int main(int argc, const char * argv[]) {
// the integral of 1/sqrt(1-x^2) is arcsin(x)
double exact = asin(0.99) - asin(0);
double a = 0.0;
double b = 0.99;
std::vector<double> nodes;
nodes.push_back(101);
nodes.push_back(201);
nodes.push_back(1001);
nodes.push_back(2001);
CompTrapRule ctp(&f, &fDoublePrime, a, b, nodes);
std::vector<double> results = ctp.getResult();
std::vector<double> hSteps = ctp.getHStep();
std::vector<double> errorBounds = ctp.getErrorBound();
std::cout << "Exact Value: " << exact << std::endl;
for(unsigned i = 0; i < results.size(); i++){
std::cout << "Composite Trapezoidal Rule approximation: " << std::setprecision(9)
<< results[i] << " with h step of " << hSteps[i] << ", an absolute erorr of "
<< absoluteError(exact, results[i]) << ", and error bound of "
<< errorBounds[i] << '.' << std::endl;
}
std::vector<double> extrp = extrapolation(results);
for(unsigned i = 0; i < extrp.size(); i++){
std::cout << "Richardson's Extrapolation approximation: " << std::setprecision(9)
<< extrp[i] << " with an absolute error of " << absoluteError(exact, extrp[i]) << std::endl;
}
return 0;
}
int main(){
int i, N;
char c, file[100];
// check that gnuplot is present on the system
int gnupl = control();
if(gnupl == 1){
printf("\nYou need gnuplot to graph the results.");
printf("\nInstall it with: sudo apt-get install gnuplot\n\n");
exit(2);
}
printf("Enter the name or path of file: ");
fgets(file,sizeof(file),stdin);
file[strlen(file)-1] = '\0';
// the file's lines number is the number of points to be saved
N = linesFile(file);
if(N <= 2){
printf("\nError: insufficient data number.\n");
exit(2);
}
// creating data's arrays
double *x = calloc(N,sizeof(double));
double *y = calloc(N,sizeof(double));
double *errors = calloc(N,sizeof(double));
if(x == NULL || y == NULL || errors == NULL){
perror("\nerror");
printf("\n");
exit(1);
}
// reading from file
FILE *inputFile = fopen(file,"r");
if(inputFile == NULL){
perror("\nError");
exit(1);
}
for(i=0; i<N; i++){
fscanf(inputFile,"%lf %lf %lf\n",&x[i],&y[i],&errors[i]);
}
fclose(inputFile);
// determine linear coefficients
double M = Mbest(N,x,y,errors);
double Q = Qbest(N,x,y,errors,M);
double sigmaM = fabs(uM(N,x,y,errors,M,Q));
double sigmaQ = fabs(uQ(N,x,errors,sigmaM));
// defining best sigma(Y) and correlation coefficient
double sigmaY = fabs(bestSigma(N,x,y,M,Q)); // <-- residuals analysis
double cov = covariance(N,x,y);
double cor = correlation(N,x,y);
double lCov = linearParamCovariance(N,mean(x,N),sigma(x,N,mean(x,N)),sigmaY,M,Q);
double lCor = linearParamCorrelation(N,x);
// Chi-square test
int freedomDegrees = N - 2; // infer 2 parameters (): M and Q
double chi2 = 0, rChi2;
for(i=0; i<N; i++){
chi2 += pow(y[i] - ((M * x[i]) + Q),2) / pow(errors[i],2);
}
rChi2 = chi2 / freedomDegrees;
printf("\nThe best linear fit Y = mX + q is:");
printf("\nm = %.3lf\tsigma(m) = %.3lf\nq = %.3lf\tsigma(q) = %.3lf",M,sigmaM,Q,sigmaQ);
printf("\n\nBest sigma(Y) = %.3lf",sigmaY);
printf("\nCov(X,Y) = %.3lf",cov);
printf("\nCor(X,Y) = %.3lf",cor);
printf("\nCov(m,c) = %.3lf",lCov);
printf("\nCor(m,c) = %.3lf",lCor);
//printf("\nChi square = %.3lf",chi2);
printf("\nReduced Chi square = %.3lf",rChi2);
// interpolation and extrapolation
int choice;
double pointX, pointY, sigmaPointY, alpha;
printf("\n\nDo you want to extrapolate a point with the calculated linear regression? (1 = YES | 0 = NO): ");
scanf("%d",&choice);
if(choice == 1){
extrapolation(N,x,errors,sigmaY,M,Q);
}
// creating fit
printf("\nPlotting fit...\n");
FILE *data = fopen("data.dat","w");
if(data == NULL){
perror("\nError");
exit(1);
}
// writing experimental datas
for(i=0; i<N; i++){
fprintf(data,"%lf %lf %lf\n",x[i],y[i],errors[i]);
}
fclose(data);
// creating fit points
//fit(M,Q,x,N); // gnuplot feature
free(x);
free(y);
return 0;
}
