double Dspline_pos4(double t, double t1, double p1, double t2, double p2, double t3, double p3, double t4, double p4, int ss, double dudt, int id) {
double uout;
double uspline_pos4;
double suspline4;
double ps[4];
ps[0] = p1;
ps[1] = p2;
ps[2] = p3;
ps[3] = p4;
uspline_pos4 = spline_pos4(t, t1, p1, t2, p2, t3, p3, t4, p4, ss, dudt);
suspline4 = Dspline4(t, t1, p1, t2, p2, t3, p3, t4, p4, ss, dudt, id);
uout = suspline4 * uspline_pos4 * log(10.0);
uout = uout / ps[id-1] / log(10.0);
return(uout);
}
/**
* parameter derivative of positive spline function with 4 nodes
*
* @param id argument index for differentiation
* @param t point at which the spline should be evaluated
* @param t1 location of node 1
* @param p1 spline value at node 1
* @param t2 location of node 2
* @param p2 spline value at node 2
* @param t3 location of node 3
* @param p3 spline value at node 3
* @param t4 location of node 4
* @param p4 spline value at node 4
* @param ss flag indicating whether slope at first node should be user defined
* @param dudt user defined slope at first node
*
* @return dspline(t)dp(id)
*
*/
double Dspline_pos4(int id, double t, double t1, double p1, double t2, double p2, double t3, double p3, double t4, double p4, int ss, double dudt) {
double uout;
double uspline_pos4;
double suspline4;
double ps[4];
int did;
ps[0] = p1;
ps[1] = p2;
ps[2] = p3;
ps[3] = p4;
did = floor(id/2-1);
uspline_pos4 = spline_pos4(t, t1, p1, t2, p2, t3, p3, t4, p4, ss, dudt);
suspline4 = Dspline4(id, t, t1, p1, t2, p2, t3, p3, t4, p4, ss, dudt);
uout = suspline4 * uspline_pos4 * log(10.0);
uout = uout / ps[did] / log(10.0);
return(uout);
}