U f{j @sdZddlZddlmZddlZddlZddlm Z ddl m Z m Z m Z ddlmZddlmZddlmZdd lmZmZdd lmZdd lmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%e&dd ddgddddgddddgddddggZ'e(ej)ej*ej+ej,ej-ej.ej/ej0ej1ej2d Z3dde34DZ5ej2dej)dej6dej7dej,dej*dej+dej8dej9dej1dej0dej.dej-dej:dej;dd diZd#d$Z?dd(d)Z@dd*d+ZAdd-d.ZBdd/d0ZCdd1d2ZDd3d4ZEd5d6ZFdd7d8ZGdd9d:ZHddd?ZJd@dAZKeddCdDZLedBddEdFdGZMdHdIZNddJdKZOdLdMZPddNdOZQdPdQZRdRdSZSdTdUZTdVdWZUdXdYZVdZd[ZWd\d]ZXd^d_ZYd`daZZGdbdcdce[Z\dddeZ]Gdfdgdge[Z^dhdiZ_djdkZ`e dldmZae dndoZbdpdqZcdrdsZdddtduZedvdwZfdxdyZgdzd{Zhd|d}Zie dd~dZjdddZke!dddZlddZmddZnddZoddZpdZqddZrddZsddZtddZuddZvedddZwddZxedddZydS)z$Helpers for various transformations.Ndeepcopy)jitmean_get_img_fdata)FIFF) fiff_open)read_tag)start_and_end_filewrite_coord_trans)_handle_default) check_fnameloggerverbose _ensure_int_validate_type _path_likeget_subjects_dirfill_doc _check_fname _check_option_require_versionwrapped_stdout) megmriZ mri_voxelheadmni_talrasZfs_talZctf_headZctf_megunknowncCsi|]\}}||qSr!).0keyvalr!r!M/var/www/html/bwave/python/venv/lib/python3.8/site-packages/mne/transforms.py +sr&r z MEG deviceZisotrakZhpirzMRI (surface RAS)z MRI voxelz MRI slicez MRI displayzCTF MEG devicezCTF/4D/KIT headzRAS (non-zero origin)z MNI TalairachzTalairach (MNI z > 0)zTalairach (MNI z < 0)cCsRt|tr>|tkr4td|ddtdt|}n t|dd}t|S)z+Convert string or int coord frame into int.zUnknown coordinate frame z , expected "z", ""zcoordinate framez a str or int) isinstancestr _str_to_frame ValueErrorjoinkeysrint)cfr!r!r% _to_const?s     r0csfeZdZdZdfdd ZddZddd Zdd d Zed d Z eddZ ddZ ddZ Z S) TransformaA transform. Parameters ---------- fro : str | int The starting coordinate frame. See notes for valid coordinate frames. to : str | int The ending coordinate frame. See notes for valid coordinate frames. trans : array-like, shape (4, 4) | None The transformation matrix. If None, an identity matrix will be used. Notes ----- Valid coordinate frames are 'meg','mri','mri_voxel','head','mri_tal','ras' 'fs_tal','ctf_head','ctf_meg','unknown' Ncsttt|t|}t|}|dkr0tdn t|tj}|jdkrXt d|j||d<||d<||d<dS)Nr2r2z(Transformation must be shape (4, 4) not fromtotrans) superr1__init__r0npeyeasarrayZfloat64shaper+)selffror5r6 __class__r!r%r8_s   zTransform.__init__c CsHtjdd2djt|dt|d|ddW5QRSQRXdS)NT)suppressz!{to}> {trans}r4r5r6)r>r5r6)r9Z printoptionsformat_coord_frame_namer=r!r!r%__repr__ls   zTransform.__repr__cCsDt|toB|d|dkoB|d|dkoBtj|d|d||dS)aSCheck for equality. Parameter --------- other : instance of Transform The other transform. rtol : float Relative tolerance. atol : float Absolute tolerance. Returns ------- eq : bool True if the transforms are equal. r4r5r6)rtolatol)r(r1r9allcloser=otherrGrHr!r!r%__eq__rs zTransform.__eq__cCs ||k S)aYCheck for inequality. Parameter --------- other : instance of Transform The other transform. rtol : float Relative tolerance. atol : float Absolute tolerance. Returns ------- eq : bool True if the transforms are not equal. r!rJr!r!r%__ne__szTransform.__ne__cCs t|dS)zThe "from" frame as a string.r4rCrDr!r!r%from_strszTransform.from_strcCs t|dS)zThe "to" frame as a string.r5rNrDr!r!r%to_strszTransform.to_strcCst||dS)zSave the transform as -trans.fif file. Parameters ---------- fname : str The name of the file, which should end in '-trans.fif'. N) write_trans)r=fnamer!r!r%saveszTransform.savecCst|S)zMake a copy of the transform.rrDr!r!r%copyszTransform.copy)N)rFrF)rFrF)__name__ __module__ __qualname____doc__r8rErLrMpropertyrOrPrSrT __classcell__r!r!r?r%r1Ls      r1cCstt|dS)z/Map integers to human-readable (verbose) names.r )_verbose_framesgetr.)Zcframer!r!r%rCsrCCoordinate transformation: minfoc Cstt|}||djt|dt|ddt|dD]Z\}}|dkrX|dkrXdnd }|dkrhd nd }|d |d |d|d||d|fq {to}r4r5r>r5r6mmg@@? mmz# % 8.6f % 8.6f % 8.6f %7.2f%srr)getattrrrBrC enumerate) tprefixZunitslevelZlog_functittscaletextr!r!r%_print_coord_transs   rpcCs||dkr&dtjkrtjd}ntdtt||d}t|dkrXtdj|dnt|dkrttdj|d|dS) NZSUBJECTz$SUBJECT environment variable not setz *-trans.fifrz/Could not find the transformation for {subject})subjectz,Found multiple transformations for {subject}r) osenvironr+globopr,len RuntimeErrorrB)rq subjects_dirZ trans_fnamesr!r!r% _find_transs     ryTcCsht|tr|d}t|}|jdkr.|St||ddddfj}|rd||dddf7}|S)aApply a transform matrix to an array of points. Parameters ---------- trans : array, shape = (4, 4) | instance of Transform Transform matrix. pts : array, shape = (3,) | (n, 3) Array with coordinates for one or n points. move : bool If True (default), apply translation. Returns ------- transformed_pts : shape = (3,) | (n, 3) Transformed point(s). r6rNra)r(dictr9r;sizerTdotT)r6ptsmoveZout_ptsr!r!r% apply_transs   rc Cst|}t|}t|}t|}t|}t|}tj||| |||||||||dg|||||||| ||||dg| ||||dgddddggtd} | S)zCreate an array with a 4 dimensional rotation matrix. Parameters ---------- x, y, z : scalar Rotation around the origin (in rad). Returns ------- r : array, shape = (4, 4) The rotation matrix. rrdtyper9cossinarrayfloat xyzZcos_xZcos_yZcos_zZsin_xZsin_yZsin_zrr!r!r%rotations(       rc Cst|}t|}t|}t|}t|}t|}tj||| |||||||||g|||||||| ||||g| ||||ggtd} | S)zCreate an array with a 3 dimensional rotation matrix. Parameters ---------- x, y, z : scalar Rotation around the origin (in rad). Returns ------- r : array, shape = (3, 3) The rotation matrix. rrrr!r!r% rotation3ds"      rcCs|tj|}td}d|ddkrDd|d<d|d<d|d<ndd|d}dd||d |d |d<d||d |d |d <|d |d <d||d |d |d <dd||d |d |d<|d |d<|d  |d<|d  |d<d||d |d |d |d |d<t||jtddksRttj |ddkslttj||d d d gdkst|S)a,Compute a rotation matrix to align [ 0 0 1] with supplied target z axis. Parameters ---------- target_z_axis : array, shape (1, 3) z axis. computed matrix (r) will map [0 0 1] to target_z_axis Returns ------- r : array, shape (3, 3) The rotation matrix. rararcrfg-q=rrrrrfrfrrrrrrfrrrrfrfrrfrra) r9linalgnormzerosanyr|r}identityAssertionErrordet)Z target_z_axisrfr!r!r%rotation3d_align_z_axis/s,        &&rcCst|d|d}t|dd|dd}t|d |}t|}t|}t||d||d||d ||d }|||fS) aFind rotation angles from a transformation matrix. Parameters ---------- m : array, shape >= (3, 3) Rotation matrix. Only the top left 3 x 3 partition is accessed. Returns ------- x, y, z : float Rotation around x, y and z axes. rrrrfrrrrrr)r9arctan2sqrtrr)r^rc2rs1c1rr!r!r%rotation_anglesXs   4rcCs:tj|dddgd|ddgdd|dgddddggtd}|S)zCreate an array with a scaling matrix. Parameters ---------- x, y, z : scalar Scaling factors. Returns ------- s : array, shape = (4, 4) The scaling matrix. rrrr9rr)rrrsr!r!r%scalingns    rcCs:tjddd|gddd|gddd|gddddggtd}|S)zCreate an array with a translation matrix. Parameters ---------- x, y, z : scalar Translation parameters. Returns ------- m : array, shape = (4, 4) The translation matrix. rrrr)rrrr^r!r!r% translations    rrc Cs<t|tr|}t|}n t|}|}~t|tr>|}t|}n t|}|}~d|d|d}t|ttfsr|g}t}t} t|D]h\} } t| tst|d| d| dh||hkr| | q| dj t| dt| ddg7} qt |d krt|d d | ||d }|d|kr8t |}|S) z$Ensure we have the proper transform.z"trans must be a Transform between z<->z, gotz Noner4r5z {fro}->{to}r`r z, r)r(r)r* _frame_to_strlisttuplerhr1r+appendrBrvr,invert_transform) r6r>r5rOZ from_constrPZto_constZerr_stridxmissesrlZ this_transr!r!r% _ensure_transsH         rcCstdf}|r|d7}t||dt|rt|}|dkrNtttddd}t|sht d|dt |d d krt |}qt |}|jd ks|jd krtd |dt|||}n.t|tr|}d}n|dkstt||}d}t|||}||fS)z5Get mri_head_t (from=mri, to=head) from mri filename.z path-likeNr6Z fsaveragedatazfsaverage-trans.fifz trans file "z " not foundr)z.fifz.gzrfr3zFile "z" did not have 4x4 entrieszinstance of TransformNr)r1rrr)rur,dirname__file__isfileIOErrorsplitext read_transr9Z genfromtxtndimr<rwr(rr)r6r>r5 allow_nonetypesZfro_to_trir!r!r% _get_transs4        rcCst|}t|}|d|krBtdj|dt|d|t|d|d|dkrtdj|dt|d|dt|dd|d|krtdj|dt|d|t|dt||t|d |d S) a7Combine two transforms. Parameters ---------- t_first : dict First transform. t_second : dict Second transform. fro : int From coordinate frame. to : int To coordinate frame. Returns ------- trans : dict Combined transformation. r4z3From mismatch: {fro1} ("{cf1}") != {fro2} ("{cf2}"))Zfro1cf1fro2cf2r5zMTransform mismatch: t1["to"] = {to1} ("{cf1}"), t2["from"] = {fro2} ("{cf2}"))to1rrrz/To mismatch: {to1} ("{cf1}") != {to2} ("{cf2}"))rrZto2rr6)r0rwrBrCr1r9r|)Zt_firstZt_secondr>r5r!r!r%combine_transformss8      rFc Cst|ddd}t|\}}}t}|8|D],}|jtjkr,|t||jj |s,qZq,W5QRXt |dkrxt d|r|S|dS)aRead a ``-trans.fif`` file. Parameters ---------- fname : path-like The name of the file. return_all : bool If True, return all transformations in the file. False (default) will only return the first. .. versionadded:: 0.15 %(verbose)s Returns ------- trans : dict | list of dict The transformation dictionary from the fif file. See Also -------- write_trans mne.transforms.Transform readT) overwriteZ must_existrz+This does not seem to be a -trans.fif file.) rr rkindrZFIFF_COORD_TRANSrr posrrvr)rRZ return_allrfidtree directoryr6rir!r!r%r s  r)rrc Cs:t|ddt||d}t|}t||W5QRXdS)a%Write a -trans.fif file. Parameters ---------- fname : path-like The name of the file, which should end in ``-trans.fif``. trans : dict Trans file data, as returned by read_trans. %(overwrite)s %(verbose)s See Also -------- read_trans r6)z -trans.fifz -trans.fif.gzz _trans.fifz _trans.fif.gz)rRrN)rrr r )rRr6rrrr!r!r%rQ2s   rQcCs t|d|dtj|dS)zInvert a transformation between coordinate systems. Parameters ---------- trans : dict Transform to invert. Returns ------- inv_trans : dict Inverse transform. r5r4r6)r1r9rinv)r6r!r!r%rJs rcCs|r t|n|}t|trB|tkr:tdtt|ft|}|d|krR|St|t|d|}||d<t ||d|d<d|krt ||ddd|d<|S)aTransform surface to the desired coordinate system. Parameters ---------- surf : dict Surface. dest : 'meg' | 'mri' | 'head' | int Destination coordinate system. Can be an integer for using FIFF types. trans : dict | list of dict Transformation to use (or a list of possible transformations to check). copy : bool If False (default), operate in-place. Returns ------- res : dict Transformed source space. z dest must be one of %s, not "%s" coord_framerrnnF)r) rr(r)r*KeyErrorrr-rr.r)Zsurfdestr6rTr!r!r%transform_surface_toZs  rcCst|}t|}t|}|||fD]"}|jdksBt|dkr(tdq(||}|tj|}|t||||}||}|tj|}t||} | \} } } t | | | } t ||| dddgf}t ddddgd}t ||f}t|| }|S)aConstruct a transformation matrix to the MNE head coordinate system. Construct a transformation matrix from an arbitrary RAS coordinate system to the MNE head coordinate system, in which the x axis passes through the two preauricular points, and the y axis passes through the nasion and is normal to the x axis. (see mne manual, pg. 97) Parameters ---------- nasion : array_like, shape (3,) Nasion point coordinate. lpa : array_like, shape (3,) Left peri-auricular point coordinate. rpa : array_like, shape (3,) Right peri-auricular point coordinate. Returns ------- trans : numpy.array, shape = (4, 4) Transformation matrix to MNE head space. rrazAPoints have to be provided as one dimensional arrays of length 3.r)r2r) r9r;rrvr+rrr|crossrvstackreshapehstack)ZnasionZlpaZrpaptrightZ right_unitoriginZanteriorZ anterior_unitZ superior_unitrrrZ origin_transZtrans_lZtrans_rZ rot_transr6r!r!r%get_ras_to_neuromag_transs&        rc Cst|ddd}t|dddd}tt||dd}tt||tddgd|dt||tddgd|dt||tddgd|dd}|S)zCGet the transforms to a coordinate frame from device, head and mri.rrr dev_head_trr`)rrr)rrrrzrr1)r_r6rZ head_mri_trZ mri_dev_tZto_cf_tr!r!r%_get_transforms_to_coord_frames.rcCst|}|jdkr"|jddks&ttt|df}ttj||dd|dddf<t |dddfdk|dddfd}t |dddf|dddf|dddf<t |dddf||dddf<t |}|S)a]Convert Cartesian coordinates to spherical coordinates. Parameters ---------- cart_pts : ndarray, shape (n_points, 3) Array containing points in Cartesian coordinates (x, y, z) Returns ------- sph_pts : ndarray, shape (n_points, 3) Array containing points in spherical coordinates (rad, azimuth, polar) rfrraZaxisNr) r9 atleast_2drr<remptyrvrsumwhererZarccosZ nan_to_num)Zcartoutrr!r!r% _cart_to_sphs $*0& rcCst|}|jdkr"|jddks&ttt|df}|dddft|dddf|dddf<|dddft|dddf}|t|dddf|dddf<|t|dddf|dddf<|S)a^Convert spherical coordinates to Cartesion coordinates. Parameters ---------- sph_pts : ndarray, shape (n_points, 3) Array containing points in spherical coordinates (rad, azimuth, polar) Returns ------- cart_pts : ndarray, shape (n_points, 3) Array containing points in Cartesian coordinates (x, y, z) rfrraNr) r9rrr<rrrvrr)Zsph_ptsZcart_ptsZxyr!r!r% _sph_to_carts 2&&&rcCst|t}|d|S)aCompute the number of multipolar moments (spherical harmonics). Equivalent to :footcite:`DarvasEtAl2006` Eq. 32. .. note:: This count excludes ``degree=0`` (for ``order=0``). Parameters ---------- order : array-like Expansion orders, often ``[int_order, ext_order]``. Returns ------- M : ndarray Number of moments due to each order. rf)r9r;r.)orderr!r!r%_get_n_momentss rc Cstj|||f}t|t|}}t|t|}} t|| | ||g|| |||g|t|| gg} td| |} | S)aConvert spherical partial derivatives to cartesian coords. Note: Because we are dealing with partial derivatives, this calculation is not a static transformation. The transformation matrix itself is dependent on azimuth and polar coord. See the 'Spherical coordinate sytem' section here: wikipedia.org/wiki/Vector_fields_in_cylindrical_and_spherical_coordinates Parameters ---------- az : ndarray, shape (n_points,) Array containing spherical coordinates points (azimuth). pol : ndarray, shape (n_points,) Array containing spherical coordinates points (polar). sph_grads : ndarray, shape (n_points, 3) Array containing partial derivatives at each spherical coordinate (radius, azimuth, polar). Returns ------- cart_grads : ndarray, shape (n_points, 3) Array containing partial derivatives in Cartesian coordinates (x, y, z) z ijk,kj->ki)r9Zc_rrr zeros_likeeinsum) azpolZg_radZg_azZg_polZ sph_gradsZc_asZs_asZc_psZs_psr6Z cart_gradsr!r!r%_sph_to_cart_partials srcCs||||dS)z:Get the index into S_in or S_out given a degree and order.rr!)degrr!r!r% _deg_ord_idx/srcCs$|dks t||drdndS)z8Get the negative spherical harmonic from a positive one.rrfrrc)rZconjshrr!r!r% _sh_negate5s rcCs8|dkrt|Std|dkr(tjntj|SdS)aConvert complex to real basis functions. Parameters ---------- sh : array-like Spherical harmonics. Must be from order >=0 even if negative orders are used. order : int Order (usually 'm') of multipolar moment. Returns ------- real_sh : array-like The real version of the spherical harmonics. Notes ----- This does not include the Condon-Shortely phase. r@N)r9realrimagrr!r!r%_sh_complex_to_real;s rcCs<|dkr|dS|ddt||dtdSdS)agConvert real spherical harmonic pair to complex. Parameters ---------- shs : ndarray, shape (2, ...) The real spherical harmonics at ``[order, -order]``. order : int Order (usually 'm') of multipolar moment. Returns ------- sh : array-like, shape (...) The complex version of the spherical harmonics. ry?rrN)r9signr)Zshsrr!r!r%_sh_real_to_complexUsrcCsddlm}tt|t|df}t|dD]n}t|dD]\}|||||}t|||ddt||f<|dkrBtt ||| |ddt|| f<qBq2|S)z=Compute complex spherical harmonics of spherical coordinates.r)sph_harmrN) Z scipy.specialrr9rrvrrangerrr)rrrrrZdegreeZorder_sphr!r!r%_compute_sph_harmjs rc@s(eZdZdZdddZed ddZdS) _TPSWarpaTransform points using thin-plate spline (TPS) warping. Notes ----- Based on the method by :footcite:`Bookstein1989` and adapted from code by Wang Lin (wanglin193@hotmail.com>). References ---------- .. footbibliography:: MbP?c Csddlm}ddlm}|jd|jdkr8dks>nt|jd|jdksVtt|||d}tjt |jddf|fdd}t t ||gt |j t d gg}tj|t d fdd} ||t|jd7}||_||| d|_|S) Nrrcdistrra sqeuclideanrrr3)r2ra)scipyrscipy.spatial.distancerr<r_tpsr9 concatenateonesrrr}rr:rT _destinationlstsq_weights) r=source destinationregrrdistsPLYr!r!r%fits  &" z _TPSWarp.fitNc Cstdt|fddlm}|jddks2tt|}t t |jd|j jddd}t t ||t ||D]P\}}t|||j d}t|t|jddf|f} t| |j|dd<qz|dkrt|S) aApply the warp. Parameters ---------- pts : shape (n_transform, 3) Source points to warp to the destination. Returns ------- dest : shape (n_transform, 3) The transformed points. zTransforming %s pointsrrrraggArN)rr_rvrrr<rr9rmaxr.rzipZ array_splitrrrr|r r) r=r~rrrZn_splitsZthis_outZthis_ptsrrr!r!r% transforms"     z_TPSWarp.transform)r)N)rUrVrWrXrrrr!r!r!r%rs rcCs0t|}|dk}||}|t|||<|S)z)Thin-plate function (r ** 2) * np.log(r).r)r9rlog)ZdistsqrmaskZvalidr!r!r%rs  rc@s4eZdZdZddZed d d Zedd d ZdS)_SphericalSurfaceWarpaBWarp surfaces via spherical harmonic smoothing and thin-plate splines. Notes ----- This class can be used to warp data from a source subject to a destination subject, as described in :footcite:`DarvasEtAl2006`. The procedure is: 1. Perform a spherical harmonic approximation to the source and destination surfaces, which smooths them and allows arbitrary interpolation. 2. Choose a set of matched points on the two surfaces. 3. Use thin-plate spline warping (common in 2D image manipulation) to generate transformation coefficients. 4. Warp points from the source subject (which should be inside the original surface) to the destination subject. .. versionadded:: 0.14 References ---------- .. footbibliography:: cs:d}tds|d7}n|dtfdddD7}|S)Nzz9fit %d->%d pts using match=%s (%d pts), order=%s, reg=%s>c3s|]}j|VqdSr) _fit_params)r"r#rDr!r% sz1_SphericalSurfaceWarp.__repr__..Zn_srcZn_destmatchZn_matchrr )hasattrr)r=repr!rDr%rEs   z_SphericalSurfaceWarp.__repr__r2h㈵>Toct5Nc Cszddlm}ddlm} ddlm} | |dddd } td t d } } |rtd t d d|D}| |ddd} || }t dd|D}| |ddd} || }tdt | dd t | dd ft t |t ||t | ||d|_|jd|jdkr"d ks(nt||_tdt|j}t|j}t| j}~ td|t|f|dd}t|f|dd}t|f|dd}|||dd}|||dd}tdt ||f|}tt|||d<|}tt|||d<t|j}|| 7}t|j}|| 7}t||||_t ||g|_td|S)arFit the warp from source points to destination points. Parameters ---------- source : array, shape (n_src, 3) The source points. destination : array, shape (n_dest, 3) The destination points. order : int Order of the spherical harmonic fit. reg : float Regularization of the TPS warp. center : bool If True, center the points by fitting a sphere to points that are in a reasonable region for head digitization. match : str The uniformly-spaced points to match on the two surfaces. Can be "ico#" or "oct#" where "#" is an integer. The default is "oct5". %(verbose)s Returns ------- inst : instance of SphericalSurfaceWarp The warping object (for chaining). rrr) _fit_sphere)_check_spacingF)rrfrzComputing TPS warpraz Centering datacSs(g|] }|ddkr |ddks|qS)rfgưrgư>r!r"pr!r!r% 4s z-_SphericalSurfaceWarp.fit..)ZdispcSs(g|] }|ddkr |ddks|qS)rfrrr!r$r!r!r%r&8s z Using centers %s -> %sNrz' Converting to spherical coordinatesz< Computing spherical harmonic approximation with order %sz0 Matching %d points (%s) on smoothed surfaces[done])rrZbemr"Z source_spacer#rr_r9rrZ array_strrzrvrr<rrTrrr}rr absr|rrrrZ_matched)r=r r rr centerrrrr"r#Zmatch_rrZ src_centerZ dest_centerZhspZsrc_rad_az_polZdest_rad_az_polZmatch_rad_az_polZsrc_sphZdest_sphZ match_sphZ src_coeffsZ dest_coeffsr!r!r%rsr       *         z_SphericalSurfaceWarp.fitcCs |j|S)a&Transform arbitrary source points to the destination. Parameters ---------- source : ndarray, shape (n_pts, 3) Source points to transform. They do not need to be the same points that were used to generate the model, although ideally they will be inside the convex hull formed by the original source points. %(verbose)s Returns ------- destination : ndarray, shape (n_pts, 3) The points transformed to the destination space. )rr)r=r rr!r!r%rfsz_SphericalSurfaceWarp.transform)r2r Tr!N)N)rUrVrWrXrErrrr!r!r!r%rs  VrcCstt|df}|jddkr|dddft|dddf|dddf<|dddft|dddf|dddf<nr|dddft|dddf}|t|dddf|dddf<|t|dddf|dddf<|S)z)Transform polar coordinates to cartesian.rfrNr)r9rrvr<rr)rrdr!r!r% _pol_to_cart~s24&&&r+cCsx|jdkr|jddksttt|df}t|dddf |dddf<tj|dddf|dddf<|S)z5Convert 2D topo coordinates to spherical coordinates.rfrraNr)rr<rr9rrvZdeg2radpi)Ztoporr!r!r% _topo_to_sphs $"r-cCsB|d|d|d}}}||||||}}}td|||d}t|}d||} d||} d||} d||} d||} d||}t|jddd }|||||d <| | |d <| | |d <| | |d <|||||d<|| |d<| | |d<|| |d<|||||d<|S)aIConvert a set of quaternions to rotations. Parameters ---------- quat : array, shape (..., 3) The q1, q2, and q3 (x, y, z) parameters of a unit quaternion. Returns ------- rot : array, shape (..., 3, 3) The corresponding rotation matrices. See Also -------- rot_to_quat .r.r.rfrcrFrfNrr).rr).rr).rrf).rr).rr).rrf).rfr).rfr).rfrf)r9maximumrrr<)quatbcr*ZbbccddZaaaZab_2Zac_2Zad_2Zbc_2Zbd_2Zcd_2rr!r!r% quat_to_rots*             r8cCstjt|d}t|ddkr.tdd|d|d|d}|t|jjkrt |d}|d |d |}|d |d |}|d |d|}n<|d|dkr&|d|dkr&t d|d|d|dd}d|}|d|d |}|d |d |}n|d|dkrt d|d|d|dd }|d|d |}d|}|d |d |}nVt d|d|d|dd}|d |d |}|d |d |}d|}t |||fS)z)Convert a rotation matrix to quaternions.rrcrz3Matrix is not a pure rotation, got determinant != 1rr2rrfrarg?) r9rrrr(r+Zfinforepsrr)rotrrirZqxZqyZqzr!r!r%_one_rot_to_quats0$&&&r?cCs&||jddd}ttd|S)a_Convert a set of rotations to quaternions. Parameters ---------- rot : array, shape (..., 3, 3) The rotation matrices to convert. Returns ------- quat : array, shape (..., 3) The q1, q2, and q3 (x, y, z) parameters of the corresponding unit quaternions. See Also -------- quat_to_rot N) r)rr<r9Zapply_along_axisr?)r>r!r!r% rot_to_quatsrBcCsT|jdksttd}t|dd|ddddf<|dd|dddf<|S)N)r<r2ra)r<rr9r:r8)r2affiner!r!r%_quat_to_affines   rDcCsF|dkrtdn|}t| |}t|}dttjj|dd|S)zDCompute the ang between two quaternions w/3-element representations.Nrarfrr)r9r _quat_mult _quat_realrrr)rrrZz0r!r!r%_angle_between_quatss rGcCs^|jddkst|jdttd|d|d|d|d|d|ddS)z(Get the real part of our 3-element quat.rrarcr.r/r0rF)r<rr9rr1)r2r!r!r%rFs rFc Cs:|jd|jdkr dks&ntt|}t|}tt||j}|d|d}}|d|d}}|d|d} } |||||| | ||d<|||| ||| ||d<|| ||||| ||d<||||||| | } t| } t| | d} || dtjf9}|S)Nrrar.r/r0r.) r<rrFr9r broadcastrrnewaxis) onetwoZw1Zw2rx1Zx2y1y2Zz1Zz2wZsignsr!r!r%rEs&$$$  rEcCs@td|d |dg|dd|d g|d |ddggS)z5Compute the skew-symmetric cross product of a vector.rFrfrr)r9r)r7r!r!r%_skew_symmetric_cross,srPcCsjtd}t||}t|dr&|St||}t||}t|}||t||d||7}|S)z6Find the rotation matrix that maps unit vector a to b.rarFr)r9r:rrIr|rP)r7r3Rvrr4Zvxr!r!r%_find_vector_rotation1s      rScCsJ|j|jkst|jdkst|jddks0t|dkrnt|dd}t|dd}t|j|}||jd}nPt|||j df}t|j|d}t|j|d}t|j||}|t ||}||j} t | d| d| d g} t |} t d } | | d <| | dddf<| | dddf<||j| td| ddddf<tj| \} }t d }|ddd f|dd<|ddkr|ddt|d9<t|dd}|r"||}||}||9}||9}|dk r||9}||9}tt|t|}nd}||t|||dd<||fS)z/Fit matched points using an analytical formula.rfrraNrrrrrr3rr<r)rrrc)r<rrrr9r|r}rrr{outerrtracerr:reighrr8r)r%rweightsrnZmu_pZmu_xdotsZweights_ZSigma_pxZA_ijDeltaZ tr_Sigma_pxQ_rRr2r>Zdev_xZdev_prr!r!r%_fit_matched_pointsAsN     (  r\cCsddlm}|jdkr$|jddks(t|dkr@t|jd}|dksPt|}|dkrnt dS||}t t |dtj f|fd }||ddtj f9}t d ||}||dddd f}|t||dkd9}|dd}|S) z"Average unit quaternions properly.rrrfr)rar2Nra.rz ij,ik->jk)rrrr<rr9rallrrrrFrIrrVr)ZquatsrWrrAZavg_quatr!r!r%_average_quatss       r_cCsLt|dd}t|ddt||ddd}t|ddd }td d t|d S) zRead a subject's RAS to MNI transform. Parameters ---------- subject : str The subject. %(subjects_dir)s Returns ------- ras_mni_t : instance of Transform The transform from RAS to MNI (in mm). T)rxZ raise_errorr)rqrZ transformsz talairach.xfmrz(FreeSurfer Talairach transformation filerrr)rrrur,rr1 _read_fs_xfm)rqrxrRr!r!r%read_ras_mni_ts  rac Cs|dstt|d}td|d}t|D]@\}}|dkr\|}td|f|dt||kr4qq4td|t }t|D]6\}}d d |d  D}| ||d krqqtd W5QRX| ddddgt j |td}||fS)z-Read a Freesurfer transform from a .xfm file.z.xfmrz)Reading FreeSurfer talairach.xfm file: %sZLinear_Transformrz Found: %rNz8Failed to find "Linear_Transform" string in xfm file: %scSsg|] }t|qSr!r)r"rr!r!r%r&sz _read_fs_xfm..z ;rfz,Could not find enough linear transform linesrFrcr)endswithropenrdebugrhstriprvr+rsplitrr9rr) rRrcomplilinerxfmiiZdigsr!r!r%r`s.  r`c Cst|d|}||dd|ddt|ddD]@\}}ddd |D}||d krjd nd 7}||dq@W5QRXdS) z,Write a Freesurfer transform to a .xfm file.wbz Ttransform_Type = Linear; asciizLinear_Transform = NrrcSsg|] }d|qS)z%0.6fr!)r"partr!r!r%r&sz!_write_fs_xfm..rf z; )rdwriteencoderhr,)rRrkrrrirjr!r!r% _write_fs_xfms rscCst|j}|d|d|d}}}t|}tjd||||dd|||||ddtjd|||||ddtjd||||dd|||||dd|S)Nr.r/r0rfr)r)r9rr<rFrZarcsin)r2eulerrrrrOr!r!r%_quat_to_eulers 8"8ruc Cs0t|j}|dd|dd|dd}}}t|t|}}~t|t|}}~t|t|} } ~t||| ||| } t| r| dkrdn| } n d| | dk<| dtjf} ||| ||| |d<||| ||| |d<||| ||| |d<|| 9}|S)Nr.rfr/r0rrc.)r9rr<rrrZisscalarrI) rtr2phithetapsiZcphiZsphiZcthetaZsthetaZcpsiZspsiZmultr!r!r%_euler_to_quats$ (  ry)rrigidrCsdrcCst|tttddfdtd|}|D]\}}td|t|dk r(tddtj |t d D}tdt |d t |d t |d kr|d }|D]}|d krtd |q|||<q(|S)NnumericzoomsZtransform_zoomsz zooms keycss|]}t|VqdSrrb)r"rr!r!r%rsz"_validate_zooms..rz len(zooms[))rrarrazZooms must be > 1, got )rrzrrr itemsr_ORDERED_STEPSr9rrravelreprrvr+)r}r#r$Z this_zoomr!r!r%_validate_zoomss     rcCs\t|tttdfdtd|}|D]0\}}td|ttdt|dt |dq&|S)NniterZtransform_niterz niter keyz len(niter[z]))rrfra) rrzrrr rrrrrv)rr#valuer!r!r%_validate_niter)s   rcCst|tttfdtttdtddtdtddd}t|trftd|ddd||}t |D],\}}d|d }t|t|t||tqntt |d d d }t||krt d |d|dt t |t |krt dt|S)NpipelinerzrrC)r]ZrigidsZaffineszwhen str)extraz pipeline[]cSs t|Sr)rindex)rr!r!r%Az$_validate_pipeline..)r#z-Steps in pipeline are out of order, expected z but got z insteadz(Steps in pipeline should not be repeated)rr)rrrzrrr(rrhsortedr+rvset)rZpipeline_defaultsrlstepnameZordered_pipeliner!r!r%_validate_pipeline2s4    rcCs,d||tj|tj|S)Nd)rr9rr)r7r3r!r!r% _compute_r2KsrcCsZddlm}|jdd}|j}t|}|dk rF|||||\}}||}||fS)Nr)reslicera)Zdipy.align.reslicerheader get_zoomsrCrr)Zimgr}rZ img_zoomsZ img_affiner!r!r%_reslice_normalizePs  rr]cCst|||||ddS)amAlign two volumes using an affine and, optionally, SDR. Parameters ---------- %(moving)s %(static)s %(pipeline)s zooms : float | tuple | dict | None The voxel size of volume for each spatial dimension in mm. If None (default), MRIs won't be resliced (slow, but most accurate). Can be a tuple to provide separate zooms for each dimension (X/Y/Z), or a dict with keys ``['translation', 'rigid', 'affine', 'sdr']`` (each with values that are float`, tuple, or None) to provide separate reslicing/accuracy for the steps. %(niter)s %(verbose)s Returns ------- %(reg_affine)s %(sdr_morph)s Notes ----- This function is heavily inspired by and extends :func:`dipy.align.affine_registration `. .. versionadded:: 0.24 Nrf)_compute_volume_registration)movingstaticrr}rrr!r!r%compute_volume_registration[s!rc%Csltdddtdddddl}tj6ddlm}ddlm}m }m } m } m } m } m} W5QRXt||jjd t||jjd t|jdd }t|}t|}t|}td d}d}t|| g| g| gd }tdddg}d}dddg}d}t|D]L\}}|dks6|||||dkr||dk rptd||d|dt||}ntd|d|}t|||\}}t|||\}}td|d|dkrT||}|||j||j|}||}| j d |t!t"t#d|dd}| $|||}t%ddd|&||||}W5QRX||} nt'||}!t%ddd0|||||d d!|||||!||d" \} }W5QRX|d#kr tj()|dd d f}"t*t+t,d t-|dd dd f}#td$|"d%d&|d'kr td(|#d%d)| j|jks6t.|t/|| }$td*|$d%d+q|||j||j|fS),Nnibabel SDR morph2.1.0dipy0.10.1r AffineMap)affine_registrationcenter_of_massrrzrCimwarpmetricsrrrazComputing registration...)rrzrCg@rcrFrr2rfrzReslicing to zooms=z for z ...zUsing original zooms for z Optimizing :r{)dimZ sigma_diffZradiusz T)indentZ cull_newlines ZMI)ZnbinsmetricrZ level_itersZsigmasfactorsZstarting_affine)rrzz Translation: z6.1frdrzz Rotation: °u R²: %)0rrr9ZtestingZsuppress_warningsdipy.align.imaffinerZ dipy.alignrrrrzrCrrrZ spatialimages SpatialImagerrrrrrrr_rzrrhrr<rZCCMetricrr.ceilZ"SymmetricDiffeomorphicRegistrationroptimizerrrZrad2degrGrrBrr)%rrrr}rZnibrrrrrzrCrrZ original_zoom reg_affine sdr_morphZpipeline_optionsZ sigmas_mmZ sigma_diff_mmrZ current_zoomirZ static_zoomed static_affineZ moving_zoomed moving_affineZsigma_diff_vox affine_maprr{Z moved_zoomedZ sigmas_voxdistZangler2r!r!r%rs    .  $        rlinearrFcCstdddtdddddlm}ddlm}dd lm} t||d t||d t|tj d t d |j dt||dfdt|dt fdd} t |t r|dstd|t|dd} td|j} tj|jtd}| dk rt|| }td| d|||8}t|j|j}} | ||j | |j | } | j||d}|dk rtd|j||tj| |j | d}||7}||| }td|S)a Apply volume registration. Uses registration parameters computed by :func:`~mne.transforms.compute_volume_registration`. Parameters ---------- %(moving)s %(static)s %(reg_affine)s %(sdr_morph)s interpolation : str Interpolation to be used during the interpolation. Can be "linear" (default) or "nearest". cval : float | str The constant value to assume exists outside the bounds of the ``moving`` image domain. Can be a string percentage like ``'1%%'`` to use the given percentile of image data as the constant value. %(verbose)s Returns ------- reg_img : instance of SpatialImage The image after affine (and SDR, if provided) registration. Notes ----- .. versionadded:: 0.24 rrrrrr)r)DiffeomorphicMaprrrrzreg_affine.shape)r3Nrr|cvalrz!cval must end with % if str, got rz Applying affine registration ...rzUsing a lower bound at the z percentile: ) interpolationzAppling SDR warp ...)rZimage_world2gridZ out_shapeZout_grid2worldr')rZnibabel.spatialimagesrZdipy.align.imwarprrrrr9Zndarrayrr<r)r(rcr+rrr_rCr;ZdataobjZ percentilerrr)rrrrrrrrrrpercrrrZreg_dataZreg_imgr!r!r%apply_volume_registrationsX!                 r)r]r^r_)N)T)rrr)rrr)rrr)rrr)rr)rrT)FN)F)r)N)NF)N)N)r]NNN)NrrFN)zrXrros.pathpathrurtnumpyr9rTrfixesrrrZ io.constantsrZio.openr Zio.tagr Zio.writer r defaultsr utilsrrrrrrrrrrrrrZ als_ras_transrzZFIFFV_COORD_DEVICEZFIFFV_COORD_MRIZFIFFV_MNE_COORD_MRI_VOXELZFIFFV_COORD_HEADZFIFFV_MNE_COORD_MNI_TALZFIFFV_MNE_COORD_RASZFIFFV_MNE_COORD_FS_TALZFIFFV_MNE_COORD_CTF_HEADZFIFFV_MNE_COORD_CTF_DEVICEZFIFFV_COORD_UNKNOWNr*rrZFIFFV_COORD_ISOTRAKZFIFFV_COORD_HPIZFIFFV_COORD_MRI_SLICEZFIFFV_COORD_MRI_DISPLAYZFIFFV_MNE_COORD_FS_TAL_GTZZFIFFV_MNE_COORD_FS_TAL_LTZr[r0r1rCrpryrrrrrrrrrrrrQrrrrrrrrrrrrrobjectrrrr+r-r8r?rBrDrGrFrErPrSr\r_rar`rsruryrrrrrrrrrr!r!r!r%s      8"   i   )   ) ") ' &4 #3?   * #   A ( "     $R