int broyden(void (*f)(double *x, double *fv, int n),
double *x0, double *f0, int n, double *eps, int *iter)
{
double **A,*x1,*f1,*s,d,tmp;
int i,j,k;
// Allocate temporary memory
x1 = new double [n];
f1 = new double [n];
s = new double [n];
A = new double *[n];
for (i=0;i<n;i++) {
A[i] = new double [n];
}
// Create identity matrix for startup (consider Jacobian alternative)
for (i=0;i<n;i++) {
for (j=0;j<n;j++) {
A[i][j] = 0.0;
}
A[i][i] = 1.0;
}
// Main loop
for (k=0;k< *iter;k++){
f(x0,f0,n);
gelimd2(A,f0,s,n); // Signs of 'f0', 's' are reversed
d = 0.0;
for (i=0;i<n;i++) {
x1[i] = x0[i] - s[i];
d += s[i]*s[i];
}
if (d <= fabs(*eps)) break;
f(x1,f1,n);
// Update A
for (i=0;i<n;i++) {
tmp = f1[i]+f0[i];
for (j=0;j<n;j++) {
tmp -= A[i][j]*s[j];
}
for (j=0;j<n;j++) {
A[i][j] -= tmp*s[j]/d;
}
}
for (i=0;i<n;i++) {
f0[i] = f1[i];
x0[i] = x1[i];
}
}
*iter = k;
// Deallocate memory
for (i=0;i<n;i++) {
delete [] A[i];
}
delete [] A;
delete [] x1;
delete [] f1;
delete [] s;
return 0;
}
int fsolve::broyden(void (*f)(double *x,double *fv,int n),
double *x0,double *f0,int n,double *eps,int *iter)
{
double **A,*x1,*f1,*s,d,tmp;
int i,j,k;
int error_code = 1;
// Allocate temporary memory
x1 = new double [n];
f1 = new double [n];
s = new double [n];
A = new double *[n];
for (i=0;i<n;i++) {
A[i] = new double [n];
}
// Create identity matrix for startup (consider Jacobian alternative)
for (i=0;i<n;i++) {
for (j=0;j<n;j++) {
A[i][j] = 0.0;
}
A[i][i] = 1.0;
}
// Main loop
double n_sqr_eps = float(n) * *eps * *eps;
for (k=0;k< *iter;k++){
f(x0,f0,n);
gelimd2(A,f0,s,n); // Signs of 'f0', 's' are reversed
d = 0.0;
for (i=0;i<n;i++) {
x1[i] = x0[i] - s[i];
d += s[i]*s[i];
}
// If the RMS of the residuals is less than the solution tolerance, we're done
if (d <= n_sqr_eps)
{
error_code = 0;
break;
}
f(x1,f1,n);
// Update A
for (i=0;i<n;i++) {
tmp = f1[i]+f0[i];
for (j=0;j<n;j++) {
tmp -= A[i][j]*s[j];
}
for (j=0;j<n;j++) {
A[i][j] -= tmp*s[j]/d;
}
}
for (i=0;i<n;i++) {
f0[i] = f1[i];
x0[i] = x1[i];
}
}
// Replace maximum iterations with the number of iterations
// required to find the solution
*iter = k;
// Deallocate memory
for (i=0;i<n;i++) {
delete [] A[i];
}
delete [] A;
delete [] x1;
delete [] f1;
delete [] s;
// Error codes are:
// 0: successfully converged
// 1: didn't converge within tolerance
return error_code;
}
