statsmodels.stats.correlation_tools.corr_nearest(corr, threshold=1e-15, n_fact=100)[source]

Find the nearest correlation matrix that is positive semi-definite.

The function iteratively adjust the correlation matrix by clipping the eigenvalues of a difference matrix. The diagonal elements are set to one.

corrndarray, (k, k)

initial correlation matrix


clipping threshold for smallest eigenvalue, see Notes

n_factint or float

factor to determine the maximum number of iterations. The maximum number of iterations is the integer part of the number of columns in the correlation matrix times n_fact.

corr_newndarray, (optional)

corrected correlation matrix


The smallest eigenvalue of the corrected correlation matrix is approximately equal to the threshold. If the threshold=0, then the smallest eigenvalue of the correlation matrix might be negative, but zero within a numerical error, for example in the range of -1e-16.

Assumes input correlation matrix is symmetric.

Stops after the first step if correlation matrix is already positive semi-definite or positive definite, so that smallest eigenvalue is above threshold. In this case, the returned array is not the original, but is equal to it within numerical precision.

Last update: May 14, 2024