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/****************************************************** *************Chi-square fitting************** Polynomial Fitting ******************************************************/ #include<stdio.h> #include<math.h> /******* Function that performs Gauss-Elimination and returns the Upper triangular matrix and solution of equations: There are two options to do this in C. 1. Pass the augmented matrix (a) as the parameter, and calculate and store the upperTriangular(Gauss-Eliminated Matrix) in it. 2. Use malloc and make the function of pointer type and return the pointer. This program uses the first option. ********/ void gaussEliminationLS(int m, int n, double a[m][n], double x[n-1]){ int i,j,k; for(i=0;i<m-1;i++){ //Partial Pivoting for(k=i+1;k<m;k++){ //If diagonal element(absolute vallue) is smaller than any of the terms below it if(fabs(a[i][i])<fabs(a[k][i])){ //Swap the rows for(j=0;j<n;j++){ double temp; temp=a[i][j]; a[i][j]=a[k][j]; a[k][j]=temp; } } } //Begin Gauss Elimination for(k=i+1;k<m;k++){ double term=a[k][i]/ a[i][i]; for(j=0;j<n;j++){ a[k][j]=a[k][j]-term*a[i][j]; } } } //Begin Back-substitution for(i=m-1;i>=0;i--){ x[i]=a[i][n-1]; for(j=i+1;j<n-1;j++){ x[i]=x[i]-a[i][j]*x[j]; } x[i]=x[i]/a[i][i]; } } /******* Function that prints the elements of a matrix row-wise Parameters: rows(m),columns(n),matrix[m][n] *******/ void printMatrix(int m, int n, double matrix[m][n]){ int i,j; for(i=0;i<m;i++){ for(j=0;j<n;j++){ printf("%lf\t",matrix[i][j]); } printf("\n"); } } main(){ //no. of data-points int N; //degree of polynomial int n; printf("Enter the no. of data-points:\n"); scanf("%d",&N); //arrays to store the c and y-axis data-points double x[N], y[N]; printf("Enter the x-axis values:\n"); int i,j; for(i=0;i<N;i++){ scanf("%lf",&x[i]); } printf("Enter the y-axis values:\n"); for(i=0;i<N;i++){ scanf("%lf",&y[i]); } printf("Enter the degree of polynomial to be used:\n"); scanf("%d",&n); // an array of size 2*n+1 for storing N, Sig xi, Sig xi^2, ...., etc. which are the independent components of the normal matrix double X[2*n+1]; for(i=0;i<=2*n;i++){ X[i]=0; for(j=0;j<N;j++){ X[i]=X[i]+pow(x[j],i); } } //the normal augmented matrix double B[n+1][n+2]; // rhs double Y[n+1]; for(i=0;i<=n;i++){ Y[i]=0; for(j=0;j<N;j++){ Y[i]=Y[i]+pow(x[j],i)*y[j]; } } for(i=0;i<=n;i++){ for(j=0;j<=n;j++){ B[i][j]=X[i+j]; } } for(i=0;i<=n;i++){ B[i][n+1]=Y[i]; } double A[n+1]; printf("The polynomial fit is given by the equation:\n"); printMatrix(n+1,n+2,B); gaussEliminationLS(n+1,n+2,B,A); for(i=0;i<=n;i++){ printf("%lfx^%d+",A[i],i); } }

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