IGLib
1.7.2
The IGLib base library EXTENDED - with other lilbraries and applications.
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Represents an interval on the real number line. More...
Public Member Functions | |
bool | OpenContains (double x) |
Determines whether the argument lies in the open interval. More... | |
bool | ClosedContains (double x) |
Determines whether the argument lies in the closed interval. More... | |
override bool | Equals (object obj) |
Determines whether a given object is an equal interval. More... | |
override int | GetHashCode () |
override string | ToString () |
Produces a string representation of the interval. More... | |
Static Public Member Functions | |
static Interval | FromEndpoints (double a, double b) |
Creates a new interval, given its endpoints. More... | |
static Interval | FromEndpointAndWidth (double endpoint, double width) |
Creates a new interval, given its lower endpoint and width. More... | |
static Interval | FromMidpointAndWidth (double midpoint, double width) |
Creates a new interval, given its midpoint and width. More... | |
static bool | operator== (Interval i1, Interval i2) |
Determines whether two intervals are equal. More... | |
static bool | operator!= (Interval i1, Interval i2) |
Determines whether two intervals are not equal. More... | |
Public Attributes | |
double | b |
double | w |
Properties | |
double | LeftEndpoint [get] |
Gets the left (lower) endpoint of the interval. More... | |
double | RightEndpoint [get] |
Gets the right (upper) endpoint of the interval. More... | |
double | Width [get] |
Gets the width of the interval. More... | |
double | Midpoint [get] |
Gets the mid-point of the interval. More... | |
Private Member Functions | |
Interval (double a, double b, double w) | |
Private Attributes | |
double | a |
Represents an interval on the real number line.
Use the static methods FromEndpoints, FromMidpointAndWidth, and FromEndpointAndWidth to instantiate intervals.
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inlineprivate |
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inline |
Determines whether the argument lies in the open interval.
x | The argument. |
Referenced by Test.IntervalTest.IntervalOpenContains().
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inline |
Determines whether the argument lies in the closed interval.
x | The argument. |
Referenced by Test.MultiIntegrateTest.BallVolumeIntegrals(), Test.SampleTest.BetaFit(), Test.SampleTest.BetaFitUncertainty(), Test.BinaryContingencyTableTest.BinaryContingencyNullTest(), Test.BinaryContingencyTableTest.BinaryContingencyTest(), Test.BivariateSampleTest.BivariateLinearRegression(), Test.BivariateSampleTest.BivariatePolynomialRegression(), Test.ContingencyTableTest.ContingencyTableProbabilitiesAndUncertainties(), Test.MultiIntegrateTest.DoubleIntegrals(), Test.SampleTest.ExponentialFit(), Test.SampleTest.ExponentialFitUncertainty(), Test.DataSetTest.FitDataToLinearFunctionTest(), Test.DataSetTest.FitDataToLineTest(), Test.DataSetTest.FitDataToPolynomialTest(), Test.DataSetTest.FitDataToPolynomialUncertaintiesTest(), Test.DataSetTest.FitDataToProportionalityTest(), Test.DataSetTest.FitToFunctionPolynomialCompatibilityTest(), Test.SampleTest.GammaFit(), Test.SampleTest.GammaFitUncertainty(), Test.MultiIntegrateTest.GaussianIntegrals(), Test.IntervalTest.IntervalClosedContains(), Test.NullDistributionTests.KendallNullDistributionTest(), Test.NullDistributionTests.KolmogorovNullDistributionTest(), Test.NullDistributionTests.KuiperNullDistributionTest(), Test.BivariateSampleTest.LinearLogisticRegression(), Test.SampleTest.LognormalFit(), Test.MultivariateSampleTest.MultivariateLinearRegressionTest(), Test.MultivariateSampleTest.MultivariateNormalSummaryStatistics(), Test.SampleTest.NormalFit(), Test.SampleTest.NormalFitUncertainties(), Test.SampleTest.SampleKuiperTest(), Test.SampleTest.SampleMaximumLikelihoodFit(), Test.SampleTest.SampleMoments(), Test.SampleTest.SamplePopulationMomentEstimateVariances(), Test.MultiIntegrateTest.SeperableIntegrals(), Test.SampleTest.SignTestDistribution(), Test.NullDistributionTests.SpearmanNullDistributionTest(), Test.MultiIntegrateTest.SteinmetzVolume(), Test.SampleTest.TTestDistribution(), Test.NullDistributionTests.TwoSampleKolmogorovNullDistributionTest(), Test.SampleTest.WaldFitUncertainties(), Test.MultiIntegrateTest.WatsonIntegrals(), Test.SampleTest.WeibullFit(), Test.SampleTest.WeibullFitUncertainties(), and Test.MultiIntegrateTest.ZetaIntegrals().
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inlinestatic |
Creates a new interval, given its endpoints.
a | The left (lower) endpoint of the interval. |
b | The right (upper) endpoint of the interval. |
If width of the interval is very much smaller than its endpoint values, accuracy will be better maintained by constructing the interval using one endpoint and its width.
Referenced by Test.MultiExtremumTest.Ackley(), Test.AdvancedMathTest.AiryBairyIntegral(), Test.AdvancedMathTest.AiryIntegral(), Test.AdvancedMathTest.AiryIntegrals(), Test.OrthogonalPolynomialsTest.AssociatedLaguerreOrthonormality(), Test.OrthogonalPolynomialsTest.AssociatedLegendreOrthonormalityL(), Test.AdvancedMathTest.BesselJ0Integral(), Test.AdvancedMathTest.BesselKapteynIntegral(), Test.AdvancedMathTest.BesselLipshitzIntegral(), Test.AdvancedMathTest.BesselWeberIntegral(), Test.AdvancedMathTest.BesselY0Integral(), Test.AdvancedMathTest.BetaIntegral(), Test.MultiExtremumTest.Bukin(), Test.AdvancedMathTest.CatalanIntegralTest(), Test.AdvancedMathTest.ClausenIntegral(), Test.AdvancedMathTest.DawsonIntegralTest(), Test.AdvancedMathTest.DiLogExpIntegral(), Test.AdvancedMathTest.DiLogLogIntegral(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.DiscreteAsContinuousDistribution(), Test.DistributionTest.DistributionProbabilityIntegral(), Test.MultiExtremumTest.Easom(), Test.AdvancedMathTest.EllipticEIntegration(), Test.AdvancedMathTest.EllipticFIntegral(), Test.AdvancedMathTest.EllipticFIntegration(), Test.AdvancedMathTest.EllipticKCatalanIntegral(), Test.AdvancedMathTest.EllipticKIntegration(), Test.AdvancedMathTest.ErfcIntegral(), Test.AdvancedMathTest.ErfIntegralTest(), Meta.Numerics.Statistics.BinaryContingencyTable.FisherExactTest(), Test.DataSetTest.FitDataToLinearFunctionTest(), Test.DataSetTest.FitDataToLineChiSquaredTest(), Test.DataSetTest.FitDataToLineTest(), Test.DataSetTest.FitDataToPolynomialChiSquaredTest(), Test.DataSetTest.FitDataToPolynomialTest(), Test.DataSetTest.FitDataToProportionalityTest(), Test.DataSetTest.FitToFunctionLinearCompatibilityTest(), Test.DataSetTest.FitToFunctionPolynomialCompatibilityTest(), Test.AdvancedMathTest.FresnelCIntegralTest(), Test.AdvancedMathTest.FresnelSIntegralTest(), Test.IntervalTest.FromTest(), Test.AdvancedMathTest.GammaIntegral(), Test.MultiIntegrateTest.GaussianIntegrals(), Test.DistributionTest.GetDistributions(), Test.MultiExtremumTest.GoldsteinPrice(), Test.MultiExtremumTest.Griewank(), Test.OrthogonalPolynomialsTest.HermiteOrthonormality(), Test.AdvancedMathTest.IntegerBesselJIntegral(), Test.AdvancedMathTest.IntegralCiSiIntegrals(), Test.AdvancedMathTest.IntegralEIntegral(), Test.AdvancedMathTest.IntegralSiDefinition(), Meta.Numerics.Analysis.FunctionMath.Integrate(), Meta.Numerics.Analysis.MultiFunctionMath.Integrate(), Test.IntervalTest.IntervalClosedContains(), Test.IntervalTest.IntervalEndpoints(), Test.IntervalTest.IntervalFromEndpoints(), Test.IntervalTest.IntervalMidpoint(), Test.IntervalTest.IntervalOpenContains(), Test.IntervalTest.IntervalWidth(), Test.IntervalTest.IntervalZeroWidth(), Test.AdvancedMathTest.InverseErfIntegralTest(), Test.MultiIntegrateTest.IsingIntegrals(), Meta.Numerics.Statistics.BivariateSample.KendallTauTest(), Meta.Numerics.Statistics.Sample.KolmogorovSmirnovTest(), Test.OrthogonalPolynomialsTest.LaguerreOrthonormality(), Meta.Numerics.Statistics.Distributions.Distribution.LeftProbability(), Test.OrthogonalPolynomialsTest.LegendreOrthonormality(), Test.AdvancedMathTest.ModifiedBesselIntegralTest(), Meta.Numerics.Statistics.Distributions.DiscreteInterval.operator Interval(), Test.MultiExtremumTest.PackCirclesInCircle(), Test.MultiExtremumTest.PackCirclesInSquare(), Test.MultiExtremumTest.PackSpheresInCube(), Test.AdvancedMathTest.PolyGammaIntegral(), Test.AdvancedMathTest.PolyLogIntegration(), Test.PolynomialTest.PolynomialCalculus(), Test.AdvancedMathTest.RealBesselJIntegral(), Test.RootsTest.RootOfEi(), Test.RootsTest.RootOfJ0(), Test.SampleTest.SampleKolmogorovSmirnovTest(), Test.MultiExtremumTest.Schwefel(), Meta.Numerics.Statistics.BivariateSample.SpearmanRhoTest(), FutureTest.FutureTest.STA(), Test.MultiIntegrateTest.SymmetricUnitCube(), FutureTest.FutureTest.TestNormalOrderStatistic(), FutureTest.FutureTest.TestOldMinimization(), Test.MultiExtremumTest.ThompsonProblem(), Test.SpinTest.ThreeJLegendreIntegral(), Test.IntervalTest.ToTest(), Meta.Numerics.Statistics.Distributions.UniformDistribution.UniformDistribution(), Test.MultiIntegrateTest.UnitCube(), Test.MultiIntegrateTest.WatsonIntegrals(), Test.OrthogonalPolynomialsTest.ZernikeBessel(), and Test.OrthogonalPolynomialsTest.ZernikeOrthonormality().
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inlinestatic |
Creates a new interval, given its lower endpoint and width.
endpoint | The left (lower) endpoint of the interval. |
width | The width of the interval. |
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inlinestatic |
Creates a new interval, given its midpoint and width.
midpoint | The midpoint of the interval. |
width | The width of the interval. |
Referenced by Meta.Numerics.UncertainValue.ConfidenceInterval(), and Test.IntervalTest.IntervalFromMidpointAndWidth().
Determines whether two intervals are equal.
i1 | The first interval. |
i2 | The second interval. |
References Meta.Numerics.Interval.a, and Meta.Numerics.Interval.w.
Determines whether two intervals are not equal.
i1 | The first interval. |
i2 | The second interval. |
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inline |
Determines whether a given object is an equal interval.
obj | An object. |
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inline |
Referenced by Test.IntervalTest.IntervalFromEndpoints().
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inline |
Produces a string representation of the interval.
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private |
Referenced by Meta.Numerics.Interval.operator==().
double Meta.Numerics.Interval.b |
double Meta.Numerics.Interval.w |
Referenced by Meta.Numerics.Interval.operator==().
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get |
Gets the left (lower) endpoint of the interval.
Referenced by Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.ComputeEffectiveBin(), Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DistributionTest.DistributionProbabilityIntegral(), Meta.Numerics.Analysis.FunctionMath.FindMaximum(), Meta.Numerics.Analysis.FunctionMath.FindMinimum(), Meta.Numerics.Analysis.FunctionMath.FindZero(), Test.IntervalTest.FromTest(), Meta.Numerics.Analysis.FunctionMath.Integrate(), Meta.Numerics.Analysis.MultiFunctionMath.Integrate(), Test.IntervalTest.IntervalEndpoints(), Test.IntervalTest.IntervalFromEndpoints(), Test.IntervalTest.IntervalFromMidpointAndWidth(), Test.IntervalTest.IntervalZeroWidth(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.LeftProbability(), Test.DistributionTest.OutsideDistributionSupport(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.ProbabilityDensity(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.RightProbability(), and Test.SampleTest.SampleInterquartileRange().
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get |
Gets the right (upper) endpoint of the interval.
Referenced by Test.DiscreteDistributionTest.DiscreteContinuousAgreement(), Test.DistributionTest.DistributionProbabilityIntegral(), Meta.Numerics.Analysis.FunctionMath.FindMaximum(), Meta.Numerics.Analysis.FunctionMath.FindMinimum(), Meta.Numerics.Analysis.FunctionMath.FindZero(), Meta.Numerics.Analysis.FunctionMath.Integrate(), Meta.Numerics.Analysis.MultiFunctionMath.Integrate(), Test.IntervalTest.IntervalEndpoints(), Test.IntervalTest.IntervalFromEndpoints(), Test.IntervalTest.IntervalFromMidpointAndWidth(), Test.IntervalTest.IntervalZeroWidth(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.LeftProbability(), Test.DistributionTest.OutsideDistributionSupport(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.ProbabilityDensity(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.RightProbability(), Test.SampleTest.SampleInterquartileRange(), and Test.IntervalTest.ToTest().
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get |
Gets the width of the interval.
Referenced by Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.ComputeEffectiveBin(), Test.DistributionTest.DistributionProbabilityIntegral(), Test.IntervalTest.IntervalFromEndpoints(), Test.IntervalTest.IntervalFromMidpointAndWidth(), Test.IntervalTest.IntervalWidth(), Test.IntervalTest.IntervalZeroWidth(), Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.MomentAboutMean(), and Meta.Numerics.Statistics.Distributions.DiscreteAsContinuousDistribution.ProbabilityDensity().
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get |
Gets the mid-point of the interval.
Referenced by Test.IntervalTest.IntervalFromMidpointAndWidth(), Test.IntervalTest.IntervalMidpoint(), and Test.IntervalTest.IntervalZeroWidth().