def euler(t, g, y0, h):
f = tensor(g(t), "j", "d")
o = tensor(ones(N), "j", "u")
T = tensor(tri(N), "ij", "dd")
y = y0 + f * h * T * o
t = append(t, t[-1]+h)
y.arr = append(array([y0]),y.arr)
return handle_3d(t, y.arr)
def RK5(t, g, y0, h):
def k(x):
a = (23*g(x) +125*g(x+h/3.) - 81*g(x+2*h/3) + 125*g(x+4.*h/5.)) / 192.
return a
f = tensor(k(t), "j", "d")
o = tensor(ones(N), "j", "u")
T = tensor(tri(N), "ij", "dd")
y = y0 + f * h * T * o
t = append(t,t[-1]+h)
y.arr = append(array([y0]),y.arr)
return handle_3d(t, y.arr)
def RK2(t, g, y0, h):
def k(x):
a = (g(x) + g(x+h)) / 2.
return a
f = tensor(k(t), "j", "d")
o = tensor(ones(N), "j", "u")
T = tensor(tri(N), "ij", "dd")
y = y0 + f * h * T * o
t = append(t, t[-1]+h)
y.arr = append(array([y0]),y.arr)
return handle_3d(t, y.arr)
def RK4(t, g, y0, h):
def k(x, y):
k1 = g(x, y)
k2 = g(x+0.5*h, y+0.5*k1)
k3 = g(x+0.5*h, y+0.5*k2)
k4 = g(x+h, y+0.5*k3)
a = (k1 + 2*k2 + 2*k3 + k4)/6.
return a
f = tensor(k(t), "j", "d")
o = tensor(ones(N), "j", "u")
y = y0 + f.convolve(o, idx="j") * h
t = append(t, t[-1]+h)
y.arr = append(array([y0]),y.arr)
return handle_3d(t, y.arr)
def RK4_tensor_poor(x, g, y0, h, sidx="i", didx="z", **kwarg):
x.transpose([sidx, 0])
prey = y0
xlst = []
ylst = []
for i in xrange(x.len(sidx)):
tmpx = x[i]
tmpy = prey
k1 = g(tmpx, tmpy, **kwarg)
k2 = g(tmpx+0.5*h, tmpy+0.5*h*k1, **kwarg)
k3 = g(tmpx+0.5*h, tmpy+0.5*h*k2, **kwarg)
k4 = g(tmpx+h, tmpy+h*k3, **kwarg)
f = (k1 + 2*k2 + 2*k3 + k4)/6.
tmpy = prey + f * h
xlst += [tmpx]
ylst += [tmpy]
prey = tmpy
return tensor(xlst, sidx, x.ud[0]), tensor(ylst, sidx, x.ud[0])
def RK4_tensor(x, g, y0, h, sidx="i", didx="z", **kwarg):
def k(x, y0, **kwarg):
k1 = g(x, y0, **kwarg)
k2 = g(x+0.5*h, y0+0.5*k1, **kwarg)
k3 = g(x+0.5*h, y0+0.5*k2, **kwarg)
k4 = g(x+h, y0+0.5*k3, **kwarg)
a = (k1 + 2*k2 + 2*k3 + k4)/6.
return a
f = k(x, y0, **kwarg) * h
N = f.len(sidx)
o = tensor(ones(N), didx, "u")
y = f.convolve(o, idx=sidx)
#y = y0 + f.convolve(o, idx=sidx)
#x = x << x[-1] + h
#y = y0.append(y, sidx)
return x, y
