source: src/main/java/bargainingchips/utilityfunctions/UF_BezierPriceBezierQuantity.java@ 341

package bargainingchips.utilityfunctions;

import bargainingchips.Bundle;
import bargainingchips.BundleBuilder;
import bargainingchips.Chip;
import bargainingchips.ChipIssueValue;
import bargainingchips.ChipIssueValueBuilder;
import bargainingchips.wishlist.WishList;
import bargainingchips.wishlist.WishListBuilder;

/**
 * 
 * This utility function inputs {@link wishList} (i.e., quantity of each desired {@link Chip}), and the curves for price 
 * and quantity ranges per each {@link Chip} as peaked curves. The curves are in a Bezier form.
 * The buyer would designate a series of `n' prices per each {@link Chip}, and then a Bezier function (of rank `n') is 
 * applied to determine the value of the offered price. That is the buyer inputs an array of prices per each desired 
 * {@link Chip} (i.e., in {@link wishList}). The prices could be in integer or real format, determined by type T[] 
 * (i.e, `Integer[]' or `Double[]', etc).
 * For quantity, similarly, the buyer may accept, with degrees of satisfaction, offered quantity around the peak (introduced 
 * via {@link wishList}) per each {@link Chip}. That is, this Bezier curve is of rank `n+1', i.e. `n' points plus wished quantity.   
 * It is worth to mention that this function considers the importance of issues (i.e., for price, quantity, etc.) 
 * as well as the importance of Chips (i.e., colors) with respect to each other.
 *  
 * 
 * @author Faria Nassiri-Mofakham
 *
 */

public class UF_BezierPriceBezierQuantity<T> implements UtilityFunction {

        // T for the type of `price' data points

        private WishList wishlist;                                                      // the exact wished quantity per each Chip 
        // Other parts of the buyer's preferences are assigned with desirability degrees of a variety of prices and quantities per each Chip. 
        private int n;                                                                          // number or data points at Bezier curve
        private ChipIssueValue<Integer[]> bezierQuantity;       // list of `n' data points determining the quantity curve. 
                                                                                                                // It could give an asymmetric deviation around desired quantity 
                                                                                                                // of the Chip; quantities less than or more than the exact qty per chip.
        private ChipIssueValue<T[]> bezierPrice;                        // list of `n' data points of type T determining the price curve
        private ChipIssueValue<Double> lambdaC;                         // importance of each Chip (i.e, color)
        private double lambdaP,lambdaQ;                                         // importance of issues (i.e., price, quantity, etc)


        public UF_BezierPriceBezierQuantity(WishList w, int m, ChipIssueValue<T[]> bz, ChipIssueValue<Integer[]> qtyDev, ChipIssueValue<Double> lc, double lp, double lq)
        {
                wishlist=w;
                n=m;
                bezierQuantity=qtyDev;
                bezierPrice=bz;
                lambdaC=lc; 
                lambdaP=lp; 
                lambdaQ=lq;
        }

        @Override
        public Double getUtility(Bundle b) 
        {
                double sumWeightedPrice = 0.0;
                double sumWeightedQty = 0.0;

                if (b!=null)
                {                       
                        for (Chip c : wishlist)
                        {
                                int desiredQ = wishlist.getQuantity(c);
                                T[] desiredP = bezierPrice.getUnitValue(c);
                                if (desiredP.length > n) 
                                        throw new IllegalStateException("\n\n[Warning] UF_BezierPriceAndBezierQuantity::getUtility(Bundle). Input only "+n+" price data points! "+ desiredP);                           
                                
                                Double importanceC= lambdaC.getUnitValue(c);

                                Integer[] devC= bezierQuantity.getUnitValue(c);
                                if (devC.length > n) 
                                        throw new IllegalStateException("\n\n[Warning] UF_BezierPriceAndBezierQuantity::getUtility(Bundle). Input totally "+ (n-1) +" quantity data points around the exact wished! "+ desiredQ);                               

                                Integer offeredQ = b.getQuantity(c);
                                if (offeredQ == null)
                                        offeredQ = 0;
                                Double offeredP= b.getUnitPrice(c);

                                sumWeightedPrice += importanceC * bezier(desiredP, offeredP);
                                sumWeightedQty += importanceC * bezier(desiredQ, devC, offeredQ);
                        }
                        double u = lambdaP * sumWeightedPrice + lambdaQ * sumWeightedQty;                                                               
                        return ( (u>1) ? 1 : ( (u<0) ? 0 : u) );
                }
                return 0.0;
        }

        /**
         * @param input parameter (e.g., an offered price per a {@link Chip}, 
         *                and `n' data points of type T (e.g., as of Double[], Integer[], etc).
         * 
         * @return Bezier value of rank `n' for the offered parameter.
         **/
        private double bezier(T[] desired, Double offered)  
        {
                double bez = 0.0;
                int n= desired.length;
                for (int i=0; i<n; i++)
                {
                        bez = ( (offered < (double) desired[0]) ? 1.0 : ( (offered > (double) desired[n-1]) ? 0.0 : comb(n,i)*Math.pow(1-offered, n)*Math.pow(i, n)*(double)desired[i]));
                }
                return ( (bez>1) ? 1 : (bez<0) ? 0 : bez);
        }
        
        /**
         * @param input parameter (e.g., an offered quantity per a {@link Chip}, and `n+1' data points.
         * 
         * @return Bezier value of rank `n+1' for the offered parameter.
         **/
        private double bezier(Integer q, Integer[] desired, Integer offered)  
        {
                double bez = 0.0;
                int n = desired.length;
                Integer[] data = new Integer[n+1];
                for (int i = 0; i < (int)Math.ceil(n/2); i++)
                {
                        data[i] = desired[i];
                        data[n-i] = desired[n-1-i];
                }
                data[(int)Math.ceil(n/2)] = q;
                for (int i=0; i<n+1; i++)
                {
                        bez = ( (offered < data[0]) ? 1.0 : ( (offered > data[n]) ? 0.0 : comb(n+1,i)*Math.pow(1-offered, n+1)*Math.pow(i, n+1)*data[i]));
                }
                return ( (bez>1) ? 1 : (bez<0) ? 0 : bez);
        }
        
        /**
         * @return combination of `m' and `k'
         **/
        private int comb(int m, int k)  
        {
                return fc(m)/(fc(m-k)*fc(k));
        }

        /**
         * @return factorial of `m'
         **/
        private int fc(int m) {  
                int result = 1;
                for (; m > 1; m--) {
                        result *= m;
                }
                return result;
        }
        
        /**
         * @return an String list of values assigned to a single variable, e.g. list of quantities or prices of a {@link Chip}
         **/
        private String writeT(ChipIssueValue<T[]> t)
        {               
                String s = "{";
                T[] j;
                if (t!=null) 
                {
                        for (Chip c: t)
                        {
                                s += " " + c.toString() + "={";
                                j = t.getUnitValue(c);
                                for (int k=0; k<j.length; k++)                                                          
                                        s += j[k].toString()+((k<j.length-1) ? ", " : "");
                                s += "}";
                        }       
                }
                s += " }";
                return s;
        }
        
        private String writeI(ChipIssueValue<Integer[]> t)
        {               
                String s = "{";
                Integer[] j;
                if (t!=null) 
                {
                        for (Chip c: t)
                        {
                                s += " " + c.toString() + "={";
                                j = t.getUnitValue(c);
                                for (int k=0; k<j.length; k++)                                                          
                                        s += j[k].toString()+((k<j.length-1) ? ", " : "");
                                s += "}";
                        }       
                }
                s += " }";
                return s;
        }
        
        @Override
        public String toString()
        {       
                return this.getClass().getSimpleName() + ": WishList " + wishlist + ": BezierPrice "+ writeT(bezierPrice)+ ": BezierQuantity "+ writeI(bezierQuantity) + ": Colors' weights "+ lambdaC + ": Issue Price's weight "+ lambdaP + ": Issue Quantity's weight " + lambdaQ;
        }

        public static void main(String[] args) 
        {
                WishList wishlist = new WishListBuilder().addWish("Green", 4).addWish("Yellow", 6).addWish("Orange", 40).build();
                int m=4;
                ChipIssueValue<Double[]> prices = new ChipIssueValueBuilder<Double[]>().addIssue("Green", new Double[] {3.0, 3.5, 4.8, 5.0}).addIssue("Yellow", new Double[] {5.0, 5.2, 6.2, 8.0}).addIssue("Orange", new Double[] {1.0, 1.8, 2.5, 3.0}).build();
                ChipIssueValue<Integer[]> deviations = new ChipIssueValueBuilder<Integer[]>().addIssue("Green", new Integer[] {2,1,2,3}).addIssue("Yellow", new Integer[] {3,2,2,3}).addIssue("Orange", new Integer[] {10,2,5,10}).build();
                ChipIssueValue<Double> wC = new ChipIssueValueBuilder<Double>().addIssue("Green", 0.5).addIssue("Yellow", 0.3).addIssue("Orange", 0.2).build();
                double wP = 0.6;
                double wQ = 0.4;

                UF_BezierPriceBezierQuantity<Double> u = new UF_BezierPriceBezierQuantity<Double> (wishlist, m, prices, deviations, wC, wP, wQ);
                System.out.println(u);

                Bundle offer = new BundleBuilder()
                                .addStack("Green", 2.0, 3)
                                .addStack("Yellow", 5.0, 4)
                                .addStack("Orange", 1.0, 17)
//---                           
//                              .addStack("Green", 3.0, 4)              //should give utility 1.0 in weighted additive
//                              .addStack("Yellow", 5.0, 6)
//                              .addStack("Orange", 1.0, 40)
//---                           
//                              .addStack("Green", 10.0, 1)             //should give utility 0.0 in weighted additive
//                              .addStack("Yellow", 10.0, 1)
//                              .addStack("Orange", 10.0, 1)    
//---
//                              .addStack("Red", 1.0, 6)
//                              .addStack("Green", 3.0, 15)
//                              .addStack("Purple", 0.10, 10)                           
                                .build();
                System.out.println(u.getUtility(offer));
        }
}