double * rk4sd(derivative f, double y0, double end, int n,
double abs_tol, double rel_tol){
double h = end / n;
double y, x, d0, d;
double step1, step2;
double xvalues[n], yvalues[n];
double * answers = (double*)malloc(2 * n * sizeof(double*));
int i;
yvalues[0] = y0;
xvalues[0] = 0;
for(i=1; i < n; i++){
x = xvalues[i - 1];
y = yvalues[i - 1];
step1 = rk4step(f, x, y, h);
step2 = rk4step(f, x, y, h/2);
step2 = rk4step(f, x + h/2, step2, h/2);
d0 = abs(step2 - step2);
d = rel_tol * step1 + abs_tol;
if(d0 < d){
xvalues[i] = x + h;
yvalues[i] = step1;
continue;
}
h = h * pow(d / d0, 0.2);
xvalues[i] = x + h;
yvalues[i] = rk4step(f, x, y, h);
}
for(i=0; i<n; i++){
answers[2*i] = xvalues[i];
answers[2*i + 1] = yvalues[i];
}
return answers;
}
double * rk4(derivative f, double y0, double end, int n){
double h = end / n;
double * yvalues = (double *)malloc(n * sizeof(double));
int i;
yvalues[0] = y0;
for(i=1; i < n; i++){
yvalues[i] = rk4step(f, (i - 1) * h, yvalues[i-1], h);
}
return yvalues;
}
void mexFunction(int nlhs, mxArray* plhs[], int nrhs, const mxArray* prhs[])
{
double* dt;
double* x;
double* xout;
int N, M, n;
int i;
if (nlhs != 1 || nrhs != 2)
mexErrMsgTxt("L3_step_c: wrong number of input or output arguments");
dt = mxGetPr(prhs[0]);
x = mxGetPr(prhs[1]);
N = mxGetN(prhs[1]);
M = mxGetM(prhs[1]);
n = N * M;
plhs[0] = mxCreateDoubleMatrix(M, N, mxREAL);
xout = mxGetPr(plhs[0]);
for (i = 0; i < n; ++i)
xout[i] = x[i];
rk4step(0.0, dt[0], n, xout, xout);
}
