org.drip.spline.pchip

Class LocalMonotoneCkGenerator

java.lang.Object

org.drip.spline.pchip.LocalMonotoneCkGenerator

public class LocalMonotoneCkGenerator
extends java.lang.Object

LocalMonotoneCkGenerator generates customized Local Stretch by trading off Ck 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 Extrema 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. - Verify if the given Quintic Polynomial is Monotone using the Hyman89 Algorithm, and generate it if necessary.

Author:

Lakshmi Krishnamurthy

Field Summary

Fields

Modifier and Type	Field and 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 and Description
static double[]	AkimaC1(double[] adblPredictorOrdinate, double[] adblResponseValue) Generate a Akima C1 Array from the specified Array of Predictor Ordinates and the Response Values.
static double[]	ApplyMonotoneFilter(double[] adblC1, double[] adblLinearC1) Apply the Monotone Filter in the Input C1 Entry
static double[]	BesselC1(double[] adblPredictorOrdinate, double[] adblResponseValue) 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[] adblPredictorOrdinate, double[] adblResponseValue, java.lang.String strGeneratorType, boolean bEliminateSpuriousExtrema, boolean bApplyMonotoneFilter) Generate the Local Control Stretch in accordance with the desired Customization Parameters
static LocalMonotoneCkGenerator	Create(int[] aiPredictorOrdinate, double[] adblResponseValue, java.lang.String strGeneratorType, boolean bEliminateSpuriousExtrema, boolean bApplyMonotoneFilter) Generate the Local Control Stretch in accordance with the desired Customization Parameters
static double[]	EliminateSpuriousExtrema(double[] adblC1, double[] adblLinearC1) Eliminate the Spurious Extrema in the Input C1 Entry
static double[]	HarmonicC1(double[] adblPredictorOrdinate, double[] adblResponseValue) 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[] adblPredictorOrdinate, double[] adblResponseValue) Generate a Huynh Le Floch Limiter C1 Array from the specified Array of Predictor Ordinates and the Response Values.
static double[]	Hyman83C1(double[] adblPredictorOrdinate, double[] adblResponseValue) 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[] adblPredictorOrdinate, double[] adblResponseValue) 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[] adblPredictorOrdinate, double[] adblResponseValue, double[] adblFirstDerivative, double[] adblSecondDerivative) 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[] adblPredictorOrdinate, double[] adblResponseValue) Generate a Kruger C1 Array from the specified Array of Predictor Ordinates and the Response Values.
static double[]	LinearC1(double[] adblPredictorOrdinate, double[] adblResponseValue) Generate a Vanilla C1 Array from the specified Array of Predictor Ordinates and the Response Values
static double[]	VanLeerLimiterC1(double[] adblPredictorOrdinate, double[] adblResponseValue) Generate a Van Leer Limiter C1 Array from the specified Array of Predictor Ordinates and the Response Values.
static boolean	VerifyHyman89QuinticMonotonicity(double[] adblPredictorOrdinate, double[] adblResponseValue, double[] adblFirstDerivative, double[] adblSecondDerivative) 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 Detail

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

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Constant Field Values

C1_BESSEL

public static final java.lang.String C1_BESSEL

C1 Type: Bessel

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Constant Field Values

C1_HARMONIC

public static final java.lang.String C1_HARMONIC

C1 Type: Harmonic

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Constant Field Values

C1_HUYNH_LE_FLOCH

public static final java.lang.String C1_HUYNH_LE_FLOCH

C1 Type: Huynh - Le Floch Limiter

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Constant Field Values

C1_HYMAN83

public static final java.lang.String C1_HYMAN83

C1 Type: Hyman83

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Constant Field Values

C1_HYMAN89

public static final java.lang.String C1_HYMAN89

C1 Type: Hyman89

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Constant Field Values

C1_KRUGER

public static final java.lang.String C1_KRUGER

C1 Type: Kruger

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Constant Field Values

C1_MONOTONE_CONVEX

public static final java.lang.String C1_MONOTONE_CONVEX

C1 Type: Monotone Convex

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Constant Field Values

C1_VAN_LEER

public static final java.lang.String C1_VAN_LEER

C1 Type: Van Leer Limiter

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Constant Field Values

Method Detail

EliminateSpuriousExtrema

public static final double[] EliminateSpuriousExtrema(double[] adblC1,
                                                      double[] adblLinearC1)

Eliminate the Spurious Extrema in the Input C1 Entry

Parameters:

adblC1 - The C1 Array in which the Spurious Extrema is to be eliminated

adblLinearC1 - Array of the Linear C1 Entries

Returns:

The C1 Array with the Spurious Extrema eliminated

ApplyMonotoneFilter

public static final double[] ApplyMonotoneFilter(double[] adblC1,
                                                 double[] adblLinearC1)

Apply the Monotone Filter in the Input C1 Entry

Parameters:

adblC1 - The C1 Array in which the Monotone Filter is to be applied

adblLinearC1 - Array of the Linear C1 Entries

Returns:

The C1 Array with the Monotone Filter applied

LinearC1

public static final double[] LinearC1(double[] adblPredictorOrdinate,
                                      double[] adblResponseValue)

Generate a Vanilla C1 Array from the specified Array of Predictor Ordinates and the Response Values

Parameters:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

BesselC1

public static final double[] BesselC1(double[] adblPredictorOrdinate,
                                      double[] adblResponseValue)

Generate a Bessel C1 Array from the specified Array of Predictor Ordinates and the Response Values

Parameters:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

Hyman83C1

public static final double[] Hyman83C1(double[] adblPredictorOrdinate,
                                       double[] adblResponseValue)

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:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

Hyman89C1

public static final double[] Hyman89C1(double[] adblPredictorOrdinate,
                                       double[] adblResponseValue)

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:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

HarmonicC1

public static final double[] HarmonicC1(double[] adblPredictorOrdinate,
                                        double[] adblResponseValue)

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:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

VanLeerLimiterC1

public static final double[] VanLeerLimiterC1(double[] adblPredictorOrdinate,
                                              double[] adblResponseValue)

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:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

HuynhLeFlochLimiterC1

public static final double[] HuynhLeFlochLimiterC1(double[] adblPredictorOrdinate,
                                                   double[] adblResponseValue)

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:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

KrugerC1

public static final double[] KrugerC1(double[] adblPredictorOrdinate,
                                      double[] adblResponseValue)

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:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

AkimaC1

public static final double[] AkimaC1(double[] adblPredictorOrdinate,
                                     double[] adblResponseValue)

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:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

Returns:

The C1 Array

VerifyHyman89QuinticMonotonicity

public static final boolean VerifyHyman89QuinticMonotonicity(double[] adblPredictorOrdinate,
                                                             double[] adblResponseValue,
                                                             double[] adblFirstDerivative,
                                                             double[] adblSecondDerivative)
                                                      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:

adblPredictorOrdinate - Array of Predictor Ordinates

adblResponseValue - Array of Response Values

adblFirstDerivative - Array of First Derivatives

adblSecondDerivative - 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[] adblPredictorOrdinate,
                                                      double[] adblResponseValue,
                                                      double[] adblFirstDerivative,
                                                      double[] adblSecondDerivative)

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:

adblPredictorOrdinate - Array of Predictor Ordinates

adblResponseValue - Array of Response Values

adblFirstDerivative - Array of First Derivatives

adblSecondDerivative - Array of Second Derivatives

Returns:

The C1 Slope Quintic Stretch

Create

public static final LocalMonotoneCkGenerator Create(double[] adblPredictorOrdinate,
                                                    double[] adblResponseValue,
                                                    java.lang.String strGeneratorType,
                                                    boolean bEliminateSpuriousExtrema,
                                                    boolean bApplyMonotoneFilter)

Generate the Local Control Stretch in accordance with the desired Customization Parameters

Parameters:

adblPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

strGeneratorType - The C1 Generator Type

bEliminateSpuriousExtrema - TRUE - Eliminate Spurious Extrema

bApplyMonotoneFilter - TRUE - Apply Monotone Filter

Returns:

Instance of the Local Control Stretch

Create

public static final LocalMonotoneCkGenerator Create(int[] aiPredictorOrdinate,
                                                    double[] adblResponseValue,
                                                    java.lang.String strGeneratorType,
                                                    boolean bEliminateSpuriousExtrema,
                                                    boolean bApplyMonotoneFilter)

Generate the Local Control Stretch in accordance with the desired Customization Parameters

Parameters:

aiPredictorOrdinate - The Predictor Ordinate Array

adblResponseValue - The Response Value Array

strGeneratorType - The C1 Generator Type

bEliminateSpuriousExtrema - TRUE - Eliminate Spurious Extrema

bApplyMonotoneFilter - TRUE - Apply Monotone Filter

Returns:

Instance of the Local Control Stretch

C1

public double[] C1()

Retrieve the C1 Array

Returns:

The C1 Array