Adapted SVD API to match numpy API

[brownbaerchen]

Due Diligence

• General:
  • title of the PR is suitable to appear in the Release Notes
• Implementation:
  • unit tests: all split configurations tested
  • unit tests: multiple dtypes tested
  • NEW unit tests: MPS tested (1 MPI process, 1 GPU)
  • benchmarks: created for new functionality
  • benchmarks: performance improved or maintained
  • documentation updated where needed

Description

As detailed in #2054, the APIs of heat and numpy differ for svd in that heat returns $V$ and numpy returns $V^T$ in the decomposition $A = U S V^T$. This PR changes the heat API for svd and related functions to match the numpy API.

Issue/s resolved: #2054

Changes proposed:

• Breaking API change: svd and related functions return $V^T$ instead of $V$ as before
• Small refactor of heat.core.linalg.svd
• Add test that the heat and numpy svd APIs match
• Fix a few small typos in documentation

Type of change

• Bug fix
• Breaking change

[github-actions]

Thank you for the PR!

[github-actions]

Thank you for the PR!

[github-actions]

Thank you for the PR!

[JuanPedroGHM]

Benchmarks results - Sponsored by perun

FTPx86-AMD-Milan-Mi250 - CPU - N4 - RUNTIME

Function	Value [s]	Change %	30 day avg. [s]	Last entrie [s]
randomized_svd_split1	0.0265715	13.5628	0.023398	0.0188619
randomized_eigh_split1	0.0163582	-12.9075	0.0187826	0.0214194
concatenate	0.245544	15.8791	0.211896	0.205057
apply_inplace_min_max_scaler_and_inverse	0.00617962	43.2365	0.00431428	0.00476065
apply_inplace_max_abs_scaler_and_inverse	0.000629711	-56.5208	0.00144831	0.000590229

---

FTPx86-AMD-Milan-Mi250 - GPU - N4 - RUNTIME

Function	Value [s]	Change %	30 day avg. [s]	Last entrie [s]
matmul_split_0	0.132893	19.3944	0.111306	0.111222
randomized_eigh_split0	0.0624381	-11.3498	0.070432	0.0617291
apply_inplace_min_max_scaler_and_inverse	0.00765181	56.0069	0.00490479	0.00240822
apply_inplace_max_abs_scaler_and_inverse	0.00189343	-21.779	0.00242061	0.00257225
apply_inplace_normalizer	0.0130144	28.5156	0.0101267	0.0143566
convolution_array_distributed	0.013139	-24.0842	0.0173073	0.0171062
convolution_array_distributed_stride	0.0238228	-28.1879	0.0331738	0.0346745
convolution_batch_processing	0.0103748	96.1258	0.00528989	0.00284004

---

Grafana Dashboard
Last updated: 2026-01-07T11:54:29Z

[codecov]

Codecov Report

❌ Patch coverage is 98.50746% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 91.68%. Comparing base (a2994ab) to head (9e2e29f).

Files with missing lines	Patch %	Lines
heat/core/linalg/svdtools.py	94.11%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main    #2089      +/-   ##
==========================================
- Coverage   91.69%   91.68%   -0.01%     
==========================================
  Files          89       89              
  Lines       13943    13946       +3     
==========================================
+ Hits        12785    12787       +2     
- Misses       1158     1159       +1     

Flag	Coverage Δ
unit	91.68% <98.50%> (-0.01%)	⬇️

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