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transform an ill-conditioned quadratic matrix to a positive semidefinite matrix

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Transform an ill-conditioned quadratic matrix into a positive semi-definite matrix.


The scipy-psdm git repo is available as PyPi package

pip install scipy-psdm


Lurie-Goldberg Algorithm to transform an ill-conditioned quadratic matrix into a positive semi-definite matrix.

import scipy_psdm as psdm
import numpy as np

# A matrix with subjectively set correlations
mat = [[ 1.   , -0.948,  0.099, -0.129],
       [-0.948,  1.   , -0.591,  0.239],
       [ 0.099, -0.591,  1.   ,  0.058],
       [-0.129,  0.239,  0.058,  1.   ]]
mat = np.array(mat)

# Convert to a positive semi-definite matrix
rho = psdm.approximate_correlation_matrix(mat)

Generate correlated random numbers

import scipy_psdm as psdm
X, rho = psdm.randcorr(n_obs=100, n_vars=5, random_state=42)

# compare
import numpy as np
print(np.corrcoef(X, rowvar=False).round(3))

Check the examples folder for notebooks.


Install a virtual environment

python3 -m venv .venv
source .venv/bin/activate
pip3 install -r requirements.txt
pip3 install -r requirements-dev.txt
pip3 install -r requirements-demo.txt

(If your git repo is stored in a folder with whitespaces, then don’t use the subfolder .venv. Use an absolute path without whitespaces.)

Python commands

  • Start virtual env: source .venv/bin/activate

  • Jupyter for the examples: jupyter lab

  • Check syntax: flake8 --ignore=F401 --exclude=$(grep -v '^#' .gitignore | xargs | sed -e 's/ /,/g')

  • Run Unit Tests: pytest -v


pandoc --from markdown --to rst -s -o README.rst
python sdist
twine upload -r pypi dist/*

Clean up

find . -type f -name "*.pyc" | xargs rm
find . -type d -name "__pycache__" | xargs rm -r
rm -r .pytest_cache
rm -r .venv


Please open an issue for support.


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