U f{jJ@sddlZddlmZddlZddlmZddlm Z ddl m Z m Z m Z mZddZd$d d Zd%d d Ze d&ddZddZddZdejZddejZddZeddZddZddZed d!Zd"d#ZdS)'N)legendre) parallel_func)loggerverbose_get_extra_data_pathfill_doccCsZ|}|}d|d|||d||}||||}|d|||}|||fS)z9Compute the next Legendre polynomial and its derivatives.r)nxp0Zp01Zp0dZp0ddZold_p0Zold_p0dr r U/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mne/forward/_lead_dots.py_next_legen_ders $rdcCst||dS)z*Get Legendre polynomials expanded about x.r )rZ legvander)r n_coeffr r r _get_legen"src Cstt||df}t||D]\}}|dddf|dddf|dddf}}}d|g|dd<ddg|dd<ddg|dd<td|D]H}t||||d||d||d||d\||<||<||<qq|S)z5Get Legendre polynomial derivatives expanded about x.Nrr r?g)npemptylenzipranger) Zxxrcoeffscr Zp0sZp0dsZp0ddsr r r r_get_legen_der's 4 rF Nc CsN|ddkrtdttd}t|s6t||dkrjt|d||f}t}d}|d|d f} n(t|d ||f}t}d }|d|f} t |r|rt d |t d d|d} || |t j} |st|d} | | W5QRXn6t d|t|ddd} t | t j} W5QRX| | _t jd|td} |dkrt}|r|| d| dd| dn|| d| d||d| d||d| d| ddddddddgf} t |ddddgddfj}t |}|} n4d| dd| d| } | ddddf} | | fS)zDReturn a (generated) LUT of Legendre (derivative) polynomial coeffs.rrzn_interp must be evenZtablesmegzlegder_%s_%s.binz derivativer rzlegval_%s_%s.binzGenerating Legendre%s table...wbzReading Legendre%s table...rb) buffering)Zdtype@rg@N) RuntimeErroropjoinrisdirosmakedirsrrisfilerinforZlinspaceZastypeZfloat32openwritetobytesfromfileshapearangefloatlistappendarrayTZascontiguousarraycopy)ch_typevolume_integralrZn_interpZ force_calcrfnameZleg_funZ extra_strZ lut_shapeZx_interplutZfidn_factZn_factsr r r_get_legen_table5sT         r>c Csddt|jd}ttd|j||jgg}t|j}t|dd|ddD]p\}}||||} t|||ddtj fd|jdf} tj | d| d| | 9} t | ||||<qZ|S) z?Lead field dot products using Legendre polynomial (P_n) series.rrNr r axisout) maxr1r concatenater2sizerrtilenewaxiscumproddot) betacthetalut_funr=n_chunklimss0startstoprZbetansr r r _comp_sum_eegns ",rSc Cst|jdt|f}ddt|jd}ttd|j||jgg}t|dd|ddD]\}} t ||| tj |jddf} | d||| 9<tj | d| dtj d | ||||| |dd|| fd qf|S) aiLead field dot products using Legendre polynomial (P_n) series. Parameters ---------- beta : array, shape (n_points * n_points, 1) Coefficients of the integration. ctheta : array, shape (n_points * n_points, 1) Cosine of the angle between the sensor integration points. lut_fun : callable Look-up table for evaluating Legendre polynomials. n_fact : array Coefficients in the integration sum. volume_integral : bool If True, compute volume integral. Returns ------- sums : array, shape (4, n_points * n_points) The results. r r?r@rrNr rAz ji,jk,ijk->ki)rC) rrr1rrDrEr2rFrrGrHrIeinsum) rKrLrMr=r:sumsrNrOrQrRZbbetar r r_comp_sums_megs""$rVg+&=rg@c #Cs|dkrt|t|f} d}nt|f} d}t| }t|}t|}t|}td||}t|dd||ddtjddf}|tjddddf}|ddtjf|tjddf}|||}| dkrt||| | | }d|j |_ td||}td||}td||}td||}td||}|||}||||}|||d d |||d||||d |||||||d }|t |9}| r||9}n.t ||| | }|j |_ |t 9}||}d } |t|9}|dk r6||ddtjf9}t |D]@\}!}"tj|dd| | t|"f|d ||!<| t|"7} q>|S)a=Lead field dot product computation for M/EEG in the sphere model. Parameters ---------- r : float The integration radius. It is used to calculate beta as: beta = (r * r) / (lr1 * lr2). rr1 : array, shape (n_points x 3) Normalized position vectors of integrations points in first sensor. rr2s : list Normalized position vector of integration points in second sensor. lr1 : array, shape (n_points x 1) Magnitude of position vector of integration points in first sensor. lr2s : list Magnitude of position vector of integration points in second sensor. cosmags1 : array, shape (n_points x 1) Direction of integration points in first sensor. cosmags2s : list Direction of integration points in second sensor. w1 : array, shape (n_points x 1) | None Weights of integration points in the first sensor. w2s : list Weights of integration points in the second sensor. volume_integral : bool If True, compute volume integral. lut : callable Look-up table for evaluating Legendre polynomials. n_fact : array Coefficients in the integration sum. ch_type : str The channel type. It can be 'meg' or 'eeg'. Returns ------- result : float The integration sum. Nr z ik,jk->ijr r)z ik,ijk->ijz jk,ijk->ijrr$rrrB)rrrrErTZcliprHrVflattenr1 _meg_constrS _eeg_const enumeratesum)#rZrr1_origZrr2sZlr1Zlr2scosmags1Z cosmags2sZw1Zw2sr:r<r=r9Z out_shapeZsum_axisrCZrr2Zlr2cosmags2ctZrr1Zlr1lr2rKrUZn1c1Zn1c2Zn2c1Zn2c2Zn1n2Zpart1Zpart2resultoffsetiiZw2r r r_fast_sphere_dot_r0sb'     $       *rec sdkrdfdd|DddDddtDdd|Ddd|D tt|\}}| f d d ttt|D} tj| d d } | S) aPerform the lead field dot product integrations. Parameters ---------- intrad : float The integration radius. It is used to calculate beta as: beta = (intrad * intrad) / (r1 * r2). volume : bool If True, perform volume integral. coils : list of dict The coils. r0 : array, shape (3 x 1) The origin of the sphere. ch_type : str The channel type. It can be 'meg' or 'eeg'. lut : callable Look-up table for evaluating Legendre polynomials. n_fact : array Coefficients in the integration sum. %(n_jobs)s Returns ------- products : array, shape (n_coils, n_coils) The integration products. eegffffff?cs&g|]}|dtjddfqSZrmagNrrH.0Zcoilr0r r @sz!_do_self_dots..cSs$g|]}ttj||ddqSr rXrsqrtr]rkr^r r rrnAscSs&g|]\}}||ddtjfqSNrirkr^Zrlr r rrnBscSsg|] }|dqSZcosmagr rjr r rrnCscSsg|] }|dqSwr rjr r rrnDsc 3s(|] } | VqdSrsr rkidx) r9cosmagsintradr<r=p_funrlensrmagsvolumewsr r Fs z _do_self_dots..rrX)rr_do_self_dots_subsetr array_splitr2rr]) r{rcoilsrmr9r<r=n_jobsparallelprodsproductsr ) r9rzr{r<r=r|rmr}r~rrr _do_self_dots!src Cstt|t|f} | D]|} | d} t||| |d| || |d| || |d| || |d| |||| } | | | d| f<| | d| | f<q| S)z Parallelize.r N)rzerosrre)r{r~r}rzrrr<r=r9ryrci1Zci2resr r rrMs*    rcs|dkr|d}fdd|D}fdd|D} dd|D} dd| D} ddt|| D}d dt| | D} d d|D} d d|D} d d|D}d d|D}tt|t| f}tt|D]D}t|||| | || |||| || |||| }|||ddf<q|S)aCompute lead field dot product integrations between two coil sets. The code is a direct translation of MNE-C code found in `mne_map_data/lead_dots.c`. Parameters ---------- intrad : float The integration radius. It is used to calculate beta as: beta = (intrad * intrad) / (r1 * r2). volume : bool If True, compute volume integral. coils1 : list of dict The original coils. coils2 : list of dict The coils to which data is being mapped. r0 : array, shape (3 x 1). The origin of the sphere. ch_type : str The channel type. It can be 'meg' or 'eeg' lut : callable Look-up table for evaluating Legendre polynomials. n_fact : array Coefficients in the integration sum. Returns ------- products : array, shape (n_coils, n_coils) The integration products. rfrgcs&g|]}|dtjddfqSrhrirjrlr rrnsz"_do_cross_dots..cs&g|]}|dtjddfqSrhrirjrlr rrnscSs$g|]}ttj||ddqSrorprrr r rrnscSs$g|]}ttj||ddqSrorprrr r rrnscSs&g|]\}}||ddtjfqSrsrirtr r rrnscSs&g|]\}}||ddtjfqSrsrirtr r rrnscSsg|] }|dqSrvr rjr r rrnscSsg|] }|dqSrvr rjr r rrnscSsg|] }|dqSrur rjr r rrnscSsg|] }|dqSrur rjr r rrnsN)rrrrrre)r{rZcoils1Zcoils2rmr9r<r=Zrmags1Zrmags2Zrlens1Zrlens2Zws1Zws2r_r`rrrr rlr_do_cross_dots]s> rc s&fdd|D dd D ddt D dd|Ddd|Dd ddkrhd |d |tjddf ttj d d  ddtjf |d | tt| \} } |  fddttt | D} tj| dd } | S)aBCompute the map construction products. Parameters ---------- intrad : float The integration radius. It is used to calculate beta as: beta = (intrad * intrad) / (r1 * r2) volume : bool If True, compute a volume integral. coils : list of dict The coils. surf : dict The surface on which the field is interpolated. sel : array Indices of the surface vertices to select. r0 : array, shape (3 x 1) The origin of the sphere. ch_type : str The channel type. It can be 'meg' or 'eeg'. lut : callable Look-up table for Legendre polynomials. n_fact : array Coefficients in the integration sum. %(n_jobs)s Returns ------- products : array, shape (n_coils, n_coils) The integration products. cs&g|]}|dtjddfqSrhrirjrlr rrnsz$_do_surface_dots..cSs$g|]}ttj||ddqSrorprrr r rrnscSs&g|]\}}||ddtjfqSrsrirtr r rrnscSsg|] }|dqSrur rjr r rrnscSsg|] }|dqSrvr rjr r rrnsNrfrgZrrr rXnnc3s2|]*}   |VqdSrsr rx)r9rzr{lsurfr<r=r|reflr}r~rrefrsurfthis_nnrrr rrsz#_do_surface_dots..r) rrrHrqr]r_do_surface_dots_subsetrr2r) r{rrZsurfselrmr9r<r=rrrrr )r9rzr{rr<r=r|rmrr}r~rrrrrr_do_surface_dotss&" (rcCs2t|||||||d| | | | | j}|dk r.t|S)aParallelize. Parameters ---------- refl : array | None If ch_type is 'eeg', the magnitude of position vector of the virtual reference (never used). lsurf : array Magnitude of position vector of the surface points. rlens : list of arrays of length n_coils Magnitude of position vector. this_nn : array, shape (n_vertices, 3) Surface normals. cosmags : list of array. Direction of the integration points in the coils. ws : list of array Integration weights of the coils. volume : bool If True, compute volume integral. lut : callable Look-up table for evaluating Legendre polynomials. n_fact : array Coefficients in the integration sum. ch_type : str 'meg' or 'eeg' idx : array, shape (n_coils x 1) Index of coil. Returns ------- products : array, shape (n_coils, n_coils) The integration products. N)rer7NotImplementedError)r{rr~rrrr}rrzrrr<r=r9ryrr r rrs$$r)r)r)FrrFN)r)os.pathpathr&numpyrZnumpy.polynomialrrrutilsrrrrrrrr>rSrVpirZr[rerrrrrr r r r s4      83 k +: A