[markbujehein]

Adds two diffusion models, both build on DeltaLorentzianDiffusionModelBase from #279.

The models

• DiffusionInSphere: a particle diffusing inside a sphere it cannot leave. [Volino and Dianoux]
• IsotropicRotationalDiffusion: a scatterer at a fixed distance from a centre, such as a hydrogen atom in a freely tumbling molecule, moving over the surface of that sphere by rotational diffusion. [Sears]

Both give an elastic line plus a series of Lorentzians. In theory the series is infinite, so each model keeps a limited number of terms (based on how this is handled in other libraries)

• The sphere model can use up to 98 terms, the same set as Mantid, and uses 10 by default.
• The rotational model uses orders up to l_max: 6 by default (enough up to QR of about 4.3), and at most 20.

The defaults are kept low for speed. Every term adds two dependent Parameters per Q, and updating dependent Parameters slows down as their number grows, a known issue.
Users who need higher Q or a larger sphere can raise the number of terms (a warning tells them when that is needed).

Spherical Bessel functions

Both models need the Spherical Bessel Function of the First Kind:

• Inside the dependency expressions that link the components to the model parameters. These cannot call SciPy, so spherical_bessel_expression writes each function out as an ordinary formula.
• Everywhere else, through easydynamics.utils.spherical_bessel.spherical_jn. Numba is added as an optional dependency, which offers a speed-up in some cases. Without numba it uses scipy.special.spherical_jn and gives the same values.
• Two different approaches are being tried out here, and I'm not entirely sure what makes the most sense.

The Spherical Bessel Function of the First Kind allow a bunch of rotational diffusion models to now be added.

---

Related:

• Add more diffusion models #46

[easyscience]

Label error. Requires at least 1 of: [bot] release, [scope] bug, [scope] documentation, [scope] enhancement, [scope] maintenance, [scope] significant. Found:

[codecov]

Codecov Report

❌ Patch coverage is 99.57128% with 4 lines in your changes missing coverage. Please review.
✅ Project coverage is 98.40%. Comparing base (b1d6773) to head (f95da61).

Files with missing lines	Patch %	Lines
src/easydynamics/utils/spherical_bessel.py	86.20%	4 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #280      +/-   ##
===========================================
+ Coverage    98.23%   98.40%   +0.17%     
===========================================
  Files           61       70       +9     
  Lines         6227     7160     +933     
  Branches      1039     1121      +82     
===========================================
+ Hits          6117     7046     +929     
- Misses          57       61       +4     
  Partials        53       53              

Flag	Coverage Δ
unittests	98.40% <99.57%> (+0.17%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
src/easydynamics/__init__.py	100.00% <100.00%> (ø)
src/easydynamics/sample_model/__init__.py	100.00% <100.00%> (ø)
...ydynamics/sample_model/diffusion_model/__init__.py	100.00% <100.00%> (ø)
...ion_model/delta_lorentzian_diffusion_model_base.py	100.00% <100.00%> (ø)
...ample_model/diffusion_model/diffusion_in_sphere.py	100.00% <100.00%> (ø)
...e_model/diffusion_model/equivalent_sites_circle.py	100.00% <100.00%> (ø)
.../sample_model/diffusion_model/gaussian_model_3d.py	100.00% <100.00%> (ø)
..._model/diffusion_model/hall_ross_jump_diffusion.py	100.00% <100.00%> (ø)
.../diffusion_model/isotropic_rotational_diffusion.py	100.00% <100.00%> (ø)
...fusion_model/jump_sites_log_normal_distribution.py	100.00% <100.00%> (ø)
... and 2 more

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