Speed up `Expr * Expr` by Zeroto521 · Pull Request #1175 · scipopt/PySCIPOpt

Zeroto521 · 2026-01-24T08:13:20Z

This PR is at least faster 1.2x than before.

Before optimized
- First time running
  - Time taken for 50x50 matrix: 1.0127 seconds
  - Time taken for 100x100 matrix: 6.8916 second
- Second time running
  - Time taken for 50x50 matrix: 0.8220 seconds
  - Time taken for 100x100 matrix: 5.8312 seconds
- Third time running
  - Time taken for 50x50 matrix: 0.9372 seconds
  - Time taken for 100x100 matrix: 5.2823 seconds
After optimized Expr.__mul__(Expr):
- First time running
  - Time taken for 50x50 matrix: 0.5335 seconds
  - Time taken for 100x100 matrix: 6.5986 seconds
- Second time running
  - Time taken for 50x50 matrix: 0.7765 seconds
  - Time taken for 100x100 matrix: 5.2647 seconds
- Third time running
  - Time taken for 50x50 matrix: 0.6112 seconds
  - Time taken for 100x100 matrix: 6.7011 seconds
After optimized Expr.__mul__(Expr) and Term.__mul__(Term)
- First time running
  - Time taken for 50x50 matrix: 0.6092 seconds
  - Time taken for 100x100 matrix: 5.7285 seconds
- Second time running
  - Time taken for 50x50 matrix: 0.5105 seconds
  - Time taken for 100x100 matrix: 5.0206 seconds
- Third time running
  - Time taken for 50x50 matrix: 0.5816 seconds
  - Time taken for 100x100 matrix: 4.3978 seconds

from timeit import timeit

from pyscipopt import Model

m = Model()

n = 50
x = m.addMatrixVar((n, n))

cost = timeit(lambda: x @ x, number=5) / 5
print(f"Time taken for {n}x{n} matrix: {cost:.4f} seconds")

n = 100
x = m.addMatrixVar((n, n))
cost = timeit(lambda: x @ x, number=5) / 5
print(f"Time taken for {n}x{n} matrix: {cost:.4f} seconds")

Replaces Term.__add__ with Term.__mul__ and updates Expr.__mul__ to use more efficient Cython dict iteration and item access. This improves performance and correctness when multiplying expressions, especially for large term dictionaries.

Replaces the simple concatenation in Term.__mul__ with an efficient merge that maintains variable order based on pointer values. This improves performance and correctness when multiplying Term objects.

Moved the 'Speed up MatrixExpr.sum(axis=...) via quicksum' entry from the Added section to the Changed section for better categorization and clarity.

Added a new entry to the changelog noting the performance improvement for Expr * Expr operations.

src/pyscipopt/expr.pxi

Copilot

Pull request overview

This PR optimizes the multiplication of Expr objects (polynomial expressions) by using low-level C API calls and introducing a more efficient Term.__mul__ method. According to the benchmarks provided, this results in at least 1.2x speedup for matrix multiplication operations.

Changes:

Introduced Term.__mul__ method using an efficient merge algorithm for combining sorted variable tuples
Optimized Expr.__mul__ to use C-level Python dict iteration APIs (PyDict_Next, PyDict_GetItem) and skip zero coefficients
Updated CHANGELOG to document the performance improvement

Reviewed changes

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

File	Description
src/pyscipopt/expr.pxi	Implements optimized `Term.__mul__` method and refactors `Expr.__mul__` to use low-level C APIs for faster dictionary iteration and term multiplication
CHANGELOG.md	Adds entry documenting the Expr * Expr performance improvement in the Changed section

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

src/pyscipopt/expr.pxi

Corrects the Term class in scip.pyi to define __mul__ instead of __add__, updating the method signature to accept and return Term objects.

Joao-Dionisio · 2026-01-28T14:58:00Z

Can you please add a test for this change? Then we can merge, I think

Introduces test_mul to verify correct string representations of multiplied expressions involving variables and constants.

Replaces Term with CONST import from pyscipopt.scip and adds new assertions in test_mul to verify multiplication involving constants and variables. Removes redundant CONST definition.

…o expr/mul

src/pyscipopt/expr.pxi

Added an assertion to test that multiplying y by (x - x) yields the same zero term as (x - x) * y. This ensures correct handling of zero expressions in multiplication.

tests/test_expr.py

CHANGELOG.md

Documented performance enhancements for Expr * Expr and Term * Term operations, including use of C-level API and an O(n) algorithm. Also clarified method renaming from Term.__add__ to Term.__mul__.

Added a comment in the Term.__mul__ method to highlight that Term.vartuple must be sorted for correct merging. Suggests ensuring sorting in the Term constructor to avoid potential issues.

Updated the description of the Term * Term speedup to specify the use of an O(n) sort algorithm instead of Python's O(log(n)) sorted function.

Updated the changelog to fix the time complexity notation for the Term * Term sort algorithm from O(log(n)) to O(n log(n)).

…o expr/mul

src/pyscipopt/expr.pxi

CHANGELOG.md

Joao-Dionisio · 2026-01-30T08:52:10Z

Can you please run the performance experiments a bit more systematically? Maybe with multiple matrices and non-matrices, and show an average across instance size.

Zeroto521 · 2026-01-30T10:01:11Z

Can you please run the performance experiments a bit more systematically? Maybe with multiple matrices and non-matrices, and show an average across instance size.

Expr * Expr can't show the performance in different versions because we don't keep the old code. MatrixExpr performance could be tested because we use the upstream (numpy.ndarray) code.

Expr * Expr could use pytest-benchmark show the costing time.

Joao-Dionisio · 2026-01-30T13:39:34Z

No sorry, I meant in your local environment, not in the tests. I'm very close to merging, just want a final experiment that's more robust regarding the performance.

Corrected the indentation of the isinstance(other, Expr) block in the Expr class to ensure proper execution flow during multiplication operations.

Zeroto521 · 2026-02-02T02:35:04Z

This PR is 1.2x faster than master.
~~If the Expr has 0 coefficient, Expr * Expr will be much faster~~.

create 2 Expr which have 1,000 vars each
- master branch: 22.2626586000 seconds
- PR#1175: 18.5187626000 seconds
create 2 Expr which have 10,000 vars each
- master branch: 280.3718507000 seconds
- PR#1175: 240.1134093000 seconds

No sorry, I meant in your local environment, not in the tests. I'm very close to merging, just want a final experiment that's more robust regarding the performance.

Two normal Expr to multiply.

from timeit import timeit

from pyscipopt import Model, quickprod

m = Model()

n = 10_000
print(f"create 2 `Expr` which have {n:,} vars each")
x = quickprod(m.addMatrixVar(n).flat)
y = quickprod(m.addMatrixVar(n).flat)

number = 100_000
print(f"repeat {number:,} times")

cost = timeit(lambda: x * y, number=number)
print(f"XXX: {cost:.10f} seconds")

Conda Environment

# packages in environment at D:\Users\Zero\AppData\Local\miniforge3\envs\cy310:
#
# Name                            Version             Build                  Channel
bzip2                             1.0.8               h0ad9c76_8             conda-forge
ca-certificates                   2025.11.12          h4c7d964_0             conda-forge
certifi                           2025.11.12          pypi_0                 pypi
charset-normalizer                3.4.4               pypi_0                 pypi
colorama                          0.4.6               pyhd8ed1ab_1           conda-forge
cython                            3.2.3               py310h23e71ea_0        conda-forge
exceptiongroup                    1.3.1               pyhd8ed1ab_0           conda-forge
execnet                           2.1.2               pyhd8ed1ab_0           conda-forge
idna                              3.11                pypi_0                 pypi
iniconfig                         2.3.0               pyhd8ed1ab_0           conda-forge
libblas                           3.9.0               35_h5709861_mkl        conda-forge
libcblas                          3.9.0               35_h2a3cdd5_mkl        conda-forge
libexpat                          2.7.3               hac47afa_0             conda-forge
libffi                            3.5.2               h52bdfb6_0             conda-forge
libhwloc                          2.11.2              default_hc8275d1_1000  conda-forge
libiconv                          1.18                hc1393d2_2             conda-forge
liblapack                         3.9.0               35_hf9ab0e9_mkl        conda-forge
liblzma                           5.8.1               h2466b09_2             conda-forge
libpython                         0.2                 pypi_0                 pypi
libpython-static                  3.10.19             hac47afa_2_cpython     conda-forge
libsqlite                         3.51.1              hf5d6505_1             conda-forge
libxml2                           2.13.9              h741aa76_0             conda-forge
libzlib                           1.3.1               h2466b09_2             conda-forge
llvm-openmp                       21.1.8              h4fa8253_0             conda-forge
m2w64-binutils                    2.25.1              5                      conda-forge
m2w64-bzip2                       1.0.6               6                      conda-forge
m2w64-crt-git                     5.0.0.4636.2595836  2                      conda-forge
m2w64-gcc                         5.3.0               6                      conda-forge
m2w64-gcc-ada                     5.3.0               6                      conda-forge
m2w64-gcc-fortran                 5.3.0               6                      conda-forge
m2w64-gcc-libgfortran             5.3.0               6                      conda-forge
m2w64-gcc-libs                    5.3.0               7                      conda-forge
m2w64-gcc-libs-core               5.3.0               7                      conda-forge
m2w64-gcc-objc                    5.3.0               6                      conda-forge
m2w64-gmp                         6.1.0               2                      conda-forge
m2w64-headers-git                 5.0.0.4636.c0ad18a  2                      conda-forge
m2w64-isl                         0.16.1              2                      conda-forge
m2w64-libiconv                    1.14                6                      conda-forge
m2w64-libmangle-git               5.0.0.4509.2e5a9a2  2                      conda-forge
m2w64-libwinpthread-git           5.0.0.4634.697f757  2                      conda-forge
m2w64-make                        4.1.2351.a80a8b8    2                      conda-forge
m2w64-mpc                         1.0.3               3                      conda-forge
m2w64-mpfr                        3.1.4               4                      conda-forge
m2w64-pkg-config                  0.29.1              2                      conda-forge
m2w64-toolchain                   5.3.0               7                      conda-forge
m2w64-tools-git                   5.0.0.4592.90b8472  2                      conda-forge
m2w64-windows-default-manifest    6.4                 3                      conda-forge
m2w64-winpthreads-git             5.0.0.4634.697f757  2                      conda-forge
m2w64-zlib                        1.2.8               10                     conda-forge
mkl                               2024.2.2            h57928b3_16            conda-forge
msys2-conda-epoch                 20160418            1                      conda-forge
numpy                             2.2.6               py310h4987827_0        conda-forge
openssl                           3.6.0               h725018a_0             conda-forge
packaging                         25.0                pyh29332c3_1           conda-forge
pip                               25.3                pyh8b19718_0           conda-forge
pluggy                            1.6.0               pyhf9edf01_1           conda-forge
pthreads-win32                    2.9.1               h2466b09_4             conda-forge
pygments                          2.19.2              pyhd8ed1ab_0           conda-forge
pytest                            9.0.2               pyhcf101f3_0           conda-forge
pytest-xdist                      3.8.0               pyhd8ed1ab_0           conda-forge
python                            3.10.19             hc20f281_2_cpython     conda-forge
python_abi                        3.10                8_cp310                conda-forge
requests                          2.32.5              pypi_0                 pypi
setuptools                        80.9.0              pyhff2d567_0           conda-forge
tbb                               2021.13.0           h62715c5_1             conda-forge
tk                                8.6.13              h2c6b04d_3             conda-forge
tomli                             2.3.0               pyhcf101f3_0           conda-forge
typing_extensions                 4.15.0              pyhcf101f3_0           conda-forge
tzdata                            2025c               h8577fbf_0             conda-forge
ucrt                              10.0.26100.0        h57928b3_0             conda-forge
urllib3                           2.6.2               pypi_0                 pypi
vc                                14.3                h2b53caa_33            conda-forge
vc14_runtime                      14.44.35208         h818238b_33            conda-forge
vcomp14                           14.44.35208         h818238b_33            conda-forge
wheel                             0.45.1              pyhd8ed1ab_1           conda-forge

Do not skip terms with 0.0 coefficients when multiplying Expr objects: remove earlier zero-checks and compute product values inline in src/pyscipopt/expr.pxi. This causes zero-product terms to be retained in the resulting expression. Update tests (tests/test_expr.py) to expect the preserved zero-coefficient terms for cases like (x - x) * y and y * (x - x).

Zeroto521 added 4 commits January 24, 2026 15:36

Optimize Term multiplication in expr.pxi

b8e2249

Replaces the simple concatenation in Term.__mul__ with an efficient merge that maintains variable order based on pointer values. This improves performance and correctness when multiplying Term objects.

Update CHANGELOG to reorder quicksum optimization entry

28de39e

Moved the 'Speed up MatrixExpr.sum(axis=...) via quicksum' entry from the Added section to the Changed section for better categorization and clarity.

Update changelog with Expr multiplication speedup

8ec24a4

Added a new entry to the changelog noting the performance improvement for Expr * Expr operations.

Copilot AI review requested due to automatic review settings January 24, 2026 08:13

Copilot started reviewing on behalf of Zeroto521 January 24, 2026 08:13 View session

Zeroto521 commented Jan 24, 2026

View reviewed changes

src/pyscipopt/expr.pxi Show resolved Hide resolved

Zeroto521 commented Jan 24, 2026

View reviewed changes

src/pyscipopt/expr.pxi Show resolved Hide resolved

Copilot AI reviewed Jan 24, 2026

View reviewed changes

Zeroto521 commented Jan 24, 2026

View reviewed changes

src/pyscipopt/expr.pxi Show resolved Hide resolved

Fix Term class operator signature in type stub

fd06702

Corrects the Term class in scip.pyi to define __mul__ instead of __add__, updating the method signature to accept and return Term objects.

Zeroto521 mentioned this pull request Jan 24, 2026

Feature: Merge Expr and GenExpr #1074

Open

Zeroto521 added 4 commits January 29, 2026 09:55

Add tests for expression multiplication

faccb2c

Introduces test_mul to verify correct string representations of multiplied expressions involving variables and constants.

Merge branch 'master' into expr/mul

4271d22

Update tests for Expr multiplication behavior

27b75c1

Replaces Term with CONST import from pyscipopt.scip and adds new assertions in test_mul to verify multiplication involving constants and variables. Removes redundant CONST definition.

Merge branch 'expr/mul' of https://github.com/Zeroto521/PySCIPOpt int…

7c4d29e

…o expr/mul

Zeroto521 commented Jan 29, 2026

View reviewed changes

src/pyscipopt/expr.pxi Outdated Show resolved Hide resolved

Add test for commutativity in multiplication with zero

3e6376d

Added an assertion to test that multiplying y by (x - x) yields the same zero term as (x - x) * y. This ensures correct handling of zero expressions in multiplication.

Zeroto521 commented Jan 29, 2026

View reviewed changes

tests/test_expr.py Outdated Show resolved Hide resolved

Zeroto521 requested a review from Joao-Dionisio January 29, 2026 02:31

Joao-Dionisio reviewed Jan 29, 2026

View reviewed changes

CHANGELOG.md Outdated Show resolved Hide resolved

Zeroto521 added 6 commits January 30, 2026 10:05

Update changelog for Expr and Term multiplication improvements

923a5f6

Documented performance enhancements for Expr * Expr and Term * Term operations, including use of C-level API and an O(n) algorithm. Also clarified method renaming from Term.__add__ to Term.__mul__.

Add note about sorted vartuple requirement in Term

b4b6fbf

Added a comment in the Term.__mul__ method to highlight that Term.vartuple must be sorted for correct merging. Suggests ensuring sorting in the Term constructor to avoid potential issues.

Clarify algorithm complexity in changelog

458079b

Updated the description of the Term * Term speedup to specify the use of an O(n) sort algorithm instead of Python's O(log(n)) sorted function.

Merge branch 'master' into expr/mul

39d547d

Correct complexity notation in changelog

b646ed9

Updated the changelog to fix the time complexity notation for the Term * Term sort algorithm from O(log(n)) to O(n log(n)).

Merge branch 'expr/mul' of https://github.com/Zeroto521/PySCIPOpt int…

afede94

…o expr/mul

Joao-Dionisio reviewed Jan 30, 2026

View reviewed changes

src/pyscipopt/expr.pxi Outdated Show resolved Hide resolved

Apply suggestion from @Joao-Dionisio

1685fd2

Joao-Dionisio reviewed Jan 30, 2026

View reviewed changes

CHANGELOG.md Outdated Show resolved Hide resolved

Apply suggestion from @Joao-Dionisio

17c00c5

Zeroto521 added 2 commits January 31, 2026 11:26

Merge branch 'master' into expr/mul

5e9faa1

Fix indentation in Expr multiplication logic

347f10f

Corrected the indentation of the isinstance(other, Expr) block in the Expr class to ensure proper execution flow during multiplication operations.

Zeroto521 added 2 commits February 2, 2026 18:35

Merge branch 'master' into expr/mul

206027e

Joao-Dionisio self-requested a review February 2, 2026 10:52

Joao-Dionisio approved these changes Feb 2, 2026

View reviewed changes

Joao-Dionisio merged commit a03b00e into scipopt:master Feb 2, 2026
3 checks passed

Zeroto521 deleted the expr/mul branch February 2, 2026 10:54

Provide feedback

Saved searches

Use saved searches to filter your results more quickly

Speed up `Expr * Expr`#1175

Speed up `Expr * Expr`#1175
Joao-Dionisio merged 22 commits intoscipopt:masterfrom
Zeroto521:expr/mul

Zeroto521 commented Jan 24, 2026

Uh oh!

Uh oh!

Uh oh!

Copilot AI left a comment

Uh oh!

Uh oh!

Joao-Dionisio commented Jan 28, 2026

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Joao-Dionisio commented Jan 30, 2026

Uh oh!

Zeroto521 commented Jan 30, 2026

Uh oh!

Joao-Dionisio commented Jan 30, 2026

Uh oh!

Zeroto521 commented Feb 2, 2026 •

edited

Loading

Uh oh!

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

2 participants

Conversation

Zeroto521 commented Jan 24, 2026

Uh oh!

Uh oh!

Uh oh!

Copilot AI left a comment

Choose a reason for hiding this comment

Pull request overview

Reviewed changes

Uh oh!

Uh oh!

Joao-Dionisio commented Jan 28, 2026

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Uh oh!

Joao-Dionisio commented Jan 30, 2026

Uh oh!

Zeroto521 commented Jan 30, 2026

Uh oh!

Joao-Dionisio commented Jan 30, 2026

Uh oh!

Zeroto521 commented Feb 2, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

Uh oh!

Uh oh!

Uh oh!

Reviewers

Assignees

Labels

Projects

Milestone

Development

Uh oh!

2 participants

Zeroto521 commented Feb 2, 2026 •

edited

Loading