def calc_polytrope_butcher(n, method="rk4", zmin=0, zmax=10, imax=10, analytic=None):
f = lambda z, (w,v), dt, n : np.array([v, -2*v/z - np.power(w,n) if z>dt else -1./3.], dtype=cyb.DTYPE)
dz = (zmax - zmin)/(imax - 1)
data = np.zeros((imax, 3), dtype=cyb.DTYPE)
data[0,0:3] = [zmin, 1.0, 0.0]
l1error = 0.0
for i in range(1,imax):
z = zmin + (i-1)*dz
data[i,0] = zmin + i*dz
data[i,1:3],k = cyb.butcher(f, data[i-1,1:3], z, dz, tableau(method),fargs=(dz,n))
if analytic and z>0:
l1error += np.fabs(data[i,1]-analytic(data[i,0]))
return data, l1error*dz
from time import time
a= np.array([[ 0. , 0. , 0. ],
[ 0.5, 0.5, 0. ],
[ 0. , 0. , 1. ]], dtype=np.float64)
f = lambda z,(w,v),dt,n : np.array([ v, -1./3. if z<dt else -2*v/z-w**n], dtype=np.float64)
dt = 0.1
numsteps = 50
t = np.arange(0,numsteps + 1,dtype=np.float64)*dt
data = [[1,0],]
n=1
runtime = 0
l1err = 0
for curt in t[:-1]:
starttime = time()
data.append( butcher(f,np.array(data[-1],np.float64),curt,dt,a, fargs=(dt,n)) )
runtime += time() - starttime
if curt != 0:
l1err += np.abs(data[-1][0] - np.sin(curt)/curt)*dt
print "l1err = %f"%l1err
print "runtime = %f s"%(runtime / numsteps)
data = np.array(data)
#import pylab as py
#py.scatter(t, data[:,0])
#py.show()
