Code:

#include <stdio.h>
#include <stdlib.h>
#include <malloc.h>
#include <math.h>
#define MAX_IT 1000 /* maximum number of iterations */
#define ALPHA 1.0 /* reflection coefficient */
#define BETA 0.5 /* contraction coefficient */
#define GAMMA 2.0 /* expansion coefficient */
#define pi 3.14
double rosen(double x[], double Actual_Output[], double Input[])
{
double c[5];
double Fitted_Curve[5];
int i;
for (i = 1; i < 5; i++)
{
c[i] = -1/atanh((exp(x[0]*2*pi)-cosh(x[0]*x[1]*Actual_Output[i]))/sinh(x[0]*x[1]*Actual_Output[i]));
Fitted_Curve[i] = (1/(x[0]*x[1]))*(c[i]-asinh(sinh(c[i])*exp(x[0]*Input[i]*2*pi)));
}
}
int main()
{
double start[] = {-1.0,1.0};
double min;
double actual[5]={1.2, 2.693, 4.325, 6.131, 8.125};
double t[5]={1, 2, 3, 4, 5};
int i;
min=simplex(rosen,start,2,1.0e-4,1, actual, t);
for (i=0;i<2;i++) {
printf("%f\n",start[i]);
}
return 0;
}
double simplex(double (*func)(double[]), double start[],int n, double EPSILON, double scale, double Output, double Input)
{
int vs; /* vertex with smallest value */
int vh; /* vertex with next smallest value */
int vg; /* vertex with largest value */
int i,j,m,row;
int k; /* track the number of function evaluations */
int itr; /* track the number of iterations */
double **v; /* holds vertices of simplex */
double pn,qn; /* values used to create initial simplex */
double *f; /* value of function at each vertex */
double fr; /* value of function at reflection point */
double fe; /* value of tion at expansion point */
double fc; /* value of function at contraction point */
double *vr; /* reflection - coordinates */
double *ve; /* expansion - coordinates */
double *vc; /* contraction - coordinates */
double *vm; /* centroid - coordinates */
double min;
double fsum,favg,s,cent;
/* dynamically allocate arrays */
/* allocate the rows of the arrays */
v = (double **) malloc ((n+1) * sizeof(double *));
f = (double *) malloc ((n+1) * sizeof(double));
vr = (double *) malloc (n * sizeof(double));
ve = (double *) malloc (n * sizeof(double));
vc = (double *) malloc (n * sizeof(double));
vm = (double *) malloc (n * sizeof(double));
/* allocate the columns of the arrays */
for (i=0;i<=n;i++) {
v[i] = (double *) malloc (n * sizeof(double));
}
/* create the initial simplex */
/* assume one of the vertices is 0,0 */
pn = scale*(sqrt(n+1)-1+n)/(n*sqrt(2));
qn = scale*(sqrt(n+1)-1)/(n*sqrt(2));
for (i=0;i<n;i++) {
v[0][i] = start[i];
}
for (i=1;i<=n;i++) {
for (j=0;j<n;j++) {
if (i-1 == j) {
v[i][j] = pn + start[j];
}
else {
v[i][j] = qn + start[j];
}
}
}
/* find the initial function values */
for (j=0;j<=n;j++) {
f[j] = func(v[j],Output,Input);
}
k = n+1;
/* print out the initial values */
printf("Initial Values\n");
for (j=0;j<=n;j++) {
printf("%f %f %f\n",v[j][0],v[j][1],f[j]);
}
/* begin the main loop of the minimization */
for (itr=1;itr<=MAX_IT;itr++) {
/* find the index of the largest value */
vg=0;
for (j=0;j<=n;j++) {
if (f[j] > f[vg]) {
vg = j;
}
}
/* find the index of the smallest value */
vs=0;
for (j=0;j<=n;j++) {
if (f[j] < f[vs]) {
vs = j;
}
}
/* find the index of the second largest value */
vh=vs;
for (j=0;j<=n;j++) {
if (f[j] > f[vh] && f[j] < f[vg]) {
vh = j;
}
}
/* calculate the centroid */
for (j=0;j<=n-1;j++) {
cent=0.0;
for (m=0;m<=n;m++) {
if (m!=vg) {
cent += v[m][j];
}
}
vm[j] = cent/n;
}
/* reflect vg to new vertex vr */
for (j=0;j<=n-1;j++) {
vr[j] = (1+ALPHA)*vm[j] - ALPHA*v[vg][j];
}
fr = func(vr,Output,Input);
k++;
/* added <= */
if (fr <= f[vh] && fr > f[vs]) {
for (j=0;j<=n-1;j++) {
v[vg][j] = vr[j];
}
f[vg] = fr;
}
/* investigate a step further in this direction */
/* added <= */
if ( fr <= f[vs]) {
for (j=0;j<=n-1;j++) {
ve[j] = GAMMA*vr[j] + (1-GAMMA)*vm[j];
}
fe = func(ve,Output,Input);
k++;
/* by making fe < fr as opposed to fe < f[vs],
Rosenbrocks function takes 63 iterations as opposed
to 64 when using doubles and e = 1.0e-6. */
if (fe < fr) {
for (j=0;j<=n-1;j++) {
v[vg][j] = ve[j];
}
f[vg] = fe;
}
else {
for (j=0;j<=n-1;j++) {
v[vg][j] = vr[j];
}
f[vg] = fr;
}
}
/* check to see if a contraction is necessary */
if (fr > f[vh]) {
for (j=0;j<=n-1;j++) {
vc[j] = BETA*v[vg][j] + (1-BETA)*vm[j];
}
fc = func(vc,Output,Input);
k++;
if (fc < f[vg]) {
for (j=0;j<=n-1;j++) {
v[vg][j] = vc[j];
}
f[vg] = fc;
}
/* at this point the contraction is not successful,
we must halve the distance from vs to all the
vertices of the simplex and then continue.
10/31/97 - modified to account for ALL vertices.
*/
else {
for (row=0;row<=n;row++) {
if (row != vs) {
for (j=0;j<=n-1;j++) {
v[row][j] = v[vs][j]+(v[row][j]-v[vs][j])/2.0;
}
}
}
f[vg] = func(v[vg],Output,Input);
k++;
f[vh] = func(v[vh],Output,Input);
k++;
}
}
/* print out the value at each iteration */
printf("Iteration %d\n",itr);
for (j=0;j<=n;j++) {
printf("%f %f %f\n",v[j][0],v[j][1],f[j]);
}
/* test for convergence */
fsum = 0.0;
for (j=0;j<=n;j++) {
fsum += f[j];
}
favg = fsum/(n+1);
s = 0.0;
for (j=0;j<=n;j++) {
s += pow((f[j]-favg),2.0)/(n);
}
s = sqrt(s);
if (s < EPSILON) break;
}
/* end main loop of the minimization */
/* find the index of the smallest value */
vs=0;
for (j=0;j<=n;j++) {
if (f[j] < f[vs]) {
vs = j;
}
}
printf("The minimum was found at\n");
for (j=0;j<n;j++) {
printf("%e\n",v[vs][j]);
start[j] = v[vs][j];
}
min=func(v[vs],Output,Input);
k++;
printf("%d Function Evaluations\n",k);
printf("%d Iterations through program\n",itr);
free(f);
free(vr);
free(ve);
free(vc);
free(vm);
free(*v);
return min;
}

There are two errors (although the second occurs more than once) the first response is Code:

double simplex(double (*func)(double[]), double start[],int n, double EPSILON, double scale, double Output, double Input)

second error is