1 // Simplex.cpp : Defines the entry point for the console application. 2 // 3 4 #include "stdafx.h" 5 #include <fstream> 6 #include <iostream> 7

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1 1 // Simplex.cpp : Defines the entry point for the console application. 2 // 3 4 #include "stdafx.h" 5 #include <fstream> 6 #include <iostream> 7 #include <stdio.h> 8 #include <stdlib.h> 9 #include <math.h> 10 #include <conio.h> using namespace std; //global variables 15 int const max_parm=50,max_var=10,max_points=200; 16 int const max_vert=max_parm+1; 17 FILE *logfile; /*Function Declarations*/ 20 void calc_function(double ycalc[max_points], 21 double beta[max_parm], 22 double x[max_var][max_points],int npoint); int _tmain(int argc, _TCHAR* argv[]) 25 { 26 int const max_iter=2000; 27 double const tol=1e-6; 28 int nparm,nvar,npoint,nvert,ivert,ipoint,ivar,iparm,iter=0; 29 int iworst,ibest, nreplace, convg=0; 30 double beta[max_vert+2][max_parm], delta[max_parm],y[max_points]; 31 double x[max_var][max_points],res[max_vert+2],centroid[max_parm]; 32 double ycalc[max_points],z,rsquared,resprev; char asc[255]; 35 FILE *ascfile; printf("\tsimplex Nonlinear Least Squares Fit\n"); 38 printf("written by C. D. Keefe\nVersion 03/04\n"); 39 printf("this program will read a data file "); 40 printf("and calculate the least-squares fit.\n"); cout<<"data file? ";cin>>asc; 43 ascfile=fopen(asc,"r"); if(ascfile==null) 46 { 47 printf("\n%s does not exist.\n", asc); 48 goto exit_error; 49 } 50

2 51 //read number of independent points, variables, parameters 52 fscanf(ascfile,"%d",&npoint); 53 fscanf(ascfile,"%d",&nvar); 54 fscanf(ascfile,"%d",&nparm); //check and see if any of these exceed the maximum 57 if(npoint>max_points) 58 { 59 printf("\ntoo many points. Maximum is %d", max_points); 60 goto exit_error; 61 } if(nparm>max_parm) 64 { 65 printf("\ntoo many parameters. Maximum is %d", max_parm); 66 goto exit_error; 67 } 68 nvert=nparm+1; if(nvar>max_var) 71 { 72 printf("\ntoo many variables. Maximum is %d", max_var); 73 goto exit_error; 74 } //read initial value of parameters 77 for(iparm=0;iparm<nparm;iparm++)fscanf(ascfile,"%lg",beta[0]+iparm); //calculate incerements to parameters 80 for(iparm=0;iparm<nparm;iparm++) 81 { 82 delta[iparm]=.01*beta[0][iparm]; 83 if(delta[iparm]==0)delta[iparm]=0.01; 84 } //calculate initial set of vertices 87 for(ivert=1;ivert<nvert;ivert++) 88 { 89 //delta[ivert-1]*=2; //change one deltas each iteration 90 for(iparm=0;iparm<nparm;iparm++) 91 { 92 if(iparm==(ivert-1))beta[ivert][iparm]=beta[0][iparm]+2*delta[iparm]; 93 else beta[ivert][iparm]=beta[0][iparm]+delta[iparm]; 94 } 95 } //read input data as (x1,x2,...,y) then initial guesses or parameters 98 for(ipoint=0;ipoint<npoint;ipoint++) 99 { 100 for(ivar=0;ivar<nvar;ivar++)fscanf(ascfile,"%lg",x[ivar]+ipoint);

3 101 fscanf(ascfile,"%lg",y+ipoint); 102 } 103 fclose(ascfile); 104 //Open Log File, Overwrite if Already Exists. 105 logfile=fopen("simplex.out","w"); 106 setvbuf(logfile,null,_ionbf,0); //unbufffered output 107 fprintf(logfile,"\t\t\tlogfile FOR Nonlinear Least Squares Fit\n\n"); //calculate values of function with ititial parameter sets 110 for(ivert=nvert-1;ivert>=0;ivert--) 111 { 112 calc_function(ycalc,beta[ivert],x,npoint); 113 Z=0; 114 for(ipoint=0;ipoint<npoint;ipoint++) 115 Z+=(y[ipoint]-ycalc[ipoint])*(y[ipoint]-ycalc[ipoint]); 116 Res[ivert]=Z; 117 } 118 //find best set of parameters 119 ibest=0; 120 for(ivert=0;ivert<nvert;ivert++)if(res[ivert]<res[ibest])ibest=ivert; 121 resprev=res[ibest]; do { 125 iter++; //check if max ietartions exceeded if(iter>max_iter) 130 { 131 printf("\nmaximum iteration exceeded."); 132 fprintf(logfile,"\nmaximum iteration exceeded."); 133 goto exit_error; 134 } //find best and worst set of parameters 138 iworst=ibest=0; 139 for(ivert=0;ivert<nvert;ivert++) 140 { 141 if(res[ivert]<res[ibest])ibest=ivert; 142 if(res[ivert]>res[iworst])iworst=ivert; 143 } //output parameters for current iteration 146 printf("\niteration %d: Response %lg",iter,res[ibest]); 147 fprintf(logfile,"\niteration %d: Response %lg",iter,res[ibest]); 148 fprintf(logfile,"\nbeta\t\tresponse\n"); 149 for(ivert=0;ivert<nvert;ivert++) 150 {

4 151 for(iparm=0;iparm<nparm;iparm++) 152 fprintf(logfile,"%8.6lf\t", beta[ivert][iparm]); 153 fprintf(logfile,"%8.6lf",res[ivert]); 154 if(ivert==ibest)fprintf(logfile,"\tbest"); 155 if(ivert==iworst)fprintf(logfile,"\tworst"); 156 fprintf(logfile,"\n"); 157 } //calculate centroid 160 for(iparm=0;iparm<nparm;iparm++) 161 { 162 centroid[iparm]=0; 163 for(ivert=0;ivert<nvert;ivert++) 164 if(ivert!=iworst)centroid[iparm]+=beta[ivert][iparm]; 165 centroid[iparm]/=nparm; 166 } //output centroid 169 for(iparm=0;iparm<nparm;iparm++) fprintf(logfile,"%8.6lf\t", centroid[iparm]); 170 fprintf(logfile,"\tcentroid\n"); //calculate 1st reflected point beta[nvert][iparm] 174 for(iparm=0;iparm<nparm;iparm++) 175 beta[nvert][iparm]=2*centroid[iparm]-beta[iworst][iparm]; //calculate respond for 1st reflected point 178 calc_function(ycalc,beta[nvert],x,npoint); 179 Z=0; 180 for(ipoint=0;ipoint<npoint;ipoint++) 181 Z+=(y[ipoint]-ycalc[ipoint])*(y[ipoint]-ycalc[ipoint]); 182 Res[nvert]=Z; //output 1st reflected point 185 for(iparm=0;iparm<nparm;iparm++) fprintf(logfile,"%8.6lf\t", beta[nvert][iparm]); 186 fprintf(logfile,"%8.6lf",res[nvert]); 187 fprintf(logfile,"\tfirst reflected point\n"); /*If response at 1st reflected point is less than response 191 at best point expand search*/ 192 if(res[nvert]<res[ibest]) //1st reflected point is best 193 { 194 //calculate 2nd reflected point beta[nvert+1][iparm] 195 for(iparm=0;iparm<nparm;iparm++) 196 beta[nvert+1][iparm]=3*centroid[iparm]-2*beta[iworst][iparm]; //calculate respond for 2nd reflected point 199 calc_function(ycalc,beta[nvert+1],x,npoint); 200 Z=0;

5 201 for(ipoint=0;ipoint<npoint;ipoint++) 202 Z+=(y[ipoint]-ycalc[ipoint])*(y[ipoint]-ycalc[ipoint]); 203 Res[nvert+1]=Z; //output 2nd reflected point 206 for(iparm=0;iparm<nparm;iparm++) fprintf(logfile,"%8.6lf\t", beta[nvert+1][iparm]); 207 fprintf(logfile,"%8.6lf",res[nvert+1]); 208 fprintf(logfile,"\tsecond reflected point\n"); /*if response at 2nd reflected point is less than 1st reflected point 211 replace worst point with 2nd reflected point otherwise 1st reflected 212 point replaces worst point */ nreplace=nvert; 215 if(res[nvert+1]<res[nvert])nreplace=nvert+1; 216 for(iparm=0;iparm<nparm;iparm++) 217 beta[iworst][iparm]=beta[nreplace][iparm]; 218 Res[iworst]=Res[nreplace]; 219 } 220 else if(res[nvert]<res[iworst]) //1st reflected not the worst 221 { 222 //replace worst point with 1st reflected point 223 nreplace=nvert; 224 for(iparm=0;iparm<nparm;iparm++) 225 beta[iworst][iparm]=beta[nreplace][iparm]; 226 Res[iworst]=Res[nreplace]; 227 } 228 else //1st reflected point is worst -- contract 229 { 230 //calculate contracted point beta[nvert+1][iparm] 231 for(iparm=0;iparm<nparm;iparm++) 232 beta[nvert+1][iparm]=0.5*(centroid[iparm]+beta[iworst][iparm]); //calculate respond for contracted point 235 calc_function(ycalc,beta[nvert+1],x,npoint); 236 Z=0; 237 for(ipoint=0;ipoint<npoint;ipoint++) 238 Z+=(y[ipoint]-ycalc[ipoint])*(y[ipoint]-ycalc[ipoint]); 239 //Res[nvert+1]=sqrt(Z/(npoint-1)); 240 Res[nvert+1]=Z; //output contracted point 243 for(iparm=0;iparm<nparm;iparm++) fprintf(logfile,"%8.6lf\t", beta[nvert+1][iparm]); 244 fprintf(logfile,"%8.6lf",res[nvert+1]); 245 fprintf(logfile,"\tcontracted point\n"); /*if response at contracted point is less than the worst 248 replace worst with contracted point */ 249 if(res[nvert+1]<res[iworst]) 250 {

6 251 nreplace=nvert+1; 252 //replace worst point 253 for(iparm=0;iparm<nparm;iparm++) 254 beta[iworst][iparm]=beta[nreplace][iparm]; 255 Res[iworst]=Res[nreplace]; 256 } 257 else //both 1st reflected point and contracted point are worse 258 { //than worst move all sets of parameters close to best 259 for (ivert=0;ivert<nvert;ivert++) 260 for (iparm=0;iparm<nparm;iparm++) 261 if(ivert!=ibest)beta[ivert][iparm]= *(beta[ivert][iparm]+beta[ibest][iparm]); 263 } 264 } if(fabs(resprev-res[ibest])<tol)convg++; 267 else convg=0; resprev=res[ibest]; 270 }while((res[ibest]>tol)&&(convg<10)); //calculate values of function with best parameters 273 calc_function(ycalc,beta[ibest],x,npoint); Z=0; 276 Rsquared=0; 277 for(ipoint=0;ipoint<npoint;ipoint++) 278 { 279 Z+=(y[ipoint]-ycalc[ipoint])*(y[ipoint]-ycalc[ipoint]); 280 Rsquared+=y[ipoint]; 281 } 282 Rsquared=-Rsquared*Rsquared/npoint; 283 for(ipoint=0;ipoint<npoint;ipoint++)rsquared+=y[ipoint]*y[ipoint]; 284 Rsquared=1-Z/Rsquared; //converged results 287 printf("\ninterations converged. R^2 %lg",rsquared); 288 fprintf(logfile,"\niterations converged. R^2 %lg",rsquared); //Print final Betas 291 fprintf(logfile, 292 "\n\nfinal Converged Parameters\nk\tbeta"); 293 for(iparm=0;iparm<nparm;iparm++) 294 fprintf(logfile,"\n%d\t%lg",iparm,beta[ibest][iparm]); //finish up 297 fclose(logfile); 298 printf("\npress any Key to Exit..."); 299 getch(); 300

7 301 return EXIT_SUCCESS; //error handling 304 exit_error: printf("\nerror during run, program aborted.\n"); 305 if(logfile!=null) 306 { 307 fprintf(logfile, "\nerror during run, program aborted.\n"); 308 fclose(logfile); 309 } 310 getch(); 311 return EXIT_FAILURE; 312 }

Program Organization and Comments

C / C++ PROGRAMMING Program Organization and Comments Copyright 2013 Dan McElroy Programming Organization The layout of a program should be fairly straight forward and simple. Although it may just look