def __init__(self,N=100,L=10.0,d=1,q=1):
self.N = N
self.L = L
self.d = d
self.radial = True
x = np.linspace(L,0,N,endpoint=False)[::-1]
method = 'uniform'
method = 'geometric'
if method == 'uniform':
x = np.linspace(L,0,N,endpoint=False)[::-1]
elif method == 'geometric':
x = np.linspace(1,0,N,endpoint=False)[::-1]
x = x**q
x = x*L
else:
n = int(np.floor(np.log2(N)))
kappa = 1/4
x = np.array([kappa*L,L])
for i in range(n):
y = (x[1:-1] + x[2:])/2
x = np.hstack((x,y,kappa*x[0]))
x.sort()
self.N = len(x)
N = self.N
if d==1:
x = np.linspace(-L/2,L/2,N)
self.deltam = np.zeros_like(x)
self.deltam[1:] = x[1:] - x[:-1]
# cas particulier d = 1
if d == 1:
self.deltam[0] = self.deltam[1]
else:
self.deltam[0] = x[0]
self.deltap = np.zeros_like(self.deltam)
self.deltap[:-1]= self.deltam[1:]
self.deltap[-1] = self.deltam[-1]
self.delta = (self.deltap+self.deltam)/2
# fd ou fe. d=2, l=0 est hard-code
self.method = 'fe'
self.x = x
if d == 1:
self.ds = np.ones_like(x)
else:
self.ds = functions.surf_nsphere(d) * x**(d-1)
def integral(gam,d):
return surf_nsphere(d) / 2 * gamma(gam+d/2+1)*gamma(d/2)/gamma(gam+d+1)