double tangent_h(double x, double h, double& y, double yguess)
{
y = find_y_at_h(x, h,yguess);
double dx = dfx(x,y);
double dy = dfx(y,x);
assert(dy != 0);
return -dx/dy;
}
double find_y_at_h(double x, double h, double yguess)
{
double y = yguess;
assert(0.000001*(x*x+y*y)-0.0015*(x+y)+0.7 > 0);
double fy = f(x, yguess);
while(fabs(fy-h)>tol){
double slope = dfx(yguess, x);
double deltay = (fy-h) /slope;
if(fabs(deltay) > 50)
deltay= deltay >0?50:-50;
yguess -= deltay;
fy = f(x, yguess);
}
return yguess;
}
static VALUE method_newton(VALUE self, VALUE pmts, VALUE exps,
VALUE guess, VALUE tolerance, VALUE max_iter) {
long len = RARRAY_LEN(pmts);
long max_i = NUM2INT(max_iter);
long double x0 = NUM2DBL(guess);
long double x1 = 0.0;
long double tol = NUM2DBL(tolerance);
long double err = 1e100;
VALUE *pmt_p = RARRAY_PTR(pmts);
VALUE *exp_p = RARRAY_PTR(exps);
long iter = 0;
while (err > tol && iter++ < max_i) {
x1 = x0 - (fx(x0, pmt_p, exp_p, len) / dfx(x0, pmt_p, exp_p, len));
err = fabs(x1 - x0);
x0 = MAX(x1, lower_bound);
}
return (err > tol) ? Qnil : rb_float_new(x0);
}
//assumption only one maximum, giving two ends, find max
void binary_search(double x1, double y1, double x2, double y2, double& retx, double& rety)
{
double dydx=(y2-y1)/(x2-x1);
double df1 = dfx(x1,y1) + dydx * dfx(y1,x1);
double df2 = dfx(x2, y2)+ dydx * dfx(y2, x2);
assert(df1 * df2 < 0);
double xmid = 0, ymid=0;
while(fabs(x2-x1)> 1e-12){
xmid = (x1+x2)/2.0;
ymid = (y1+y2)/2.0;
double df3 = dfx(xmid, ymid)+dydx*dfx(ymid,xmid);
if(df3 * df1 > 0){
x1 = xmid;
y1 = ymid;
}else{
x2 = xmid;
y2 = ymid;
}
}
retx = (x1+x2)/2;
rety = (y1+y2)/2;
}
int main()
{
/*
{
double xstart = 1400, ystart = 1400;
double xfinal = 1561.907083805850789, yfinal = 672.892772938465328;
int nseg = 1000;
double retx, rety;
double dx = (xfinal- xstart)/nseg;
double dy = (yfinal- ystart)/nseg;
for(int i = 0; i <= nseg; ++i){
//binary_search(1400, 1400, 1600, ystart+i*dy, retx, rety);
printf("%d %30.15f\n", i, f(xstart+dx*i, ystart+i*dy));
}
binary_search(xstart, ystart, xfinal, yfinal, retx, rety);
printf("%30.15f\n", f(retx, rety));
exit(1);
}
*/
double PI = 4.0*atan(1.0);
double ret1, ret2;
double radius = sqrt(17.0/40)*1000;
//first find the fmin, minimum height
binary_search(0,0, 1600, 0, ret1, ret2 );
double barrierx = ret1;
double maxh = f(ret1, 0);
printf("%30.15f, %30.15f %30.15f\n", ret1, f(ret1, 0), dfx(ret1, 0));
//second, find the path to the barrier
//double y200 = 0;
//double x200 = find_tangent(maxh, 300, barrierx, -100,y200 );
double x200, y200, x1400, y1400, tp;
find_barrier_200(barrierx, maxh, x200, y200);
printf("data 200| %30.15f %30.15f %30.15f\n", x200, y200, f(x200, y200)-maxh);
printf("part2 %30.15f %30.15f %30.15f\n", f(x200, y200)-maxh, tangent_h(x200, maxh, tp, y200), (y200-200)/(x200-200) );
find_barrier_1400(700, maxh, x1400,y1400);
// x1400 = find_barrier_eq_h(1410, 1600, maxh, ret1);
// y1400 = find_y_at_h(x1400, maxh, 1600);
printf("data 1400 %30.15f %30.15f %30.15f\n", x1400, y1400, f(x1400, y1400)-maxh);
printf("part 2 %30.15f %30.15f %30.15f\n", f(x1400, y1400)-maxh, tangent_h(x1400, maxh,tp, y1400), (y1400-1400)/(x1400-1400) );
int nseg = 1000000;
double y0 = y200;
double total = sqrt((x200-200)*(x200-200)+(y200-200)*(y200-200));
total += sqrt((x1400-1400)*(x1400-1400)+(y1400-1400)*(y1400-1400));
//{
// double xstart = 1600, ystart = 900;
// double xfinal = 1400, yfinal = 1400;
// int nseg = 1000;
// double dx = (xfinal- xstart)/nseg;
// double dy = (yfinal- ystart)/nseg;
// for(int i = 0; i <= nseg; ++i){
// printf("%d %30.15f\n", i, f(xstart+i*dx, ystart+i*dy));
// }
// exit(1);
//}
//total += sqrt((x200-barrierx)*(x200-barrierx)+y200*y200);
double dx = (1561.907083805850789 -x200)/nseg;
for(unsigned int i=1; i<=nseg;++i){
double y1 = find_y_at_h(x200+i*dx, maxh, y0);
//printf("%30.15f %30.15f %30.15f\n", x200+i*dx, y1, f(x200+i*dx, y1));
double ds = dx*dx+ (y1-y0)*(y1-y0);
ds= sqrt(ds);
total += ds;
y0= y1;
}
//printf("------------------");
nseg = 1000000;
double x4 = 1561.907083805850789;
dx = (x4 - x1400)/nseg;
y0 = find_y_at_h(x1400, maxh, y1400);
for(unsigned int i=1; i<= nseg;++i){
double y1 = find_y_at_h(x1400+i*dx, maxh, y0);
//printf("%30.15f %30.15f %30.15f\n", x4+i*dx, y1, f(x4+i*dx, y1));
double ds = dx*dx+ (y1-y0)*(y1-y0);
ds= sqrt(ds);
total += ds;
y0= y1;
}
printf("%30.15f\n", total);
}
