VPMR C++ Implementation

Call For Help

more performant parallel SVD algorithm: eigen only provides sequential SVD
alternative integration: currently only Gauss-Legendre quadrature is available

What Is This?

This is a C++ implementation of the VPMR algorithm to compute the approximation of arbitrary smooth kernel. A Python package is also provided.

Check the reference paper 10.1007/s10915-022-01999-1 and the original MATLAB implementation for more details.

In short, the algorithm tries to find a summation of exponentials to approximate a given kernel function. In mathematical terms, it looks for a set of $m_j$ and $s_j$ such that

$$ \max_{t\in{}I}\left|g(t)-\sum_jm_j\exp(-s_jt)\right|<\epsilon. $$

In the above, $g(t)$ is the given kernel function and $\epsilon$ is the prescribed tolerance.

Dependency

The following libraries are required:

gmp for multiple precision arithmetic
mpfr for multiple-precision floating-point computations
tbb for parallel computing

The following libraries are included:

mpreal mpreal type C++ wrapper, included
Eigen for matrix decomposition, included
exprtk for expression parsing, included
exprtk-custom-types for mpreal support, included

How To

If the application needs to be compiled on your machine (build the binary from source, python wheels are not available, etc.), you need to install the compiler and three libraries.

On RPM-based Linux distributions (using dnf), you need to sudo dnf install -y gcc-c++ tbb-devel mpfr-devel gmp-devel.
On DEB-based Linux distributions (using apt), you need to sudo apt install -y g++ libtbb-dev libmpfr-dev libgmp-dev.
On macOS, you need to brew install gcc tbb mpfr gmp.

If the binary is available (run the pre-compiled binary, python wheels are available, etc.), you only need the runtimes of three libraries. You can find the exact names on pkgs.org by searching tbb, gmp and mpfr.

Docker

You can simply pull the image using the following command.

docker pull tlcfem/vpmr
# or using GitHub Container Registry
docker pull ghcr.io/tlcfem/vmpr

Just use it as you would normally do with any other docker images. For example,

docker run tlcfem/vpmr -n 30

To build the image locally, use the provided Dockerfile.

wget -q https://raw.githubusercontent.com/TLCFEM/vpmr/master/https://raw.githubusercontent.com/TLCFEM/vpmr/master/resource/Dockerfile
docker build -t vpmr -f Dockerfile .

Python Package

On most platforms (Linux and macOS), wheels are available, simply install the package with pip.

pip install pyvpmr

If the corresponding wheel is not available, the package will be compiled, which takes a few minutes. The execution of the algorithm always requires available gmp, mpfr and tbb libraries.

Jumpstart

import numpy as np

from pyvpmr import vpmr, plot


def kernel(x):
    return np.exp(-x ** 2 / 4)


if __name__ == '__main__':
    m, s = vpmr(n=50, k='exp(-t^2/4)')
    plot(m, s, kernel)

Standalone Binary

All available options are:

Usage: vpmr [options]

Options:

    -n, --max-terms             <int>     number of terms (default: 10)
    -c, --max-exponent          <int>     maximum exponent (default: 4)
    -d, --precision-bits        <int>     number of precision bits (default: 512)
    -q, --quadrature-order      <int>     quadrature order (default: 500)
    -m, --precision-multiplier  <float>   precision multiplier (default: 1.05)
    -e, --tolerance             <float>   tolerance (default: 1E-8)
    -k, --kernel                <string>  file name of kernel function (default uses: exp(-t^2/4))
    -s, --singular-values                 print singular values
    -w, --weights                         print weights
    -h, --help                            print this help message

The minimum required precision can be estimated by the parameter $n$. The algorithm involves the computation of $C(4n,k)$ and $2^{4n}$. The number of precision bits shall be at least $4n+\log_2C(4n,2n)$. In the implementation, this number will be further multiplied by the parameter $m$.

Example

The default kernel is exp(-t^2/4). One can run the application with the following command:

./vpmr -n 30

The output is:

Using the following parameters:
       terms = 30.
    exponent = 4.
   precision = 355.
 quad. order = 500.
  multiplier = 1.0500e+00.
   tolerance = 1.0000e-08.
      kernel = exp(-t*t/4).

[1/6] Computing weights... [60/60]
[2/6] Solving Lyapunov equation...
[3/6] Solving SVD...
[4/6] Transforming (P=+11)...
[5/6] Solving eigen decomposition...
[6/6] Done with 11 final terms.

M = 
+2.3132817597168739e+01-2.8586221856566439e-105j
-1.1577276470339980e+01+1.2090460362812458e+01j
-1.1577276470339980e+01-1.2090460362812458e+01j
-1.5850953326980194e-01+6.1693993683365882e+00j
-1.5850953326980194e-01-6.1693993683365882e+00j
+7.3529603986874903e-01+7.5750538019498470e-01j
+7.3529603986874903e-01-7.5750538019498470e-01j
-6.6807938653881516e-02+1.0261144687127986e-02j
-6.6807938653881516e-02-1.0261144687127986e-02j
+8.8910386408859823e-04+2.2917263647765330e-04j
+8.8910386408859823e-04-2.2917263647765330e-04j
S = 
+2.0729005744773779e+00-0.0000000000000000e+00j
+2.0678104641951456e+00+5.6013828454286663e-01j
+2.0678104641951456e+00-5.6013828454286663e-01j
+2.0525989324387557e+00-1.1331825475504296e+00j
+2.0525989324387557e+00+1.1331825475504296e+00j
+2.0268330855090184e+00+1.7349515936847757e+00j
+2.0268330855090184e+00-1.7349515936847757e+00j
+1.9884211467751960e+00-2.3916428978210722e+00j
+1.9884211467751960e+00+2.3916428978210722e+00j
+1.9308660033206897e+00-3.1676394473339076e+00j
+1.9308660033206897e+00+3.1676394473339076e+00j

Running time: 1987 ms.

exp(-t^2/4)

Arbitrary Kernel

For arbitrary kernel, it is necessary to provide the kernel function in a text file. The file should contain the kernel expressed as a function of variable t.

The exprtk is used to parse the expression and compute the value. The provided kernel function must be valid and supported by exprtk. Check the documentation regarding how to write a valid expression.

For example, to compute the approximation of exp(-t^2/10), one can create a file kernel.txt with the following content:

exp(-t*t/10)

In the following, the kernel function is echoed to a file and then used as an input to the application.

echo "exp(-t*t/10)" > kernel.txt
 ./vpmr -n 60 -k kernel.txt -e 1e-12

exp(-t^2/10)

Performance

The majority of the algorithm is parallelised to extract the maximum performance. The following is a typical performance profile on a i7-10750H platform using the ./vpmr -n 80.

profiling

Compilation

Windows

Use the following instructions based on MSYS2, or follow the Linux instructions below with WSL.

# install necessary packages
pacman -S git mingw-w64-x86_64-cmake mingw-w64-x86_64-tbb mingw-w64-x86_64-gcc mingw-w64-x86_64-ninja mingw-w64-x86_64-gmp mingw-w64-x86_64-mpfr
# clone the repository
git clone --recurse-submodules --depth 1 https://github.com/TLCFEM/vpmr.git
cd vpmr
# apply patch to enable parallel evaluation of some loops in SVD
cd eigen && git apply --ignore-space-change --ignore-whitespace ../parallelize.patch && cd ..
# configure and compile
cmake -G Ninja -DCMAKE_BUILD_TYPE=Release .
ninja

Linux

The following is based on Fedora.

sudo dnf install gcc g++ cmake git tbb-devel mpfr-devel gmp-devel -y
git clone --recurse-submodules --depth 1 https://github.com/TLCFEM/vpmr.git
cd vpmr
cd eigen && git apply --ignore-space-change --ignore-whitespace ../parallelize.patch && cd ..
cmake -DCMAKE_BUILD_TYPE=Release .
make

Metadata

Release files for pyvpmr 0

For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.

Built distributions (wheels)

Table of built distributions (wheels) for pyvpmr 0
File	Interpreter	ABI	Platform	Reset
pyvpmr-0-cp314-cp314t-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.14	CPython 3.14 free-threading	macOS 15.0+ x86-64	Details
pyvpmr-0-cp314-cp314t-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.14	CPython 3.14 free-threading	macOS 15.0+ ARM64	Details
pyvpmr-0-cp314-cp314t-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.14	CPython 3.14 free-threading	macOS 14.0+ x86-64	Details
pyvpmr-0-cp314-cp314t-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.14	CPython 3.14 free-threading	macOS 14.0+ ARM64	Details
pyvpmr-0-cp314-cp314-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.14	CPython 3.14	macOS 15.0+ x86-64	Details
pyvpmr-0-cp314-cp314-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.14	CPython 3.14	macOS 15.0+ ARM64	Details
pyvpmr-0-cp314-cp314-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.14	CPython 3.14	macOS 14.0+ x86-64	Details
pyvpmr-0-cp314-cp314-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.14	CPython 3.14	macOS 14.0+ ARM64	Details
pyvpmr-0-cp313-cp313-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.13	CPython 3.13	macOS 15.0+ x86-64	Details
pyvpmr-0-cp313-cp313-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.13	CPython 3.13	macOS 15.0+ ARM64	Details
pyvpmr-0-cp313-cp313-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.13	CPython 3.13	macOS 14.0+ x86-64	Details
pyvpmr-0-cp313-cp313-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.13	CPython 3.13	macOS 14.0+ ARM64	Details
pyvpmr-0-cp312-cp312-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.12	CPython 3.12	macOS 15.0+ x86-64	Details
pyvpmr-0-cp312-cp312-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.12	CPython 3.12	macOS 15.0+ ARM64	Details
pyvpmr-0-cp312-cp312-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.12	CPython 3.12	macOS 14.0+ x86-64	Details
pyvpmr-0-cp312-cp312-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.12	CPython 3.12	macOS 14.0+ ARM64	Details
pyvpmr-0-cp311-cp311-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.11	CPython 3.11	macOS 15.0+ x86-64	Details
pyvpmr-0-cp311-cp311-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.11	CPython 3.11	macOS 15.0+ ARM64	Details
pyvpmr-0-cp311-cp311-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.11	CPython 3.11	macOS 14.0+ x86-64	Details
pyvpmr-0-cp311-cp311-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.11	CPython 3.11	macOS 14.0+ ARM64	Details
pyvpmr-0-cp310-cp310-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.10	CPython 3.10	macOS 15.0+ x86-64	Details
pyvpmr-0-cp310-cp310-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.10	CPython 3.10	macOS 15.0+ ARM64	Details
pyvpmr-0-cp310-cp310-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.10	CPython 3.10	macOS 14.0+ x86-64	Details
pyvpmr-0-cp310-cp310-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.10	CPython 3.10	macOS 14.0+ ARM64	Details
pyvpmr-0-cp39-cp39-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.9	CPython 3.9	macOS 15.0+ x86-64	Details
pyvpmr-0-cp39-cp39-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.9	CPython 3.9	macOS 15.0+ ARM64	Details
pyvpmr-0-cp39-cp39-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.9	CPython 3.9	macOS 14.0+ x86-64	Details
pyvpmr-0-cp39-cp39-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.9	CPython 3.9	macOS 14.0+ ARM64	Details
pyvpmr-0-cp38-cp38-macosx_15_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.8	CPython 3.8	macOS 15.0+ x86-64	Details
pyvpmr-0-cp38-cp38-macosx_15_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.8	CPython 3.8	macOS 15.0+ ARM64	Details
pyvpmr-0-cp38-cp38-macosx_14_0_x86_64.whl 4.0 MB Mar 22, 2026	CPython 3.8	CPython 3.8	macOS 14.0+ x86-64	Details
pyvpmr-0-cp38-cp38-macosx_14_0_arm64.whl 3.7 MB Mar 22, 2026	CPython 3.8	CPython 3.8	macOS 14.0+ ARM64	Details

Total release size: 122.8 MB

Release files / pyvpmr-0-cp314-cp314t-macosx_15_0_x86_64.whl

Download URL	pyvpmr-0-cp314-cp314t-macosx_15_0_x86_64.whl
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Release files / pyvpmr-0-cp314-cp314t-macosx_15_0_arm64.whl

Download URL	pyvpmr-0-cp314-cp314t-macosx_15_0_arm64.whl
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Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Release files / pyvpmr-0-cp314-cp314t-macosx_14_0_x86_64.whl

Download URL	pyvpmr-0-cp314-cp314t-macosx_14_0_x86_64.whl
Size	4.0 MB
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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing configuration: github.com/TLCFEM/vpmr/blob/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68/.github/workflows/wheels.yml
Publishing logs: github.com/TLCFEM/vpmr/actions/runs/23393963006/attempts/1

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Release files / pyvpmr-0-cp314-cp314t-macosx_14_0_arm64.whl

Download URL	pyvpmr-0-cp314-cp314t-macosx_14_0_arm64.whl
Size	3.7 MB
Tags	CPython 3.14 CPython 3.14 free-threading macOS 14.0+ ARM64
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Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing configuration: github.com/TLCFEM/vpmr/blob/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68/.github/workflows/wheels.yml
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Release files / pyvpmr-0-cp314-cp314-macosx_15_0_x86_64.whl

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Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Release files / pyvpmr-0-cp314-cp314-macosx_15_0_arm64.whl

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Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Identity

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Release files / pyvpmr-0-cp310-cp310-macosx_14_0_x86_64.whl

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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Release files / pyvpmr-0-cp310-cp310-macosx_14_0_arm64.whl

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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

Workflow

Publishing configuration: github.com/TLCFEM/vpmr/blob/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68/.github/workflows/wheels.yml
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Artifact

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Release files / pyvpmr-0-cp39-cp39-macosx_15_0_x86_64.whl

Download URL	pyvpmr-0-cp39-cp39-macosx_15_0_x86_64.whl
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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Release files / pyvpmr-0-cp39-cp39-macosx_15_0_arm64.whl

Download URL	pyvpmr-0-cp39-cp39-macosx_15_0_arm64.whl
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Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Artifact

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Release files / pyvpmr-0-cp39-cp39-macosx_14_0_x86_64.whl

Download URL	pyvpmr-0-cp39-cp39-macosx_14_0_x86_64.whl
Size	4.0 MB
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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing logs: github.com/TLCFEM/vpmr/actions/runs/23393963006/attempts/1

Artifact

Subject: pyvpmr-0-cp39-cp39-macosx_14_0_x86_64.whl
SHA-256 checksum: 0d7eca993049a0bfbbee2c3f897036ede32d037af382eca578213fc1dcad6096 Verifying attestations

Release files / pyvpmr-0-cp39-cp39-macosx_14_0_arm64.whl

Download URL	pyvpmr-0-cp39-cp39-macosx_14_0_arm64.whl
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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Release files / pyvpmr-0-cp38-cp38-macosx_15_0_x86_64.whl

Download URL	pyvpmr-0-cp38-cp38-macosx_15_0_x86_64.whl
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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Release files / pyvpmr-0-cp38-cp38-macosx_15_0_arm64.whl

Download URL	pyvpmr-0-cp38-cp38-macosx_15_0_arm64.whl
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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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SHA-256 checksum: 9175832e27299151b856f4cf75d222806b782739159d36f8b5dbe0e9fba956f4 Verifying attestations

Release files / pyvpmr-0-cp38-cp38-macosx_14_0_x86_64.whl

Download URL	pyvpmr-0-cp38-cp38-macosx_14_0_x86_64.whl
Size	4.0 MB
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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

Workflow

Publishing configuration: github.com/TLCFEM/vpmr/blob/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68/.github/workflows/wheels.yml
Publishing logs: github.com/TLCFEM/vpmr/actions/runs/23393963006/attempts/1

Artifact

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SHA-256 checksum: 939686d1f768723d7402323937c4c3e6d7026fbb975618ef28ec96bd8350eab9 Verifying attestations

Release files / pyvpmr-0-cp38-cp38-macosx_14_0_arm64.whl

Download URL	pyvpmr-0-cp38-cp38-macosx_14_0_arm64.whl
Size	3.7 MB
Tags	CPython 3.8 macOS 14.0+ ARM64
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Upload date	Mar 22, 2026
Uploaded using Trusted Publishing? What is trusted publishing?	Yes
Uploaded via	`twine/6.1.0 CPython/3.13.7`

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Identity

Publishing platform: GitHub Actions
Publishing repository: github.com/TLCFEM/vpmr
Publishing commit: github.com/TLCFEM/vpmr/tree/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68

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Publishing configuration: github.com/TLCFEM/vpmr/blob/1ed40d5cedacb4d27f8fb15819b7a8aa9c8b9c68/.github/workflows/wheels.yml
Publishing logs: github.com/TLCFEM/vpmr/actions/runs/23393963006/attempts/1

Artifact

Subject: pyvpmr-0-cp38-cp38-macosx_14_0_arm64.whl
SHA-256 checksum: 29b38fb9d6614e2317347808d961d17b48f3b99990ff79f9205770b28b377f20 Verifying attestations

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pyvpmr 0

VPMR C++ Implementation

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Release files / pyvpmr-0-cp314-cp314t-macosx_15_0_x86_64.whl

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Release files / pyvpmr-0-cp314-cp314t-macosx_15_0_arm64.whl

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Release files / pyvpmr-0-cp314-cp314t-macosx_14_0_x86_64.whl

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Release files / pyvpmr-0-cp314-cp314t-macosx_14_0_arm64.whl

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Release files / pyvpmr-0-cp314-cp314-macosx_15_0_x86_64.whl

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Release files / pyvpmr-0-cp314-cp314-macosx_15_0_arm64.whl

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Release files / pyvpmr-0-cp314-cp314-macosx_14_0_x86_64.whl

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Release files / pyvpmr-0-cp314-cp314-macosx_14_0_arm64.whl