Add sobol sampler as well as tests and demonstrating notebook - #325
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Samuel-Vangu wants to merge 2 commits into
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Add sobol sampler as well as tests and demonstrating notebook#325Samuel-Vangu wants to merge 2 commits into
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🟡 Changes recommended
Moderate correctness, performance, validation-order, and notebook comparison issues remain unresolved.
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Pull request overview
Adds Sobol sampling for equal-weight integration over hypercubes and parallelepipeds.
Changes:
- Implements and exports the
Sobolgrid. - Adds validation, mapping, integration, and reproducibility tests.
- Adds a comparative example notebook.
File summaries
| File | Description |
|---|---|
src/grid/sobol.py |
Implements Sobol sampling and affine domain mapping. |
src/grid/tests/test_sobol.py |
Tests Sobol behavior, mapping, and integration. |
src/grid/__init__.py |
Exports the new Sobol class. |
Review details
Suppressed comments (1)
src/grid/tests/test_sobol.py:210
- The test comment attributes the changed first point to Owen scrambling, but the wrapped SciPy sampler uses LMS+shift. Please keep the behavioral explanation aligned with the actual sampler.
With randomize=True, Owen scrambling is applied and even the first
- Files reviewed: 3/4 changed files
- Comments generated: 6
- Review effort level: Balanced
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| " sobol_err_cut.append(np.mean(trial_sobol_cut))\n", | ||
| " mc_err_cut.append(np.mean(trial_mc_cut))\n", | ||
| "\n", | ||
| " m_tensor = int(round(N ** (1 / DIM)))\n", |
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| # Generate Sobol points in the unit cube [0, 1)^d | ||
| points_unit = self._generate_sobol_points(n_points, dimension, seed, randomize) |
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| points = origin + points_unit @ axes | ||
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|
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| # Volume of the parallelepiped | ||
| volume = np.abs(np.linalg.det(axes)) |
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| if isinstance(index, int): | ||
| return Grid(np.array([self.points[index]]), np.array([self.weights[index]])) |
| "id": "9be9ecff", | ||
| "metadata": {}, | ||
| "source": [ | ||
| "[](https://colab.research.google.com/github/theochem/grid/blob/master/examples/Sobol.ipynb)" |
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| randomize : bool, optional | ||
| If True (default), applies Owen scrambling to the sequence. If | ||
| False, generates the unscrambled (deterministic) Sobol' sequence. |
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Adds a
Sobolsampling class for integration on (hyper)cubic grids,following up on the discussion in #322.
What's included
src/grid/sobol.py:Sobol(n_points, dimension, seed=None, randomize=True, origin=None, axes=None). Wrapsscipy.stats.qmc.Sobol(already agriddependency), generating points via
random_base2for the balanceproperties of the digital-net construction;
n_pointsmust therefore be apower of 2.
randomize=Falsegives the deterministic, unscrambledsequence (whose first point is always the origin);
randomize=Trueapplies Owen scrambling. Supports mapping onto an arbitrary parallelepiped
via
origin/axes.src/grid/tests/test_sobol.py: tests covering validation, weights, domainmapping, integration accuracy, reproducibility, and properties specific to
Sobol' sequences (origin as first point when unrandomized, the nesting
property between an N-point and a 2N-point design).
examples/: comparesSobolagainst baselinesalready in
grid(plain Monte Carlo,Tensor1DGrids/Trapezoidal) on twochemistry-motivated integrands -- a product of Gaussian-type functions
(smooth) and a spherical interaction-cutoff indicator (discontinuous) --
to show honestly where Sobol's low-discrepancy advantage holds and where
it doesn't.