def div(X):
if X.shape==(1,):
shape=()
else:
shape=X.shape[:-1]
assert(X.shape[-1]==X.dim)
assert(X.order==1)
dX=Tensor(shape=shape, N=X.N, Fourier=True, fft_form=X.fft_form)
if X.Fourier:
FX=X
else:
F=DFT(N=X.N, fft_form=X.fft_form)
FX=F(X)
dim=len(X.N)
freq=Grid.get_freq(X.N, X.Y, fft_form=FX.fft_form)
strfreq='xyz'
coef=2*np.pi*1j
for ii in range(X.dim):
mul_str='{0},...{1}->...{1}'.format(strfreq[ii], strfreq[:dim])
dX.val+=np.einsum(mul_str, coef*freq[ii], FX.val[ii], dtype=np.complex)
if not X.Fourier:
iF=DFT(N=X.N, inverse=True, fft_form=dX.fft_form)
dX=iF(dX)
dX.name='div({0})'.format(X.name[:10])
return dX
def div(X):
if X.shape == (1, ):
shape = ()
else:
shape = X.shape[:-1]
assert (X.shape[-1] == X.dim)
assert (X.order == 1)
dX = Tensor(shape=shape, N=X.N, Fourier=True, fft_form=X.fft_form)
if X.Fourier:
FX = X
else:
F = DFT(N=X.N, fft_form=X.fft_form)
FX = F(X)
dim = len(X.N)
freq = Grid.get_freq(X.N, X.Y, fft_form=FX.fft_form)
strfreq = 'xyz'
coef = 2 * np.pi * 1j
for ii in range(X.dim):
mul_str = '{0},...{1}->...{1}'.format(strfreq[ii], strfreq[:dim])
dX.val += np.einsum(mul_str,
coef * freq[ii],
FX.val[ii],
dtype=np.complex)
if not X.Fourier:
iF = DFT(N=X.N, inverse=True, fft_form=dX.fft_form)
dX = iF(dX)
dX.name = 'div({0})'.format(X.name[:10])
return dX
def grad(X):
if X.shape==(1,):
shape=(X.dim,)
else:
shape=X.shape+(X.dim,)
name='grad({0})'.format(X.name[:10])
gX=Tensor(name=name, shape=shape, N=X.N,
Fourier=True, fft_form=X.fft_form)
if X.Fourier:
FX=X
else:
F=DFT(N=X.N, fft_form=X.fft_form) # TODO:change to X.fourier()
FX=F(X)
dim=len(X.N)
freq=Grid.get_freq(X.N, X.Y, fft_form=X.fft_form)
strfreq='xyz'
coef=2*np.pi*1j
val=np.empty((X.dim,)+X.shape+X.N_fft, dtype=np.complex)
for ii in range(X.dim):
mul_str='{0},...{1}->...{1}'.format(strfreq[ii], strfreq[:dim])
val[ii]=np.einsum(mul_str, coef*freq[ii], FX.val, dtype=np.complex)
if X.shape==(1,):
gX.val=np.squeeze(val)
else:
gX.val=np.moveaxis(val, 0, X.order)
if not X.Fourier:
iF=DFT(N=X.N, inverse=True, fft_form=gX.fft_form)
gX=iF(gX)
gX.name='grad({0})'.format(X.name[:10])
return gX
def grad(X):
if X.shape==(1,):
shape=(X.dim,)
else:
shape=X.shape+(X.dim,)
name='grad({0})'.format(X.name[:10])
gX=Tensor(name=name, shape=shape, N=X.N,
Fourier=True, fft_form=X.fft_form)
if X.Fourier:
FX=X
else:
F=DFT(N=X.N, fft_form=X.fft_form) # TODO:change to X.fourier()
FX=F(X)
dim=len(X.N)
freq=Grid.get_freq(X.N, X.Y, fft_form=X.fft_form)
strfreq='xyz'
coef=2*np.pi*1j
val=np.empty((X.dim,)+X.shape+X.N_fft, dtype=np.complex)
for ii in range(X.dim):
mul_str='{0},...{1}->...{1}'.format(strfreq[ii], strfreq[:dim])
val[ii]=np.einsum(mul_str, coef*freq[ii], FX.val, dtype=np.complex)
if X.shape==(1,):
gX.val=np.squeeze(val)
else:
gX.val=np.moveaxis(val, 0, X.order)
if not X.Fourier:
iF=DFT(N=X.N, inverse=True, fft_form=gX.fft_form)
gX=iF(gX)
gX.name='grad({0})'.format(X.name[:10])
return gX