+ * than the instance limits
+ */
+ public double getPartialDerivative(final int ... orders)
+ throws DimensionMismatchException, NumberIsTooLargeException {
+ return data[compiler.getPartialDerivativeIndex(orders)];
+ }
+
+ /** Get all partial derivatives.
+ * @return a fresh copy of partial derivatives, in an array sorted according to
+ * {@link DSCompiler#getPartialDerivativeIndex(int...)}
+ */
+ public double[] getAllDerivatives() {
+ return data.clone();
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure add(final double a) {
+ final DerivativeStructure ds = new DerivativeStructure(this);
+ ds.data[0] += a;
+ return ds;
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ */
+ @Override
+ public DerivativeStructure add(final DerivativeStructure a)
+ throws DimensionMismatchException {
+ compiler.checkCompatibility(a.compiler);
+ final DerivativeStructure ds = new DerivativeStructure(this);
+ compiler.add(data, 0, a.data, 0, ds.data, 0);
+ return ds;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure subtract(final double a) {
+ return add(-a);
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ */
+ @Override
+ public DerivativeStructure subtract(final DerivativeStructure a)
+ throws DimensionMismatchException {
+ compiler.checkCompatibility(a.compiler);
+ final DerivativeStructure ds = new DerivativeStructure(this);
+ compiler.subtract(data, 0, a.data, 0, ds.data, 0);
+ return ds;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure multiply(final int n) {
+ return multiply((double) n);
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure multiply(final double a) {
+ final DerivativeStructure ds = new DerivativeStructure(this);
+ for (int i = 0; i < ds.data.length; ++i) {
+ ds.data[i] *= a;
+ }
+ return ds;
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ */
+ @Override
+ public DerivativeStructure multiply(final DerivativeStructure a)
+ throws DimensionMismatchException {
+ compiler.checkCompatibility(a.compiler);
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.multiply(data, 0, a.data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure divide(final double a) {
+ final DerivativeStructure ds = new DerivativeStructure(this);
+ for (int i = 0; i < ds.data.length; ++i) {
+ ds.data[i] /= a;
+ }
+ return ds;
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ */
+ @Override
+ public DerivativeStructure divide(final DerivativeStructure a)
+ throws DimensionMismatchException {
+ compiler.checkCompatibility(a.compiler);
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.divide(data, 0, a.data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure remainder(final double a) {
+ final DerivativeStructure ds = new DerivativeStructure(this);
+ ds.data[0] = FastMath.IEEEremainder(ds.data[0], a);
+ return ds;
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure remainder(final DerivativeStructure a)
+ throws DimensionMismatchException {
+ compiler.checkCompatibility(a.compiler);
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.remainder(data, 0, a.data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure negate() {
+ final DerivativeStructure ds = new DerivativeStructure(compiler);
+ for (int i = 0; i < ds.data.length; ++i) {
+ ds.data[i] = -data[i];
+ }
+ return ds;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure abs() {
+ if (Double.doubleToLongBits(data[0]) < 0) {
+ // we use the bits representation to also handle -0.0
+ return negate();
+ } else {
+ return this;
+ }
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure ceil() {
+ return new DerivativeStructure(compiler.getFreeParameters(),
+ compiler.getOrder(),
+ FastMath.ceil(data[0]));
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure floor() {
+ return new DerivativeStructure(compiler.getFreeParameters(),
+ compiler.getOrder(),
+ FastMath.floor(data[0]));
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure rint() {
+ return new DerivativeStructure(compiler.getFreeParameters(),
+ compiler.getOrder(),
+ FastMath.rint(data[0]));
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public long round() {
+ return FastMath.round(data[0]);
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure signum() {
+ return new DerivativeStructure(compiler.getFreeParameters(),
+ compiler.getOrder(),
+ FastMath.signum(data[0]));
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure copySign(final DerivativeStructure sign){
+ long m = Double.doubleToLongBits(data[0]);
+ long s = Double.doubleToLongBits(sign.data[0]);
+ if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
+ return this;
+ }
+ return negate(); // flip sign
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure copySign(final double sign) {
+ long m = Double.doubleToLongBits(data[0]);
+ long s = Double.doubleToLongBits(sign);
+ if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
+ return this;
+ }
+ return negate(); // flip sign
+ }
+
+ /**
+ * Return the exponent of the instance value, removing the bias.
+ * <p>
+ * For double numbers of the form 2<sup>x</sup>, the unbiased
+ * exponent is exactly x.
+ * </p>
+ * @return exponent for instance in IEEE754 representation, without bias
+ */
+ public int getExponent() {
+ return FastMath.getExponent(data[0]);
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure scalb(final int n) {
+ final DerivativeStructure ds = new DerivativeStructure(compiler);
+ for (int i = 0; i < ds.data.length; ++i) {
+ ds.data[i] = FastMath.scalb(data[i], n);
+ }
+ return ds;
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure hypot(final DerivativeStructure y)
+ throws DimensionMismatchException {
+
+ compiler.checkCompatibility(y.compiler);
+
+ if (Double.isInfinite(data[0]) || Double.isInfinite(y.data[0])) {
+ return new DerivativeStructure(compiler.getFreeParameters(),
+ compiler.getFreeParameters(),
+ Double.POSITIVE_INFINITY);
+ } else if (Double.isNaN(data[0]) || Double.isNaN(y.data[0])) {
+ return new DerivativeStructure(compiler.getFreeParameters(),
+ compiler.getFreeParameters(),
+ Double.NaN);
+ } else {
+
+ final int expX = getExponent();
+ final int expY = y.getExponent();
+ if (expX > expY + 27) {
+ // y is neglectible with respect to x
+ return abs();
+ } else if (expY > expX + 27) {
+ // x is neglectible with respect to y
+ return y.abs();
+ } else {
+
+ // find an intermediate scale to avoid both overflow and underflow
+ final int middleExp = (expX + expY) / 2;
+
+ // scale parameters without losing precision
+ final DerivativeStructure scaledX = scalb(-middleExp);
+ final DerivativeStructure scaledY = y.scalb(-middleExp);
+
+ // compute scaled hypotenuse
+ final DerivativeStructure scaledH =
+ scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();
+
+ // remove scaling
+ return scaledH.scalb(middleExp);
+
+ }
+
+ }
+ }
+
+ /**
+ * Returns the hypotenuse of a triangle with sides {@code x} and {@code y}
+ * - sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ * avoiding intermediate overflow or underflow.
+ *
+ * <ul>
+ * <li> If either argument is infinite, then the result is positive infinity.</li>
+ * <li> else, if either argument is NaN then the result is NaN.</li>
+ * </ul>
+ *
+ * @param x a value
+ * @param y a value
+ * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ public static DerivativeStructure hypot(final DerivativeStructure x, final DerivativeStructure y)
+ throws DimensionMismatchException {
+ return x.hypot(y);
+ }
+
+ /** Compute composition of the instance by a univariate function.
+ * @param f array of value and derivatives of the function at
+ * the current point (i.e. [f({@link #getValue()}),
+ * f'({@link #getValue()}), f''({@link #getValue()})...]).
+ * @return f(this)
+ * @exception DimensionMismatchException if the number of derivatives
+ * in the array is not equal to {@link #getOrder() order} + 1
+ */
+ public DerivativeStructure compose(final double ... f)
+ throws DimensionMismatchException {
+ if (f.length != getOrder() + 1) {
+ throw new DimensionMismatchException(f.length, getOrder() + 1);
+ }
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.compose(data, 0, f, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure reciprocal() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.pow(data, 0, -1, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure sqrt() {
+ return rootN(2);
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure cbrt() {
+ return rootN(3);
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure rootN(final int n) {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.rootN(data, 0, n, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public Field<DerivativeStructure> getField() {
+ return new Field<DerivativeStructure>() {
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure getZero() {
+ return new DerivativeStructure(compiler.getFreeParameters(), compiler.getOrder(), 0.0);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure getOne() {
+ return new DerivativeStructure(compiler.getFreeParameters(), compiler.getOrder(), 1.0);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public Class<? extends FieldElement<DerivativeStructure>> getRuntimeClass() {
+ return DerivativeStructure.class;
+ }
+
+ };
+ }
+
+ /** Compute a<sup>x</sup> where a is a double and x a {@link DerivativeStructure}
+ * @param a number to exponentiate
+ * @param x power to apply
+ * @return a<sup>x</sup>
+ * @since 3.3
+ */
+ public static DerivativeStructure pow(final double a, final DerivativeStructure x) {
+ final DerivativeStructure result = new DerivativeStructure(x.compiler);
+ x.compiler.pow(a, x.data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure pow(final double p) {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.pow(data, 0, p, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure pow(final int n) {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.pow(data, 0, n, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure pow(final DerivativeStructure e)
+ throws DimensionMismatchException {
+ compiler.checkCompatibility(e.compiler);
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.pow(data, 0, e.data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure exp() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.exp(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure expm1() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.expm1(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure log() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.log(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure log1p() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.log1p(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** Base 10 logarithm.
+ * @return base 10 logarithm of the instance
+ */
+ @Override
+ public DerivativeStructure log10() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.log10(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure cos() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.cos(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure sin() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.sin(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure tan() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.tan(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure acos() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.acos(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure asin() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.asin(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure atan() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.atan(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure atan2(final DerivativeStructure x)
+ throws DimensionMismatchException {
+ compiler.checkCompatibility(x.compiler);
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.atan2(data, 0, x.data, 0, result.data, 0);
+ return result;
+ }
+
+ /** Two arguments arc tangent operation.
+ * @param y first argument of the arc tangent
+ * @param x second argument of the arc tangent
+ * @return atan2(y, x)
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ public static DerivativeStructure atan2(final DerivativeStructure y, final DerivativeStructure x)
+ throws DimensionMismatchException {
+ return y.atan2(x);
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure cosh() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.cosh(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure sinh() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.sinh(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure tanh() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.tanh(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure acosh() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.acosh(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure asinh() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.asinh(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** {@inheritDoc}
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure atanh() {
+ final DerivativeStructure result = new DerivativeStructure(compiler);
+ compiler.atanh(data, 0, result.data, 0);
+ return result;
+ }
+
+ /** Convert radians to degrees, with error of less than 0.5 ULP
+ * @return instance converted into degrees
+ */
+ public DerivativeStructure toDegrees() {
+ final DerivativeStructure ds = new DerivativeStructure(compiler);
+ for (int i = 0; i < ds.data.length; ++i) {
+ ds.data[i] = FastMath.toDegrees(data[i]);
+ }
+ return ds;
+ }
+
+ /** Convert degrees to radians, with error of less than 0.5 ULP
+ * @return instance converted into radians
+ */
+ public DerivativeStructure toRadians() {
+ final DerivativeStructure ds = new DerivativeStructure(compiler);
+ for (int i = 0; i < ds.data.length; ++i) {
+ ds.data[i] = FastMath.toRadians(data[i]);
+ }
+ return ds;
+ }
+
+ /** Evaluate Taylor expansion a derivative structure.
+ * @param delta parameters offsets (Δx, Δy, ...)
+ * @return value of the Taylor expansion at x + Δx, y + Δy, ...
+ * @throws MathArithmeticException if factorials becomes too large
+ */
+ public double taylor(final double ... delta) throws MathArithmeticException {
+ return compiler.taylor(data, 0, delta);
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final DerivativeStructure[] a, final DerivativeStructure[] b)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double[] aDouble = new double[a.length];
+ for (int i = 0; i < a.length; ++i) {
+ aDouble[i] = a[i].getValue();
+ }
+ final double[] bDouble = new double[b.length];
+ for (int i = 0; i < b.length; ++i) {
+ bDouble[i] = b[i].getValue();
+ }
+ final double accurateValue = LinearCombination.value(aDouble, bDouble);
+
+ // compute a simple value, with all partial derivatives
+ DerivativeStructure simpleValue = a[0].getField().getZero();
+ for (int i = 0; i < a.length; ++i) {
+ simpleValue = simpleValue.add(a[i].multiply(b[i]));
+ }
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(simpleValue.getFreeParameters(), simpleValue.getOrder(), all);
+
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final double[] a, final DerivativeStructure[] b)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double[] bDouble = new double[b.length];
+ for (int i = 0; i < b.length; ++i) {
+ bDouble[i] = b[i].getValue();
+ }
+ final double accurateValue = LinearCombination.value(a, bDouble);
+
+ // compute a simple value, with all partial derivatives
+ DerivativeStructure simpleValue = b[0].getField().getZero();
+ for (int i = 0; i < a.length; ++i) {
+ simpleValue = simpleValue.add(b[i].multiply(a[i]));
+ }
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(simpleValue.getFreeParameters(), simpleValue.getOrder(), all);
+
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final DerivativeStructure a1, final DerivativeStructure b1,
+ final DerivativeStructure a2, final DerivativeStructure b2)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double accurateValue = LinearCombination.value(a1.getValue(), b1.getValue(),
+ a2.getValue(), b2.getValue());
+
+ // compute a simple value, with all partial derivatives
+ final DerivativeStructure simpleValue = a1.multiply(b1).add(a2.multiply(b2));
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(getFreeParameters(), getOrder(), all);
+
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final double a1, final DerivativeStructure b1,
+ final double a2, final DerivativeStructure b2)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double accurateValue = LinearCombination.value(a1, b1.getValue(),
+ a2, b2.getValue());
+
+ // compute a simple value, with all partial derivatives
+ final DerivativeStructure simpleValue = b1.multiply(a1).add(b2.multiply(a2));
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(getFreeParameters(), getOrder(), all);
+
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final DerivativeStructure a1, final DerivativeStructure b1,
+ final DerivativeStructure a2, final DerivativeStructure b2,
+ final DerivativeStructure a3, final DerivativeStructure b3)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double accurateValue = LinearCombination.value(a1.getValue(), b1.getValue(),
+ a2.getValue(), b2.getValue(),
+ a3.getValue(), b3.getValue());
+
+ // compute a simple value, with all partial derivatives
+ final DerivativeStructure simpleValue = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3));
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(getFreeParameters(), getOrder(), all);
+
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final double a1, final DerivativeStructure b1,
+ final double a2, final DerivativeStructure b2,
+ final double a3, final DerivativeStructure b3)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double accurateValue = LinearCombination.value(a1, b1.getValue(),
+ a2, b2.getValue(),
+ a3, b3.getValue());
+
+ // compute a simple value, with all partial derivatives
+ final DerivativeStructure simpleValue = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3));
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(getFreeParameters(), getOrder(), all);
+
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final DerivativeStructure a1, final DerivativeStructure b1,
+ final DerivativeStructure a2, final DerivativeStructure b2,
+ final DerivativeStructure a3, final DerivativeStructure b3,
+ final DerivativeStructure a4, final DerivativeStructure b4)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double accurateValue = LinearCombination.value(a1.getValue(), b1.getValue(),
+ a2.getValue(), b2.getValue(),
+ a3.getValue(), b3.getValue(),
+ a4.getValue(), b4.getValue());
+
+ // compute a simple value, with all partial derivatives
+ final DerivativeStructure simpleValue = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3)).add(a4.multiply(b4));
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(getFreeParameters(), getOrder(), all);
+
+ }
+
+ /** {@inheritDoc}
+ * @exception DimensionMismatchException if number of free parameters
+ * or orders do not match
+ * @since 3.2
+ */
+ @Override
+ public DerivativeStructure linearCombination(final double a1, final DerivativeStructure b1,
+ final double a2, final DerivativeStructure b2,
+ final double a3, final DerivativeStructure b3,
+ final double a4, final DerivativeStructure b4)
+ throws DimensionMismatchException {
+
+ // compute an accurate value, taking care of cancellations
+ final double accurateValue = LinearCombination.value(a1, b1.getValue(),
+ a2, b2.getValue(),
+ a3, b3.getValue(),
+ a4, b4.getValue());
+
+ // compute a simple value, with all partial derivatives
+ final DerivativeStructure simpleValue = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3)).add(b4.multiply(a4));
+
+ // create a result with accurate value and all derivatives (not necessarily as accurate as the value)
+ final double[] all = simpleValue.getAllDerivatives();
+ all[0] = accurateValue;
+ return new DerivativeStructure(getFreeParameters(), getOrder(), all);
+
+ }
+
+ /**
+ * Test for the equality of two derivative structures.
+ * <p>
+ * Derivative structures are considered equal if they have the same number
+ * of free parameters, the same derivation order, and the same derivatives.
+ * </p>
+ * @param other Object to test for equality to this
+ * @return true if two derivative structures are equal
+ * @since 3.2
+ */
+ @Override
+ public boolean equals(Object other) {
+
+ if (this == other) {
+ return true;
+ }
+
+ if (other instanceof DerivativeStructure) {
+ final DerivativeStructure rhs = (DerivativeStructure)other;
+ return (getFreeParameters() == rhs.getFreeParameters()) &&
+ (getOrder() == rhs.getOrder()) &&
+ MathArrays.equals(data, rhs.data);
+ }
+
+ return false;
+
+ }
+
+ /**
+ * Get a hashCode for the derivative structure.
+ * @return a hash code value for this object
+ * @since 3.2
+ */
+ @Override
+ public int hashCode() {
+ return 227 + 229 * getFreeParameters() + 233 * getOrder() + 239 * MathUtils.hash(data);
+ }
+
+ /**
+ * Replace the instance with a data transfer object for serialization.
+ * @return data transfer object that will be serialized
+ */
+ private Object writeReplace() {
+ return new DataTransferObject(compiler.getFreeParameters(), compiler.getOrder(), data);
+ }
+
+ /** Internal class used only for serialization. */
+ private static class DataTransferObject implements Serializable {
+
+ /** Serializable UID. */
+ private static final long serialVersionUID = 20120730L;
+
+ /** Number of variables.
+ * @serial
+ */
+ private final int variables;
+
+ /** Derivation order.
+ * @serial
+ */
+ private final int order;
+
+ /** Partial derivatives.
+ * @serial
+ */
+ private final double[] data;
+
+ /** Simple constructor.
+ * @param variables number of variables
+ * @param order derivation order
+ * @param data partial derivatives
+ */
+ DataTransferObject(final int variables, final int order, final double[] data) {
+ this.variables = variables;
+ this.order = order;
+ this.data = data;
+ }
+
+ /** Replace the deserialized data transfer object with a {@link DerivativeStructure}.
+ * @return replacement {@link DerivativeStructure}
+ */
+ private Object readResolve() {
+ return new DerivativeStructure(variables, order, data);
+ }
+
+ }
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiator.java
new file mode 100644
index 0000000..c008751
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/FiniteDifferencesDifferentiator.java
@@ -0,0 +1,393 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import java.io.Serializable;
+
+import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
+import org.apache.commons.math4.legacy.analysis.UnivariateMatrixFunction;
+import org.apache.commons.math4.legacy.analysis.UnivariateVectorFunction;
+import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
+import org.apache.commons.math4.legacy.exception.NotPositiveException;
+import org.apache.commons.math4.legacy.exception.NumberIsTooLargeException;
+import org.apache.commons.math4.legacy.exception.NumberIsTooSmallException;
+import org.apache.commons.math4.legacy.util.FastMath;
+
+/** Univariate functions differentiator using finite differences.
+ * <p>
+ * This class creates some wrapper objects around regular
+ * {@link UnivariateFunction univariate functions} (or {@link
+ * UnivariateVectorFunction univariate vector functions} or {@link
+ * UnivariateMatrixFunction univariate matrix functions}). These
+ * wrapper objects compute derivatives in addition to function
+ * values.
+ * </p>
+ * <p>
+ * The wrapper objects work by calling the underlying function on
+ * a sampling grid around the current point and performing polynomial
+ * interpolation. A finite differences scheme with n points is
+ * theoretically able to compute derivatives up to order n-1, but
+ * it is generally better to have a slight margin. The step size must
+ * also be small enough in order for the polynomial approximation to
+ * be good in the current point neighborhood, but it should not be too
+ * small because numerical instability appears quickly (there are several
+ * differences of close points). Choosing the number of points and
+ * the step size is highly problem dependent.
+ * </p>
+ * <p>
+ * As an example of good and bad settings, lets consider the quintic
+ * polynomial function {@code f(x) = (x-1)*(x-0.5)*x*(x+0.5)*(x+1)}.
+ * Since it is a polynomial, finite differences with at least 6 points
+ * should theoretically recover the exact same polynomial and hence
+ * compute accurate derivatives for any order. However, due to numerical
+ * errors, we get the following results for a 7 points finite differences
+ * for abscissae in the [-10, 10] range:
+ * <ul>
+ * <li>step size = 0.25, second order derivative error about 9.97e-10</li>
+ * <li>step size = 0.25, fourth order derivative error about 5.43e-8</li>
+ * <li>step size = 1.0e-6, second order derivative error about 148</li>
+ * <li>step size = 1.0e-6, fourth order derivative error about 6.35e+14</li>
+ * </ul>
+ * <p>
+ * This example shows that the small step size is really bad, even simply
+ * for second order derivative!</p>
+ *
+ * @since 3.1
+ */
+public class FiniteDifferencesDifferentiator
+ implements UnivariateFunctionDifferentiator, UnivariateVectorFunctionDifferentiator,
+ UnivariateMatrixFunctionDifferentiator, Serializable {
+
+ /** Serializable UID. */
+ private static final long serialVersionUID = 20120917L;
+
+ /** Number of points to use. */
+ private final int nbPoints;
+
+ /** Step size. */
+ private final double stepSize;
+
+ /** Half sample span. */
+ private final double halfSampleSpan;
+
+ /** Lower bound for independent variable. */
+ private final double tMin;
+
+ /** Upper bound for independent variable. */
+ private final double tMax;
+
+ /**
+ * Build a differentiator with number of points and step size when independent variable is unbounded.
+ * <p>
+ * Beware that wrong settings for the finite differences differentiator
+ * can lead to highly unstable and inaccurate results, especially for
+ * high derivation orders. Using very small step sizes is often a
+ * <em>bad</em> idea.
+ * </p>
+ * @param nbPoints number of points to use
+ * @param stepSize step size (gap between each point)
+ * @exception NotPositiveException if {@code stepsize <= 0} (note that
+ * {@link NotPositiveException} extends {@link NumberIsTooSmallException})
+ * @exception NumberIsTooSmallException {@code nbPoint <= 1}
+ */
+ public FiniteDifferencesDifferentiator(final int nbPoints, final double stepSize)
+ throws NotPositiveException, NumberIsTooSmallException {
+ this(nbPoints, stepSize, Double.NEGATIVE_INFINITY, Double.POSITIVE_INFINITY);
+ }
+
+ /**
+ * Build a differentiator with number of points and step size when independent variable is bounded.
+ * <p>
+ * When the independent variable is bounded (tLower < t < tUpper), the sampling
+ * points used for differentiation will be adapted to ensure the constraint holds
+ * even near the boundaries. This means the sample will not be centered anymore in
+ * these cases. At an extreme case, computing derivatives exactly at the lower bound
+ * will lead the sample to be entirely on the right side of the derivation point.
+ * </p>
+ * <p>
+ * Note that the boundaries are considered to be excluded for function evaluation.
+ * </p>
+ * <p>
+ * Beware that wrong settings for the finite differences differentiator
+ * can lead to highly unstable and inaccurate results, especially for
+ * high derivation orders. Using very small step sizes is often a
+ * <em>bad</em> idea.
+ * </p>
+ * @param nbPoints number of points to use
+ * @param stepSize step size (gap between each point)
+ * @param tLower lower bound for independent variable (may be {@code Double.NEGATIVE_INFINITY}
+ * if there are no lower bounds)
+ * @param tUpper upper bound for independent variable (may be {@code Double.POSITIVE_INFINITY}
+ * if there are no upper bounds)
+ * @exception NotPositiveException if {@code stepsize <= 0} (note that
+ * {@link NotPositiveException} extends {@link NumberIsTooSmallException})
+ * @exception NumberIsTooSmallException {@code nbPoint <= 1}
+ * @exception NumberIsTooLargeException {@code stepSize * (nbPoints - 1) >= tUpper - tLower}
+ */
+ public FiniteDifferencesDifferentiator(final int nbPoints, final double stepSize,
+ final double tLower, final double tUpper)
+ throws NotPositiveException, NumberIsTooSmallException, NumberIsTooLargeException {
+
+ if (nbPoints <= 1) {
+ throw new NumberIsTooSmallException(stepSize, 1, false);
+ }
+ this.nbPoints = nbPoints;
+
+ if (stepSize <= 0) {
+ throw new NotPositiveException(stepSize);
+ }
+ this.stepSize = stepSize;
+
+ halfSampleSpan = 0.5 * stepSize * (nbPoints - 1);
+ if (2 * halfSampleSpan >= tUpper - tLower) {
+ throw new NumberIsTooLargeException(2 * halfSampleSpan, tUpper - tLower, false);
+ }
+ final double safety = FastMath.ulp(halfSampleSpan);
+ this.tMin = tLower + halfSampleSpan + safety;
+ this.tMax = tUpper - halfSampleSpan - safety;
+
+ }
+
+ /**
+ * Get the number of points to use.
+ * @return number of points to use
+ */
+ public int getNbPoints() {
+ return nbPoints;
+ }
+
+ /**
+ * Get the step size.
+ * @return step size
+ */
+ public double getStepSize() {
+ return stepSize;
+ }
+
+ /**
+ * Evaluate derivatives from a sample.
+ * <p>
+ * Evaluation is done using divided differences.
+ * </p>
+ * @param t evaluation abscissa value and derivatives
+ * @param t0 first sample point abscissa
+ * @param y function values sample {@code y[i] = f(t[i]) = f(t0 + i * stepSize)}
+ * @return value and derivatives at {@code t}
+ * @exception NumberIsTooLargeException if the requested derivation order
+ * is larger or equal to the number of points
+ */
+ private DerivativeStructure evaluate(final DerivativeStructure t, final double t0,
+ final double[] y)
+ throws NumberIsTooLargeException {
+
+ // create divided differences diagonal arrays
+ final double[] top = new double[nbPoints];
+ final double[] bottom = new double[nbPoints];
+
+ for (int i = 0; i < nbPoints; ++i) {
+
+ // update the bottom diagonal of the divided differences array
+ bottom[i] = y[i];
+ for (int j = 1; j <= i; ++j) {
+ bottom[i - j] = (bottom[i - j + 1] - bottom[i - j]) / (j * stepSize);
+ }
+
+ // update the top diagonal of the divided differences array
+ top[i] = bottom[0];
+
+ }
+
+ // evaluate interpolation polynomial (represented by top diagonal) at t
+ final int order = t.getOrder();
+ final int parameters = t.getFreeParameters();
+ final double[] derivatives = t.getAllDerivatives();
+ final double dt0 = t.getValue() - t0;
+ DerivativeStructure interpolation = new DerivativeStructure(parameters, order, 0.0);
+ DerivativeStructure monomial = null;
+ for (int i = 0; i < nbPoints; ++i) {
+ if (i == 0) {
+ // start with monomial(t) = 1
+ monomial = new DerivativeStructure(parameters, order, 1.0);
+ } else {
+ // monomial(t) = (t - t0) * (t - t1) * ... * (t - t(i-1))
+ derivatives[0] = dt0 - (i - 1) * stepSize;
+ final DerivativeStructure deltaX = new DerivativeStructure(parameters, order, derivatives);
+ monomial = monomial.multiply(deltaX);
+ }
+ interpolation = interpolation.add(monomial.multiply(top[i]));
+ }
+
+ return interpolation;
+
+ }
+
+ /** {@inheritDoc}
+ * <p>The returned object cannot compute derivatives to arbitrary orders. The
+ * value function will throw a {@link NumberIsTooLargeException} if the requested
+ * derivation order is larger or equal to the number of points.
+ * </p>
+ */
+ @Override
+ public UnivariateDifferentiableFunction differentiate(final UnivariateFunction function) {
+ return new UnivariateDifferentiableFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double value(final double x) throws MathIllegalArgumentException {
+ return function.value(x);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure value(final DerivativeStructure t)
+ throws MathIllegalArgumentException {
+
+ // check we can achieve the requested derivation order with the sample
+ if (t.getOrder() >= nbPoints) {
+ throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);
+ }
+
+ // compute sample position, trying to be centered if possible
+ final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;
+
+ // compute sample points
+ final double[] y = new double[nbPoints];
+ for (int i = 0; i < nbPoints; ++i) {
+ y[i] = function.value(t0 + i * stepSize);
+ }
+
+ // evaluate derivatives
+ return evaluate(t, t0, y);
+
+ }
+
+ };
+ }
+
+ /** {@inheritDoc}
+ * <p>The returned object cannot compute derivatives to arbitrary orders. The
+ * value function will throw a {@link NumberIsTooLargeException} if the requested
+ * derivation order is larger or equal to the number of points.
+ * </p>
+ */
+ @Override
+ public UnivariateDifferentiableVectorFunction differentiate(final UnivariateVectorFunction function) {
+ return new UnivariateDifferentiableVectorFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double[]value(final double x) throws MathIllegalArgumentException {
+ return function.value(x);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure[] value(final DerivativeStructure t)
+ throws MathIllegalArgumentException {
+
+ // check we can achieve the requested derivation order with the sample
+ if (t.getOrder() >= nbPoints) {
+ throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);
+ }
+
+ // compute sample position, trying to be centered if possible
+ final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;
+
+ // compute sample points
+ double[][] y = null;
+ for (int i = 0; i < nbPoints; ++i) {
+ final double[] v = function.value(t0 + i * stepSize);
+ if (i == 0) {
+ y = new double[v.length][nbPoints];
+ }
+ for (int j = 0; j < v.length; ++j) {
+ y[j][i] = v[j];
+ }
+ }
+
+ // evaluate derivatives
+ final DerivativeStructure[] value = new DerivativeStructure[y.length];
+ for (int j = 0; j < value.length; ++j) {
+ value[j] = evaluate(t, t0, y[j]);
+ }
+
+ return value;
+
+ }
+
+ };
+ }
+
+ /** {@inheritDoc}
+ * <p>The returned object cannot compute derivatives to arbitrary orders. The
+ * value function will throw a {@link NumberIsTooLargeException} if the requested
+ * derivation order is larger or equal to the number of points.
+ * </p>
+ */
+ @Override
+ public UnivariateDifferentiableMatrixFunction differentiate(final UnivariateMatrixFunction function) {
+ return new UnivariateDifferentiableMatrixFunction() {
+
+ /** {@inheritDoc} */
+ @Override
+ public double[][] value(final double x) throws MathIllegalArgumentException {
+ return function.value(x);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public DerivativeStructure[][] value(final DerivativeStructure t)
+ throws MathIllegalArgumentException {
+
+ // check we can achieve the requested derivation order with the sample
+ if (t.getOrder() >= nbPoints) {
+ throw new NumberIsTooLargeException(t.getOrder(), nbPoints, false);
+ }
+
+ // compute sample position, trying to be centered if possible
+ final double t0 = FastMath.max(FastMath.min(t.getValue(), tMax), tMin) - halfSampleSpan;
+
+ // compute sample points
+ double[][][] y = null;
+ for (int i = 0; i < nbPoints; ++i) {
+ final double[][] v = function.value(t0 + i * stepSize);
+ if (i == 0) {
+ y = new double[v.length][v[0].length][nbPoints];
+ }
+ for (int j = 0; j < v.length; ++j) {
+ for (int k = 0; k < v[j].length; ++k) {
+ y[j][k][i] = v[j][k];
+ }
+ }
+ }
+
+ // evaluate derivatives
+ final DerivativeStructure[][] value = new DerivativeStructure[y.length][y[0].length];
+ for (int j = 0; j < value.length; ++j) {
+ for (int k = 0; k < y[j].length; ++k) {
+ value[j][k] = evaluate(t, t0, y[j][k]);
+ }
+ }
+
+ return value;
+
+ }
+
+ };
+ }
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/GradientFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/GradientFunction.java
new file mode 100644
index 0000000..c9c9d33
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/GradientFunction.java
@@ -0,0 +1,66 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.MultivariateVectorFunction;
+
+/** Class representing the gradient of a multivariate function.
+ * <p>
+ * The vectorial components of the function represent the derivatives
+ * with respect to each function parameters.
+ * </p>
+ * @since 3.1
+ */
+public class GradientFunction implements MultivariateVectorFunction {
+
+ /** Underlying real-valued function. */
+ private final MultivariateDifferentiableFunction f;
+
+ /** Simple constructor.
+ * @param f underlying real-valued function
+ */
+ public GradientFunction(final MultivariateDifferentiableFunction f) {
+ this.f = f;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public double[] value(double[] point) {
+
+ // set up parameters
+ final DerivativeStructure[] dsX = new DerivativeStructure[point.length];
+ for (int i = 0; i < point.length; ++i) {
+ dsX[i] = new DerivativeStructure(point.length, 1, i, point[i]);
+ }
+
+ // compute the derivatives
+ final DerivativeStructure dsY = f.value(dsX);
+
+ // extract the gradient
+ final double[] y = new double[point.length];
+ final int[] orders = new int[point.length];
+ for (int i = 0; i < point.length; ++i) {
+ orders[i] = 1;
+ y[i] = dsY.getPartialDerivative(orders);
+ orders[i] = 0;
+ }
+
+ return y;
+
+ }
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/JacobianFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/JacobianFunction.java
new file mode 100644
index 0000000..4795950
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/JacobianFunction.java
@@ -0,0 +1,70 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.MultivariateMatrixFunction;
+
+/** Class representing the Jacobian of a multivariate vector function.
+ * <p>
+ * The rows iterate on the model functions while the columns iterate on the parameters; thus,
+ * the numbers of rows is equal to the dimension of the underlying function vector
+ * value and the number of columns is equal to the number of free parameters of
+ * the underlying function.
+ * </p>
+ * @since 3.1
+ */
+public class JacobianFunction implements MultivariateMatrixFunction {
+
+ /** Underlying vector-valued function. */
+ private final MultivariateDifferentiableVectorFunction f;
+
+ /** Simple constructor.
+ * @param f underlying vector-valued function
+ */
+ public JacobianFunction(final MultivariateDifferentiableVectorFunction f) {
+ this.f = f;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public double[][] value(double[] point) {
+
+ // set up parameters
+ final DerivativeStructure[] dsX = new DerivativeStructure[point.length];
+ for (int i = 0; i < point.length; ++i) {
+ dsX[i] = new DerivativeStructure(point.length, 1, i, point[i]);
+ }
+
+ // compute the derivatives
+ final DerivativeStructure[] dsY = f.value(dsX);
+
+ // extract the Jacobian
+ final double[][] y = new double[dsY.length][point.length];
+ final int[] orders = new int[point.length];
+ for (int i = 0; i < dsY.length; ++i) {
+ for (int j = 0; j < point.length; ++j) {
+ orders[j] = 1;
+ y[i][j] = dsY[i].getPartialDerivative(orders);
+ orders[j] = 0;
+ }
+ }
+
+ return y;
+
+ }
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/MultivariateDifferentiableFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/MultivariateDifferentiableFunction.java
new file mode 100644
index 0000000..e6c0504
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/MultivariateDifferentiableFunction.java
@@ -0,0 +1,42 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.MultivariateFunction;
+import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
+
+/**
+ * Extension of {@link MultivariateFunction} representing a
+ * multivariate differentiable real function.
+ * @since 3.1
+ */
+public interface MultivariateDifferentiableFunction extends MultivariateFunction {
+
+ /**
+ * Compute the value for the function at the given point.
+ *
+ * @param point Point at which the function must be evaluated.
+ * @return the function value for the given point.
+ * @exception MathIllegalArgumentException if {@code point} does not
+ * satisfy the function's constraints (wrong dimension, argument out of bound,
+ * or unsupported derivative order for example)
+ */
+ DerivativeStructure value(DerivativeStructure[] point)
+ throws MathIllegalArgumentException;
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/MultivariateDifferentiableVectorFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/MultivariateDifferentiableVectorFunction.java
new file mode 100644
index 0000000..31426eb4
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/MultivariateDifferentiableVectorFunction.java
@@ -0,0 +1,43 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.MultivariateVectorFunction;
+import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
+
+
+/**
+ * Extension of {@link MultivariateVectorFunction} representing a
+ * multivariate differentiable vectorial function.
+ * @since 3.1
+ */
+public interface MultivariateDifferentiableVectorFunction
+ extends MultivariateVectorFunction {
+
+ /**
+ * Compute the value for the function at the given point.
+ * @param point point at which the function must be evaluated
+ * @return function value for the given point
+ * @exception MathIllegalArgumentException if {@code point} does not
+ * satisfy the function's constraints (wrong dimension, argument out of bound,
+ * or unsupported derivative order for example)
+ */
+ DerivativeStructure[] value(DerivativeStructure[] point)
+ throws MathIllegalArgumentException;
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradient.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradient.java
new file mode 100644
index 0000000..4deb958
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/SparseGradient.java
@@ -0,0 +1,937 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import java.io.Serializable;
+import java.util.Collections;
+import java.util.HashMap;
+import java.util.Map;
+
+import org.apache.commons.numbers.arrays.LinearCombination;
+import org.apache.commons.numbers.core.Precision;
+import org.apache.commons.math4.legacy.Field;
+import org.apache.commons.math4.legacy.FieldElement;
+import org.apache.commons.math4.legacy.RealFieldElement;
+import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
+import org.apache.commons.math4.legacy.util.FastMath;
+import org.apache.commons.math4.legacy.util.MathUtils;
+
+/**
+ * First derivative computation with large number of variables.
+ * <p>
+ * This class plays a similar role to {@link DerivativeStructure}, with
+ * a focus on efficiency when dealing with large number of independent variables
+ * and most computation depend only on a few of them, and when only first derivative
+ * is desired. When these conditions are met, this class should be much faster than
+ * {@link DerivativeStructure} and use less memory.
+ * </p>
+ *
+ * @since 3.3
+ */
+public class SparseGradient implements RealFieldElement<SparseGradient>, Serializable {
+
+ /** Serializable UID. */
+ private static final long serialVersionUID = 20131025L;
+
+ /** Value of the calculation. */
+ private double value;
+
+ /** Stored derivative, each key representing a different independent variable. */
+ private final Map<Integer, Double> derivatives;
+
+ /** Internal constructor.
+ * @param value value of the function
+ * @param derivatives derivatives map, a deep copy will be performed,
+ * so the map given here will remain safe from changes in the new instance,
+ * may be null to create an empty derivatives map, i.e. a constant value
+ */
+ private SparseGradient(final double value, final Map<Integer, Double> derivatives) {
+ this.value = value;
+ this.derivatives = new HashMap<>();
+ if (derivatives != null) {
+ this.derivatives.putAll(derivatives);
+ }
+ }
+
+ /** Internal constructor.
+ * @param value value of the function
+ * @param scale scaling factor to apply to all derivatives
+ * @param derivatives derivatives map, a deep copy will be performed,
+ * so the map given here will remain safe from changes in the new instance,
+ * may be null to create an empty derivatives map, i.e. a constant value
+ */
+ private SparseGradient(final double value, final double scale,
+ final Map<Integer, Double> derivatives) {
+ this.value = value;
+ this.derivatives = new HashMap<>();
+ if (derivatives != null) {
+ for (final Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+ this.derivatives.put(entry.getKey(), scale * entry.getValue());
+ }
+ }
+ }
+
+ /** Factory method creating a constant.
+ * @param value value of the constant
+ * @return a new instance
+ */
+ public static SparseGradient createConstant(final double value) {
+ return new SparseGradient(value, Collections.<Integer, Double> emptyMap());
+ }
+
+ /** Factory method creating an independent variable.
+ * @param idx index of the variable
+ * @param value value of the variable
+ * @return a new instance
+ */
+ public static SparseGradient createVariable(final int idx, final double value) {
+ return new SparseGradient(value, Collections.singletonMap(idx, 1.0));
+ }
+
+ /**
+ * Find the number of variables.
+ * @return number of variables
+ */
+ public int numVars() {
+ return derivatives.size();
+ }
+
+ /**
+ * Get the derivative with respect to a particular index variable.
+ *
+ * @param index index to differentiate with.
+ * @return derivative with respect to a particular index variable
+ */
+ public double getDerivative(final int index) {
+ final Double out = derivatives.get(index);
+ return (out == null) ? 0.0 : out;
+ }
+
+ /**
+ * Get the value of the function.
+ * @return value of the function.
+ */
+ public double getValue() {
+ return value;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public double getReal() {
+ return value;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient add(final SparseGradient a) {
+ final SparseGradient out = new SparseGradient(value + a.value, derivatives);
+ for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+ final int id = entry.getKey();
+ final Double old = out.derivatives.get(id);
+ if (old == null) {
+ out.derivatives.put(id, entry.getValue());
+ } else {
+ out.derivatives.put(id, old + entry.getValue());
+ }
+ }
+
+ return out;
+ }
+
+ /**
+ * Add in place.
+ * <p>
+ * This method is designed to be faster when used multiple times in a loop.
+ * </p>
+ * <p>
+ * The instance is changed here, in order to not change the
+ * instance the {@link #add(SparseGradient)} method should
+ * be used.
+ * </p>
+ * @param a instance to add
+ */
+ public void addInPlace(final SparseGradient a) {
+ value += a.value;
+ for (final Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+ final int id = entry.getKey();
+ final Double old = derivatives.get(id);
+ if (old == null) {
+ derivatives.put(id, entry.getValue());
+ } else {
+ derivatives.put(id, old + entry.getValue());
+ }
+ }
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient add(final double c) {
+ final SparseGradient out = new SparseGradient(value + c, derivatives);
+ return out;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient subtract(final SparseGradient a) {
+ final SparseGradient out = new SparseGradient(value - a.value, derivatives);
+ for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+ final int id = entry.getKey();
+ final Double old = out.derivatives.get(id);
+ if (old == null) {
+ out.derivatives.put(id, -entry.getValue());
+ } else {
+ out.derivatives.put(id, old - entry.getValue());
+ }
+ }
+ return out;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient subtract(double c) {
+ return new SparseGradient(value - c, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient multiply(final SparseGradient a) {
+ final SparseGradient out =
+ new SparseGradient(value * a.value, Collections.<Integer, Double> emptyMap());
+
+ // Derivatives.
+ for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+ out.derivatives.put(entry.getKey(), a.value * entry.getValue());
+ }
+ for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+ final int id = entry.getKey();
+ final Double old = out.derivatives.get(id);
+ if (old == null) {
+ out.derivatives.put(id, value * entry.getValue());
+ } else {
+ out.derivatives.put(id, old + value * entry.getValue());
+ }
+ }
+ return out;
+ }
+
+ /**
+ * Multiply in place.
+ * <p>
+ * This method is designed to be faster when used multiple times in a loop.
+ * </p>
+ * <p>
+ * The instance is changed here, in order to not change the
+ * instance the {@link #add(SparseGradient)} method should
+ * be used.
+ * </p>
+ * @param a instance to multiply
+ */
+ public void multiplyInPlace(final SparseGradient a) {
+ // Derivatives.
+ for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+ derivatives.put(entry.getKey(), a.value * entry.getValue());
+ }
+ for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+ final int id = entry.getKey();
+ final Double old = derivatives.get(id);
+ if (old == null) {
+ derivatives.put(id, value * entry.getValue());
+ } else {
+ derivatives.put(id, old + value * entry.getValue());
+ }
+ }
+ value *= a.value;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient multiply(final double c) {
+ return new SparseGradient(value * c, c, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient multiply(final int n) {
+ return new SparseGradient(value * n, n, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient divide(final SparseGradient a) {
+ final SparseGradient out = new SparseGradient(value / a.value, Collections.<Integer, Double> emptyMap());
+
+ // Derivatives.
+ for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+ out.derivatives.put(entry.getKey(), entry.getValue() / a.value);
+ }
+ for (Map.Entry<Integer, Double> entry : a.derivatives.entrySet()) {
+ final int id = entry.getKey();
+ final Double old = out.derivatives.get(id);
+ if (old == null) {
+ out.derivatives.put(id, -out.value / a.value * entry.getValue());
+ } else {
+ out.derivatives.put(id, old - out.value / a.value * entry.getValue());
+ }
+ }
+ return out;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient divide(final double c) {
+ return new SparseGradient(value / c, 1.0 / c, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient negate() {
+ return new SparseGradient(-value, -1.0, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public Field<SparseGradient> getField() {
+ return new Field<SparseGradient>() {
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient getZero() {
+ return createConstant(0);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient getOne() {
+ return createConstant(1);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public Class<? extends FieldElement<SparseGradient>> getRuntimeClass() {
+ return SparseGradient.class;
+ }
+
+ };
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient remainder(final double a) {
+ return new SparseGradient(FastMath.IEEEremainder(value, a), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient remainder(final SparseGradient a) {
+
+ // compute k such that lhs % rhs = lhs - k rhs
+ final double rem = FastMath.IEEEremainder(value, a.value);
+ final double k = FastMath.rint((value - rem) / a.value);
+
+ return subtract(a.multiply(k));
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient abs() {
+ if (Double.doubleToLongBits(value) < 0) {
+ // we use the bits representation to also handle -0.0
+ return negate();
+ } else {
+ return this;
+ }
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient ceil() {
+ return createConstant(FastMath.ceil(value));
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient floor() {
+ return createConstant(FastMath.floor(value));
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient rint() {
+ return createConstant(FastMath.rint(value));
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public long round() {
+ return FastMath.round(value);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient signum() {
+ return createConstant(FastMath.signum(value));
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient copySign(final SparseGradient sign) {
+ final long m = Double.doubleToLongBits(value);
+ final long s = Double.doubleToLongBits(sign.value);
+ if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
+ return this;
+ }
+ return negate(); // flip sign
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient copySign(final double sign) {
+ final long m = Double.doubleToLongBits(value);
+ final long s = Double.doubleToLongBits(sign);
+ if ((m >= 0 && s >= 0) || (m < 0 && s < 0)) { // Sign is currently OK
+ return this;
+ }
+ return negate(); // flip sign
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient scalb(final int n) {
+ final SparseGradient out = new SparseGradient(FastMath.scalb(value, n), Collections.<Integer, Double> emptyMap());
+ for (Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+ out.derivatives.put(entry.getKey(), FastMath.scalb(entry.getValue(), n));
+ }
+ return out;
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient hypot(final SparseGradient y) {
+ if (Double.isInfinite(value) || Double.isInfinite(y.value)) {
+ return createConstant(Double.POSITIVE_INFINITY);
+ } else if (Double.isNaN(value) || Double.isNaN(y.value)) {
+ return createConstant(Double.NaN);
+ } else {
+
+ final int expX = FastMath.getExponent(value);
+ final int expY = FastMath.getExponent(y.value);
+ if (expX > expY + 27) {
+ // y is negligible with respect to x
+ return abs();
+ } else if (expY > expX + 27) {
+ // x is negligible with respect to y
+ return y.abs();
+ } else {
+
+ // find an intermediate scale to avoid both overflow and underflow
+ final int middleExp = (expX + expY) / 2;
+
+ // scale parameters without losing precision
+ final SparseGradient scaledX = scalb(-middleExp);
+ final SparseGradient scaledY = y.scalb(-middleExp);
+
+ // compute scaled hypotenuse
+ final SparseGradient scaledH =
+ scaledX.multiply(scaledX).add(scaledY.multiply(scaledY)).sqrt();
+
+ // remove scaling
+ return scaledH.scalb(middleExp);
+
+ }
+
+ }
+ }
+
+ /**
+ * Returns the hypotenuse of a triangle with sides {@code x} and {@code y}
+ * - sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ * avoiding intermediate overflow or underflow.
+ *
+ * <ul>
+ * <li> If either argument is infinite, then the result is positive infinity.</li>
+ * <li> else, if either argument is NaN then the result is NaN.</li>
+ * </ul>
+ *
+ * @param x a value
+ * @param y a value
+ * @return sqrt(<i>x</i><sup>2</sup> +<i>y</i><sup>2</sup>)
+ */
+ public static SparseGradient hypot(final SparseGradient x, final SparseGradient y) {
+ return x.hypot(y);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient reciprocal() {
+ return new SparseGradient(1.0 / value, -1.0 / (value * value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient sqrt() {
+ final double sqrt = FastMath.sqrt(value);
+ return new SparseGradient(sqrt, 0.5 / sqrt, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient cbrt() {
+ final double cbrt = FastMath.cbrt(value);
+ return new SparseGradient(cbrt, 1.0 / (3 * cbrt * cbrt), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient rootN(final int n) {
+ if (n == 2) {
+ return sqrt();
+ } else if (n == 3) {
+ return cbrt();
+ } else {
+ final double root = FastMath.pow(value, 1.0 / n);
+ return new SparseGradient(root, 1.0 / (n * FastMath.pow(root, n - 1)), derivatives);
+ }
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient pow(final double p) {
+ return new SparseGradient(FastMath.pow(value, p), p * FastMath.pow(value, p - 1), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient pow(final int n) {
+ if (n == 0) {
+ return getField().getOne();
+ } else {
+ final double valueNm1 = FastMath.pow(value, n - 1);
+ return new SparseGradient(value * valueNm1, n * valueNm1, derivatives);
+ }
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient pow(final SparseGradient e) {
+ return log().multiply(e).exp();
+ }
+
+ /** Compute a<sup>x</sup> where a is a double and x a {@link SparseGradient}
+ * @param a number to exponentiate
+ * @param x power to apply
+ * @return a<sup>x</sup>
+ */
+ public static SparseGradient pow(final double a, final SparseGradient x) {
+ if (a == 0) {
+ if (x.value == 0) {
+ return x.compose(1.0, Double.NEGATIVE_INFINITY);
+ } else if (x.value < 0) {
+ return x.compose(Double.NaN, Double.NaN);
+ } else {
+ return x.getField().getZero();
+ }
+ } else {
+ final double ax = FastMath.pow(a, x.value);
+ return new SparseGradient(ax, ax * FastMath.log(a), x.derivatives);
+ }
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient exp() {
+ final double e = FastMath.exp(value);
+ return new SparseGradient(e, e, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient expm1() {
+ return new SparseGradient(FastMath.expm1(value), FastMath.exp(value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient log() {
+ return new SparseGradient(FastMath.log(value), 1.0 / value, derivatives);
+ }
+
+ /** Base 10 logarithm.
+ * @return base 10 logarithm of the instance
+ */
+ @Override
+ public SparseGradient log10() {
+ return new SparseGradient(FastMath.log10(value), 1.0 / (FastMath.log(10.0) * value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient log1p() {
+ return new SparseGradient(FastMath.log1p(value), 1.0 / (1.0 + value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient cos() {
+ return new SparseGradient(FastMath.cos(value), -FastMath.sin(value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient sin() {
+ return new SparseGradient(FastMath.sin(value), FastMath.cos(value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient tan() {
+ final double t = FastMath.tan(value);
+ return new SparseGradient(t, 1 + t * t, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient acos() {
+ return new SparseGradient(FastMath.acos(value), -1.0 / FastMath.sqrt(1 - value * value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient asin() {
+ return new SparseGradient(FastMath.asin(value), 1.0 / FastMath.sqrt(1 - value * value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient atan() {
+ return new SparseGradient(FastMath.atan(value), 1.0 / (1 + value * value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient atan2(final SparseGradient x) {
+
+ // compute r = sqrt(x^2+y^2)
+ final SparseGradient r = multiply(this).add(x.multiply(x)).sqrt();
+
+ final SparseGradient a;
+ if (x.value >= 0) {
+
+ // compute atan2(y, x) = 2 atan(y / (r + x))
+ a = divide(r.add(x)).atan().multiply(2);
+
+ } else {
+
+ // compute atan2(y, x) = +/- pi - 2 atan(y / (r - x))
+ final SparseGradient tmp = divide(r.subtract(x)).atan().multiply(-2);
+ a = tmp.add(tmp.value <= 0 ? -FastMath.PI : FastMath.PI);
+
+ }
+
+ // fix value to take special cases (+0/+0, +0/-0, -0/+0, -0/-0, +/-infinity) correctly
+ a.value = FastMath.atan2(value, x.value);
+
+ return a;
+
+ }
+
+ /** Two arguments arc tangent operation.
+ * @param y first argument of the arc tangent
+ * @param x second argument of the arc tangent
+ * @return atan2(y, x)
+ */
+ public static SparseGradient atan2(final SparseGradient y, final SparseGradient x) {
+ return y.atan2(x);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient cosh() {
+ return new SparseGradient(FastMath.cosh(value), FastMath.sinh(value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient sinh() {
+ return new SparseGradient(FastMath.sinh(value), FastMath.cosh(value), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient tanh() {
+ final double t = FastMath.tanh(value);
+ return new SparseGradient(t, 1 - t * t, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient acosh() {
+ return new SparseGradient(FastMath.acosh(value), 1.0 / FastMath.sqrt(value * value - 1.0), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient asinh() {
+ return new SparseGradient(FastMath.asinh(value), 1.0 / FastMath.sqrt(value * value + 1.0), derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient atanh() {
+ return new SparseGradient(FastMath.atanh(value), 1.0 / (1.0 - value * value), derivatives);
+ }
+
+ /** Convert radians to degrees, with error of less than 0.5 ULP
+ * @return instance converted into degrees
+ */
+ public SparseGradient toDegrees() {
+ return new SparseGradient(FastMath.toDegrees(value), FastMath.toDegrees(1.0), derivatives);
+ }
+
+ /** Convert degrees to radians, with error of less than 0.5 ULP
+ * @return instance converted into radians
+ */
+ public SparseGradient toRadians() {
+ return new SparseGradient(FastMath.toRadians(value), FastMath.toRadians(1.0), derivatives);
+ }
+
+ /** Evaluate Taylor expansion of a sparse gradient.
+ * @param delta parameters offsets (Δx, Δy, ...)
+ * @return value of the Taylor expansion at x + Δx, y + Δy, ...
+ */
+ public double taylor(final double ... delta) {
+ double y = value;
+ for (int i = 0; i < delta.length; ++i) {
+ y += delta[i] * getDerivative(i);
+ }
+ return y;
+ }
+
+ /** Compute composition of the instance by a univariate function.
+ * @param f0 value of the function at (i.e. f({@link #getValue()}))
+ * @param f1 first derivative of the function at
+ * the current point (i.e. f'({@link #getValue()}))
+ * @return f(this)
+ */
+ public SparseGradient compose(final double f0, final double f1) {
+ return new SparseGradient(f0, f1, derivatives);
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final SparseGradient[] a,
+ final SparseGradient[] b)
+ throws DimensionMismatchException {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = a[0].getField().getZero();
+ for (int i = 0; i < a.length; ++i) {
+ out = out.add(a[i].multiply(b[i]));
+ }
+
+ // recompute an accurate value, taking care of cancellations
+ final double[] aDouble = new double[a.length];
+ for (int i = 0; i < a.length; ++i) {
+ aDouble[i] = a[i].getValue();
+ }
+ final double[] bDouble = new double[b.length];
+ for (int i = 0; i < b.length; ++i) {
+ bDouble[i] = b[i].getValue();
+ }
+ out.value = LinearCombination.value(aDouble, bDouble);
+
+ return out;
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final double[] a, final SparseGradient[] b) {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = b[0].getField().getZero();
+ for (int i = 0; i < a.length; ++i) {
+ out = out.add(b[i].multiply(a[i]));
+ }
+
+ // recompute an accurate value, taking care of cancellations
+ final double[] bDouble = new double[b.length];
+ for (int i = 0; i < b.length; ++i) {
+ bDouble[i] = b[i].getValue();
+ }
+ out.value = LinearCombination.value(a, bDouble);
+
+ return out;
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
+ final SparseGradient a2, final SparseGradient b2) {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = a1.multiply(b1).add(a2.multiply(b2));
+
+ // recompute an accurate value, taking care of cancellations
+ out.value = LinearCombination.value(a1.value, b1.value, a2.value, b2.value);
+
+ return out;
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final double a1, final SparseGradient b1,
+ final double a2, final SparseGradient b2) {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = b1.multiply(a1).add(b2.multiply(a2));
+
+ // recompute an accurate value, taking care of cancellations
+ out.value = LinearCombination.value(a1, b1.value, a2, b2.value);
+
+ return out;
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
+ final SparseGradient a2, final SparseGradient b2,
+ final SparseGradient a3, final SparseGradient b3) {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3));
+
+ // recompute an accurate value, taking care of cancellations
+ out.value = LinearCombination.value(a1.value, b1.value,
+ a2.value, b2.value,
+ a3.value, b3.value);
+
+ return out;
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final double a1, final SparseGradient b1,
+ final double a2, final SparseGradient b2,
+ final double a3, final SparseGradient b3) {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3));
+
+ // recompute an accurate value, taking care of cancellations
+ out.value = LinearCombination.value(a1, b1.value,
+ a2, b2.value,
+ a3, b3.value);
+
+ return out;
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final SparseGradient a1, final SparseGradient b1,
+ final SparseGradient a2, final SparseGradient b2,
+ final SparseGradient a3, final SparseGradient b3,
+ final SparseGradient a4, final SparseGradient b4) {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = a1.multiply(b1).add(a2.multiply(b2)).add(a3.multiply(b3)).add(a4.multiply(b4));
+
+ // recompute an accurate value, taking care of cancellations
+ out.value = LinearCombination.value(a1.value, b1.value,
+ a2.value, b2.value,
+ a3.value, b3.value,
+ a4.value, b4.value);
+
+ return out;
+
+ }
+
+ /** {@inheritDoc} */
+ @Override
+ public SparseGradient linearCombination(final double a1, final SparseGradient b1,
+ final double a2, final SparseGradient b2,
+ final double a3, final SparseGradient b3,
+ final double a4, final SparseGradient b4) {
+
+ // compute a simple value, with all partial derivatives
+ SparseGradient out = b1.multiply(a1).add(b2.multiply(a2)).add(b3.multiply(a3)).add(b4.multiply(a4));
+
+ // recompute an accurate value, taking care of cancellations
+ out.value = LinearCombination.value(a1, b1.value,
+ a2, b2.value,
+ a3, b3.value,
+ a4, b4.value);
+
+ return out;
+
+ }
+
+ /**
+ * Test for the equality of two sparse gradients.
+ * <p>
+ * Sparse gradients are considered equal if they have the same value
+ * and the same derivatives.
+ * </p>
+ * @param other Object to test for equality to this
+ * @return true if two sparse gradients are equal
+ */
+ @Override
+ public boolean equals(Object other) {
+
+ if (this == other) {
+ return true;
+ }
+
+ if (other instanceof SparseGradient) {
+ final SparseGradient rhs = (SparseGradient)other;
+ if (!Precision.equals(value, rhs.value, 1)) {
+ return false;
+ }
+ if (derivatives.size() != rhs.derivatives.size()) {
+ return false;
+ }
+ for (final Map.Entry<Integer, Double> entry : derivatives.entrySet()) {
+ if (!rhs.derivatives.containsKey(entry.getKey())) {
+ return false;
+ }
+ if (!Precision.equals(entry.getValue(), rhs.derivatives.get(entry.getKey()), 1)) {
+ return false;
+ }
+ }
+ return true;
+ }
+
+ return false;
+
+ }
+
+ /**
+ * Get a hashCode for the derivative structure.
+ * @return a hash code value for this object
+ * @since 3.2
+ */
+ @Override
+ public int hashCode() {
+ return 743 + 809 * MathUtils.hash(value) + 167 * derivatives.hashCode();
+ }
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableFunction.java
new file mode 100644
index 0000000..1adf189
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableFunction.java
@@ -0,0 +1,43 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
+import org.apache.commons.math4.legacy.exception.DimensionMismatchException;
+
+/** Interface for univariate functions derivatives.
+ * <p>This interface represents a simple function which computes
+ * both the value and the first derivative of a mathematical function.
+ * The derivative is computed with respect to the input variable.</p>
+ * @see UnivariateDifferentiableFunction
+ * @see UnivariateFunctionDifferentiator
+ * @since 3.1
+ */
+public interface UnivariateDifferentiableFunction extends UnivariateFunction {
+
+ /** Simple mathematical function.
+ * <p>{@link UnivariateDifferentiableFunction} classes compute both the
+ * value and the first derivative of the function.</p>
+ * @param t function input value
+ * @return function result
+ * @exception DimensionMismatchException if t is inconsistent with the
+ * function's free parameters or order
+ */
+ DerivativeStructure value(DerivativeStructure t)
+ throws DimensionMismatchException;
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableMatrixFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableMatrixFunction.java
new file mode 100644
index 0000000..49d5106
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableMatrixFunction.java
@@ -0,0 +1,40 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.UnivariateMatrixFunction;
+import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
+
+/**
+ * Extension of {@link UnivariateMatrixFunction} representing a univariate differentiable matrix function.
+ *
+ * @since 3.1
+ */
+public interface UnivariateDifferentiableMatrixFunction
+ extends UnivariateMatrixFunction {
+
+ /**
+ * Compute the value for the function.
+ * @param x the point for which the function value should be computed
+ * @return the value
+ * @exception MathIllegalArgumentException if {@code x} does not
+ * satisfy the function's constraints (argument out of bound, or unsupported
+ * derivative order for example)
+ */
+ DerivativeStructure[][] value(DerivativeStructure x) throws MathIllegalArgumentException;
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableVectorFunction.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableVectorFunction.java
new file mode 100644
index 0000000..0304675
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateDifferentiableVectorFunction.java
@@ -0,0 +1,40 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.UnivariateVectorFunction;
+import org.apache.commons.math4.legacy.exception.MathIllegalArgumentException;
+
+/**
+ * Extension of {@link UnivariateVectorFunction} representing a univariate differentiable vectorial function.
+ *
+ * @since 3.1
+ */
+public interface UnivariateDifferentiableVectorFunction
+ extends UnivariateVectorFunction {
+
+ /**
+ * Compute the value for the function.
+ * @param x the point for which the function value should be computed
+ * @return the value
+ * @exception MathIllegalArgumentException if {@code x} does not
+ * satisfy the function's constraints (argument out of bound, or unsupported
+ * derivative order for example)
+ */
+ DerivativeStructure[] value(DerivativeStructure x) throws MathIllegalArgumentException;
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateFunctionDifferentiator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateFunctionDifferentiator.java
new file mode 100644
index 0000000..c9ef9c1
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateFunctionDifferentiator.java
@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.UnivariateFunction;
+
+/** Interface defining the function differentiation operation.
+ * @since 3.1
+ */
+public interface UnivariateFunctionDifferentiator {
+
+ /** Create an implementation of a {@link UnivariateDifferentiableFunction
+ * differential} from a regular {@link UnivariateFunction function}.
+ * @param function function to differentiate
+ * @return differential function
+ */
+ UnivariateDifferentiableFunction differentiate(UnivariateFunction function);
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateMatrixFunctionDifferentiator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateMatrixFunctionDifferentiator.java
new file mode 100644
index 0000000..fe21d51
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateMatrixFunctionDifferentiator.java
@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.commons.math4.legacy.analysis.differentiation;
+
+import org.apache.commons.math4.legacy.analysis.UnivariateMatrixFunction;
+
+/** Interface defining the function differentiation operation.
+ * @since 3.1
+ */
+public interface UnivariateMatrixFunctionDifferentiator {
+
+ /** Create an implementation of a {@link UnivariateDifferentiableMatrixFunction
+ * differential} from a regular {@link UnivariateMatrixFunction matrix function}.
+ * @param function function to differentiate
+ * @return differential function
+ */
+ UnivariateDifferentiableMatrixFunction differentiate(UnivariateMatrixFunction function);
+
+}
diff --git a/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateVectorFunctionDifferentiator.java b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateVectorFunctionDifferentiator.java
new file mode 100644
index 0000000..5fb7ff7
--- /dev/null
+++ b/commons-math-legacy/src/main/java/org/apache/commons/math4/legacy/analysis/differentiation/UnivariateVectorFunctionDifferentiator.java
@@ -0,0 +1,33 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements. See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License. You may obtain a copy of the License at
+ *
+ * http://www.apache.org/licenses/LICENSE-2.0
... 529851 lines suppressed ...