o Rŀg0@s2dZddlZddlmZddZGdddZdS)aEStructural alignment using Quaternion Characteristic Polynomial (QCP). QCPSuperimposer finds the best rotation and translation to put two point sets on top of each other (minimizing the RMSD). This is eg. useful to superimpose crystal structures. QCP stands for Quaternion Characteristic Polynomial, which is used in the algorithm. Algorithm and original code described in: Theobald DL. Rapid calculation of RMSDs using a quaternion-based characteristic polynomial. Acta Crystallogr A. 2005 Jul;61(Pt 4):478-80. doi: 10.1107/S0108767305015266. Epub 2005 Jun 23. PMID: 15973002. N) PDBExceptioncd Cstt||j}tt||j}t|j|}||d}|\ }}} } } } } }}||}| | }||}||}| | }| | }| | }||}| | }d| || |}|||||}d|||||||||}d|| || | | ||| || || | ||| | }| | }| |}|| }| |} | | }!|| }"|| }#|| }$||||}%| }&|! }'|" }(|#|})|%|%|||||&| |"|$||'||"|$||&|||#||'| ||)| |||$||(| ||)| | |!|$||(||!|#|}*d}+|},d}-t|+D]:}.|,}/|,|,}0|0||,}1|1|}2|2|,|*}3d|0|,|1|2}4|3|4|-}5t|,|5},|,|/|-|,krrn q9td|+ddt||,|d}6|#||,}7| }8|'}9|"}:| };|$||,}<|}=|}>|9}?|=}@| |||,}A|}B|:}C|>}D|B}E||#|,}F|A|F|E|B}G|@|F|D|B}H|@|E|D|A}I|?|E|C|A}J|?|F|C|B}K|?|D|C|@}L|<|G|=|H|>|I}M|; |G|=|K|>|J}N|;|H|<|K|>|L}O|; |I|<|J|=|L}P|M|M|N|N|O|O|P|P}Qd }R|Q|RkrF|8|G|9|H|:|I}M|7 |G|9|K|:|J}N|7|H|8|K|:|L}O|7 |I|8|J|9|L}P|M|M|N|N|O|O|P|P}Q|Q|RkrF|9|>|:|=}S|8|>|:|<}T|8|=|9|<}U|7|>|:|;}V|7|=|9|;}W|7|<|8|;}X|D|S|E|T|F|U}M|C |S|E|V|F|W}N|C|T|D|V|F|X}O|C |U|D|W|E|X}P|M|M|N|N|O|O|P|P}Q|Q|RkrF|@|S|A|T|B|U}M|? |S|A|V|B|W}N|?|T|@|V|B|X}O|? |U|@|W|A|X}P|M|M|N|N|O|O|P|P}Q|Q|RkrFtd }Y|6|Y|M|N|O|PgfS|Qd}Z|M|Z}M|N|Z}N|O|Z}O|P|Z}P|M|M}[|N|N}0|O|O}\|P|P}]|N|O}^|M|P}_|P|N}`|M|O}a|O|P}b|M|N}ct d }Y|[|0|\|]|Yd d <d |^|_|Yd d<d |`|a|Yd d <d |^|_|Ydd <|[|0|\|]|Ydd<d |b|c|Ydd <d |`|a|Yd d <d |b|c|Yd d<|[|0|\|]|Yd d <|6|Y|M|N|O|PffS)zImplement the QCP code in Python. Input coordinate arrays must be centered at the origin and have shape Nx3. Variable names match (as much as possible) the C implementation. g?g@gg @2gdy=z&Newton-Rhapson did not converge after z iterationsgư>)rrr) nptracedotTflattenrangeabsprinteyezeros)dcoords1coords2natomsG1G2AE0SxxSxySxzSyxSyySyzSzxSzySzzSxx2Syy2Szz2Sxy2Syz2Sxz2Syx2Szy2Szx2SyzSzymSyySzz2Sxx2Syy2Szz2Syz2Szy2C2C1SxzpSzxSyzpSzySxypSyxSyzmSzySxzmSzxSxymSyxSxxpSyySxxmSyySxy2Sxz2Syx2Szx2 negSxzpSzx negSxzmSzx negSxymSyx SxxpSyy_p_SzzC0nr_itmxEigenVevalprec_oldgx2baff_primedeltarmsda11a12a13a14a21a22a23a24a31a32a33a34a41a42a43a44 a3344_4334 a3244_4234 a3243_4233 a3143_4133 a3144_4134 a3142_4132q1q2q3q4qsqrevecprec a1324_1423 a1224_1422 a1223_1322 a1124_1421 a1123_1321 a1122_1221rotnormqa2y2z2xyazzxayyzaxruB/var/www/html/myenv/lib/python3.10/site-packages/Bio/PDB/qcprot.pyqcpsF  (                          rwc@s`eZdZdZddZddZddZdd Zd d Zd d Z ddZ ddZ ddZ ddZ dS)QCPSuperimposera Quaternion Characteristic Polynomial (QCP) Superimposer. QCPSuperimposer finds the best rotation and translation to put two point sets on top of each other (minimizing the RMSD). This is eg. useful to superimposing 3D structures of proteins. QCP stands for Quaternion Characteristic Polynomial, which is used in the algorithm. Reference: Douglas L Theobald (2005), "Rapid calculation of RMSDs using a quaternion-based characteristic polynomial.", Acta Crystallogr A 61(4):478-480 cCs |dS)zInitialize the class.N)_reset_propertiesselfrururv__init__s zQCPSuperimposer.__init__cCs.d|_d|_d|_d|_d|_d|_d|_dS)zFReset all relevant properties to None to avoid conflicts between runs.N)reference_coordscoordstransformed_coordsrjtranrmsinit_rmsrzrururvrys z!QCPSuperimposer._reset_propertiescCsxt|t|ks Jdtjdd|Dtjd}tjdd|Dtjd}||||||_||_ dS)a=Prepare alignment between two atom lists. Put (translate/rotate) the atoms in fixed on the atoms in moving, in such a way that the RMSD is minimized. :param fixed: list of (fixed) atoms :param moving: list of (moving) atoms :type fixed,moving: [L{Atom}, L{Atom},...] z*Fixed and moving atom lists differ in sizecSg|]}|qSru get_coord.0rCrururv z-QCPSuperimposer.set_atoms..)dtypecSrrurrrururvrrN) lenrarrayfloat64setrunget_rmsr get_rotranrotran)r{fixedmoving fix_coord mov_coordrururv set_atomss   zQCPSuperimposer.set_atomscCs6|jdur td|j\}}|D]}|||qdS)zCApply the QCP rotation matrix/translation vector to a set of atoms.Nz)No transformation has been calculated yet)rr transform)r{ atom_listrjratomrururvapplys  zQCPSuperimposer.applycCsH|||_||_|j\|_}|j|jkrtd|dkr"tddS)aSet the coordinates to be superimposed. coords will be put on top of reference_coords. - reference_coords: an NxDIM array - coords: an NxDIM array DIM is the dimension of the points, N is the number of points to be superimposed. z*Coordinates must have the same dimensions.rzCoordinates must be Nx3 arrays.N)ryr}r~shape_natomsr)r{r}r~n_dimrururvr"s   zQCPSuperimposer.setcCs|jdus |jdurtd|j}|j}tj|dd}tj|dd}||8}||8}t|||j\|_|_ }|t ||j |_ dS)z Superimpose the coordinate sets.NNo coordinates set.raxis) r~r}rcopyrmeanrwrrrjr r)r{r~ coords_ref com_coordscom_refr?rururvr9s  zQCPSuperimposer.runcCsL|jdus |jdurtd|jdurtdt|j|j|j|_|jS)z#Get the transformed coordinate set.NrNothing is superimposed yet.)r~r}rrjrr rrrzrururvget_transformedLs  zQCPSuperimposer.get_transformedcCs|jdur td|j|jfS)z@Return right multiplying rotation matrix and translation vector.Nr)rjrrrzrururvrWs  zQCPSuperimposer.get_rotrancCsT|jdur td|jdur'|j|j}tttj||dd|j|_|jS)zCReturn the root mean square deviation of untransformed coordinates.NzNo coordinates set yet.rr)r~rrr}rsqrtsumr)r{diffrururv get_init_rms]s   &zQCPSuperimposer.get_init_rmscCs|jdur td|jS)z7Root mean square deviation of superimposed coordinates.NzNothing superimposed yet.)rrrzrururvrgs zQCPSuperimposer.get_rmsN)__name__ __module__ __qualname____doc__r|ryrrrrrrrrrurururvrxs    rx)rnumpyrBio.PDB.PDBExceptionsrrwrxrurururvs  D