U f»{jÊ ã@sLddlmZddlZddlmZmZmZmZed dd„ƒZ edd d „ƒZ dS)é)ÚsqrtNé)Úcheck_random_stateÚloggerÚverboseÚfill_docéèçü©ñÒMbP?cCs¦|jd}t|ƒ}| ||¡}|tj |d¡}t |j|¡}t ||j¡} tj} t |ƒD]F} t t ||¡| ¡} tj | d¡} t | | ƒ|kr”q¢| | }| } qZ| S)a–Find the largest singular value for the matrix kron(C.T, A). It uses power iterations. Parameters ---------- A : array An array C : array An array max_iter : int Maximum number of iterations %(random_state)s Returns ------- L : float largest singular value Notes ----- http://en.wikipedia.org/wiki/Power_iteration rZfro) ÚshaperZrandnÚnpÚlinalgÚnormÚdotÚTÚinfÚrangeÚabs)ÚAÚCÚmax_iterÚtolZ random_stateZAS_sizeÚrngÚBZATAZCCTZL0Ú_ÚYÚL©rú`/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mne/inverse_sparse/mxne_debiasing.pyÚpower_iteration_kron s   rçíµ ÷Æ°>écCsb|jd}dt||ƒ}t |¡} t |¡} d} t|ƒD]ü} | } |t || |¡}| tjt |j|¡|dd|} |dkr¬tj|   d|¡dd} t  | |dg¡j  ¡} t  | d¡} | }ddt dd| d ƒ} |  d ¡|d| }| || | } tj | | tj¡}||kr8t d | ||f¡q^q8tj | | tj¡}t d |||f¡| S) a‹Compute scaling to correct amplitude bias. It solves the following optimization problem using FISTA: min 1/2 * (|| M - GDX ||fro)^2 s.t. D >= 1 and D is a diagonal matrix Reference for the FISTA algorithm: Amir Beck and Marc Teboulle A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, SIAM J. Imaging Sci., 2(1), 183-202. (20 pages) http://epubs.siam.org/doi/abs/10.1137/080716542 Parameters ---------- M : array measurement data. G : array leadfield matrix. X : array reconstructed time courses with amplitude bias. max_iter : int Maximum number of iterations. tol : float The tolerance on convergence. n_orient : int The number of orientations (1 for fixed and 3 otherwise). %(verbose)s Returns ------- D : array Debiasing weights. rgš™™™™™ñ?gð?r )Zaxiséÿÿÿÿgà?g@rgz?Debiasing converged after %d iterations max(|D - D0| = %e < %e)zHDebiasing did not converge after %d iterations! max(|D - D0| = %e >= %e))r rr ZonesrrÚsumrZmeanZreshapeZtileZravelÚmaximumrÚfillr r rrÚinfo)ÚMÚGÚXrrZn_orientrÚ n_sourcesZlipschitz_constantÚDrÚtÚiZD0ÚRÚt0ÚdtZDdiffrrrÚ compute_bias8s:$    $   ÿÿr0)rr r)rrr N) ÚmathrÚnumpyr Úutilsrrrrrr0rrrrÚs  +