CXS Class

class CXS(n, L=1.0, dq=1.0, f_probe=None, f_mask=None)

Bases: Module

Base class to compute the coherent X-ray scattering pattern of an object.

Parameters:

n (int) – Dimension of reciprocal-space pattern n x n for dq = 1 (default). When dq < 1, the new dimension n will be recomputed and saved as an attribute.
L (float) – Length of the real-space simulation box (L x L).
dq (float) – Sampling in reciprocal space, i.e. the fraction of \(2 \pi/L\) at which to sample. Default is dq = 1, corresponding to a spacing of \(2 \pi/L\).
f_probe (float) – Standard deviation of the Gaussian probe intensity as a fraction of L.
f_mask (float) – Radius of center beam stop as a fraction of n.

Variables:

cmap (matplotlib.colors.Colormap) – Default colormap for plotting.
gmap (matplotlib.colors.Colormap) – cmap with an opacity gradient.
q (torch.tensor) – 1-D tensor of reciprocal space coordinates determined by the dimension n and sampling dq.
n (int) – Recomputed dimension of reciprocal-space pattern n x n for the input sampling dq.
Q (torch.tensor) – 2-D tensor of shape (n x n, 2) containing the reciprocal space coordinate grid.
mask (torch.tensor) – Boolean tensor storing the masked detector pixels.
probe (torch.nn.Conv2d) – Convolution operator for convolving the reciprocal space pattern with the probe.

center_crop(y, k)

Crop y down to its central k x k pixels.

Parameters:

y (torch.tensor) – Tensor to crop.
k (int) – Target dimension, k x k.

Returns:

y – Cropped tensor.

Return type:

torch.tensor of shape (...,k,k)

plot_example(ode, y, ntype=None, vmin=None, vmax=None, lmax=None)

Plot images visualizing the scattering conditions of a given example.

Parameters:

ode (ode) – ODE object of the system.
y (torch.tensor) – Solution of the system to plot.
ntype (str) –
Type of normalization to apply when displaying the image. The options are:
- none – No normalization
- sym – Symmetric linear normalization scale
- unit – Linear normalization between 0 and 1
- mod – Linear normalization modulo \(2 \pi\)
- log – Logarithmic normalization scale
- symlog – Symmetric logarithmic normalization scale
- None – Linear normalization between the min. and max. values of y
The default is None.
vmin (float, optional) – Minimum normalization value.
vmax (float, optional) – Maximum normalization value.
lmax (float, optional) – Maximum intensity, proxy for maximum expected event frequency of Poisson process. The default value is None, corresponding to the ideal scattered intensity without Poisson sampling.

Returns:

fig – Figure object.

Return type:

matplotlib.figure

plot_probe(ax, ec='white')

Plot the real and, optionally, reciprocal space views of the probe.

Parameters:: ax (matplotlib.axes) – Axis or list of axis objects on which to display the image(s).
Returns:: sm – List of scalar mappables storing the color scales of the two plots.
Return type:: list

shapes(): Print detector and probe shapes.

class CXSGrid(N, n, L=1.0, dq=1.0, f_probe=None, f_mask=None, f=None, w=None, c=None, k=0)

Bases: CXS

Class to compute the coherent X-ray scattering pattern of an object on a uniform grid.

Parameters:

N (int) – Dimension of real-space grid N x N.
n (int) – Dimension of reciprocal-space pattern n x n for dq = 1 (default). When dq < 1, the new dimension n will be recomputed and saved as an attribute.
L (float) – Length of the real-space simulation box (L x L).
dq (float) – Sampling in reciprocal space, i.e. the fraction of \(2 \pi/L\) at which to sample. Default is dq = 1, corresponding to a spacing of \(2 \pi/L\).
f_probe (float) – Standard deviation of the Gaussian probe intensity as a fraction of L.
f_mask (float) – Radius of center beam stop as a fraction of n.
f (str) – Form factor function to use. Current options are phase or none (identity).
w (list) – List of relative weights on input channels.
c (list) – List of relative weights on non-magnetic and magnetic scattering channels.

Variables:

cmap (matplotlib.colors.Colormap) – Default colormap for plotting.
gmap (matplotlib.colors.Colormap) – cmap with an opacity gradient.
q (torch.tensor) – 1-D tensor of reciprocal space coordinates determined by the dimension n and sampling dq.
n (int) – Recomputed dimension of reciprocal-space pattern n x n for the input sampling dq.
Q (torch.tensor) – 2-D tensor of shape (n x n, 2) containing the reciprocal space coordinate grid.
mask (torch.tensor) – Boolean tensor storing the masked detector pixels.
probe (torch.nn.Conv2d) – Convolution operator for convolving the reciprocal space pattern with the probe.

I_xmcd(y)

Magnetic scattering channel intensity.

Parameters:: y (torch.tensor) – Tensor of orientations over the real-space grid.
Returns:: I – Scattered intensity.
Return type:: torch.tensor

I_xnm()

Non-magnetic scattering channel intensity.

Returns:: I – Scattered intensity.
Return type:: torch.tensor

f_none(y)

Identity form factor.

Parameters:: y (torch.tensor) – Tensor of phases at which to evaluate the form factor.
Returns:: f – Form factor evaluated at each point in y.
Return type:: torch.tensor of shape y.shape

f_phase(y)

Orientation-dependent form factor.

Parameters:: y (torch.tensor) – Tensor of phases at which to evaluate the form factor.
Returns:: f – Form factor evaluated at each point in y.
Return type:: torch.tensor of shape y.shape

forward(y)

Compute the total scattered intensity.

Parameters:: y (torch.tensor) – Tensor of orientations over the real-space grid.
Returns:: I – Scattered intensity.
Return type:: torch.tensor

class CXSPoint(R, n, L=1.0, dq=1.0, f_probe=None, f_mask=None, c=None)

Bases: CXS

Class to compute the coherent X-ray scattering pattern of a point cloud of spherical objects.

Parameters:

R (int) – Radius of spherical objects.
n (int) – Dimension of reciprocal-space pattern n x n for dq = 1 (default). When dq < 1, the new dimension n will be recomputed and saved as an attribute.
L (float) – Length of the real-space simulation box (L x L).
dq (float) – Sampling in reciprocal space, i.e. the fraction of \(2 \pi/L\) at which to sample. Default is dq = 1, corresponding to a spacing of \(2 \pi/L\).
f_probe (float) – Standard deviation of the Gaussian probe intensity as a fraction of L.
f_mask (float) – Radius of center beam stop as a fraction of n.
c (list) – List of relative weights on non-magnetic and magnetic scattering channels.

Variables:

cmap (matplotlib.colors.Colormap) – Default colormap for plotting.
gmap (matplotlib.colors.Colormap) – cmap with an opacity gradient.
q (torch.tensor) – 1-D tensor of reciprocal space coordinates determined by the dimension n and sampling dq.
n (int) – Recomputed dimension of reciprocal-space pattern n x n for the input sampling dq.
Q (torch.tensor) – 2-D tensor of shape (n x n, 2) containing the reciprocal space coordinate grid.
mask (torch.tensor) – Boolean tensor storing the masked detector pixels.
probe (torch.nn.Conv2d) – Convolution operator for convolving the reciprocal space pattern with the probe.

I_xmcd(ys)

Magnetic scattering channel intensity.

Parameters:: ys (List of torch.tensors) – List of tensors giving the orientations as well as the real and imaginary parts of the phase term.
Returns:: I – Scattered intensity.
Return type:: torch.tensor

I_xnm(ys)

Non-magnetic scattering channel intensity.

Parameters:: ys (List of torch.tensors) – List of tensors of the real and imaginary parts of the phase term.
Returns:: I – Scattered intensity.
Return type:: torch.tensor

f_coreshell(q, Rc, Rs, pc, ps, pa)

Normalized form factor of a core-shell particle.

Parameters:

q (torch.tensor) – Tensor of reciprocal-space points at which to evaluate the form factor.
Rc (float) – Radius of core.
Rs (float) – Radius of shell.
pc (float) – Scattering length density of core.
ps (float) – Scattering length density of shell.
pa (float) – Scattering length density of solvent.

Returns:

f – Form factor evaluated at each point in q.

Return type:

torch.tensor of shape q.shape

f_phase(y)

Orientation-dependent form factor.

Parameters:: y (torch.tensor) – Tensor of phases at which to evaluate the form factor.
Returns:: f – Form factor evaluated at each point in y.
Return type:: torch.tensor of shape y.shape

f_sphere(q, R)

Normalized form factor of a sphere.

Parameters:

q (torch.tensor) – Tensor of reciprocal-space points at which to evaluate the form factor.
R (float) – Radius of sphere.

Returns:

f – Form factor evaluated at each point in q.

Return type:

torch.tensor of shape q.shape

forward(y)

Compute the total scattered intensity.

Parameters:: y (torch.tensor) – Tensor of particle coordinates. The final dimension should correspond to orientations, if applicable.
Returns:: I – Scattered intensity.
Return type:: torch.tensor