Add summary statistics to ProductMeasure

[Laasya-73]

This PR adds combined summary statistics to ProductMeasure.

ProductMeasure now derives statistics for its independent marginal blocks by:

• concatenating marginal means
• concatenating marginal variances
• concatenating marginal standard deviations
• constructing a block-diagonal covariance matrix from the marginal covariance matrices

This allows users to access statistics for the complete product distribution directly instead of calculating them separately for each marginal.

Changes

• Added combined summary-statistic support to ProductMeasure.
• Added block-diagonal covariance construction for independent marginal blocks.
• Added tests for one-dimensional and multidimensional marginal combinations.
• Added coverage for scalar one-dimensional statistics.
• Added tests for behavior when marginal statistics are unavailable.

[codecov]

Codecov Report

❌ Patch coverage is 96.22642% with 2 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.70%. Comparing base (dc3d923) to head (536d3cd).

Files with missing lines	Patch %	Lines
qmcpy/true_measure/product_measure.py	96.22%	2 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #608      +/-   ##
===========================================
+ Coverage    88.65%   88.70%   +0.04%     
===========================================
  Files          104      104              
  Lines         8508     8561      +53     
===========================================
+ Hits          7543     7594      +51     
- Misses         965      967       +2     

Flag	Coverage Δ
alltests	88.70% <96.22%> (+0.04%)	⬆️

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

Files with missing lines	Coverage Δ
qmcpy/true_measure/product_measure.py	96.42% <96.22%> (-0.19%)	⬇️

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[Copilot]

Pull request overview

Adds combined summary statistics to ProductMeasure.

Changes:

• Concatenates marginal means, variances, and standard deviations.
• Constructs block-diagonal covariance matrices.
• Adds coverage for scalar, multidimensional, ordering, and unavailable-statistic cases.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 1 comment.

File	Description
qmcpy/true_measure/product_measure.py	Implements combined statistics.
test/test_product_measure.py	Tests statistic aggregation and errors.

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[Copilot]

Fixed in commit Fix ProductMeasure.covariance to preserve sparse blocks. The covariance property now:

• Skips toarray() on sparse blocks, preserving their shape for validation
• Uses sparse.block_diag(blocks, format="dia") and sets .data.setflags(write=False) when all blocks are sparse
• Falls back to the dense path (with toarray() only at that point) when blocks are mixed sparse/dense

[fjhickernell]

tried it with the AreWeThereYet notebook for MATH 565 and it worked like a charm.

[fjhickernell]

@Laasya-73, running by copilot once more but it looks ready for you to squash and merge.

[Copilot]

Pull request overview

Copilot reviewed 2 out of 2 changed files in this pull request and generated 2 comments.

[Copilot]

Fixed in the latest commit. The covariance result is now converted to a dense array via toarray() when sparse before passing to assert_allclose.

[Copilot]

Fixed in the latest commit. The immutability loop now checks value.data.flags for sparse matrices and value.flags for dense arrays.

[Copilot]

Pull request overview

Copilot reviewed 2 out of 2 changed files in this pull request and generated no new comments.

Suppressed comments (1)

Previously missed (1) — in code that hasn't changed since the last review.

qmcpy/true_measure/product_measure.py:267

• Return a protected view here, not the owned array itself. An owned array made read-only with setflags(write=False) can be made writable again by calling result.setflags(write=True), whereas the established statistics contract explicitly checks that this raises (test/test_true_measures.py:221-225). The mixed sparse/dense covariance path therefore exposes a mutable result unlike the other dense statistics.

        return self._read_only_array(covariance)

[sou-cheng-choi]

@Laasya-73

A dense block densifies an otherwise sparse covariance:

from qmcpy import ProductMeasure, DummySampler, Uniform, Gaussian
    from scipy import sparse
    import numpy as np
    d = 128
    product = ProductMeasure(
        DummySampler(d + 2),
        [Uniform(DummySampler(d)),
         Gaussian(DummySampler(2), covariance=np.array([[1.0, 0.5], [0.5, 1.0]]))])
    covariance = product.covariance
    sparse_equivalent = sparse.block_diag(
        [marginal.covariance for marginal in product.marginals],
        format="csr")

[sou-cheng-choi]

See example above.