source: src/main/java/agents/anac/y2015/agentBuyogV2/flanagan/interpolation/QuadriCubicSpline.java

/**********************************************************
*
*   QuadriCubicSpline.java
*
*   Class for performing an interpolation on the tabulated
*   function y = f(x1,x2,x3,x4) using a natural quadricubic spline
*   Assumes second derivatives at end points = 0 (natural spine)
*
*   WRITTEN BY: Dr Michael Thomas Flanagan
*
*   DATE:       May 2003
*   UPDATE  July 2007, 4 December 2007, 21 September 2008, 12 October 2009, 31 October 2009
*
*   DOCUMENTATION:
*   See Michael Thomas Flanagan's Java library on-line web page:
*   http://www.ee.ucl.ac.uk/~mflanaga/java/QuadriCubicSpline.html
*   http://www.ee.ucl.ac.uk/~mflanaga/java/
*
*   Copyright (c) 2003 - 2009   Michael Thomas Flanagan
*
*   PERMISSION TO COPY:
*
* Permission to use, copy and modify this software and its documentation for NON-COMMERCIAL purposes is granted, without fee,
* provided that an acknowledgement to the author, Dr Michael Thomas Flanagan at www.ee.ucl.ac.uk/~mflanaga, appears in all copies
* and associated documentation or publications.
*
* Redistributions of the source code of this source code, or parts of the source codes, must retain the above copyright notice, this list of conditions
* and the following disclaimer and requires written permission from the Michael Thomas Flanagan:
*
* Redistribution in binary form of all or parts of this class 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 and requires written permission from the Michael Thomas Flanagan:
*
* Dr Michael Thomas Flanagan makes no representations about the suitability or fitness of the software for any or for a particular purpose.
* Dr Michael Thomas Flanagan shall not be liable for any damages suffered as a result of using, modifying or distributing this software
* or its derivatives.
*
***************************************************************************************/

package agents.anac.y2015.agentBuyogV2.flanagan.interpolation;

import agents.anac.y2015.agentBuyogV2.flanagan.math.Fmath;

public class QuadriCubicSpline{

        private int nPoints = 0;                                    // no. of x1 tabulated points
        private int mPoints = 0;                                    // no. of x2 tabulated points
        private int lPoints = 0;                                    // no. of x3 tabulated points
        private int kPoints = 0;                                    // no. of x4 tabulated points

        private double[][][][] y = null;                        // y=f(x1,x2,x3,x4) tabulated function
        private double[] x1 = null;                             // x1 in tabulated function f(x1,x2,x3,x4)
        private double[] x2 = null;                             // x2 in tabulated function f(x1,x2,x3,x4)
        private double[] x3 = null;                             // x3 in tabulated function f(x1,x2,x3,x4)
        private double[] x4 = null;                             // x4 in tabulated function f(x1,x2,x3,x4)
        private double[] xMin = new double[4];                  // minimum values of x1, x2, x3 and x4
        private double[] xMax = new double[4];                  // maximum values of x1, x2, x3 and x4

        private TriCubicSpline[] tcsn = null;                   // nPoints array of TriCubicSpline instances
        private CubicSpline csm = null;                         // CubicSpline instance
        private double[][][][] d2ydx2inner = null;                   // inner matrix of second derivatives
        private boolean derivCalculated = false;                // = true when the called triicubic spline derivatives have been calculated
        private boolean averageIdenticalAbscissae = false;      // if true: the the ordinate values for identical abscissae are averaged
                                                                // If false: the abscissae values are separated by 0.001 of the total abscissae range;
        private static double potentialRoundingError = 5e-15;   // potential rounding error used in checking wheter a value lies within the interpolation bounds (static value)
        private static boolean roundingCheck = true;            // = true: points outside the interpolation bounds by less than the potential rounding error rounded to the bounds limit (static value)


        // Constructor
        public QuadriCubicSpline(double[] x1, double[] x2, double[] x3, double[] x4, double[][][][] y){
                this.nPoints=x1.length;
                this.mPoints=x2.length;
                this.lPoints=x3.length;
                this.kPoints=x4.length;
                if(this.nPoints!=y.length)throw new IllegalArgumentException("Arrays x1 and y-row are of different length " + this.nPoints + " " + y.length);
                if(this.mPoints!=y[0].length)throw new IllegalArgumentException("Arrays x2 and y-column are of different length "+ this.mPoints + " " + y[0].length);
                if(this.lPoints!=y[0][0].length)throw new IllegalArgumentException("Arrays x3 and y-column are of different length "+ this.mPoints + " " + y[0][0].length);
                if(this.kPoints!=y[0][0][0].length)throw new IllegalArgumentException("Arrays x4 and y-column are of different length "+ this.kPoints + " " + y[0][0][0].length);
                if(this.nPoints<3 || this.mPoints<3 || this.lPoints<3 || this.kPoints<3)throw new IllegalArgumentException("The tabulated 4D array must have a minimum size of 3 X 3 X 3 X 3");

                this.csm = new CubicSpline(this.nPoints);
                this.tcsn = TriCubicSpline.oneDarray(this.nPoints, this.mPoints, this.lPoints, this.kPoints);
                this.x1 = new double[this.nPoints];
                this.x2 = new double[this.mPoints];
                this.x3 = new double[this.lPoints];
                this.x4 = new double[this.kPoints];

                this.y = new double[this.nPoints][this.mPoints][this.lPoints][this.kPoints];
                this.d2ydx2inner = new double[this.nPoints][this.mPoints][this.lPoints][this.kPoints];
                for(int i=0; i<this.nPoints; i++){
                        this.x1[i]=x1[i];
                }
                this.xMin[0] = Fmath.minimum(this.x1);
                this.xMax[0] = Fmath.maximum(this.x1);

                for(int j=0; j<this.mPoints; j++){
                        this.x2[j]=x2[j];
                }
                this.xMin[1] = Fmath.minimum(this.x2);
                this.xMax[1] = Fmath.maximum(this.x2);

                for(int j=0; j<this.lPoints; j++){
                        this.x3[j]=x3[j];
                }
                this.xMin[2] = Fmath.minimum(this.x3);
                this.xMax[2] = Fmath.maximum(this.x3);

                for(int j=0; j<this.kPoints; j++){
                        this.x4[j]=x4[j];
                }
                this.xMin[3] = Fmath.minimum(this.x4);
                this.xMax[3] = Fmath.maximum(this.x4);

                for(int i =0; i<this.nPoints; i++){
                        for(int j=0; j<this.mPoints; j++){
                            for(int k=0; k<this.lPoints; k++){
                                for(int l=0; l<this.kPoints; l++){
                                        this.y[i][j][k][l]=y[i][j][k][l];
                                    }
                                }
                        }
                }

                double[][][] yTempml = new double[this.mPoints][this.lPoints][this.kPoints];
            for(int i=0; i<this.nPoints; i++){
                        for(int j=0; j<this.mPoints; j++){
                            for(int k=0; k<this.lPoints; k++){
                            for(int l=0; l<this.kPoints; l++){
                                    yTempml[j][k][l]=y[i][j][k][l];
                                }
                            }
                        }
                        this.tcsn[i].resetData(x2,x3,x4,yTempml);
                        d2ydx2inner[i] = this.tcsn[i].getDeriv();
                }
                double[] yTempm = new double[nPoints];
                this.derivCalculated = true;
        }

        //  METHODS

        // Reset rounding error check option
        // Default option: points outside the interpolation bounds by less than the potential rounding error rounded to the bounds limit
        // This method causes this check to be ignored and an exception to be thrown if any point lies outside the interpolation bounds
        public static void noRoundingErrorCheck(){
            QuadriCubicSpline.roundingCheck = false;
            TriCubicSpline.noRoundingErrorCheck();
            BiCubicSpline.noRoundingErrorCheck();
            CubicSpline.noRoundingErrorCheck();
        }

        // Reset potential rounding error value
        // Default option: points outside the interpolation bounds by less than the potential rounding error rounded to the bounds limit
        // The default value for the potential rounding error is 5e-15*times the 10^exponent of the value outside the bounds
            // This method allows the 5e-15 to be reset
        public static void potentialRoundingError(double potentialRoundingError){
            QuadriCubicSpline.potentialRoundingError = potentialRoundingError;
            TriCubicSpline.potentialRoundingError(potentialRoundingError);
            BiCubicSpline.potentialRoundingError(potentialRoundingError);
            CubicSpline.potentialRoundingError(potentialRoundingError);
        }

        // Reset the default handing of identical abscissae with different ordinates
        // from the default option of separating the two relevant abscissae by 0.001 of the range
        // to avraging the relevant ordinates
        public void averageIdenticalAbscissae(){
            this.averageIdenticalAbscissae = true;
            for(int i=0; i<this.tcsn.length; i++)this.tcsn[i].averageIdenticalAbscissae();
            this.csm.averageIdenticalAbscissae();
        }

            // Get minimum limits
        public double[] getXmin(){
            return this.xMin;
        }

        // Get maximum limits
        public double[] getXmax(){
            return this.xMax;
        }

        // Get limits to x
        public double[] getLimits(){
            double[] limits = {xMin[0], xMax[0], xMin[1], xMax[1], xMin[2], xMax[2], xMin[3], xMax[3]};
            return limits;
        }

        // Display limits to x
        public void displayLimits(){
            System.out.println(" ");
            for(int i=0; i<2; i++){
                System.out.println("The limits to the x array " + i + " are " + xMin[i] + " and " + xMax[i]);
            }
            System.out.println(" ");
        }

        //      Returns an interpolated value of y for values of x1, x2, x3 and x4
        //      from a tabulated function y=f(x1,x2,x3,x4)
        public double interpolate(double xx1, double xx2, double xx3, double xx4){


                double[] yTempm = new double[nPoints];
                for (int i=0;i<nPoints;i++){
                        yTempm[i]=this.tcsn[i].interpolate(xx2, xx3, xx4);
                }
                this.csm.resetData(x1,yTempm);
                return this.csm.interpolate(xx1);
        }


        // Get inner matrix of derivatives
        // Primarily used by PolyCubicSpline
        public double[][][][] getDeriv(){
            return this.d2ydx2inner;
        }

        // Set inner matrix of derivatives
        // Primarily used by PolyCubicSpline
        public void setDeriv(double[][][][] d2ydx2){
            this.d2ydx2inner = d2ydx2;
            this.derivCalculated = true;
        }
}