?»??»?/*
	This function use non linear method calculate parameters
	for arrhenius equation
*/
//#include "stdafx.h"

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>

//#include "tools.h"


#define kOVERh 2.083674e+10
//#define kb=3.16683e-6

double matinv(double **a, int n);
void functn(int n, int m, double *a, double * x, double *f, double **g);
void  arrhenius(int n, int m, double *a, double *x, double *y);
double matinv(double **a, int n);

double *dvector(long num);
void free_dvector(double *vec);
double **dmatrix(long nrow, long ncol);
void free_dmatrix(double **matr);

int main (int argc, char * argv[]){

	double a[3];
	double x[]={300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200, 1300, 1400, 1500, 2000,  2500};
	double y[]={5.16E-04, 1.12E+01, 4.79E+03, 2.83E+05, 5.40E+06, 5.01E+07, 2.87E+08, 1.18E+09, 3.74E+09, 9.89E+09, 2.26E+10, 4.59E+10, 8.50E+10, 7.45E+11, 2.76E+12};
	double kb=3.16683e-6;
	int i;

	a[0] = log(kOVERh);
	a[1] = 0.0001;
	a[2] = 0.0462833/kb;
	int n=15;
	int m=3;
	
	for (i=0;i<n ; i++)
	{
		printf("Temp[%d]= %4.0lf , \t rate [ %d ] = %12.5lE \n", i+1, x[i], i+1, y[i]);
	}

	for (i=0;i<n ;i++ )
	{
		y[i]=log(y[i]);
	}

	arrhenius(n, m, a, x, y);
	printf("%4.1lf\n",x[0]);
	printf("%4.1lE\n",y[0]);

	

	printf("A = %12.5lE\n",exp(a[0]) );
	printf("n = %12.5lf \n", a[1]);
	printf("Ea/R= %12.5lE\n", a[2]);
	
	return (EXIT_SUCCESS);

}


void  arrhenius(int n, int m, double *a, double *x, double *y)
{
	int i,icount,j,l;
	int itmax=10000;
	


	double h;
	double *f, *w, **g, **p;
	double z[4],dif,d;
	double test,delta;
	
	f=dvector(n);
	w=dvector(n);
	g=dmatrix(4,n);
	p=dmatrix(4,4);
	
	h=1.0;

	
	for(icount=0;icount<itmax;icount++) {
		
		functn(n,m,a,x,f,g);
		
		for(i=0;i<m;i++) {
			
			z[i]=0.0;
			
			for(j=0;j<m;j++){
				p[i][j]=0.0;
			}
			
		}
		
		for(i=0;i<n;i++){
			w[i]=1.0;
			for(j=0;j<m;j++){
				for(l=0;l<=j;l++){
					p[j][l]=p[j][l]+w[i]*g[j][i]*g[l][i];
				}
			}
		}
		
		for(i=1;i<m;i++){
			l=i-1;
			for(j=0;j<l;j++){
				p[j][i]=p[i][j];
			}
		}
		
		for(i=0;i<n;i++){
			dif=y[i]-f[i];
			for(j=0;j<m;j++){
				z[j] = z[j]+w[i]*dif*g[j][i];
			}
		}
		
		d=matinv(p,m);
		
		
		if(d ==0.0) {
			printf("The coefficient matrix is singlar \n");
			printf("When calculating parameters for arrhenius equation\n");
			printf("To solve this problem, you may need input more \n");
			printf("temperatures\n");
			printf("The program stop\n");
			exit(1);
		}
		
		test=0.0;
		for(i=0;i<m;i++){
			delta=0.0;
			for(j=0;j<m;j++){
				delta =delta + p[i][j]*z[j];
			}
			test = test + fabs(delta/a[i]);
			a[i] = a[i] + h*delta;
		}
	}
	free_dvector(f);
	free_dvector(w);
	free_dmatrix(g);
	free_dmatrix(p);

}

void functn(int n, int m, double *a, double * x, double *f, double **g)
{
	int i;
	double par1, par2,par3,t;
	
	par1=a[0];
	par2=a[1];
	par3=a[2];
		
	for(i=0;i<n;i++){
		t=x[i];
		f[i]    = par1+par2*log(t)-par3/t;
		g[0][i] = 1.0;
		g[1][i] = log(t);
		g[2][i] = -(1.0/t);
	}
}


double *dvector(long num)
     /* Allocate n double vector with numer num */

{
	double *vec;
	
	vec = new double [num];
  
	//vec=(double *)malloc((size_t)(num*sizeof(double)));
	if(!vec){
		printf(" Double Allocation Error");
		exit(1);
	}
	
    
	return vec;
  
}

double **dmatrix(long nrow, long ncol)
     /* Allocate a Matrix with nrow rows and ncol colums */

{
	long i;
	double **matr;
	
	matr = new (double * [nrow]);
	matr[0] = new double [nrow*ncol];

	for(i=1;i<nrow;i++) matr[i]=matr[i-1]+ncol;
	if(!matr){
		printf(" Double Allocation Error");
		exit(1);
	}
	
  	return matr;
}

void free_dmatrix(double **matr)

{

	delete matr[0];
	delete matr;	
	//	free((char *) (matr[0]));
	//	free((char *) (matr));
}

void free_dvector(double *vec)
     /* Free an integer vector */

{
	delete vec;
	//	free((char *)(vec));
}

double matinv(double **a, int n)
{
	
	int i,j,k,irow=0,icolum=0,l,l1,nswap,jrow,jcolum;
	double tol,amax,swap,pivot,t,d;
	int ipv[10][3];
	
	d=1.0;
	tol=1.0e-35;
	
	for(j=0;j<n;j++){
		ipv[j][2]=0;
	}
	
	for(i=0;i<n;i++){
		amax=0.0;
		
		for(j=0;j<n;j++){
			if(ipv[j][2] == 1) continue;
			for(k=0;k<n;k++){
				if(ipv[k][2] == 1) continue;
				if(amax >= fabs(a[j][k])) continue;
				irow=j;
				icolum=k;
				amax = fabs(a[j][k]);
			}
		}
		
		if(amax <= tol){
			d = 0.0;
			return d;
		}
		
		ipv[icolum][2] = 1;
		ipv[i][0] = irow;
		ipv[i][1] = icolum;
		
		if(irow != icolum) {
			for(l=0;l<n;l++){
				swap = a[irow][l];
				a[irow][l]=a[icolum][l];
				a[icolum][l]=swap;
			}
		}
		
		pivot = a[icolum][icolum];
		d=d*pivot;
		a[icolum][icolum] = 1.0;
		
		for(l=0;l<n;l++){
			a[icolum][l] = a[icolum][l]/pivot;
		}
		
		for(l1=0;l1<n;l1++){
			if(l1 == icolum) continue;
			t = a[l1][icolum];
			a[l1][icolum] = 0.0;
			for(l=0;l<n;l++){
				a[l1][l] = a[l1][l] - a[icolum][l]*t;
			}
		}
	}  //i loop
	
	nswap = 0;
	
	for(i=0;i<n;i++){
		l=n-i-1;
		if(ipv[l][0] == ipv[l][1]) continue;
		jrow = ipv[l][0];
		jcolum = ipv[l][1];
		nswap += 1;
		
		for(k=0;k<n;k++){
			swap = a[k][jrow];
			a[k][jrow] = a[k][jcolum];
			a[k][jcolum]=swap;
		}
	}
	
	d = d*pow(-1.0,nswap);
	return d;
	
}