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 :class:`.TensorProductSpace` class.
"""
N = self.N
if fast is True:
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(N + 1, dtype=u.dtype)
Np = N if not N % 2 == 0 else N + 1
k1 = np.fft.fftfreq(Np, 1. / Np).astype(int)
convolve.convolve_real_1D(u, v, uv, k1)
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 :class:`.TensorProductSpace` class.
"""
N = self.N
if fast is True:
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(N+1, dtype=u.dtype)
Np = N if not N % 2 == 0 else N+1
k1 = np.fft.fftfreq(Np, 1./Np).astype(int)
convolve.convolve_real_1D(u, v, uv, k1)
#u1 = np.hstack((u, np.conj(u[1:][::-1])))
#if N % 2 == 0:
#u1[N//2:N//2+2] *= 0.5
#v1 = np.hstack((v, np.conj(v[1:][::-1])))
#if N % 2 == 0:
#v1[N//2:N//2+2] *= 0.5
#for m in range(N):
#vc = np.roll(v1, -(m+1))
#s = u1*vc[::-1]
#ki = k1 + np.roll(k1, -(m+1))[::-1]
#z0 = np.argwhere(ki == m)
#z1 = np.argwhere(ki == m-N)
#uv[m] = np.sum(s[z0])
#uv[m-N] = np.sum(s[z1])
#for m in k1:
#for n in k1:
#p = m + n
#if p >= 0:
#if N % 2 == 0:
#if abs(m) == N//2:
#um = u[abs(m)]*0.5
#elif m >= 0:
#um = u[m]
#else:
#um = np.conj(u[abs(m)])
#if abs(n) == N//2:
#vn = v[abs(n)]*0.5
#elif n >= 0:
#vn = v[n]
#else:
#vn = np.conj(v[abs(n)])
#else:
#if m >= 0:
#um = u[m]
#elif m < 0:
#um = np.conj(u[abs(m)])
#if n >= 0:
#vn = v[n]
#elif n < 0:
#vn = np.conj(v[abs(n)])
#uv[p] += um*vn
return uv