Chief hat geschrieben:Die Berechnung mit Fortran kann Contravariant übernehmen.
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Chief hat geschrieben:Die Berechnung mit Fortran kann Contravariant übernehmen.
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# Looping mit Gravitationspotential:
restart; Digits:=15;
Looping:=proc()
global r,g,m,phi,dphi,t,v,x,y,U,v_o,E,v_u,dt,ml;
r:=10;g:=9.81;m:=1; ml:=6371000^2*9.81; # ml=m_Erde*Lambda
phi:=evalf(-1/2*Pi);
t:=0; x:=0; y:=-10;dt:=0.00001; U:=evalf(2*r*Pi);
v_o:=sqrt(r*ml/6371020^2); E:=-m*ml*(1/6371020-1/6371000)+m/2*v_o^2; v_u:=sqrt(2*E/m);
x:=r*cos(phi);
y:=r*sin(phi);
# print([t,phi,v_u,x,y]);
printf("%f\n%f\n",x,y);
while phi <= 4.712388981 do
v:=sqrt(2/m*(E+ml*(1/(6371000+r+y)-1/6371000)));
dphi:=evalf(v*dt*2*Pi/U);
phi:=phi+dphi;
x:=r*cos(phi);
y:=r*sin(phi);
t:=t+dt;
if round(t/0.02)-t/0.02=0 then # Ausgabe alle 0.02s
# print([t,phi,v,x,y]);
printf("%f\n%f\n",x,y);
fi;
od;
# print([t,phi,v,x,y]); # vollständige Umdrehung
printf("%f\n%f\n",x,y);
end;
Looping();
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solkar hat geschrieben:Ich möchte vorschlagen, dass wir die Diskussion über Programmierung und Programmiersprachen im "Looping"-Thread
weiterführen; dort sind wir näher an der konkreten Fallstudie.
Solkar hat geschrieben:Kann man da eigentlich Unicode-Bezeichner verwenden, also singemäss z.B.
- Code: Alles auswählen
φ = π
statt
- Code: Alles auswählen
phi = PI
schreiben?
Aber Deine letzte Bemerkung zum Tuning gibt mir zu denken - da würd ich dann doch lieber glattes C als eckiges Haskell schreiben wollen...
#include <cmath>
#include <iostream>
#include <cstdlib>
using namespace std;
#define DIM 2
#define g 9.81
#define r 10.0
typedef struct {
double vektor[DIM];
} Vektor;
/* Vektor + Vektor */
Vektor operator+(Vektor a, Vektor b);
/* Skalar * Vektor */
Vektor operator*(double ska, Vektor vek);
/* "Rechte Seite" der DGL
* d^2 phi/dt^2 = - (g/r) sin(phi)
* Zerlegung in zwei gekoppelte DGL erster Ordnung
* d phi/dt = omega
* d omega/dt = - (g/r) sin(phi)
*/
Vektor f(Vektor vek);
/* Ein Zeitschritt mit Runge-Kutta vierter Ordnung*/
Vektor rk4(double dt, Vektor phi);
int main(int argc, char **argv) {
double dt, t, tMax;
Vektor phi;
if (argc != 5) {
cerr << "looping dt tMax phi0 omega0" << endl;
exit(EXIT_FAILURE);
}
dt = atof(argv[1]);
tMax = atof(argv[2]);
phi.vektor[0] = atof(argv[3]);
phi.vektor[1] = atof(argv[4]);
t = 0.0;
while (t<tMax) {
cout << t << "\t" << phi.vektor[0] << "\t" << phi.vektor[1] << endl;
phi = rk4(dt, phi);
t += dt;
}
exit(EXIT_SUCCESS);
}
Vektor rk4(double dt, Vektor phi) {
Vektor k1, k2, k3, k4;
k1 = dt*f(phi);
k2 = dt*f(phi + 0.5*k1);
k3 = dt*f(phi + 0.5*k2);
k4 = dt*f(phi + k3);
return phi + 1.0/6.0*(k1 + 2.0*k2 + 2.0*k3 + k4);
}
Vektor operator+(Vektor a, Vektor b) {
Vektor erg;
erg.vektor[0] = a.vektor[0] + b.vektor[0];
erg.vektor[1] = a.vektor[1] + b.vektor[1];
return erg;
}
Vektor operator*(double ska, Vektor vek){
Vektor erg;
erg.vektor[0] = ska*vek.vektor[0];
erg.vektor[1] = ska*vek.vektor[1];
return erg;
}
Vektor f(Vektor vek) {
Vektor erg;
erg.vektor[0] = vek.vektor[1];
erg.vektor[1] = -(g/r)*sin(vek.vektor[0]);
return erg;
}
#!/usr/bin/python
import sys
from math import *
from numpy import *
g = 9.81
r = 10.0
def f(phi):
return array([phi[1], -g/r*sin(phi[0])])
def rk4(dt, phi):
k1 = dt*f(phi)
k2 = dt*f(phi + 0.5*k1)
k3 = dt*f(phi + 0.5*k2)
k4 = dt*f(phi + k3)
return phi + 1.0/6.0*(k1 + 2.0*k2 + 2.0*k3 + k4)
if (len(sys.argv) != 5):
sys.stderr.write("./looping.py dt tMax phi0 omega0\n")
sys.exit(2)
dt = float64(sys.argv[1])
tMax = float64(sys.argv[2])
phi0 = float64(sys.argv[3])
omega0 = float64(sys.argv[4])
t = 0.0
phi = array([phi0, omega0])
while t<tMax:
print t, phi[0], phi[1]
phi = rk4(dt, phi)
t += dt
Solkar hat geschrieben:contravariant hat geschrieben:Der Aufruf ist
./looping[.py] dt tMax phi0 omega
dt ist der Zeitschritt für die Integration, tMax die maximale Integrationzeit, phi0 Startwinkel und omega0 Startwinkelgeschwindigkeit. Beide schreiben den Output als "t phi omega" nach stdout.
Ich brauche die aktuellen Parameter, die Du beim Profiling auf der Kommandozeile übergeben hast; die formalen Parameter sieht man ja im Code.
Grüsse, Solkar
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