RiNdZddlZddlmZddlZdZdZdZeZ dZ dZ d Z d Z Gd d Z d ededej"fdZd edej"fdZd edej"fdZd edej"fdZdedededej"fdZdedededej"fdZdedej"fdZdededefdZdej"deeeeffdZej8dej: Zej8dej: Zej8dej: Z ej8dej: Z! d+d!ej"d"ej"d#ej"d$e"deej"ej"dzff d%Z#d ej"dej"fd&Z$d ej"dej"fd'Z%d+d(ej"d)e&d$e"dej"fd*Z'y),z3Vector class, including rotation-related functions.N)Optionalcd}t|d|dz |krt|d|dz |krt|d|dz |kryt|d|dz|krQt|d|dz|kr:t|d|dz|kr#t|d|d z|d zd z |krd }nYtj}nHd tj|dz z}t d|}t d|}tj |}|dkrdtdd d fS|tjkrB|d|dz }|d|dz }|d|dz }t|||}|j||fS|d}|d } |d } || kDr:|| kDr5tj|| z | z d z}|dd|zz }|dd|zz }ns| |kDr:| | kDr5tj| |z | z d z}|dd|zz }|dd|zz }n4tj| |z | z d z}|dd|zz }|dd|zz }t|||}|jtj|fS)zReturn angles, axis pair that corresponds to rotation matrix m. The case where ``m`` is the identity matrix corresponds to a singularity where any rotation axis is valid. In that case, ``Vector([1, 0, 0])``, is returned. h㈵>rrrrr rrr r rrrrrr r rg?rgV瞯<r ) absnppitracemaxminarccosVector normalizesqrt) mepsangletxyzaxism00m11m22s G/home/agent/.friday_env/lib/python3.12/site-packages/Bio/PDB/vectors.py m2rotaxisr*s C AdGag $ $!D'! "S ( $!D'! "S ( $!D'! "S (AdGag%&,AdGag%&,AdGag%$/!34s:EEEE 288A;? # AJ 1I !  u}F1aO##  dGag  dGag  dGag aA d{ggg 9sc C#-.A$1q5!A$1q5!A 3Y39c C#-.A$1q5!A$1q5!Ac C#-.A$1q5!A$1q5!AaA uud{c|j}|j}|j|}|||tj|zzz S)a2Vector to axis method. Return the vector between a point and the closest point on a line (ie. the perpendicular projection of the point on the line). :type line: L{Vector} :param line: vector defining a line :type point: L{Vector} :param point: vector defining the point ) normalizednormr mathcos)linepoint norm_pointr s r)vector_to_axisr4SsF ?? DJ JJu E 4J%89 99r+c|j}tj|}tj|}d|z }|j \}}}tj d}||z|z|z|d<||z|z||zz |d<||z|z||zz|d<||z|z||zz|d<||z|z|z|d<||z|z||zz |d<||z|z||zz |d <||z|z||zz|d <||z|z|z|d <|S) aGCalculate left multiplying rotation matrix. Calculate a left multiplying rotation matrix that rotates theta rad around vector. :type theta: float :param theta: the rotation angle :type vector: L{Vector} :param vector: the rotation axis :return: The rotation matrix, a 3x3 NumPy array. Examples -------- >>> from numpy import pi >>> from Bio.PDB.vectors import rotaxis2m >>> from Bio.PDB.vectors import Vector >>> m = rotaxis2m(pi, Vector(1, 0, 0)) >>> Vector(1, 2, 3).left_multiply(m) r)rrrrr rrr r r r)r-rr0sin get_arrayzeros) thetavectorcsr!r"r#r$rots r) rotaxis2mr>fs70   F u A u A AA GAq! ((6 CA A CIA AE!CIA AE!CIA AE!CIA A CIA AE!CIA AE!CIA AE!CIA A CI Jr+c||j}|j}||z jdkrtjdS||z }|j |j }d|_tjd}|dtj|tj|zz }|S)aReturn a (left multiplying) matrix that mirrors p onto q. :type p,q: L{Vector} :return: The mirror operation, a 3x3 NumPy array. Examples -------- >>> from Bio.PDB.vectors import refmat >>> p, q = Vector(1, 2, 3), Vector(2, 3, 5) >>> mirror = refmat(p, q) >>> qq = p.left_multiply(mirror) >>> print(q) >>> print(qq) rr)rrr ) r-r.ridentityrr7shapedot transpose)pqpqbirefs r)refmatrJs$ A A A||~{{1~ QBLLN AAG AA a"&&BLLO,, ,C Jr+c^tjt|| t|| }|S)aReturn a (left multiplying) matrix that rotates p onto q. :param p: moving vector :type p: L{Vector} :param q: fixed vector :type q: L{Vector} :return: rotation matrix that rotates p onto q :rtype: 3x3 NumPy array Examples -------- >>> from Bio.PDB.vectors import rotmat >>> p, q = Vector(1, 2, 3), Vector(2, 3, 5) >>> r = rotmat(p, q) >>> print(q) >>> print(p) >>> p.left_multiply(r) )rrBrJ)rDrEr=s r)rotmatrLs)2 &&A2q1" .C Jr+c8||z }||z }|j|S)zCalculate angle method. Calculate the angle between 3 vectors representing 3 connected points. :param v1, v2, v3: the tree points that define the angle :type v1, v2, v3: L{Vector} :return: angle :rtype: float )r )v1v2v3s r) calc_anglerQs$ bB bB 88B<r+c||z }||z }||z }||z}||z}||z} |j|} |j| dkDr| } | S#t$rY| SwxYw)a Calculate dihedral angle method. Calculate the dihedral angle between 4 vectors representing 4 connected points. The angle is in ]-pi, pi]. :param v1, v2, v3, v4: the four points that define the dihedral angle :type v1, v2, v3, v4: L{Vector} gMbP?)r ZeroDivisionError) rNrOrPv4abcbdbuvwr s r) calc_dihedralr[s bB bB bB BA BA 1A GGAJE 88A; FE L   L sA AAceZdZdZddZdZdZdZdZdZ d Z d Z d Z d Z d ZdZdZdZdZdZdZdZdZdZy)rz 3D vector.Nc|7|5t|dk7r tdtj|d|_ytj|||fd|_y)zInitialize the class.Nrz0Vector: x is not a list/tuple/array of 3 numbersd)len ValueErrorrarray_arselfr"r#r$s r)__init__zVector.__init__sN 91v{ !STTxx3'DHxxAq 3/DHr+c@|j\}}}d|dd|dd|ddS)zReturn vector 3D coordinates.zrbrcs r)__repr__zVector.__repr__ s2((1a!C1S'Ac7!44r+c2|j }t|S)zReturn Vector(-x, -y, -z).)rbr)rdas r)__neg__zVector.__neg__s XXIayr+ct|tr$|j|jz}t|S|jtj|z}t|S)z%Return Vector+other Vector or scalar. isinstancerrbrrardotherrks r)__add__zVector.__add__L eV $599$Aay288E?*Aayr+ct|tr$|j|jz }t|S|jtj|z }t|S)z%Return Vector-other Vector or scalar.rnrps r)__sub__zVector.__sub__rsr+cFt|j|jzS)z#Return Vector.Vector (dot product).)sumrb)rdrqs r)__mul__zVector.__mul__&s488eii'((r+c\|jtj|z }t|S)zReturn Vector(coords/a).)rbrrar)rdr"rks r) __truediv__zVector.__truediv__*s" HHrxx{ "ayr+c(t|tr|j\}}}|j\}}}tjj tj ||f||ff}tjj tj ||f||ff } tjj tj ||f||ff} t|| | S|jtj |z}t|S)z6Return VectorxVector (cross product) or Vectorxscalar.)rorrbrlinalgdetra) rdrqrkrGr;r^efc1c2c3s r)__pow__zVector.__pow__/s eV $hhGAq!iiGAq!rxx!Q!Q(89:B))--1a&1a&)9 :;;Brxx!Q!Q(89:B"b"% %288E?*A!9 r+c |j|S)zReturn value of array index i.rhrdrHs r) __getitem__zVector.__getitem__<sxx{r+c"||j|<y)zAssign values to array index i.Nrh)rdrHvalues r) __setitem__zVector.__setitem__@s r+c||jvS)zValidate if i is in array.rhrs r) __contains__zVector.__contains__DsDHH}r+cltjt|j|jzS)zReturn vector norm.)rrrwrbrds r)r.z Vector.normHs#wws488dhh./00r+cXtt|j|jzS)zReturn square of vector norm.)rrwrbrs r)normsqz Vector.normsqLs3txx$((*+,,r+cj|jr#|j|jz |_yy)zNormalize the Vector object. Changes the state of ``self`` and doesn't return a value. If you need to chain function calls or create a new object use the ``normalized`` method. N)r.rbrs r)rzVector.normalizePs( 99;xx$))+-DH r+cF|j}|j|S)zwReturn a normalized copy of the Vector. To avoid allocating new objects use the ``normalize`` method. )copyr)rdrYs r)r-zVector.normalizedZs IIK r+c|j}|j}||z||zz }t|d}td|}tj|S)z!Return angle between two vectors.rr)r.rrrr)rdrqn1n2r;s r)r z Vector.anglecsN YY[ ZZ\ E\b2g & 1I AJyy|r+c@tj|jS)z,Return (a copy of) the array of coordinates.)rrarbrs r)r7zVector.get_arraymsxx!!r+cXtj||j}t|S)zReturn Vector=Matrix x Vector.rrBrbrrdmatrixrks r) left_multiplyzVector.left_multiplyqs FF6488 $ayr+cXtj|j|}t|S)zReturn Vector=Vector x Matrix.rrs r)right_multiplyzVector.right_multiplyvs FF488V $ayr+c,t|jS)z!Return a deep copy of the Vector.)rrbrs r)rz Vector.copy{sdhhr+)NN)__name__ __module__ __qualname____doc__rerirlrrrurxrzrrrrr.rrr-r r7rrrr+r)rrsi 05  ) 1-."   r+r angle_radsr%returnctj|}tj|}d|k(r2tj|| ddf||ddfddftj Sd|k(r2tj|d|dfd| d|dfdftj Stjdd|| dfd||dfdftj S) zGenerate a 4x4 single-axis NumPy rotation matrix. :param float angle_rads: the desired rotation angle in radians :param char axis: character specifying the rotation axis r$r)rrrrrrrrdtyper#)rrrr)rrrr)r/r0r6rrafloat64)rr%cosangsinangs r) homog_rot_mtxrs XXj !F XXj !F d{xx&!Q'A&   **   xxFA&!VQ'   **  xxFVGQ'FFA&   **  r+mtxctj|}tj|}|x|d<|d<||d<| |d<y)z/Update existing Z rotation matrix to new angle.rrrrNr/r0r6rrrrs r)set_Z_homog_rot_mtxrD XXj !F XXj !F""CID CICIr+ctj|}tj|}|x|d<|d<||d<| |d<y)z/Update existing Y rotation matrix to new angle.rrr r Nrrs r)set_Y_homog_rot_mtxrrr+ctj|}tj|}|x|d<|d<||d<| |d<y)z/Update existing X rotation matrix to new angle.rrr r Nrrs r)set_X_homog_rot_mtxrrr+r"r#r$cltjddd|fddd|fddd|fdftjS)z[Generate a 4x4 NumPy translation matrix. :param x, y, z: translation in each axis rrrrrrar)r"r#r$s r)homog_trans_mtxrs@ 88 Q11a|aAq\<@jj r+c"||d<||d<||d<y)z1Update existing translation matrix to new values.)rr)rr)r rNr)r"r#r$rs r)set_homog_trans_mtxrsCICICIr+scalecptj|dddgd|ddgdd|dggdgtjS)zSGenerate a 4x4 NumPy scaling matrix. :param float scale: scale multiplier rrrr)rs r)homog_scale_mtxrsC 88 Aq Aua+aE1-=|Ljj r+c|dkrdnd}|dkrdnd}d|k7rd|k7rtj||Sd|k7rtjdz |zS|dkrtjSdS)Nrgg?rg@)rarctan2r)r"r#sign_ysign_xs r) _get_azimuthrs~WT#FWT#F FqAv 1a AvUUS[6 !  !3,  -0 r+xyzcttjj|}d|k(ryt |d|d}tj |d|z }|||fS)zCompute spherical coordinates (r, azimuth, polar_angle) for X,Y,Z point. :param array xyz: column vector (3 row x 1 column NumPy array) :return: tuple of r, azimuth, polar_angle for input coordinate r)rrrrr )floatrr|r.rr)rrazimuth polar_angles r)get_spherical_coordinatesrs\ biinnS!"AAv3q63q6*G3q6A:.K w $$r+ra0a1a2revct}t}t}t}t |d |d |d |||z }t |} t | d |t| d |tjtjt} | j|}t|d|d} t | |tj| } |s| dfSt | |t| d|t | d|t |d|d|d|tjtjtjt} | | fS)aGenerate transformation matrix to coordinate space defined by 3 points. New coordinate space will have: acs[0] on XZ plane acs[1] origin acs[2] on +Z axis :param NumPy column array x3 acs: X,Y,Z column input coordinates x3 :param bool rev: if True, also return reverse transformation matrix (to return from coord_space) :returns: 4x4 NumPy array, x2 if rev=True rrr N) gtmgmrygmrzgmrz2rrrrrBr) rrrrtmmrymrzmrz2rDscmtazimuth2mrs r) coord_spacersG4 B C C DAAA3 RA "1 %BA$A$ $((3- B r AAaD!A$'H 4( 2B 4x $'1s#1s#1r!ubeR0 $((5/* +B r6Mr+c.tj|jdddf}tjd|d<tj|x|ddddf<|ddddf<tj ||ddddf<|ddddf |ddddf<|S)zCreate [entries] NumPy Z rotation matrices for [entries] angles. :param entries: int number of matrices generated. :param angle_rads: NumPy array of angles :returns: entries x 4 x 4 homogeneous rotation matrices rr.NrremptyrAr@r0r6)rrzs r) multi_rot_Zrvs :##A&1- .Bkk!nBsG "z 22Bq!QwK"Q1W+&&$Bq!QwKaAg;,Bq!QwK Ir+c.tj|jdddf}tjd|d<tj|x|ddddf<|ddddf<tj ||ddddf<|ddddf |ddddf<|S)zCreate [entries] NumPy Y rotation matrices for [entries] angles. :param entries: int number of matrices generated. :param angle_rads: NumPy array of angles :returns: entries x 4 x 4 homogeneous rotation matrices rr.Nr r)rrys r) multi_rot_Yrs :##A&1- .Bkk!nBsG "z 22Bq!QwK"Q1W+&&$Bq!QwKaAg;,Bq!QwK Ir+a3dLenc$tj|ddf}tjd|d<|dddddf |dddddf<|dddf|dddfz }tjj |d}tj |dddf|dddf}tj tj|dddf||dk7 }t| }t| } tj| tj||} tj| |dddfjd ddjd d}tj |dddf|dddf} t| } |stj| | ddStj| | dd} t| } t|}t|}|dddddf|dddddf<||z|z| z}tj| |gS) aGenerate [dLen] transform matrices to coord space defined by 3 points. New coordinate space will have: acs[0] on XZ plane acs[1] origin acs[2] on +Z axis :param NumPy array [entries]x3x3 [entries] XYZ coords for 3 atoms :param bool rev: if True, also return reverse transformation matrix (to return from coord_space) :returns: [entries] 4x4 NumPy arrays, x2 if rev=True r.Nrrrr )r%)wherer) rrr@r|r.rrdividerrmatmulreshapera)rrrrrDrrrrrrrrz2rrrrs r)multi_coord_spacers 4A, Bkk!nBsG1ac ]NBq!A#qyM 1a42ad8A qq!Ajj1a4!AqD'*G))BIIa1gqQ?@K gX B k\ "B 2ryyR( )B "bAh&&r1a0199"a@Azz!AqD'1QT7+H xi C yybe$$ 31 B x D k "C g Cq!QqSyMBq!A#qyM cC$ B 88RH r+)F)(rr/typingrnumpyrr*r4r>rotaxisrJrLrQr[rrstrndarrayrrrrrrrrtuplerr@rrrrrboolrrrintrrr+r)rsp: @F:&*Z >:"6  D& e& 3& 2::& RE E E u5RZZ5Uu2::5RZZ E e   %2:: %%ue8K2L %bkk!2::&r{{1BJJ'r{{1BJJ' ARZZ(AFd d d(* d9=d 2::rzzD( ()dN BJJ 2::  BJJ 2::  E"**ECEdErzzEr+