M/Ph:dZddlZgdZd dZdZdZ d d ZdS) z* Linear Algebra solvers and other helpers N) logdet_symmstationary_solvetransf_constraints matrix_sqrtFcddlm}|r,tj||jkst d||d\}}dtjtj| zS)z Return log(det(m)) asserting positive definiteness of m. Parameters ---------- m : array_like 2d array that is positive-definite (and symmetric) Returns ------- logdet : float The log-determinant of m. rlinalgzm is not symmetric.T)lower) scipyr npallT ValueError cho_factorsumlogdiagonal)m check_symmr c_s X/var/www/html/test/jupyter/venv/lib/python3.11/site-packages/statsmodels/tools/linalg.pyrr s4va13h 4233 3   Qd  + +DAq RVBF1::<<(( ) ) ))c 0|dd}|j}|jdkr |dddf}|ddddf}tdt|D].}|d|ddd}||ddftj||z dtj||dddz z }|tj|ddd|z }tj||dddffd}|t|dz krn{||} | tj||z dtj||dddz z }|||dddzz }tj|tj|f}0|dkr |dddf}|S)aH Solve a linear system for a Toeplitz correlation matrix. A Toeplitz correlation matrix represents the covariance of a stationary series with unit variance. Parameters ---------- r : array_like A vector describing the coefficient matrix. r[0] is the first band next to the diagonal, r[1] is the second band, etc. b : array_like The right-hand side for which we are solving, i.e. we solve Tx = b and return b, where T is the Toeplitz coefficient matrix. Returns ------- The solution to the linear system. rN)axis)ndimrangelenr dotouter concatenater_) rbdbdimxjrfazrns rrr s* 1Q3B &Cv{{ aaagJ !A#qqq& A 1c!ff   + + qsVDDbD\ q!!!tWrvb!}} $RVB44R4-A-A)A B DDbD1%% % NAqqqqz? 3 3 3 A ?? E qT "&R.. QBtttH)=)=%= > 2ddd8O ^QaM * * axx aaadG Hrcddlm}|jd}|t j|\}}|dd|df}|S)ause QR to get transformation matrix to impose constraint Parameters ---------- constraints : ndarray, 2-D restriction matrix with one constraints in rows Returns ------- transf : ndarray transformation matrix to reparameterize so that constraint is imposed Notes ----- This is currently and internal helper function for GAM. API not stable and will most likely change. The code for this function was taken from patsy spline handling, and corresponds to the reparameterization used by Wood in R's mgcv package. See Also -------- statsmodels.base._constraints.TransformRestriction : class to impose constraints by reparameterization used by `_fit_constrained`. rrN)r r shapeqrr transpose) constraintsr rqrtransfs rrrPs\8!A 99R\+.. / /DAq qqq!""uXF MrV瞯rMs   ****,- - - `!!!H;@: : : : : : r