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

/**********************************************************
*
*   TriCubicSpline.java
*
*   Class for performing an interpolation on the tabulated
*   function y = f(x1,x2,x3) using a natural tricubic spline
*   Assumes second derivatives at end points = 0 (natural spine)
*
*   WRITTEN BY: Dr Michael Thomas Flanagan
*
*   DATE:       May 2002
*   UPDATE: 20 May 2003, 17 February 2006, 27 July 2007, 4 December 2007, 31 October 2009, 5 January 2011
*
*   DOCUMENTATION:
*   See Michael Thomas Flanagan's Java library on-line web page:
*   http://www.ee.ucl.ac.uk/~mflanaga/java/TriCubicSpline.html
*   http://www.ee.ucl.ac.uk/~mflanaga/java/
*
*   Copyright (c) 2003 - 2011  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, Michael Thomas Flanagan at http:\\www.ee.ucl.ac.uk/~mflanaga, appears in all copies.
*
*   Dr Michael Thomas Flanagan makes no representations about the suitability
*   or fitness of the software for any or for a particular purpose.
*   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 TriCubicSpline{

        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 double[][][] y = null;                          // y=f(x1,x2) tabulated function
        private double[] x1 = null;                             // x1 in tabulated function f(x1,x2,x3)
        private double[] x2 = null;                             // x2 in tabulated function f(x1,x2,x3)
        private double[] x3 = null;                             // x3 in tabulated function f(x1,x2,x3)
        private double[] xMin = new double[3];                  // minimum values of x1, x2 and x3
        private double[] xMax = new double[3];                  // maximum values of x1, x2 and x3
        private BiCubicSpline[] bcsn = null;                    // nPoints array of BiCubicSpline instances
        private CubicSpline csm = null;                         // CubicSpline instance
        private double[][][] d2ydx2inner = null;                // inner matrix of second derivatives
        private boolean derivCalculated = false;                // = true when the called bicubic 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 TriCubicSpline(double[] x1, double[] x2, double[] x3, double[][][] y){
                this.nPoints=x1.length;
                this.mPoints=x2.length;
                this.lPoints=x3.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.nPoints<3 || this.mPoints<3 || this.lPoints<3)throw new IllegalArgumentException("The tabulated 3D array must have a minimum size of 3 X 3 X 3");

                this.csm = new CubicSpline(this.nPoints);
                this.bcsn = BiCubicSpline.oneDarray(this.nPoints, this.mPoints, this.lPoints);
                this.x1 = new double[this.nPoints];
                this.x2 = new double[this.mPoints];
                this.x3 = new double[this.lPoints];
                this.y = new double[this.nPoints][this.mPoints][this.lPoints];
                this.d2ydx2inner = new double[this.nPoints][this.mPoints][this.lPoints];
                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 i =0; i<this.nPoints; i++){
                        for(int j=0; j<this.mPoints; j++){
                            for(int k=0; k<this.lPoints; k++){
                                    this.y[i][j][k]=y[i][j][k];
                                }
                        }
                }

                double[][] yTempml = new double[this.mPoints][this.lPoints];
            for(int i=0; i<this.nPoints; i++){

                        for(int j=0; j<this.mPoints; j++){
                            for(int k=0; k<this.lPoints; k++){
                                yTempml[j][k]=y[i][j][k];
                            }
                        }
                        this.bcsn[i].resetData(x2,x3,yTempml);
                        this.d2ydx2inner[i] = this.bcsn[i].getDeriv();
                }
                derivCalculated = true;
        }

        // Constructor with data arrays initialised to zero
        // Primarily for use by QuadriCubicSpline
        public TriCubicSpline(int nP, int mP, int lP){
                this.nPoints=nP;
                this.mPoints=mP;
                this.lPoints=lP;
                if(this.nPoints<3 || this.mPoints<3 || this.lPoints<3)throw new IllegalArgumentException("The data matrix must have a minimum size of 3 X 3 X 3");

                this.csm = new CubicSpline(this.nPoints);
                this.bcsn = BiCubicSpline.oneDarray(this.nPoints, this.mPoints, this.lPoints);
                this.x1 = new double[this.nPoints];
                this.x2 = new double[this.mPoints];
                this.x3 = new double[this.lPoints];
                this.y = new double[this.nPoints][this.mPoints][this.lPoints];
                this.d2ydx2inner = new double[this.nPoints][this.mPoints][this.lPoints];
        }

        //  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(){
            TriCubicSpline.roundingCheck = false;
            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){
            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.bcsn.length; i++)this.bcsn[i].averageIdenticalAbscissae();
            this.csm.averageIdenticalAbscissae();
        }

        // Returns a new TriCubicSpline setting internal array size to nP x mP x lP and all array values to zero with natural spline default
        // Primarily for use in this.oneDarray for QuadriCubicSpline
        public static TriCubicSpline zero(int nP, int mP, int lP){
                if(nP<3 || mP<3 || lP<3)throw new IllegalArgumentException("A minimum of three x three x three data points is needed");
                TriCubicSpline aa = new TriCubicSpline(nP, mP, lP);
                return aa;
        }

        // Create a one dimensional array of TriCubicSpline objects of length nP each of internal array size mP x lP xkP
        // Primarily for use in quadriCubicSpline
        public static TriCubicSpline[] oneDarray(int nP, int mP, int lP, int kP){
                if(mP<3 || lP<3 || kP<3)throw new IllegalArgumentException("A minimum of three x three x three data points is needed");
                TriCubicSpline[] a = new TriCubicSpline[nP];
                for(int i=0; i<nP; i++){
                        a[i]=TriCubicSpline.zero(mP, lP, kP);
                }
                return a;
        }


            // Resets the x1, x2, x3, y data arrays
            // Primarily for use in QuadriCubicSpline
        public void resetData(double[] x1, double[] x2, double[] x3, double[][][] y){
                if(x1.length!=y.length)throw new IllegalArgumentException("Arrays x1 and y row are of different length");
                if(x2.length!=y[0].length)throw new IllegalArgumentException("Arrays x2 and y column are of different length");
                if(x3.length!=y[0][0].length)throw new IllegalArgumentException("Arrays x3 and y column are of different length");
                if(this.nPoints!=x1.length)throw new IllegalArgumentException("Original array length not matched by new array length");
                if(this.mPoints!=x2.length)throw new IllegalArgumentException("Original array length not matched by new array length");
                if(this.lPoints!=x3.length)throw new IllegalArgumentException("Original array length not matched by new array length");

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

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

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

                this.csm = new CubicSpline(this.nPoints);
                this.bcsn = BiCubicSpline.oneDarray(this.nPoints, this.mPoints, this.lPoints);
                double[][] yTempml = new double[this.mPoints][this.lPoints];
            for(int i=0; i<this.nPoints; i++){

                        for(int j=0; j<this.mPoints; j++){
                            for(int k=0; k<this.lPoints; k++){
                                yTempml[j][k]=y[i][j][k];
                            }
                        }
                        this.bcsn[i].resetData(x2,x3,yTempml);
                        this.d2ydx2inner[i] = this.bcsn[i].getDeriv();
                }
                derivCalculated = true;
        }

            // 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]};
            return limits;
        }

        // Display limits to x
        public void displayLimits(){
            System.out.println(" ");
            for(int i=0; i<3; 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 and x3
        //      from a tabulated function y=f(x1,x2,x3)
        public double interpolate(double xx1, double xx2, double xx3){

                double[] yTempm = new double[nPoints];

                for (int i=0;i<nPoints;i++){
                        yTempm[i]=this.bcsn[i].interpolate(xx2, xx3);
                }

                this.csm.resetData(x1,yTempm);
                return this.csm.interpolate(xx1);
        }

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

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