source: src/main/java/bargainingchips/utilityfunctions/UF_BezierPriceGaussianQuantity.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;

//import bargainingchips.utilityfunctions.helperMethods;

/**
* 
* This utility function inputs {@link wishList} (i.e., quantity of each desired {@link Chip}), and price per each 
* {@link Chip} as peaked curves. 
* For quantity, the buyer may accept, with degrees of satisfaction, offered quantity around the peak, which is 
* determined by the deviation from the peak per each {@link Chip}. It is in a Guassian form. 
* For the price, 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).
* 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_BezierPriceGaussianQuantity<T> implements UtilityFunction {
        // `T' for the type of price data points, and `n' for the number of 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 ChipIssueValue<Integer> qtyDeviation;   // sigma_c. A symmetric deviation for quantities less than or more than the exact qty per chip.
        private int n;                                                                  // number of price data points at Bezier curve
        private ChipIssueValue<T[]> bezierPrice;                // list of `n' data points of type T determining the price curve
        private ChipIssueValue<Double> lambdaC;                 // kappa_c and lambda_c
        private double lambdaP,lambdaQ;                                 // lambda_p and lambda_q


        public UF_BezierPriceGaussianQuantity(WishList w, int m, ChipIssueValue<T[]> bz, ChipIssueValue<Integer> qtyDev, ChipIssueValue<Double> lc, double lp, double lq)
        {
                wishlist=w;
                qtyDeviation=qtyDev;
                n=m;
                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_BezierPriceAndGaussianQuantity::getUtility(Bundle). Input only "+n+" price data points! "+ desiredP);                         
                                
                                Double importanceC= lambdaC.getUnitValue(c);
                                int devC= qtyDeviation.getUnitValue(c);

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

                                sumWeightedPrice += importanceC * bezier(desiredP, offeredP);
                                sumWeightedQty += importanceC / (devC * 2 * Math.sqrt(Math.PI)) * Math.pow(Math.E, -0.5 * Math.pow((offeredQ - desiredQ)/devC, 2));
                        }
                        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;
                // n is 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);
        }
        
        /**
         * @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;
        }
        
        @Override
        public String toString()
        {       
                return this.getClass().getSimpleName() + ": WishList " + wishlist + ": BezierPrice "+ writeT(bezierPrice)+ ": QtyDeviations "+ qtyDeviation + ": 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", 1).addIssue("Yellow", 1).addIssue("Orange", 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_BezierPriceGaussianQuantity<Double> u = new UF_BezierPriceGaussianQuantity<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));
        }
}