U f{j @sddlZddlmZddlZddlmZddlmZm Z m Z m Z m Z m Z mZddlmZmZmZmZeddd Zd d ZdHd dZdIddZddZddZe dJddZe dKddZddZe dLd$d%Ze dMd&d'Ze dNd)d*Z d+d,Z!d-d.Z"Gd/d0d0e#Z$Gd1d2d2e#Z%dOd3d4Z&d5d6Z'dPd8d9Z(dQd:d;Z)dRdd?Z+e dTd@dAZ,e dUdDdEZ-e dVdFdGZ.dS)WN)sqrt) compute_bias)loggerverbose sum_squaredwarn_get_blas_funcs_validate_type _check_option) stft_norm1 stft_norm2stftistftcCs ttjdS)NZgemm)r npfloat64rr\/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mne/inverse_sparse/mxne_optim.py _get_dgemmsrcCs.|jd|}tjt|d||dddS)z+Compute squared L2 norms of groups inplace.rrrZaxis)shapersumpowerreshape)An_orient n_positionsrrr groups_norm2srTcCs.|jdkrdS|r|}ttt||S)z L2-inf norm.r)sizecopyrrmaxrrrr"rrr norm_l2infs  r%cCs0|jdkrdS|r|}ttt||S)z L21 norm.rr )r!r"rrrrr$rrrnorm_l21%s  r&c CsRt|dd|f|}||}t||dd}t|} d| ||} | || |fS)a,Primal objective for the mixed-norm inverse problem. See :footcite:`GramfortEtAl2012`. Parameters ---------- M : array, shape (n_sensors, n_times) The data. G : array, shape (n_sensors, n_active) The gain matrix a.k.a. lead field. X : array, shape (n_active, n_times) Sources. active_set : array of bool, shape (n_sources,) Mask of active sources. alpha : float The regularization parameter. n_orient : int Number of dipoles per locations (typically 1 or 3). Returns ------- p_obj : float Primal objective. R : array, shape (n_sensors, n_times) Current residual (M - G * X). nR2 : float Data-fitting term. GX : array, shape (n_sensors, n_times) Forward prediction. NTr"?)rdotr&r) MGX active_setalpharGXRZpenaltynR2p_objrrr _primal_l21.s r3cCs~t||||||\}}}} tt|j||dd} || } t| d} | d| d|| t|| } || } | || |fS)aPDuality gap for the mixed norm inverse problem. See :footcite:`GramfortEtAl2012`. Parameters ---------- M : array, shape (n_sensors, n_times) The data. G : array, shape (n_sensors, n_active) The gain matrix a.k.a. lead field. X : array, shape (n_active, n_times) Sources. active_set : array of bool, shape (n_sources, ) Mask of active sources. alpha : float The regularization parameter. n_orient : int Number of dipoles per locations (typically 1 or 3). Returns ------- gap : float Dual gap. p_obj : float Primal objective. d_obj : float Dual objective. gap = p_obj - d_obj. R : array, shape (n_sensors, n_times) Current residual (M - G * X). References ---------- .. footbibilography:: Fr'?r(r)r3r%rr)Tminr)r*r+r,r-r.rr2r0r1r/ dual_normscalingd_objgaprrrdgap_l21Us# &r;':0yE> c Csddlm} |j|jkr,|jd|jdks0t| |t||t|d|dd} |dk rd|j| _nt |jd|jdfj| _| ||| jj} t j | dd} | | } t ||| | ||\}}}}| | |fS) z2Solve L21 inverse problem with coordinate descent.rMultiTaskLassoFT)r.tolZ fit_interceptZmax_iterZ warm_startNrr)sklearn.linear_modelr@ndimrAssertionErrorlenrr5Zcoef_rzerosfitanyr;)r*r+r.lipschitz_constantmaxitrArinitr dgap_freqr@Zclfr,r-r:r2r9_rrr_mixed_norm_solver_cds  $  rNc * Cs|j\} } |j\} }||}|dkrzIteration %d: LinAlg Errorr) rrrFr"r)infboolemptyasfortranarrayrRrrDr5flags f_contiguousrangesliceappendascontiguousarray_bcdr;r#rdebugrravellinalgZsvdrZkrononesr3)*r*r+r.rIrJrArrKrrLZ use_accelKrMn_times n_sourcesrr,r0E highest_d_objr-alpha_lcZlast_K_XU one_ovr_lc list_G_j_cjidxir2r9r:kCuszcZX_accZ_grp_norm2_accZactive_set_accZ p_obj_accrrr_mixed_norm_solver_bcds            $        ruc Cs.tj|d|ddfdd}t} t|D]\} } t| || d|} |dd| f} || }| || d|j| |jdd|dd k}|r| d d |j| j|jdd||7}tt|}||| kr|dd || <q,t d || |d}||9}| d d |j| j|jdd||dd<d|| <q,dS) a^Implement one full pass of BCD. BCD stands for Block Coordinate Descent. This function make use of scipy.linalg.get_blas_funcs to speed reasons. Parameters ---------- G : array, shape (n_sensors, n_active) The gain matrix a.k.a. lead field. X : array, shape (n_sources, n_times) Sources, modified in place. R : array, shape (n_sensors, n_times) The residuals: R = M - G @ X, modified in place. active_set : array of bool, shape (n_sources, ) Mask of active sources, modified in place. one_ovr_lc : array, shape (n_positions, ) One over the lipschitz constants. n_orient : int Number of dipoles per positions (typically 1 or 3). n_positions : int Number of source positions. alpha_lc: array, shape (n_positions, ) alpha * (Lipschitz constants). Nrporderrr T)r.betaabrtZ overwrite_c)rrrr4F) r zeros_liker enumerater[r5rrfillr#)r+r,r0r-rjrrhrkX_j_newZdgemmrlZG_j_crmG_jX_jZ was_non_zeroZ block_normshrinkrrrr^s4      r^ 2autoFc+ Cs,|jd}||}|j\}}tt|j||dd}td|t|}tj||f|j d}d}zddl m }Wnt k rd}YnXt | td td | d | d kr|r|dkrd } nd } | d kr|dkr|stdd } |dkrtdd } | d krtdt}d}n| d ks"ttdt}t|}|dkrXtj||dd}nXt|}t|D]D}|dd|||d|f}tjjt|j|dd||<qj|dk rvt}tj }| dk r| j||fkrtd| dk r| n tj|td}ttt|j||}|| d}|dkrf||dddft |dddf!}d||<t|}tj} t|D]}!| d kr||dd|}"n4| d krd}"n$dtjj|dd|fddd}"|||dd|f||"||| || d \}}#}|#"||<t#|d}$t$||||||\}}%}&}'t%|&|}|%|} |&|%td|!d|%| ||t||f| |krtd| |fq|!|dkrttt|j|'|}|| d}|dkr||dddft |dddf}|!}d||<t#|d}(t|}tj||f|j d} t'|(|$})|| |)<qtd| |fn:||||||||dd\}}}| rt$||||||d} t(|r|rt)||dd|f||d}*||*ddtj*f9}tdt||| r|||| fS|||fSdS)a%Solve L1/L2 mixed-norm inverse problem with active set strategy. See references :footcite:`GramfortEtAl2012,StrohmeierEtAl2016, BertrandEtAl2020`. Parameters ---------- M : array, shape (n_sensors, n_times) The data. G : array, shape (n_sensors, n_dipoles) The gain matrix a.k.a. lead field. alpha : float The regularization parameter. It should be between 0 and 100. A value of 100 will lead to an empty active set (no active source). maxit : int The number of iterations. tol : float Tolerance on dual gap for convergence checking. %(verbose)s active_set_size : int Size of active set increase at each iteration. debias : bool Debias source estimates. n_orient : int The number of orientation (1 : fixed or 3 : free or loose). solver : 'cd' | 'bcd' | 'auto' The algorithm to use for the optimization. Block Coordinate Descent (BCD) uses Anderson acceleration for faster convergence. return_gap : bool Return final duality gap. dgap_freq : int The duality gap is computed every dgap_freq iterations of the solver on the active set. active_set_init : array, shape (n_dipoles,) or None The initial active set (boolean array) used at the first iteration. If None, the usual active set strategy is applied. X_init : array, shape (n_dipoles, n_times) or None The initial weight matrix used for warm starting the solver. If None, the weights are initialized at zero. Returns ------- X : array, shape (n_active, n_times) The source estimates. active_set : array, shape (new_active_set_size,) The mask of active sources. Note that new_active_set_size is the size of the active set after convergence of the solver. E : list The value of the objective function over the iterations. gap : float Final duality gap. Returned only if return_gap is True. References ---------- .. footbibliography:: rFr'z-- ALPHA MAX : %srQTrr?solver)cdbcdrrrrzcScikit-learn >= 0.12 cannot be found. Using block coordinate descent instead of coordinate descent.zxCoordinate descent is only available for fixed orientation. Using block coordinate descent instead of coordinate descentzUsing coordinate descentNzUsing block coordinate descentrrordz'Wrong dim for initialized coefficients.g)\(?)rJrArKrrLzKIteration %d :: p_obj %f :: dgap %f :: n_active_start %d :: n_active_end %drSz!Did NOT converge ! (gap: %s > %s))rJrArrKrzFinal active set size: %s)+rr%rr)r5rinfofloatrFrRrBr@ ImportErrorr strr r rNrDrurWrrVrZranormlistrT ValueErrorrUargsortraranger`r"wherer;r#r\Z searchsortedrHrnewaxis)+r*r+r.rJrAractive_set_sizedebiasrr return_gaprLZactive_set_initZX_initZ n_dipolesrrMrdZ alpha_maxr,Z has_sklearnr@Z l21_solverlcrlG_tmprfrgr-Zidx_large_corrZnew_active_idxZas_sizer:roZlc_tmpas_Zidx_old_active_setr2r9r0Zidx_active_setrmbiasrrrmixed_norm_solver9s=               "      $               rc sfddfdd} t}| dk rT| j|jdfkrTtd| j|jdff| dk r`| nt|jd}|dk}||}t|jd|jdf}t|D]}|}|}|dd|f|tjddf}|dk rDt ||krt |||d |||| | |d \}}}n$t |||d ||d| | |d \}}}n$t |||d ||d| | |d \}}}t d | | dkrH|||<|||ddtjf9}| |}d tj |t|dd|f|d d|t |}|||dkrvt||krvtt|||krvtd|qxqt|}d tj |d}||qxqt|r|rt||dd|f|d}||ddtjf9}|||fS)a(Solve L0.5/L2 mixed-norm inverse problem with active set strategy. See reference :footcite:`StrohmeierEtAl2016`. Parameters ---------- M : array, shape (n_sensors, n_times) The data. G : array, shape (n_sensors, n_dipoles) The gain matrix a.k.a. lead field. alpha : float The regularization parameter. It should be between 0 and 100. A value of 100 will lead to an empty active set (no active source). n_mxne_iter : int The number of MxNE iterations. If > 1, iterative reweighting is applied. maxit : int The number of iterations. tol : float Tolerance on dual gap for convergence checking. %(verbose)s active_set_size : int Size of active set increase at each iteration. debias : bool Debias source estimates. n_orient : int The number of orientation (1 : fixed or 3 : free or loose). dgap_freq : int or np.inf The duality gap is evaluated every dgap_freq iterations. solver : 'cd' | 'bcd' | 'auto' The algorithm to use for the optimization. weight_init : array, shape (n_dipoles,) or None The initial weight used for reweighting the gain matrix. If None, the weights are initialized with ones. Returns ------- X : array, shape (n_active, n_times) The source estimates. active_set : array The mask of active sources. E : list The value of the objective function over the iterations. References ---------- .. footbibliography:: csttt|S)N)rrrr"wrrrg*sz&iterative_mixed_norm_solver..gcsdt|SN@)rrepeatr`rrrrrgprime-sz+iterative_mixed_norm_solver..gprimeNrz?Wrong dimension for weight initialization. Got %s. Expected %s.rF)rrrJrArrLrrzactive set size %dr(fror*Convergence reached after %d reweightings!r)rrrrrbrFrZr"rrrrrrarr)r\allabsprintr|rHr)r*r+r.Z n_mxne_iterrJrArrrrrLrZ weight_initrrfweightsr-r,roZX0 active_set_0rZ _active_setrMr2rrrriterative_mixed_norm_solvers5 "  "    rMbP?cCs|jd}|jd}tj||ftjd}||} d} tdD]v} | } td| t|| }t||} t|j | }||}t t |} || } t | | | |kr<qq<| S)zQCompute lipschitz constant for FISTA. It uses a power iteration method. rrQg}Ô%ITdz$Lipschitz estimation: iteration = %d) rrrbrrZrrrealr)r5r#r)r*r+phiphiTrArrdZn_pointsZivvLitZL_oldZGvZGtGvrrrrtf_lipschitz_constantqs"    rcCs&t|rtt||SdSdS)z4Compute np.max(np.abs(A[ia])) possible with empty A.r Nrrr#r)riarrr safe_max_abss rcCs@t|r||nd}t|r(||nd}tt||S)z0Compute np.max(np.abs(A)) possible with empty A.r r)rrBZibrrrsafe_max_abs_diffsrc@s*eZdZdZddZddZd ddZd S) _PhizBHave phi stft as callable w/o using a lambda that does not pickle.c Cst||_t||_t||_t||_|dd|_|j|j|_||_ t |_ t |j|jD].\}}|j tt|||dd|dqfdS)NrrF)rr)r atleast_1dwsizetstepn_coefsrEn_dictsn_freqsn_stepsrdropszipr\reyer)selfrrrrdwstsrrr__init__s"    z _Phi.__init__csB|jdkr|jdStfdd|jDt|jSdS)Nrrcsg|] }|qSrr).0opxrr sz!_Phi.__call__..)rrrZhstackr)rrrrr__call__s  z _Phi.__call__rc Cs|dkrtd||dkr tnt}d}t|jdkr^tjt|t|jdddd}n t|g}t t|D]*}|||| d|j ||j |7}qv|S)z6Squared L2 norm if ord == 2 and L1 norm if order == 1.)rrz3Only supported norm order are 1 and 2. Got ord = %srr Nrr) rr rrErr array_splitZ atleast_2dcumsumrZrrr)rrsrZ stft_normrz_rnrrrrs  z _Phi.normN)r)__name__ __module__ __qualname____doc__rrrrrrrrsrc@s eZdZdZddZddZdS)_PhiTzEHave phi.T istft as callable w/o using a lambda that does not pickle.c Cs||_||_||_||_t|tjr,t|nd|_t |_ t |_ t |_ t |j|j|jD]p\}}}||}|j |t|||||} |j t| |||||j t| d||||q\dS)Nry?)rrrrd isinstancerZndarrayrErrrop_reop_imrr\rrr) rrrrrdnfnsrncrrrrrs8 z_PhiT.__init__cCs|jdkr*|j|jd|j|jdSt|jd|jf}tj |t |j dddd}t ||j|jD]"\}}}||j||j|7}qp|t |jSdS)Nrrrr)rrrimagrrrFrrdrrrrr)rrsZx_outrZthis_zrrrrrrs   z_PhiT.__call__N)rrrrrrrrrrrsrcCsP|jdrHt|j|ddd|jdd}|dk r>||9}|}nd}|S) zL21 norm for TF.rrrrrrNr )rrrrrr)Zrrw_spaceZl21_normrrr norm_l21_tfs  rcCs|jdrz|jd|}ttjt|dj|dfdddd}|j|dfdd}|dk rf||9}|j|dd }nd }|S) zL1 norm for TF.rrrFrvrNrrr )rrrrrrr)rrrw_timerZZ_Zl1_normrrr norm_l1_tfs rr4cCs:tt|d}tt|t|jddD].\}}d|d|j|<d||j| d<q0|dk r|dk}||}||}||}|dk rt||nt|} |dkr| S|dkrt |j |dddfdd S| dkrdS|dkr||| k} n&||t||d|||k} | dkr<| S|dk rtt || || ddd} || | }nt || ddd} || | }|| | }t ||}|dk rt ||}|jd} |dkr t|d} td| d}t|}| |dd |||}nNt|d} t|d}t||}| ||dd ||||}t||dd|d|dkd}|jr|ddn| d}| |} ||}||}|d||dd|d}t|d kr | d ||S||d| |}||t ||SdS) aWeighted epsilon norm. The weighted epsilon norm is the dual norm of:: w_{space} * (1. - l1_ratio) * ||Y||_2 + l1_ratio * ||Y||_{1, w_{time}}. where `||Y||_{1, w_{time}} = (np.abs(Y) * w_time).sum()` Warning: it takes into account the fact that Y only contains coefficients corresponding to the positive frequencies (see `stft_norm2()`): some entries will be counted twice. It is also assumed that all entries of both Y and w_time are non-negative. See :footcite:`NdiayeEtAl2016,BurdakovMerkulov2001`. Parameters ---------- Y : array, shape (n_coefs,) The input data. l1_ratio : float between 0 and 1 Tradeoff between L2 and L1 regularization. When it is 0, no temporal regularization is applied. phi : instance of _Phi The TF operator. w_space : float Scalar weight of the L2 norm. By default, it is taken equal to 1. w_time : array, shape (n_coefs, ) | None Weights of each TF coefficient in the L1 norm. If None, weights equal to 1 are used. Returns ------- nu : float The value of the dual norm evaluated at Y. References ---------- .. footbibliography:: rNrrr r4rrrg|=)rfullrEr}rrrrr#rrrrrrrrr!r)Yl1_ratiorrrZ freqs_countrnfcZnonzero_weightsZ norm_inf_YrmZidx_sortrcZp_sum_Y2Zp_sum_w2Zp_sum_YwupperZ upper_greaterZi0denomdeltarrr norm_epsilons|, $             rcCs|jd|}t|t|j|}|j|dfdd}tjj|dd}|j|dfdd}d} t|D]R} || } |dk r|| nd} |dk r|| nd } t | ||| | d }|| krf|} qf| S) aWeighted epsilon-inf norm of phi(np.dot(G.T, R)). Parameters ---------- G : array, shape (n_sensors, n_sources) Gain matrix a.k.a. lead field. R : array, shape (n_sensors, n_times) Residual. phi : instance of _Phi The TF operator. l1_ratio : float between 0 and 1 Parameter controlling the tradeoff between L21 and L1 regularization. 0 corresponds to an absence of temporal regularization, ie MxNE. n_orient : int Number of dipoles per location (typically 1 or 3). w_space : array, shape (n_positions,) or None. Weights for the L2 term of the epsilon norm. If None, weights are all equal to 1. w_time : array, shape (n_positions, n_coefs) or None Weights for the L1 term of the epsilon norm. If None, weights are all equal to 1. Returns ------- nu : float The maximum value of the epsilon norms over groups of n_orient dipoles (consecutive rows of phi(np.dot(G.T, R))). rrrrvrrr Nr4rr) rrrr)r5rrarrZr)r+r0rrrrrrZGTRPhinurmZGTRPhi_Zw_tZw_sZnorm_epsrrrnorm_epsilon_infys   rc  Cs||} t|dd|f| } || }| dk rD| |dd|}nd}| dk rd| |dd|}nd}t||||}t||||}t|}d|||||}|||}t|||||| | d}td|||}|d|d||t|| }t|| }||}||||fS)axDuality gap for the time-frequency mixed norm inverse problem. See :footcite:`GramfortEtAl2012,NdiayeEtAl2016` Parameters ---------- M : array, shape (n_sensors, n_times) The data. G : array, shape (n_sensors, n_sources) Gain matrix a.k.a. lead field. Z : array, shape (n_active, n_coefs) Sources in TF domain. active_set : array of bool, shape (n_sources, ) Mask of active sources. alpha_space : float The spatial regularization parameter. alpha_time : float The temporal regularization parameter. The higher it is the smoother will be the estimated time series. phi : instance of _Phi The TF operator. phiT : instance of _PhiT The transpose of the TF operator. n_orient : int Number of dipoles per locations (typically 1 or 3). highest_d_obj : float The highest value of the dual objective so far. w_space : array, shape (n_positions, ) Array of spatial weights. w_time : array, shape (n_positions, n_coefs) Array of TF weights. Returns ------- gap : float Dual gap p_obj : float Primal objective d_obj : float Dual objective. gap = p_obj - d_obj R : array, shape (n_sensors, n_times) Current residual (M - G * X) References ---------- .. footbibliography:: Nr(rr4r) rr)rrrrr6rr#)r*r+rr- alpha_space alpha_timerrrrgrrr,r/r0 w_time_as w_space_asZ penaltyl1Z penaltyl21r1r2rr7r8r9r:rrr dgap_l21l1s.1  & rc5s|jd}|| }t|}t|j|| dddd}|}t|dd| d}|D] }|t ||| |8}q`g}| dkr||}n|| |dddf}| dkr||}n || |}d}tj }t | D]}|D]}|| } | | }!||}"|}#|| |!}$t |$}%t |"j|||}&|&}'|%rl| |#}(|t |"|(7}|'|(7}'tj |'d})|)||kr|%rd|<d|$dd<q||&}*|%r|#|*}+n|*}+tj j|+dd},t|,||krd|<d|$dd<qtd ||t|,||d}-| dk r8d|-| |dk<|+|-tjddf9}+|+j}.t|j|+dd }/|/||krd|<d|$dd<qtd ||t|/||d}-|+|-9}+|+jd|.dd|<d |$dd<| |}0|t |"|08}q|d|dkrtfd d t |D}1t|||1||||| | || | d \}2}3}}4|2|k}||3td|dt|| ftd|2|3|f|rq|dk rt|t| ||krqq|||fS)NrrrrFrr rr4rTcs"g|]}t|r|qSrrrHrposrrrrVsz._tf_mixed_norm_solver_bcd_..rz Iteration %d :: n_active %dz% dgap %.2e :: p_obj %f :: d_obj %f)r)rrrWr]r5rZ transposer"rr)rTrZrHrarrmaximumrrrvstackrr\rrr)5r*r+rr- candidatesrrrIrrrrrrJrArLpercZtimeitrrerZGdr0activermrfZ alpha_time_lcZalpha_space_lc convergedr9rnZjjZidsZiderZZ_jZ active_set_jZ was_activeZGTRrrZ rows_normZGTR_phiZZ_j_newZcol_normrZ shape_initZrow_normZ Z_j_phi_TZdr:r2rMrrr_tf_mixed_norm_solver_bcd_s              rc$s^|j\}}|jd}|| }tt|dtj|td}g}|dk r|j||jfkrdt dt |D]D}t ||| |d| rld||| |d| <| |qlt |rވtt|t||t |g}t |}tj }tt|d}|tt|t|||||||||||| | d| d|d\}}}||7}t|dd| d}ttt t |fdd |D}t t |}|dk r||dd| }nd}| dk r| |dd| }nd}t||dd|f|tjt || td|||||dd| ||||| | | | d |d \}}}t|dd| d}|||<||7}d}|rtfd d t t D} t||| |||||| ||| \}!}"}}td |!|"|t|| f|!| krtdqq|r(tfdd t t D|}#n(tjd|jftjdtd|f}#|#|||!fS)Nrr rQz@Z_init must be None or an array with shape (n_sources, n_coefs).T)rrrrJrArrrcsg|] }|qSrr)rrmrrrrsz8_tf_mixed_norm_solver_bcd_active_set..r()rrrrJrArLrrcs"g|]}t|r|qSrrrrrrrsz1 dgap %.2e :: p_obj %f :: d_obj %f :: n_active %dz Convergence reached! cs"g|]}t|r|qSrrrrrrrs)rdictfromkeysrrrFrUrr ExceptionrZrHr\rEupdaterZvsplitrTvaluesrrrbr"rrrr complex128)$r*r+rrrIrrZ_initrrrrJrArLr n_sensorsrdrerr-riirfrr9ZE_tmprMZ candidates_rrrrrr:r2r,rrr$_tf_mixed_norm_solver_bcd_active_setls     $           r @c Cs|j\}}|j\}}||}t|}t|}t|t|krPtd||ft|jd|tt}|dd}||}t ||||}t ||||}|dkrtj ||dd}nVt |}t |D]B}|dd|||d|f}tjjt|j|dd||<qtdt|||||||d|||| dd \}}}}}t|r| rt||dd|f||d }||ddtjf9}| r||||fS|||fSdS) acSolve TF L21+L1 inverse solver with BCD and active set approach. See :footcite:`GramfortEtAl2013b,GramfortEtAl2011,BekhtiEtAl2016`. Parameters ---------- M : array, shape (n_sensors, n_times) The data. G : array, shape (n_sensors, n_dipoles) The gain matrix a.k.a. lead field. alpha_space : float The spatial regularization parameter. alpha_time : float The temporal regularization parameter. The higher it is the smoother will be the estimated time series. wsize: int or array-like Length of the STFT window in samples (must be a multiple of 4). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep) and each entry of wsize must be a multiple of 4. tstep: int or array-like Step between successive windows in samples (must be a multiple of 2, a divider of wsize and smaller than wsize/2) (default: wsize/2). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep), and each entry of tstep must be a multiple of 2 and divide the corresponding entry of wsize. n_orient : int The number of orientation (1 : fixed or 3 : free or loose). maxit : int The number of iterations. tol : float If absolute difference between estimates at 2 successive iterations is lower than tol, the convergence is reached. debias : bool Debias source estimates. return_gap : bool Return final duality gap. dgap_freq : int or np.inf The duality gap is evaluated every dgap_freq iterations. %(verbose)s Returns ------- X : array, shape (n_active, n_times) The source estimates. active_set : array The mask of active sources. E : list The value of the objective function every dgap_freq iteration. If log_objective is False or dgap_freq is np.inf, it will be empty. gap : float Final duality gap. Returned only if return_gap is True. References ---------- .. footbibliography:: WThe same number of window sizes and steps must be passed. Got tstep = %s and wsize = %srrrrNrz7Using block coordinate descent with active set approach)r rrJrArLrr)rrrrErceilastyperintrrrrVrZrarr)r5rrr rHrr) r*r+rrrrrrJrArrrrLrr rdrerrrrrrrrlrr,rr-rfr:rrrrtf_mixed_norm_solversT>            rc +s|j\} }|jd}|}t|}t|}t|t|krPtd||ft||tt}|dd}||}t ||||t ||||}dkrtj ||dd}nVt |}t |D]B}|dd||df}tjjt|j|dd||<qȇfdd fd d }fd d fdd}t}tj|td}tj|j ftjd}t |D]}|}|}|dkrd} d}!n4d||} ||}!d|!|!dk<d|!}!d|!|!dk<t||dd|f||||dd||| |!||| dd\}"}}#}$}%|#||<| dkrt |}&j|dd }'dtj|t|dd|f|"dd||&||'}(||(td|d| |(ft||rJtt||})|)|krJt d|qNnDdtj|d}(||(td|d| |(fqNqt| r| dkrt!||dd|f|"d}*|"|*ddtj"f9}"|"||fS)aVSolve TF L0.5/L1 + L0.5 inverse problem with BCD + active set approach. Parameters ---------- M: array, shape (n_sensors, n_times) The data. G: array, shape (n_sensors, n_dipoles) The gain matrix a.k.a. lead field. alpha_space: float The spatial regularization parameter. The higher it is the less there will be active sources. alpha_time : float The temporal regularization parameter. The higher it is the smoother will be the estimated time series. 0 means no temporal regularization, a.k.a. irMxNE. n_tfmxne_iter : int Number of TF-MxNE iterations. If > 1, iterative reweighting is applied. wsize : int or array-like Length of the STFT window in samples (must be a multiple of 4). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep) and each entry of wsize must be a multiple of 4. tstep : int or array-like Step between successive windows in samples (must be a multiple of 2, a divider of wsize and smaller than wsize/2) (default: wsize/2). If an array is passed, multiple TF dictionaries are used (each having its own wsize and tstep), and each entry of tstep must be a multiple of 2 and divide the corresponding entry of wsize. maxit : int The maximum number of iterations for each TF-MxNE problem. tol : float If absolute difference between estimates at 2 successive iterations is lower than tol, the convergence is reached. Also used as criterion on duality gap for each TF-MxNE problem. debias : bool Debias source estimates. n_orient : int The number of orientation (1 : fixed or 3 : free or loose). dgap_freq : int or np.inf The duality gap is evaluated every dgap_freq iterations. %(verbose)s Returns ------- X : array, shape (n_active, n_times) The source estimates. active_set : array The mask of active sources. 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