java.lang.Object

org.drip.spline.pchip.LocalMonotoneCkGenerator

public class LocalMonotoneCkGenerator
extends java.lang.Object

LocalMonotoneCkGenerator generates customized Local Stretch by trading off C^k for local control. This class implements the following variants: Akima, Bessel, Harmonic, Hyman83, Hyman89, Kruger, Monotone Convex, as well as the Van Leer and the Huynh/LeFloch limiters. It also provides the following custom control on the resulting C¹:

Eliminate the Spurious Filter in the Input C¹ Entry
Apply the Monotone Filter in the Input C¹ Entry
Generate a Vanilla C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a Bessel C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a Hyman83 C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a Hyman89 C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a Harmonic C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a van Leer Limiter C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a Huynh Le Floch Limiter C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a Kruger C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Generate a Akima C¹ Array from the specified Array of Predictor Ordinates and the Response Values
Verify if the given Quintic Polynomial is Monotone using the Hyman89 Algorithm
Generate C¹ Slope Quintic Polynomial is Monotone using the Hyman89 Algorithm
Generate the Local Control Stretch in accordance with the desired Customization Parameters
Retrieve the C¹ Array

Module	Product Core Module
Library	Fixed Income Analytics
Project	Basis Splines and Linear Compounders across a Broad Family of Spline Basis Functions
Package	Monotone Convex Themed PCHIP Splines

Author:: Lakshmi Krishnamurthy

Field Summary

Fields
Modifier and Type	Field	Description
`static java.lang.String`	`C1_AKIMA`	C¹ Type: Akima
`static java.lang.String`	`C1_BESSEL`	C¹ Type: Bessel
`static java.lang.String`	`C1_HARMONIC`	C¹ Type: Harmonic
`static java.lang.String`	`C1_HUYNH_LE_FLOCH`	C¹ Type: Huynh - Le Floch Limiter
`static java.lang.String`	`C1_HYMAN83`	C¹ Type: Hyman83
`static java.lang.String`	`C1_HYMAN89`	C¹ Type: Hyman89
`static java.lang.String`	`C1_KRUGER`	C¹ Type: Kruger
`static java.lang.String`	`C1_MONOTONE_CONVEX`	C¹ Type: Monotone Convex
`static java.lang.String`	`C1_VAN_LEER`	C¹ Type: Van Leer Limiter
`static java.lang.String`	`C1_VANILLA`	C¹ Type: Vanilla

Method Summary

Modifier and Type	Method	Description
`static double[]`	`AkimaC1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Akima C¹ Array from the specified Array of Predictor Ordinates and the Response Values.
`static double[]`	`ApplyMonotoneFilter(double[] c1Array, double[] linearC1Array)`	Apply the Monotone Filter in the Input C¹ Entry
`static double[]`	`BesselC1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Bessel C¹ Array from the specified Array of Predictor Ordinates and the Response Values
`double[]`	`C1()`	Retrieve the C¹ Array
`static LocalMonotoneCkGenerator`	`Create(double[] predictorOrdinateArray, double[] responseValueArray, java.lang.String generatorType, boolean eliminateSpuriousExtrema, boolean applyMonotoneFilter)`	Generate the Local Control Stretch in accordance with the desired Customization Parameters
`static LocalMonotoneCkGenerator`	`Create(int[] predictorOrdinateArray, double[] responseValueArray, java.lang.String generatorType, boolean eliminateSpuriousExtrema, boolean applyMonotoneFilter)`	Generate the Local Control Stretch in accordance with the desired Customization Parameters
`static double[]`	`EliminateSpuriousExtrema(double[] c1Array, double[] linearC1Array)`	Eliminate the Spurious Extrema in the Input C¹ Entry
`static double[]`	`HarmonicC1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Harmonic C¹ Array from the specified Array of Predictor Ordinates and the Response Values Fritcsh and Butland (1984) A Method for constructing local monotonic piece-wise cubic interpolants - SIAM J on Scientific and Statistical Computing 5, 300-304.
`static double[]`	`HuynhLeFlochLimiterC1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Huynh Le Floch Limiter C¹ Array from the specified Array of Predictor Ordinates and the Response Values.
`static double[]`	`Hyman83C1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Hyman83 C¹ Array from the specified Array of Predictor Ordinates and the Response Values Hyman (1983) Accurate Monotonicity Preserving Cubic Interpolation - SIAM J on Numerical Analysis 4 (4), 645-654.
`static double[]`	`Hyman89C1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Hyman89 C¹ Array from the specified Array of Predictor Ordinates and the Response Values Doherty, Edelman, and Hyman (1989) Non-negative, monotonic, or convexity preserving cubic and quintic Hermite interpolation - Mathematics of Computation 52 (186), 471-494.
`static double[]`	`Hyman89QuinticMonotoneC1(double[] predictorOrdinateArray, double[] responseValueArray, double[] firstDerivativeArray, double[] secondDerivativeArray)`	Generate C¹ Slope Quintic Polynomial is Monotone using the Hyman89 Algorithm Doherty, Edelman, and Hyman (1989) Non-negative, monotonic, or convexity preserving cubic and quintic Hermite interpolation - Mathematics of Computation 52 (186), 471-494.
`static double[]`	`KrugerC1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Kruger C¹ Array from the specified Array of Predictor Ordinates and the Response Values.
`static double[]`	`LinearC1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Vanilla C¹ Array from the specified Array of Predictor Ordinates and the Response Values
`static double[]`	`VanLeerLimiterC1(double[] predictorOrdinateArray, double[] responseValueArray)`	Generate a Van Leer Limiter C¹ Array from the specified Array of Predictor Ordinates and the Response Values.
`static boolean`	`VerifyHyman89QuinticMonotonicity(double[] predictorOrdinateArray, double[] responseValueArray, double[] firstDerivativeArray, double[] secondDerivativeArray)`	Verify if the given Quintic Polynomial is Monotone using the Hyman89 Algorithm Doherty, Edelman, and Hyman (1989) Non-negative, monotonic, or convexity preserving cubic and quintic Hermite interpolation - Mathematics of Computation 52 (186), 471-494.

Methods inherited from class java.lang.Object

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

Field Details
- C1_VANILLA
  
  public static final java.lang.String C1_VANILLA
  
  C¹ Type: Vanilla
  
  See Also:
  
  Constant Field Values
- C1_AKIMA
  
  public static final java.lang.String C1_AKIMA
  
  C¹ Type: Akima
  
  See Also:
  
  Constant Field Values
- C1_BESSEL
  
  public static final java.lang.String C1_BESSEL
  
  C¹ Type: Bessel
  
  See Also:
  
  Constant Field Values
- C1_HARMONIC
  
  public static final java.lang.String C1_HARMONIC
  
  C¹ Type: Harmonic
  
  See Also:
  
  Constant Field Values
- C1_HUYNH_LE_FLOCH
  
  public static final java.lang.String C1_HUYNH_LE_FLOCH
  
  C¹ Type: Huynh - Le Floch Limiter
  
  See Also:
  
  Constant Field Values
- C1_HYMAN83
  
  public static final java.lang.String C1_HYMAN83
  
  C¹ Type: Hyman83
  
  See Also:
  
  Constant Field Values
- C1_HYMAN89
  
  public static final java.lang.String C1_HYMAN89
  
  C¹ Type: Hyman89
  
  See Also:
  
  Constant Field Values
- C1_KRUGER
  
  public static final java.lang.String C1_KRUGER
  
  C¹ Type: Kruger
  
  See Also:
  
  Constant Field Values
- C1_MONOTONE_CONVEX
  
  public static final java.lang.String C1_MONOTONE_CONVEX
  
  C¹ Type: Monotone Convex
  
  See Also:
  
  Constant Field Values
- C1_VAN_LEER
  
  public static final java.lang.String C1_VAN_LEER
  
  C¹ Type: Van Leer Limiter
  
  See Also:
  
  Constant Field Values
Method Details
- EliminateSpuriousExtrema
  
  public static final double[] EliminateSpuriousExtrema(double[] c1Array, double[] linearC1Array)
  
  Eliminate the Spurious Extrema in the Input C¹ Entry
  
  Parameters:
  
  c1Array - The C¹ Array in which the Spurious Extrema is to be eliminated
  
  linearC1Array - Array of the Linear C¹ Entries
  
  Returns:
  
  The C¹ Array with the Spurious Extrema eliminated
- ApplyMonotoneFilter
  
  public static final double[] ApplyMonotoneFilter(double[] c1Array, double[] linearC1Array)
  
  Apply the Monotone Filter in the Input C¹ Entry
  
  Parameters:
  
  c1Array - The C¹ Array in which the Monotone Filter is to be applied
  
  linearC1Array - Array of the Linear C¹ Entries
  
  Returns:
  
  The C¹ Array with the Monotone Filter applied
- LinearC1
  
  public static final double[] LinearC1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Vanilla C¹ Array from the specified Array of Predictor Ordinates and the Response Values
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- BesselC1
  
  public static final double[] BesselC1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Bessel C¹ Array from the specified Array of Predictor Ordinates and the Response Values
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- Hyman83C1
  
  public static final double[] Hyman83C1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Hyman83 C¹ Array from the specified Array of Predictor Ordinates and the Response Values Hyman (1983) Accurate Monotonicity Preserving Cubic Interpolation - SIAM J on Numerical Analysis 4 (4), 645-654.
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- Hyman89C1
  
  public static final double[] Hyman89C1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Hyman89 C¹ Array from the specified Array of Predictor Ordinates and the Response Values Doherty, Edelman, and Hyman (1989) Non-negative, monotonic, or convexity preserving cubic and quintic Hermite interpolation - Mathematics of Computation 52 (186), 471-494.
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- HarmonicC1
  
  public static final double[] HarmonicC1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Harmonic C¹ Array from the specified Array of Predictor Ordinates and the Response Values Fritcsh and Butland (1984) A Method for constructing local monotonic piece-wise cubic interpolants - SIAM J on Scientific and Statistical Computing 5, 300-304.
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- VanLeerLimiterC1
  
  public static final double[] VanLeerLimiterC1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Van Leer Limiter C¹ Array from the specified Array of Predictor Ordinates and the Response Values. Van Leer (1974) Towards the Ultimate Conservative Difference Scheme. II - Monotonicity and Conservation combined in a Second-Order Scheme, Journal of Computational Physics 14 (4), 361-370.
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- HuynhLeFlochLimiterC1
  
  public static final double[] HuynhLeFlochLimiterC1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Huynh Le Floch Limiter C¹ Array from the specified Array of Predictor Ordinates and the Response Values. Huynh (1993) Accurate Monotone Cubic Interpolation, SIAM J on Numerical Analysis 30 (1), 57-100.
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- KrugerC1
  
  public static final double[] KrugerC1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Kruger C¹ Array from the specified Array of Predictor Ordinates and the Response Values. Kruger (2002) Constrained Cubic Spline Interpolations for Chemical Engineering Application, http://www.korf.co.uk/spline.pdf
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- AkimaC1
  
  public static final double[] AkimaC1(double[] predictorOrdinateArray, double[] responseValueArray)
  
  Generate a Akima C¹ Array from the specified Array of Predictor Ordinates and the Response Values. Akima (1970): A New Method of Interpolation and Smooth Curve Fitting based on Local Procedures, Journal of the Association for the Computing Machinery 17 (4), 589-602.
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  Returns:
  
  The C¹ Array
- VerifyHyman89QuinticMonotonicity
  
  public static final boolean VerifyHyman89QuinticMonotonicity(double[] predictorOrdinateArray, double[] responseValueArray, double[] firstDerivativeArray, double[] secondDerivativeArray) throws java.lang.Exception
  
  Verify if the given Quintic Polynomial is Monotone using the Hyman89 Algorithm Doherty, Edelman, and Hyman (1989) Non-negative, monotonic, or convexity preserving cubic and quintic Hermite interpolation - Mathematics of Computation 52 (186), 471-494.
  
  Parameters:
  
  predictorOrdinateArray - Array of Predictor Ordinates
  
  responseValueArray - Array of Response Values
  
  firstDerivativeArray - Array of First Derivatives
  
  secondDerivativeArray - Array of Second Derivatives
  
  Returns:
  
  TRUE - The given Quintic Polynomial is Monotone
  
  Throws:
  
  java.lang.Exception - Thrown if the Monotonicity cannot be determined
- Hyman89QuinticMonotoneC1
  
  public static final double[] Hyman89QuinticMonotoneC1(double[] predictorOrdinateArray, double[] responseValueArray, double[] firstDerivativeArray, double[] secondDerivativeArray)
  
  Generate C¹ Slope Quintic Polynomial is Monotone using the Hyman89 Algorithm Doherty, Edelman, and Hyman (1989) Non-negative, monotonic, or convexity preserving cubic and quintic Hermite interpolation - Mathematics of Computation 52 (186), 471-494.
  
  Parameters:
  
  predictorOrdinateArray - Array of Predictor Ordinates
  
  responseValueArray - Array of Response Values
  
  firstDerivativeArray - Array of First Derivatives
  
  secondDerivativeArray - Array of Second Derivatives
  
  Returns:
  
  The C¹ Slope Quintic Stretch
- Create
  
  public static final LocalMonotoneCkGenerator Create(double[] predictorOrdinateArray, double[] responseValueArray, java.lang.String generatorType, boolean eliminateSpuriousExtrema, boolean applyMonotoneFilter)
  
  Generate the Local Control Stretch in accordance with the desired Customization Parameters
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  generatorType - The C¹ Generator Type
  
  eliminateSpuriousExtrema - TRUE - Eliminate Spurious Extrema
  
  applyMonotoneFilter - TRUE - Apply Monotone Filter
  
  Returns:
  
  Instance of the Local Control Stretch
- Create
  
  public static final LocalMonotoneCkGenerator Create(int[] predictorOrdinateArray, double[] responseValueArray, java.lang.String generatorType, boolean eliminateSpuriousExtrema, boolean applyMonotoneFilter)
  
  Generate the Local Control Stretch in accordance with the desired Customization Parameters
  
  Parameters:
  
  predictorOrdinateArray - The Predictor Ordinate Array
  
  responseValueArray - The Response Value Array
  
  generatorType - The C¹ Generator Type
  
  eliminateSpuriousExtrema - TRUE - Eliminate Spurious Extrema
  
  applyMonotoneFilter - TRUE - Apply Monotone Filter
  
  Returns:
  
  Instance of the Local Control Stretch
- C1
  
  public double[] C1()
  
  Retrieve the C¹ Array
  
  Returns:
  
  The C¹ Array

Class LocalMonotoneCkGenerator

Field Summary

Method Summary

Methods inherited from class java.lang.Object

Field Details

C1_VANILLA

C1_AKIMA

C1_BESSEL

C1_HARMONIC

C1_HUYNH_LE_FLOCH

C1_HYMAN83

C1_HYMAN89

C1_KRUGER

C1_MONOTONE_CONVEX

C1_VAN_LEER

Method Details

EliminateSpuriousExtrema

ApplyMonotoneFilter

LinearC1

BesselC1

Hyman83C1

Hyman89C1

HarmonicC1

VanLeerLimiterC1

HuynhLeFlochLimiterC1

KrugerC1

AkimaC1

VerifyHyman89QuinticMonotonicity

Hyman89QuinticMonotoneC1

Create

Create

C1