Nufft¶

ducc0.nufft¶

ducc0.nufft.bestEpsilon(*, ndim: int, singleprec: bool, sigma_min: float = 1.1, sigma_max: float = 2.6) → float¶

Computes the smallest possible error for the given NUFFT parameters.

Parameters:

ndim (int (1-3)) – the dimensionality of the transform
singleprec (bool) – True if np.float32/np.complex64 are used, otherwise False
sigma_min (float) – minimum and maximum allowed oversampling factors 1.2 <= sigma_min < sigma_max <= 2.5
sigma_max (float) – minimum and maximum allowed oversampling factors 1.2 <= sigma_min < sigma_max <= 2.5

Returns:

the smallest possible error that can be achieved for the given parameters.

Return type:

float

ducc0.nufft.nu2u(*, points: numpy.ndarray, coord: numpy.ndarray, forward: bool, epsilon: float, nthreads: int = 1, out: numpy.ndarray = None, verbosity: int = 0, sigma_min: float = 1.2, sigma_max: float = 2.51, periodicity: object = 6.283185307179586, fft_order: bool = False) → numpy.ndarray¶

Type 1 non-uniform FFT (non-uniform to uniform)

Parameters:

points (numpy.ndarray((npoints,), dtype=numpy.complex)) – The input values at the specified non-uniform grid points
coord (numpy.ndarray((npoints, ndim), dtype=numpy.float32 or numpy.float64)) – the coordinates of the npoints non-uniform points. ndim must be the same as out.ndim Periodicity is assumed; the coordinates don’t have to lie inside a particular interval, but smaller absolute coordinate values help accuracy
forward (bool) – if True, perform the FFT with exponent -1, else +1.
epsilon (float) – desired accuracy for single precision inputs, this must be >1e-6, for double precision it must be >2e-13
nthreads (int >= 0) – the number of threads to use for the computation if 0, use as many threads as there are hardware threads available on the system
out (numpy.ndarray(1D/2D/3D, same dtype as points)) – the grid of output data Note: this is a mandatory parameter, since its shape defines the grid dimensions!
verbosity (int) – 0: no console output 1: some diagnostic console output
sigma_min (float) – minimum and maximum allowed oversampling factors 1.2 <= sigma_min < sigma_max <= 2.5
sigma_max (float) – minimum and maximum allowed oversampling factors 1.2 <= sigma_min < sigma_max <= 2.5
periodicity (float or sequence of floats) – periodicity of the coordinates
fft_order (bool) – if False, grids start with the most negative Fourier node if True, grids start with the zero Fourier mode

Returns:

the computed grid values. Identical to out.

Return type:

numpy.ndarray(1D/2D/3D, same dtype as points)

ducc0.nufft.u2nu(*, grid: numpy.ndarray, coord: numpy.ndarray, forward: bool, epsilon: float, nthreads: int = 1, out: object = None, verbosity: int = 0, sigma_min: float = 1.2, sigma_max: float = 2.51, periodicity: object = 6.283185307179586, fft_order: bool = False) → numpy.ndarray¶

Type 2 non-uniform FFT (uniform to non-uniform)

Parameters:

grid (numpy.ndarray(1D/2D/3D, dtype=complex)) – the grid of input data
coord (numpy.ndarray((npoints, ndim), dtype=numpy.float32 or numpy.float64)) – the coordinates of the npoints non-uniform points. ndim must be the same as grid.ndim Periodicity is assumed; the coordinates don’t have to lie inside a particular interval, but smaller absolute coordinate values help accuracy
forward (bool) – if True, perform the FFT with exponent -1, else +1.
epsilon (float) – desired accuracy for single precision inputs, this must be >1e-6, for double precision it must be >2e-13
nthreads (int >= 0) – the number of threads to use for the computation if 0, use as many threads as there are hardware threads available on the system
out (numpy.ndarray((npoints,), same data type as grid), optional) – if provided, this will be used to store the result
verbosity (int) – 0: no console output 1: some diagnostic console output
sigma_min (float) – minimum and maximum allowed oversampling factors
sigma_max (float) – minimum and maximum allowed oversampling factors
periodicity (float or sequence of floats) – periodicity of the coordinates
fft_order (bool) – if False, grids start with the most negative Fourier node if True, grids start with the zero Fourier mode

Returns:

the computed values at the specified non-uniform grid points. Identical to out if it was provided

Return type:

numpy.ndarray((npoints,), same data type as grid)

Wgridder

Healpix