diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
new file mode 100644
index 0000000..6803be6
--- /dev/null
+++ b/.github/workflows/ci.yml
@@ -0,0 +1,80 @@
+name: ci
+
+on:
+ push:
+ branches: ['**']
+ tags: ['**']
+ pull_request:
+ branches: ['**']
+
+jobs:
+ ruff:
+ runs-on: ubuntu-24.04
+ steps:
+ - uses: actions/checkout@v4
+ - uses: actions/setup-python@v5
+ with:
+ python-version: '3.13'
+
+ - name: Install package as dev
+ run: pip install ".[dev]"
+
+ - name: Ruff check
+ run: ruff check
+
+ - name: Ruff format
+ run: ruff format --check
+
+ mypy:
+ runs-on: ubuntu-24.04
+ strategy:
+ matrix:
+ python-version: ["3.10", "3.11", "3.12", "3.13"]
+ steps:
+ - uses: actions/checkout@v4
+ - uses: actions/setup-python@v5
+ with:
+ python-version: ${{ matrix.python-version }}
+
+ - name: Install package as dev
+ run: pip install ".[dev]"
+
+ - name: Run mypy
+ run: mypy pyrpca
+
+ test:
+ runs-on: ubuntu-24.04
+ strategy:
+ matrix:
+ python-version: ["3.10", "3.11", "3.12", "3.13"]
+ steps:
+ - uses: actions/checkout@v4
+ - uses: actions/setup-python@v5
+ with:
+ python-version: ${{ matrix.python-version }}
+
+ - name: Install package as dev
+ run: pip install ".[dev]"
+
+ - name: Run tests
+ run: pytest
+
+ deploy:
+ if: startsWith(github.ref, 'refs/tags/v')
+ needs: [ruff, mypy, test]
+ runs-on: ubuntu-24.04
+ environment:
+ name: publish
+ permissions:
+ id-token: write
+
+ steps:
+ - uses: actions/checkout@v4
+ - uses: actions/setup-python@v5
+ with:
+ python-version: '3.13'
+
+ - name: Build package
+ run: pip wheel --no-deps . -w ./dist
+ - name: Publish package distributions to PyPI
+ uses: pypa/gh-action-pypi-publish@release/v1
diff --git a/.gitignore b/.gitignore
index 0a19790..47f98d1 100644
--- a/.gitignore
+++ b/.gitignore
@@ -1,3 +1,5 @@
+.vscode/
+
# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
diff --git a/LICENSE b/LICENSE
new file mode 100644
index 0000000..d0a1fa1
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,373 @@
+Mozilla Public License Version 2.0
+==================================
+
+1. Definitions
+--------------
+
+1.1. "Contributor"
+ means each individual or legal entity that creates, contributes to
+ the creation of, or owns Covered Software.
+
+1.2. "Contributor Version"
+ means the combination of the Contributions of others (if any) used
+ by a Contributor and that particular Contributor's Contribution.
+
+1.3. "Contribution"
+ means Covered Software of a particular Contributor.
+
+1.4. "Covered Software"
+ means Source Code Form to which the initial Contributor has attached
+ the notice in Exhibit A, the Executable Form of such Source Code
+ Form, and Modifications of such Source Code Form, in each case
+ including portions thereof.
+
+1.5. "Incompatible With Secondary Licenses"
+ means
+
+ (a) that the initial Contributor has attached the notice described
+ in Exhibit B to the Covered Software; or
+
+ (b) that the Covered Software was made available under the terms of
+ version 1.1 or earlier of the License, but not also under the
+ terms of a Secondary License.
+
+1.6. "Executable Form"
+ means any form of the work other than Source Code Form.
+
+1.7. "Larger Work"
+ means a work that combines Covered Software with other material, in
+ a separate file or files, that is not Covered Software.
+
+1.8. "License"
+ means this document.
+
+1.9. "Licensable"
+ means having the right to grant, to the maximum extent possible,
+ whether at the time of the initial grant or subsequently, any and
+ all of the rights conveyed by this License.
+
+1.10. "Modifications"
+ means any of the following:
+
+ (a) any file in Source Code Form that results from an addition to,
+ deletion from, or modification of the contents of Covered
+ Software; or
+
+ (b) any new file in Source Code Form that contains any Covered
+ Software.
+
+1.11. "Patent Claims" of a Contributor
+ means any patent claim(s), including without limitation, method,
+ process, and apparatus claims, in any patent Licensable by such
+ Contributor that would be infringed, but for the grant of the
+ License, by the making, using, selling, offering for sale, having
+ made, import, or transfer of either its Contributions or its
+ Contributor Version.
+
+1.12. "Secondary License"
+ means either the GNU General Public License, Version 2.0, the GNU
+ Lesser General Public License, Version 2.1, the GNU Affero General
+ Public License, Version 3.0, or any later versions of those
+ licenses.
+
+1.13. "Source Code Form"
+ means the form of the work preferred for making modifications.
+
+1.14. "You" (or "Your")
+ means an individual or a legal entity exercising rights under this
+ License. For legal entities, "You" includes any entity that
+ controls, is controlled by, or is under common control with You. For
+ purposes of this definition, "control" means (a) the power, direct
+ or indirect, to cause the direction or management of such entity,
+ whether by contract or otherwise, or (b) ownership of more than
+ fifty percent (50%) of the outstanding shares or beneficial
+ ownership of such entity.
+
+2. License Grants and Conditions
+--------------------------------
+
+2.1. Grants
+
+Each Contributor hereby grants You a world-wide, royalty-free,
+non-exclusive license:
+
+(a) under intellectual property rights (other than patent or trademark)
+ Licensable by such Contributor to use, reproduce, make available,
+ modify, display, perform, distribute, and otherwise exploit its
+ Contributions, either on an unmodified basis, with Modifications, or
+ as part of a Larger Work; and
+
+(b) under Patent Claims of such Contributor to make, use, sell, offer
+ for sale, have made, import, and otherwise transfer either its
+ Contributions or its Contributor Version.
+
+2.2. Effective Date
+
+The licenses granted in Section 2.1 with respect to any Contribution
+become effective for each Contribution on the date the Contributor first
+distributes such Contribution.
+
+2.3. Limitations on Grant Scope
+
+The licenses granted in this Section 2 are the only rights granted under
+this License. No additional rights or licenses will be implied from the
+distribution or licensing of Covered Software under this License.
+Notwithstanding Section 2.1(b) above, no patent license is granted by a
+Contributor:
+
+(a) for any code that a Contributor has removed from Covered Software;
+ or
+
+(b) for infringements caused by: (i) Your and any other third party's
+ modifications of Covered Software, or (ii) the combination of its
+ Contributions with other software (except as part of its Contributor
+ Version); or
+
+(c) under Patent Claims infringed by Covered Software in the absence of
+ its Contributions.
+
+This License does not grant any rights in the trademarks, service marks,
+or logos of any Contributor (except as may be necessary to comply with
+the notice requirements in Section 3.4).
+
+2.4. Subsequent Licenses
+
+No Contributor makes additional grants as a result of Your choice to
+distribute the Covered Software under a subsequent version of this
+License (see Section 10.2) or under the terms of a Secondary License (if
+permitted under the terms of Section 3.3).
+
+2.5. Representation
+
+Each Contributor represents that the Contributor believes its
+Contributions are its original creation(s) or it has sufficient rights
+to grant the rights to its Contributions conveyed by this License.
+
+2.6. Fair Use
+
+This License is not intended to limit any rights You have under
+applicable copyright doctrines of fair use, fair dealing, or other
+equivalents.
+
+2.7. Conditions
+
+Sections 3.1, 3.2, 3.3, and 3.4 are conditions of the licenses granted
+in Section 2.1.
+
+3. Responsibilities
+-------------------
+
+3.1. Distribution of Source Form
+
+All distribution of Covered Software in Source Code Form, including any
+Modifications that You create or to which You contribute, must be under
+the terms of this License. You must inform recipients that the Source
+Code Form of the Covered Software is governed by the terms of this
+License, and how they can obtain a copy of this License. You may not
+attempt to alter or restrict the recipients' rights in the Source Code
+Form.
+
+3.2. Distribution of Executable Form
+
+If You distribute Covered Software in Executable Form then:
+
+(a) such Covered Software must also be made available in Source Code
+ Form, as described in Section 3.1, and You must inform recipients of
+ the Executable Form how they can obtain a copy of such Source Code
+ Form by reasonable means in a timely manner, at a charge no more
+ than the cost of distribution to the recipient; and
+
+(b) You may distribute such Executable Form under the terms of this
+ License, or sublicense it under different terms, provided that the
+ license for the Executable Form does not attempt to limit or alter
+ the recipients' rights in the Source Code Form under this License.
+
+3.3. Distribution of a Larger Work
+
+You may create and distribute a Larger Work under terms of Your choice,
+provided that You also comply with the requirements of this License for
+the Covered Software. If the Larger Work is a combination of Covered
+Software with a work governed by one or more Secondary Licenses, and the
+Covered Software is not Incompatible With Secondary Licenses, this
+License permits You to additionally distribute such Covered Software
+under the terms of such Secondary License(s), so that the recipient of
+the Larger Work may, at their option, further distribute the Covered
+Software under the terms of either this License or such Secondary
+License(s).
+
+3.4. Notices
+
+You may not remove or alter the substance of any license notices
+(including copyright notices, patent notices, disclaimers of warranty,
+or limitations of liability) contained within the Source Code Form of
+the Covered Software, except that You may alter any license notices to
+the extent required to remedy known factual inaccuracies.
+
+3.5. Application of Additional Terms
+
+You may choose to offer, and to charge a fee for, warranty, support,
+indemnity or liability obligations to one or more recipients of Covered
+Software. However, You may do so only on Your own behalf, and not on
+behalf of any Contributor. You must make it absolutely clear that any
+such warranty, support, indemnity, or liability obligation is offered by
+You alone, and You hereby agree to indemnify every Contributor for any
+liability incurred by such Contributor as a result of warranty, support,
+indemnity or liability terms You offer. You may include additional
+disclaimers of warranty and limitations of liability specific to any
+jurisdiction.
+
+4. Inability to Comply Due to Statute or Regulation
+---------------------------------------------------
+
+If it is impossible for You to comply with any of the terms of this
+License with respect to some or all of the Covered Software due to
+statute, judicial order, or regulation then You must: (a) comply with
+the terms of this License to the maximum extent possible; and (b)
+describe the limitations and the code they affect. Such description must
+be placed in a text file included with all distributions of the Covered
+Software under this License. Except to the extent prohibited by statute
+or regulation, such description must be sufficiently detailed for a
+recipient of ordinary skill to be able to understand it.
+
+5. Termination
+--------------
+
+5.1. The rights granted under this License will terminate automatically
+if You fail to comply with any of its terms. However, if You become
+compliant, then the rights granted under this License from a particular
+Contributor are reinstated (a) provisionally, unless and until such
+Contributor explicitly and finally terminates Your grants, and (b) on an
+ongoing basis, if such Contributor fails to notify You of the
+non-compliance by some reasonable means prior to 60 days after You have
+come back into compliance. Moreover, Your grants from a particular
+Contributor are reinstated on an ongoing basis if such Contributor
+notifies You of the non-compliance by some reasonable means, this is the
+first time You have received notice of non-compliance with this License
+from such Contributor, and You become compliant prior to 30 days after
+Your receipt of the notice.
+
+5.2. If You initiate litigation against any entity by asserting a patent
+infringement claim (excluding declaratory judgment actions,
+counter-claims, and cross-claims) alleging that a Contributor Version
+directly or indirectly infringes any patent, then the rights granted to
+You by any and all Contributors for the Covered Software under Section
+2.1 of this License shall terminate.
+
+5.3. In the event of termination under Sections 5.1 or 5.2 above, all
+end user license agreements (excluding distributors and resellers) which
+have been validly granted by You or Your distributors under this License
+prior to termination shall survive termination.
+
+************************************************************************
+* *
+* 6. Disclaimer of Warranty *
+* ------------------------- *
+* *
+* Covered Software is provided under this License on an "as is" *
+* basis, without warranty of any kind, either expressed, implied, or *
+* statutory, including, without limitation, warranties that the *
+* Covered Software is free of defects, merchantable, fit for a *
+* particular purpose or non-infringing. The entire risk as to the *
+* quality and performance of the Covered Software is with You. *
+* Should any Covered Software prove defective in any respect, You *
+* (not any Contributor) assume the cost of any necessary servicing, *
+* repair, or correction. This disclaimer of warranty constitutes an *
+* essential part of this License. No use of any Covered Software is *
+* authorized under this License except under this disclaimer. *
+* *
+************************************************************************
+
+************************************************************************
+* *
+* 7. Limitation of Liability *
+* -------------------------- *
+* *
+* Under no circumstances and under no legal theory, whether tort *
+* (including negligence), contract, or otherwise, shall any *
+* Contributor, or anyone who distributes Covered Software as *
+* permitted above, be liable to You for any direct, indirect, *
+* special, incidental, or consequential damages of any character *
+* including, without limitation, damages for lost profits, loss of *
+* goodwill, work stoppage, computer failure or malfunction, or any *
+* and all other commercial damages or losses, even if such party *
+* shall have been informed of the possibility of such damages. This *
+* limitation of liability shall not apply to liability for death or *
+* personal injury resulting from such party's negligence to the *
+* extent applicable law prohibits such limitation. Some *
+* jurisdictions do not allow the exclusion or limitation of *
+* incidental or consequential damages, so this exclusion and *
+* limitation may not apply to You. *
+* *
+************************************************************************
+
+8. Litigation
+-------------
+
+Any litigation relating to this License may be brought only in the
+courts of a jurisdiction where the defendant maintains its principal
+place of business and such litigation shall be governed by laws of that
+jurisdiction, without reference to its conflict-of-law provisions.
+Nothing in this Section shall prevent a party's ability to bring
+cross-claims or counter-claims.
+
+9. Miscellaneous
+----------------
+
+This License represents the complete agreement concerning the subject
+matter hereof. If any provision of this License is held to be
+unenforceable, such provision shall be reformed only to the extent
+necessary to make it enforceable. Any law or regulation which provides
+that the language of a contract shall be construed against the drafter
+shall not be used to construe this License against a Contributor.
+
+10. Versions of the License
+---------------------------
+
+10.1. New Versions
+
+Mozilla Foundation is the license steward. Except as provided in Section
+10.3, no one other than the license steward has the right to modify or
+publish new versions of this License. Each version will be given a
+distinguishing version number.
+
+10.2. Effect of New Versions
+
+You may distribute the Covered Software under the terms of the version
+of the License under which You originally received the Covered Software,
+or under the terms of any subsequent version published by the license
+steward.
+
+10.3. Modified Versions
+
+If you create software not governed by this License, and you want to
+create a new license for such software, you may create and use a
+modified version of this License if you rename the license and remove
+any references to the name of the license steward (except to note that
+such modified license differs from this License).
+
+10.4. Distributing Source Code Form that is Incompatible With Secondary
+Licenses
+
+If You choose to distribute Source Code Form that is Incompatible With
+Secondary Licenses under the terms of this version of the License, the
+notice described in Exhibit B of this License must be attached.
+
+Exhibit A - Source Code Form License Notice
+-------------------------------------------
+
+ This Source Code Form is subject to the terms of the Mozilla Public
+ License, v. 2.0. If a copy of the MPL was not distributed with this
+ file, You can obtain one at https://mozilla.org/MPL/2.0/.
+
+If it is not possible or desirable to put the notice in a particular
+file, then You may include the notice in a location (such as a LICENSE
+file in a relevant directory) where a recipient would be likely to look
+for such a notice.
+
+You may add additional accurate notices of copyright ownership.
+
+Exhibit B - "Incompatible With Secondary Licenses" Notice
+---------------------------------------------------------
+
+ This Source Code Form is "Incompatible With Secondary Licenses", as
+ defined by the Mozilla Public License, v. 2.0.
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..6fb47d9
--- /dev/null
+++ b/README.md
@@ -0,0 +1,40 @@
+# Robust principal component analysis for Python
+
+This package provides algorithms to solve the Robust Principal Component Analysis (RPCA) problem, as presented by Candès et al.[[1]](#candes2011).
+Currently, a single algorithm is implemented: it solves the Principal Component Pursuit (PCP) convex relaxation of RPCA from the same paper, using the Inexact Augmented Lagrange Multiplier (IALM) method from Lin et al.[[2]](#lin2011)[[3]](#lin2013).
+
+## Example
+```python
+from pyrpca import rpca_pcp_ialm
+
+# given an m x n data matrix
+data = ...
+
+# decide on sparsity factor.
+# this parameter is also commonly known as 'lambda'.
+sparsity_factor = 1.0 / numpy.sqrt(max(data.shape))
+
+# run the ialm algorithm.
+low_rank, sparse = rpca_pcp_ialm(data, sparsity_factor)
+```
+
+## Installing
+```shell
+pip install pyrpca
+```
+
+## Feature requests and contributing
+Pull requests and feature requests are welcome. The current version is minimal and suits my personal needs, but feel free to make suggestions. Even if the repository looks inactive, I will still respond :)
+
+## References
+1. [Emmanuel J. Candès, Xiaodong Li, Yi Ma, John Wright. Robust principal component analysis? Association for Computing Machinery 2011.](https://doi.org/10.1145/1970392.1970395) (preprint on [arXiv](https://doi.org/10.48550/arXiv.0912.3599))
+2. [Zhouchen Lin, Risheng Liu, Zhixun Su. Linearized Alternating Direction Method with Adaptive Penalty for Low-Rank Representation. arXiv 2011.](https://doi.org/10.48550/arXiv.1109.0367)
+3. [Zhouchen Lin, Minming Chen, Yi Ma. The Augmented Lagrange Multiplier Method for Exact Recovery of Corrupted Low-Rank Matrices, V3. arXiv 2013.](https://doi.org/10.48550/arXiv.1009.5055)
+
+## Acknowledgements
+Appreciation is due to various other Python implementations of RPCA that served as inspiration for this project. Below is a non-exhaustive list:
+
+- https://github.com/2020leon/rpca
+- https://github.com/dganguli/robust-pca
+- https://github.com/weilinear/PyRPCA
+- https://github.com/loiccoyle/RPCA
diff --git a/pyproject.toml b/pyproject.toml
new file mode 100644
index 0000000..da1b54f
--- /dev/null
+++ b/pyproject.toml
@@ -0,0 +1,38 @@
+[build-system]
+requires = ["setuptools >= 78", "setuptools-git-versioning >=2.1, <3"]
+build-backend = "setuptools.build_meta"
+
+[tool.setuptools-git-versioning]
+enabled = true
+
+[project]
+name = "pyrpca"
+description = "Robust principal component analysis for Python."
+dynamic = ["version"]
+readme = "README.md"
+requires-python = ">=3.10,<4"
+classifiers = [
+ "License :: OSI Approved :: Mozilla Public License 2.0 (MPL 2.0)",
+]
+dependencies = ["numpy >= 2.0.2, < 3", "scipy >= 1.15.2"]
+keywords = ["rpca", "robust pca", "robust principal component analysis"]
+authors = [{ name = "Aart Stuurman", email = "aart@astuurman.com" }]
+maintainers = [{ name = "Aart Stuurman", email = "aart@astuurman.com" }]
+license = { file = "LICENSE" }
+
+[project.optional-dependencies]
+dev = [
+ "ruff == 0.11.2",
+ "mypy == 1.15.0",
+ "pytest == 8.3.5",
+ "scipy-stubs >= 1.15.2",
+]
+
+[project.urls]
+homepage = "https://github.com/surgura/PyRPCA"
+
+[tool.setuptools]
+package-dir = { "pyrpca" = "pyrpca" }
+
+[tool.mypy]
+strict = true
diff --git a/pyrpca/__init__.py b/pyrpca/__init__.py
new file mode 100644
index 0000000..573ceb6
--- /dev/null
+++ b/pyrpca/__init__.py
@@ -0,0 +1,3 @@
+from .pcp_ialm import rpca_pcp_ialm
+
+__all__ = ["rpca_pcp_ialm"]
diff --git a/pyrpca/ialm.py b/pyrpca/ialm.py
new file mode 100644
index 0000000..e69de29
diff --git a/pyrpca/pcp_ialm.py b/pyrpca/pcp_ialm.py
new file mode 100644
index 0000000..084d054
--- /dev/null
+++ b/pyrpca/pcp_ialm.py
@@ -0,0 +1,85 @@
+import numpy.typing as npt
+from typing import Tuple
+import numpy as np
+from numpy.linalg import norm
+from scipy.linalg import svd
+
+
+def rpca_pcp_ialm(
+ observations: npt.ArrayLike,
+ sparsity_factor: float,
+ max_iter: int = 1000,
+ mu: float | None = None,
+ mu_upper_bound: float | None = None,
+ rho: float = 1.5,
+ tol: float = 1e-7,
+ verbose: bool = True,
+) -> Tuple[npt.ArrayLike, npt.ArrayLike]:
+ """
+ Solve the Principal Component Pursuit (PCP) convex relaxation of Robust PCA using the Inexact Augmented Lagrange Multiplier (IALM) method.
+
+ See README for algorithmic details and references.
+
+ Mu is updated every loop by multiplying it by `rho` until reaching `mu_upper_bound`.
+
+ Parameters:
+ observations: The m x n input matrix to decompose ('D' in the IALM paper).
+ sparsity_factor: Weight on the sparse term in the objective ('lambda' in the IALM paper).
+ max_iter: Maximum number of iterations to perform.
+ mu: Initial value for the penalty parameter. If None, defaults to 1/spectral norm of observations.
+ mu_upper_bound: Maximum allowed value for `mu`. If None, defaults to `mu * 1e7`.
+ rho: Multiplicative factor to increase `mu` in each iteration.
+ tol: Tolerance for stopping criterion (relative Frobenius norm of the residual).
+ verbose: If True, print status and debug information during optimization.
+
+ Returns:
+ low_rank_component: The recovered low-rank matrix ('A' in the IALM paper).
+ sparse_component: The recovered sparse matrix ('E' in the IALM paper).
+ """
+ if mu is None:
+ mu = float(1.25 / norm(observations, ord=2))
+ if mu_upper_bound is None:
+ mu_upper_bound = mu * 1e7
+
+ norm_fro_obs = norm(observations, ord="fro")
+
+ dual = observations / np.maximum(
+ norm(observations, ord=2), norm(observations, ord=np.inf) / sparsity_factor
+ )
+ sparse = np.zeros_like(observations)
+
+ i = 0
+ while True:
+ # compute next iteration of a
+ u, s, v = svd(observations - sparse + 1.0 / mu * dual, full_matrices=False)
+ s_thresholded = np.maximum(s - 1.0 / mu, 0)
+ low_rank = (u * s_thresholded) @ v
+
+ # compute next iteration of e
+ residual_for_sparse = observations - low_rank + 1.0 / mu * dual
+ sparse = np.sign(residual_for_sparse) * np.maximum(
+ np.abs(residual_for_sparse) - sparsity_factor / mu, 0
+ )
+
+ # calculate error
+ residual = observations - low_rank - sparse
+ err = norm(residual, ord="fro") / norm_fro_obs
+
+ i += 1
+
+ if verbose:
+ print(f"iter {i:<4} | err {err:<25} | mu {mu:<25}")
+
+ if err < tol:
+ if verbose:
+ print("Finished optimization. Error smaller than tolerance.")
+ break
+ if i == max_iter:
+ if verbose:
+ print("Finized optimization. Max iterations reached.")
+ break
+
+ # update dual and mu
+ dual = dual + mu * (residual)
+ mu = min(mu * rho, mu_upper_bound)
+ return low_rank, sparse
diff --git a/tests/test_pcp_ialm.py b/tests/test_pcp_ialm.py
new file mode 100644
index 0000000..33fb10d
--- /dev/null
+++ b/tests/test_pcp_ialm.py
@@ -0,0 +1,43 @@
+import numpy as np
+from pyrpca import rpca_pcp_ialm
+from numpy.linalg import norm
+from scipy.sparse import random as sparse_random
+
+
+def test_rpca_separates_low_rank_and_sparse():
+ np.random.seed(0)
+ m, n, rank = 500, 400, 5
+
+ # create low-rank matrix A
+ u = np.random.randn(m, rank)
+ v = np.random.randn(rank, n)
+ low_rank = u @ v
+
+ # create sparse matrix E
+ sparse = sparse_random(
+ m, n, density=0.1, format="csr", data_rvs=np.random.randn
+ ).toarray()
+
+ # create observation matrix
+ observations = low_rank + sparse
+
+ # Run RPCA
+ low_rank_recovered, sparse_recovered = rpca_pcp_ialm(
+ observations,
+ sparsity_factor=1.0 / np.sqrt(max(observations.shape)),
+ )
+
+ # check that the reconstruction is close
+ reconstruction_error = norm(
+ observations - (low_rank_recovered + sparse_recovered), ord="fro"
+ ) / norm(observations, ord="fro")
+ assert reconstruction_error < 1e-6, (
+ f"Reconstruction error too high: {reconstruction_error}"
+ )
+
+ # check that recovered matrices are low rank and sparse
+ approx_rank = np.linalg.matrix_rank(low_rank_recovered, tol=1e-3)
+ sparsity = np.count_nonzero(sparse_recovered) / sparse_recovered.size
+
+ assert approx_rank <= rank + 2, f"Recovered A not low rank: {approx_rank}"
+ assert sparsity < 0.2, f"Recovered E not sparse: sparsity={sparsity}"