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ENH: Return rank 0 for empty matrices in matrix_rank#30422

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seberg merged 11 commits into
numpy:mainfrom
false200:fix-matrix-rank-empty
Dec 19, 2025
Merged

ENH: Return rank 0 for empty matrices in matrix_rank#30422
seberg merged 11 commits into
numpy:mainfrom
false200:fix-matrix-rank-empty

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This PR fixes a bug in np.linalg.matrix_rank where empty matrices
(previously with 0 rows or 0 columns) would raise a ValueError due to
attempting a reduction operation on a zero-size array.

Changes include:

  • Return 0 for all empty matrices in matrix_rank.
  • Added tests covering all empty matrix shapes to ensure the correct behavior.

Files modified:

  • numpy/linalg/_linalg.py
  • numpy/linalg/tests/test_linalg.py

Closes #30421

Fix trailing whitespace causing lint failure and simplify the empty-matrix
rank assertion.
Comment thread numpy/linalg/_linalg.py Outdated

# Handle empty matrices - rank is 0 for matrices with 0 rows or 0 columns
if A.size == 0:
return 0

@seberg seberg Dec 12, 2025

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I wonder if we should just add initial=0 which I assume also works. The tests you added are missing the case of np.zeros((0, 5, 5)) where this return is clearly incorrect.

EDIT: Actually, while we are here, can you check if we don't return np.intp(0) on the last return? We may want to adjust the return type for the other early return as well.

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Hi @seberg, thanks for the feedback!
Added initial=0 to the S.max(... ) call as suggested, and I also added the missing np.zeros((0, 5, 5)) test.

I ran the linalg test suite locally and everything looks good.
All relevant tests passed, only the usual SKIP/XFAIL cases showed up.

WhatsApp Image 2025-12-12 at 22 58 30_538d4365
Let me know if you'd like any additional tweaks!

@false200 false200 Dec 13, 2025

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Hi @seberg , just a quick ping , all checks have passed now.

Would you mind taking a look for merge? Thanks!

@false200 false200 requested a review from seberg December 12, 2025 11:12
@seberg seberg removed their request for review December 12, 2025 11:21
@false200 false200 requested a review from seberg December 12, 2025 17:32
@seberg seberg changed the title BUG: Return rank 0 for empty matrices in matrix_rank ENH: Return rank 0 for empty matrices in matrix_rank Dec 19, 2025

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Code looks good now (I might punt on backporting, but should be OK too).
The tests could be nicer with parametrization, but it is OK.

I am not quite 100% on whether zero is always expected, so wondering if you can argue that or know some prior art?

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@seberg Thanks for the careful review and the questions
On the semantics, returning rank = 0 for empty matrices is consistent with standard linear algebra definitions and with prior art.
From a theoretical standpoint, rank is the dimension of the column (or row) space. For matrices with zero rows or zero columns, there are no columns (or no vectors at all), so the dimension of the span is 0 by definition. This is the convention used in linear algebra texts when discussing degenerate or empty linear maps.
From an SVD perspective, which matrix_rank is based on, an empty matrix has no singular values, so the count of singular values greater than the tolerance is naturally zero. Using initial=0 simply makes this behavior explicit and avoids the reduction error.
There is also prior art

  • NumPy itself already returns 0 for degenerate inputs such as np.linalg.matrix_rank(np.zeros((n,))), which aligns with this interpretation.
  • MATLAB’s rank returns 0 for empty matrices (it treats the empty singular-value set as having no values above tolerance).
  • This is consistent with the rank–nullity theorem - if the number of columns is zero, rank must be zero.

So this change doesn’t introduce a new definition so much as make the existing mathematical convention explicit and handle it robustly in code.
Happy to adjust wording or tests further if you’d like.

@false200 false200 requested a review from seberg December 19, 2025 17:48
@seberg

seberg commented Dec 19, 2025

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Cool, thanks for confirming, agreed seems rather clear convention, so let's put this in, thanks.

Should be safe for backporting, but I would probably just consider it an enhancement.

@seberg seberg merged commit c59095f into numpy:main Dec 19, 2025
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@seberg Thanks for clarifying!

@charris charris added the 09 - Backport-Candidate PRs tagged should be backported label Apr 3, 2026
charris pushed a commit to charris/numpy that referenced this pull request Apr 10, 2026
This PR fixes a bug in np.linalg.matrix_rank where empty matrices
(previously with 0 rows or 0 columns) would raise a ValueError due to
attempting a reduction operation on a zero-size array.
@charris charris removed the 09 - Backport-Candidate PRs tagged should be backported label Apr 10, 2026
charris added a commit that referenced this pull request Apr 10, 2026
ENH: Return rank 0 for empty matrices in matrix_rank (#30422)
736-c41-2c1-e464fc974 added a commit to Swiss-Armed-Forces/Loom that referenced this pull request Jun 29, 2026
This MR contains the following updates:

| Package | Type | Update | Change | OpenSSF |
|---|---|---|---|---|
| [debugpy](https://aka.ms/debugpy) ([source](https://github.com/microsoft/debugpy)) | dev | patch | `1.8.20` → `1.8.21` | [![OpenSSF Scorecard](https://api.securityscorecards.dev/projects/github.com/microsoft/debugpy/badge)](https://securityscorecards.dev/viewer/?uri=github.com/microsoft/debugpy) |
| [numpy](https://github.com/numpy/numpy) ([changelog](https://numpy.org/doc/stable/release)) | dependencies | patch | `2.4.4` → `2.4.6` | [![OpenSSF Scorecard](https://api.securityscorecards.dev/projects/github.com/numpy/numpy/badge)](https://securityscorecards.dev/viewer/?uri=github.com/numpy/numpy) |
| [pydantic-settings](https://github.com/pydantic/pydantic-settings) ([changelog](https://github.com/pydantic/pydantic-settings/releases)) | dependencies | patch | `2.14.0` → `2.14.2` | [![OpenSSF Scorecard](https://api.securityscorecards.dev/projects/github.com/pydantic/pydantic-settings/badge)](https://securityscorecards.dev/viewer/?uri=github.com/pydantic/pydantic-settings) |
| [python-multipart](https://github.com/Kludex/python-multipart) ([changelog](https://github.com/Kludex/python-multipart/blob/master/CHANGELOG.md)) | dependencies | patch | `^0.0.22` → `^0.0.32` | [![OpenSSF Scorecard](https://api.securityscorecards.dev/projects/github.com/Kludex/python-multipart/badge)](https://securityscorecards.dev/viewer/?uri=github.com/Kludex/python-multipart) |
| [types-requests](https://github.com/python/typeshed) ([changelog](https://github.com/typeshed-internal/stub_uploader/blob/main/data/changelogs/requests.md)) | dependencies | patch | `2.32.0.20240523` → `2.32.4.20260324` | [![OpenSSF Scorecard](https://api.securityscorecards.dev/projects/github.com/python/typeshed/badge)](https://securityscorecards.dev/viewer/?uri=github.com/python/typeshed) |

---

### Release Notes

<details>
<summary>microsoft/debugpy (debugpy)</summary>

### [`v1.8.21`](https://github.com/microsoft/debugpy/releases/tag/v1.8.21): debugpy v1.8.21

[Compare Source](microsoft/debugpy@v1.8.20...v1.8.21)

Fixes for:

- Return evaluate result in DAP response body instead of writing to stdout: [#&#8203;2027](microsoft/debugpy#2027)
- Prevent invalid `scopes` request from crashing debug session: [#&#8203;2026](microsoft/debugpy#2026)
- Skip uninitialized `__slots__` in variable resolver: [#&#8203;2024](microsoft/debugpy#2024)
- Handle `-c` arguments that are `bytes` instead of `str`: [#&#8203;2021](microsoft/debugpy#2021)
- Fix evaluation of variables from chained exception frames: [#&#8203;2018](microsoft/debugpy#2018)
- `ContinueRequest` with a specific `threadId` no longer resumes all threads (in-process adapter): [#&#8203;2012](microsoft/debugpy#2012)
- Avoid strong reference to exceptions during unwind: [#&#8203;2008](microsoft/debugpy#2008)
- Show error message on evaluate failures in the hover context: [#&#8203;2006](microsoft/debugpy#2006)
- Display `dlerror` output when `dlopen` fails: [#&#8203;2000](microsoft/debugpy#2000)
- Replace removed `pkgutil.get_loader` with `importlib.util.find_spec` in `get_fullname`: [#&#8203;1998](microsoft/debugpy#1998)

Enhancements:

- Add option to ignore all system exit codes: [#&#8203;2017](microsoft/debugpy#2017)
- Pull changes from pydevd up to March 2026: [#&#8203;2010](microsoft/debugpy#2010)

Infrastructure work:

- Suppress Flawfinder false positives on Cython memcpy / read-loop iterators (TSA [#&#8203;2816216](https://github.com/microsoft/debugpy/issues/2816216), [#&#8203;2816217](https://github.com/microsoft/debugpy/issues/2816217), [#&#8203;2816218](https://github.com/microsoft/debugpy/issues/2816218), [#&#8203;2816219](https://github.com/microsoft/debugpy/issues/2816219), [#&#8203;2816220](https://github.com/microsoft/debugpy/issues/2816220)): [#&#8203;2028](microsoft/debugpy#2028), [#&#8203;2029](microsoft/debugpy#2029), [#&#8203;2030](microsoft/debugpy#2030), [#&#8203;2031](microsoft/debugpy#2031), [#&#8203;2032](microsoft/debugpy#2032)

Thanks to [@&#8203;maxbachmann](https://github.com/maxbachmann), [@&#8203;mfussenegger](https://github.com/mfussenegger), and [@&#8203;sambrightman](https://github.com/sambrightman) for the commits.

</details>

<details>
<summary>numpy/numpy (numpy)</summary>

### [`v2.4.6`](https://github.com/numpy/numpy/releases/tag/v2.4.6): (May 18, 2026)

[Compare Source](numpy/numpy@v2.4.5...v2.4.6)

### NumPy 2.4.6 Release Notes

NumPy 2.4.6 is a quick release that fixes a regression discovered in the 2.4.5
release.

This release supports Python versions 3.11-3.14

#### Contributors

A total of 4 people contributed to this release. People with a "+" by their
names contributed a patch for the first time.

- !EarlMilktea
- Charles Harris
- Sebastian Berg
- Warren Weckesser

#### Pull requests merged

A total of 4 pull requests were merged for this release.

- [#&#8203;31444](numpy/numpy#31444): MAINT: Prepare 2.4.x for further development
- [#&#8203;31453](numpy/numpy#31453): BUG: Fix regression in `arr.conj()`
- [#&#8203;31459](numpy/numpy#31459): BUG: `np.linalg.svd(..., hermitian=True)` returns non-unitary...
- [#&#8203;31460](numpy/numpy#31460): BUG: Don't call INCREF/DECREF on descr in NpyStringAcquireAllocator...

### [`v2.4.5`](https://github.com/numpy/numpy/releases/tag/v2.4.5): (May 15, 2026)

[Compare Source](numpy/numpy@v2.4.4...v2.4.5)

### NumPy 2.4.5 Release Notes

NumPy 2.4.5 is a patch release that fixes bugs discovered after the 2.4.4
release, has some typing improvements, and maintains infrastructure.

This release supports Python versions 3.11-3.14

#### Contributors

A total of 17 people contributed to this release. People with a "+" by their
names contributed a patch for the first time.

- Aleksei Nikiforov
- Anarion Zuo +
- Ankit Ahlawat
- Breno Favaretto +
- Charles Harris
- Igor Krivenko +
- Ijtihed Kilani +
- Joren Hammudoglu
- Maarten Baert +
- Matti Picus
- Nathan Goldbaum
- Praneeth Kodumagulla +
- Ralf Gommers
- RoomWithOutRoof +
- Sebastian Berg
- Warren Weckesser
- div +

#### Pull requests merged

A total of 28 pull requests were merged for this release.

- [#&#8203;31093](numpy/numpy#31093): MAINT: Prepare 2.4.x for further development
- [#&#8203;31182](numpy/numpy#31182): TYP: fix `np.shape` assignability issue for python lists ([#&#8203;31171](numpy/numpy#31171))
- [#&#8203;31197](numpy/numpy#31197): ENH: Return rank 0 for empty matrices in matrix\_rank ([#&#8203;30422](numpy/numpy#30422))
- [#&#8203;31198](numpy/numpy#31198): CI/BUG: add native jobs for s390x, fix bug in `pack_inner`...
- [#&#8203;31199](numpy/numpy#31199): BUG: f2py map complex\_long\_double to NPY\_CLONGDOUBLE
- [#&#8203;31205](numpy/numpy#31205): MAINT: f2py: Stop setting re.\_MAXCACHE to 50.
- [#&#8203;31206](numpy/numpy#31206): BUG: fix heap buffer overflow in timedelta to string casts
- [#&#8203;31207](numpy/numpy#31207): MAINT: Rename ppc64le and s390x workflow ([#&#8203;31121](numpy/numpy#31121))
- [#&#8203;31208](numpy/numpy#31208): BUG: Fix matvec/vecmat in-place aliasing (out=input produces...
- [#&#8203;31209](numpy/numpy#31209): TYP: `tile`: accept numpy scalars and arrays as second argument...
- [#&#8203;31211](numpy/numpy#31211): DEP: Undo deprecation for np.dtype() signature used by old pickles...
- [#&#8203;31212](numpy/numpy#31212): REV: Manual revert of float16 svml use ([#&#8203;31178](numpy/numpy#31178))
- [#&#8203;31222](numpy/numpy#31222): TYP: `ix_` fix for boolean and non-1d input ([#&#8203;31218](numpy/numpy#31218))
- [#&#8203;31329](numpy/numpy#31329): BUG: incorrect temp elision for new-style (NEP 43) user-defined...
- [#&#8203;31330](numpy/numpy#31330): TYP: fix sliding\_window\_view axis parameter typing
- [#&#8203;31335](numpy/numpy#31335): BUG: Prevent deadlock due to downstream importing NumPy in dlopen...
- [#&#8203;31336](numpy/numpy#31336): BUG: Fix segfault in nditer.multi\_index when \_\_getitem\_\_ raises...
- [#&#8203;31338](numpy/numpy#31338): TYP: Fix ruff lint error
- [#&#8203;31357](numpy/numpy#31357): BUG: fix memory leak in np.zeros when fill-zero loop raises ([#&#8203;31320](numpy/numpy#31320))
- [#&#8203;31358](numpy/numpy#31358): BUG: np.einsum() fails with a 0-dimensional out argument and...
- [#&#8203;31379](numpy/numpy#31379): BUG: Fix signed overflow issue in npy\_gcd for INT\_MIN on s390x...
- [#&#8203;31383](numpy/numpy#31383): CI: remove Cirrus CI FreeBSD job ([#&#8203;31380](numpy/numpy#31380))
- [#&#8203;31390](numpy/numpy#31390): BUILD: newer MKL uses so.3
- [#&#8203;31391](numpy/numpy#31391): BLD/MAINT: improve support for Intel LLVM compilers
- [#&#8203;31401](numpy/numpy#31401): BUG: Avoid UB in [safe]()\[add,sub,mul] helpers ([#&#8203;31396](numpy/numpy#31396))
- [#&#8203;31402](numpy/numpy#31402): BUG: exclude \_\_pycache\_\_ directories from wheels ([#&#8203;31397](numpy/numpy#31397))
- [#&#8203;31404](numpy/numpy#31404): TYP: `_NestedSequence` type parameter default to work around...
- [#&#8203;31426](numpy/numpy#31426): TYP: Fix `DTypeLike` runtime type-checker support ([#&#8203;31425](numpy/numpy#31425))

</details>

<details>
<summary>pydantic/pydantic-settings (pydantic-settings)</summary>

### [`v2.14.2`](https://github.com/pydantic/pydantic-settings/releases/tag/v2.14.2)

[Compare Source](pydantic/pydantic-settings@v2.14.1...v2.14.2)

#### What's Changed

This is a security patch release.

- Prevent `NestedSecretsSettingsSource` from following symlinks outside `secrets_dir` by [@&#8203;hramezani](https://github.com/hramezani) in [#&#8203;889](pydantic/pydantic-settings#889)
- Prepare release 2.14.2 by [@&#8203;hramezani](https://github.com/hramezani) in [#&#8203;890](pydantic/pydantic-settings#890)

##### Security

Fixes [GHSA-4xgf-cpjx-pc3j](GHSA-4xgf-cpjx-pc3j): `NestedSecretsSettingsSource` with `secrets_nested_subdir=True` could follow a symbolic link inside `secrets_dir` pointing outside it, reading out-of-tree files into settings values and bypassing the `secrets_dir_max_size` cap. Affected versions: `>= 2.12.0, < 2.14.2`.

**Full Changelog**: <pydantic/pydantic-settings@v2.14.1...v2.14.2>

### [`v2.14.1`](https://github.com/pydantic/pydantic-settings/releases/tag/v2.14.1)

[Compare Source](pydantic/pydantic-settings@v2.14.0...v2.14.1)

#### What's Changed

- Bump the python-packages group with 4 updates by [@&#8203;dependabot](https://github.com/dependabot)\[bot] in [#&#8203;850](pydantic/pydantic-settings#850)
- Bump the python-packages group with 5 updates by [@&#8203;dependabot](https://github.com/dependabot)\[bot] in [#&#8203;854](pydantic/pydantic-settings#854)
- Bump the github-actions group with 3 updates by [@&#8203;dependabot](https://github.com/dependabot)\[bot] in [#&#8203;853](pydantic/pydantic-settings#853)
- Bump the python-packages group with 2 updates by [@&#8203;dependabot](https://github.com/dependabot)\[bot] in [#&#8203;856](pydantic/pydantic-settings#856)
- Fix field named `cls` conflicting with classmethod parameter by [@&#8203;hramezani](https://github.com/hramezani) in [#&#8203;858](pydantic/pydantic-settings#858)
- Prepare release 2.14.1 by [@&#8203;hramezani](https://github.com/hramezani) in [#&#8203;859](pydantic/pydantic-settings#859)

**Full Changelog**: <pydantic/pydantic-settings@v2.14.0...v2.14.1>

</details>

<details>
<summary>Kludex/python-multipart (python-multipart)</summary>

### [`v0.0.32`](https://github.com/Kludex/python-multipart/blob/HEAD/CHANGELOG.md#0032-2026-06-04)

[Compare Source](Kludex/python-multipart@0.0.31...0.0.32)

- Speed up partial-boundary scanning for CR/LF-dense part data [#&#8203;300](Kludex/python-multipart#300).

### [`v0.0.31`](https://github.com/Kludex/python-multipart/blob/HEAD/CHANGELOG.md#0031-2026-06-04)

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- Speed up multipart header parsing and callback dispatch [#&#8203;295](Kludex/python-multipart#295).
- Bound header field name size before validating [#&#8203;296](Kludex/python-multipart#296).
- Validate `Content-Length` is non-negative in `parse_form` [#&#8203;297](Kludex/python-multipart#297).

### [`v0.0.30`](https://github.com/Kludex/python-multipart/blob/HEAD/CHANGELOG.md#0030-2026-05-31)

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- Parse `application/x-www-form-urlencoded` bodies per the WHATWG URL standard, treating only `&` as a field separator [#&#8203;290](Kludex/python-multipart#290).
- Ignore RFC 2231/5987 extended parameters (`name*`, `filename*`) in `parse_options_header`, keeping the plain parameter authoritative per [RFC 7578 §4.2](https://datatracker.ietf.org/doc/html/rfc7578#section-4.2) [#&#8203;291](Kludex/python-multipart#291).

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- Handle malformed RFC 2231 continuations in `parse_options_header` [#&#8203;270](Kludex/python-multipart#270).

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- Speed up partial-boundary tail scan via `bytes.find` [#&#8203;281](Kludex/python-multipart#281).
- Cap multipart boundary length at 256 bytes [#&#8203;282](Kludex/python-multipart#282).

### [`v0.0.27`](https://github.com/Kludex/python-multipart/blob/HEAD/CHANGELOG.md#0027-2026-04-27)

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- Add multipart header limits [#&#8203;267](Kludex/python-multipart#267).
- Pass parse offsets via constructors [#&#8203;268](Kludex/python-multipart#268).

### [`v0.0.26`](https://github.com/Kludex/python-multipart/blob/HEAD/CHANGELOG.md#0026-2026-04-10)

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- Skip preamble before the first multipart boundary more efficiently [#&#8203;262](Kludex/python-multipart#262).
- Silently discard epilogue data after the closing multipart boundary [#&#8203;259](Kludex/python-multipart#259).

### [`v0.0.25`](https://github.com/Kludex/python-multipart/blob/HEAD/CHANGELOG.md#0025-2026-04-10)

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- Add MIME content type info to `File` [#&#8203;143](Kludex/python-multipart#143).
- Handle CTE values case-insensitively [#&#8203;258](Kludex/python-multipart#258).
- Remove custom `FormParser` classes [#&#8203;257](Kludex/python-multipart#257).
- Add `UPLOAD_DELETE_TMP` to `FormParser` config [#&#8203;254](Kludex/python-multipart#254).
- Emit `field_end` for trailing bare field names on finalize [#&#8203;230](Kludex/python-multipart#230).
- Handle multipart headers case-insensitively [#&#8203;252](Kludex/python-multipart#252).
- Apply Apache-2.0 properly [#&#8203;247](Kludex/python-multipart#247).

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- Validate `chunk_size` in `parse_form()` [#&#8203;244](Kludex/python-multipart#244).

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- Remove unused `trust_x_headers` parameter and `X-File-Name` fallback [#&#8203;196](Kludex/python-multipart#196).
- Return processed length from `QuerystringParser._internal_write` [#&#8203;229](Kludex/python-multipart#229).
- Cleanup metadata dunders from `__init__.py` [#&#8203;227](Kludex/python-multipart#227).

</details>

---

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---

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BUG: np.linalg.matrix_rank fails for empty matrices

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