statsmodels.stats.correlation_tools.corr_nearest¶
-
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.
- Parameters
- corr
ndarray
, (k
,k
) initial correlation matrix
- threshold
float
clipping threshold for smallest eigenvalue, see Notes
- n_fact
int
orfloat
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
- Returns
- corr_new
ndarray
, (optional
) corrected correlation matrix
- corr_new
See also
Notes
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.