Thereby, the common structure is given in terms of three self-contained algorithmic frameworks that are built on top of each other, namely fast Fourier transform (FFT), nonequispaced fast Fourier transform (NFFT) and NFFT based particle-mesh methods (P²NFFT). For each of these frameworks ...
Notes --- The fourier transform approach utilizes the fact that the autocorrelation function is the inverse FT of the power spectrum density. For background read the Scipy fftpack docs and for a good explanation see: http://www.ucl.ac.uk/~ucapikr/projects/KamilaSuankulova_BSc_Project.pdf...
N = self._grid.get_number_nodes() prefactor = product(array(T) / (1.0* array(N) **2))# Reshape from (1, prod_d^D N_d) to (N_1, ..., N_D) shapepotential = [pot.reshape(N)forpotinpotential]# Apply the matrix potential to the kettmp = [zeros(component.shape, dtype=compl...
equal to the length of `x` Returns --- x : `list` [`numpy.ndarray` [`float`]], of shape [(nx,), (ny,), ...] List of vectors defining a mesh such that for a function, `f`, defined on the mesh given by `y`, ifft(f) is defined on the mesh given by `x`. 0 will ...
N = self._grid.get_number_nodes() prefactor = product(array(T) / (1.0* array(N) **2))# Reshape from (1, prod_d^D N_d) to (N_1, ..., N_D) shapepotential = [pot.reshape(N)forpotinpotential]# Apply the matrix potential to the kettmp = [zeros(component.shape, dtype=compl...
the mesh given by `x`, `fft(f)` is defined on the mesh given by `y` """y = []forXinx:ifX.size >1: y.append(fftfreq(X.size, X.item(1) - X.item(0)) * (2* pi))else: y.append(array([0])) y[-1] = y[-1].astype(X.dtype, copy=False)return[fftshift(Y)forYiny...
The basic method is to compute, on the same grid, the difference vector: Δ𝑖(𝒙)=𝑢𝑠𝑢𝑏𝑖(𝒙)−𝑢ℎ𝑜𝑚𝑖(𝒙) Δi(x)=uisub(x)−uihom(x) (7) where 𝑢𝑠𝑢𝑏𝑖(𝒙)uisub(x) is the displacement vector calculated for voxels where this eigen...
where the function h ( x ) is the density function of W t i + 1 conditional on the value of W t i h ( x ) = 1 2 π Δ t m e − x 2 2 Δ t m . Lord et al. [15] explained that the method relies heavily on the Fourier transformation. We know that the method to...