def convolve(self, u, v, uv=None, fast=True):
"""Convolution of u and v.
Parameters
----------
u : array
v : array
uv : array, optional
fast : bool, optional
Whether to use fast transforms in computing convolution
Note
----
Note that this method is only valid for 1D data, and that
for multidimensional arrays one should use corresponding method
in the TensorProductSpace class.
"""
assert len(u.shape) == 1
N = self.N
if fast:
if uv is None:
uv = self.forward.output_array.copy()
assert self.padding_factor > 1.0, "padding factor must be > 3/2+1/N to perform convolution without aliasing"
u2 = self.backward.output_array.copy()
u3 = self.backward.output_array.copy()
u2 = self.backward(u, u2)
u3 = self.backward(v, u3)
uv = self.forward(u2 * u3, uv)
else:
if uv is None:
uv = np.zeros(2 * N, dtype=u.dtype)
Np = N if not N % 2 == 0 else N + 1
k = np.fft.fftfreq(Np, 1. / Np).astype(int)
convolve.convolve_1D(u, v, uv, k)
return uv
def convolve(self, u, v, uv=None, fast=True):
"""Convolution of u and v.
Parameters
----------
u : array
v : array
uv : array, optional
fast : bool, optional
Whether to use fast transforms in computing convolution
Note
----
Note that this method is only valid for 1D data, and that
for multidimensional arrays one should use corresponding method
in the TensorProductSpace class.
"""
assert len(u.shape) == 1
N = self.N
if fast:
if uv is None:
uv = self.forward.output_array.copy()
assert self.padding_factor > 1.0, "padding factor must be > 3/2+1/N to perform convolution without aliasing"
u2 = self.backward.output_array.copy()
u3 = self.backward.output_array.copy()
u2 = self.backward(u, u2)
u3 = self.backward(v, u3)
uv = self.forward(u2*u3, uv)
else:
if uv is None:
uv = np.zeros(2*N, dtype=u.dtype)
Np = N if not N % 2 == 0 else N+1
k = np.fft.fftfreq(Np, 1./Np).astype(int)
convolve.convolve_1D(u, v, uv, k)
#if N % 2 == 0:
#u = np.hstack((u[:N//2], u[N//2], u[N//2:]))
#u[N//2:N//2+2] *= 0.5
#v = np.hstack((v[:N//2], v[N//2], v[N//2:]))
#v[N//2:N//2+2] *= 0.5
#for m in range(Np):
#vc = np.roll(v, -(m+1))
#s = u*vc[::-1]
#ki = k + np.roll(k, -(m+1))[::-1]
#z0 = np.argwhere(ki == m)
#z1 = np.argwhere(ki == m-Np)
#uv[m] = np.sum(s[z0])
#uv[m-Np] = np.sum(s[z1])
#for m in k:
#for n in k:
#p = m + n
#if N % 2 == 0:
#if abs(m) == N//2:
#um = u[m]*0.5
#else:
#um = u[m]
#if abs(n) == N//2:
#vn = v[n]*0.5
#else:
#vn = v[n]
#else:
#um = u[m]
#vn = v[n]
#uv[p] += um*vn
return uv