B bH2;@sdZddlmZddlmZddlmZddlm Z m Z m Z ddl m Z ddlmZmZmZmZmZddlZddlZd d Zd d Zd dZddZddZddZddZddZddZdZ de dZ!eddZ"e"#d e dd!e dd"e dd#e dd$e dd%e dd&e dd&e dd'e dd'e dd(e dd(e dd)e dd)e dd*e dd*e dd+e dd+e dd,e dd,e dd-e dd-e dd.e dd.e dd/e dd/e dd0e dd0e dd1e dd1e dd2e dd2e dd3e dd3e dd4e dd4e dd5e dd5e dd6e dd6e dd7e dd7e dd8e dd8e dd#e dd#e dd!e dd!e dd9e dd9e dd:e dd:e dd;e dd;e dda} This module contains the functionality for carrying out geometrical calculations for molecules and molecular systems Author: Jason Swails Contributors: Copyright (C) 2014 - 2015 Jason Swails This program is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330 Boston, MA 02111-1307, USA. )division) defaultdict)unit)TINY DEG_TO_RAD RAD_TO_DEG)Vec3)picossinsqrtacosNcCst|r|tj}t|r,|tj}t|rB|tj}t|rX|tj}t|rn|tj}t|r|tj}|dtkr|dtkr|dtkrtd|t9}|t9}|t9}|ddg}|t |}|t |}||dg} |t |} |t |t |t |t |} t ||| | | | } | | | g} t |t krbd| d<t |t krxd| d<t | t krd| d<t | t krd| d<t | t krd| d<|| | ftjS)a This function takes the lengths of the unit cell vectors and the angles between them and returns 3 unit cell vectors satisfying those dimensions Parameters ---------- a : double (or length Quantity) Length of the first unit cell vector b : double (or length Quantity) Length of the second unit cell vector c : double (or length Quantity) Length of the third unit cell vector alpha : double (or angle Quantity) Angle between vectors b and c beta : double (or angle Quantity) Angle between vectors a and c gamma : double (or angle Quantity) Angle between vectors a and b Returns ------- list Quantity, list Quantity, list Quantity The 3, 3-element vectors as quantities with dimension length Notes ----- The unit cell lengths are assumed to be Angstroms if no explicit unit is given. The angles are assumed to be degrees zIStrange unit cell vector angles detected. They appear to be in radians...gr)u is_quantity value_in_unit angstromsdegreesr warningswarnrr r r absr)abcalphabetagammaavZbxZbyZbvZcxZcyZczZcvr.lib/python3.7/site-packages/parmed/geometry.py!box_lengths_and_angles_to_vectors"sH      $      $ r!c Cst|r|tj}t|r,|tj}t|rB|tj}t|d|d|d|d|d|d}t|d|d|d|d|d|d}t|d|d|d|d|d|d}t|d|d|d|d|d|d||}t|d|d|d|d|d|d||}t|d|d|d|d|d|d||}|t9}|t9}|t9}|||ftj|||ftjfS)aH This function takes the lengths of the unit cell vectors and the angles between them and returns 3 unit cell vectors satisfying those dimensions Parameters ---------- a : collection of 3 floats (or length Quantity) The first unit cell vector b : collection of 3 floats (or length Quantity) The second unit cell vector c : collection of 3 floats (or length Quantity) The third unit cell vector Returns ------- (a, b, c), (alpha, beta, gamma) Two tuples, the first is the 3 unit cell vector lengths as length-dimension Quantity objects and the second is the set of angles between the unit cell vectors as angle-dimension Quantity objects Notes ----- The unit cell lengths are assumed to be Angstroms if no explicit unit is given. rrr)rrrrr r rr) rrrZlaZlbZlcrrrrrr !box_vectors_to_lengths_and_anglesas    444<<<r"cCst|r|tj}t|r,|tj}t|rB|tj}t|}t|}t|}||t|d|d}||t|d|d}||t|d|d}|||fS)a This function puts three unit cell vectors in a reduced form where a is "mostly" in x, b is "mostly" in y, and c is "mostly" in z. This form is necessary for some programs (notably OpenMM and Gromacs) Parameters ---------- a : 3-element collection of float First unit cell vector b : 3-element collection of float Second unit cell vector c : 3-element collection of float Third unit cell vector Returns ------- red_a, red_b, red_c : Vec3, Vec3, Vec3 The reduced unit cell vectors in units of angstroms Notes ----- The implementation here is taken from the OpenMM Python application layer written by Peter Eastman rr)rrrrrround)rrrrrr reduce_box_vectorss      r$cCs,|}||jddf}tj||ddS)a. Compute the center of mass of a group of coordinates. Parameters ---------- coordinates : numpy.ndarray Coordinate array masses : numpy.ndarray Array of masses Returns ------- COM np.ndarray of shape (3,) identifying the cartesian center of mass Notes ----- This method *requires* that the parameters be passed in as numpy arrays. AttributeError's will ensue if this is not the case. Also, coordinates must be able to be reshaped to (len(masses), 3), or ValueError's will ensue r)ZweightsZaxis)ZflattenZreshapeshapenpZaverage)Z coordinatesZmassesrrr center_of_masssr(c CsLt|\}}}t|\}}}||}||} ||} ||| | | | S)a Computes the cartesian distance between two atoms. Ignores periodic boundary conditions. Parameters ---------- a1, a2 : Atom or collection of 3 coordinates The two atoms between whom the distance should be calculated Returns ------- d2 : float The square of the distance between the two atoms Notes ----- This is done in pure Python, so it should not be used for large numbers of distance calculations. For that, use numpy-vectorized routines and the numpy coordinate arrays Raises ------ TypeError if a1 or a2 are not Atom or iterable ValueError if a1 or a2 are iterable, but do not have exactly 3 items )_get_coords_from_atom_or_tuple) a1a2x1y1z1x2y2z2ZdxZdyZdzrrr distance2s r2cCst|\}}}t|\}}}t|\} } } t||||||g} t|| || || g} tt| | }tt| | }t| | ||}tt|S)a Computes the cartesian angle between three atoms. Ignores periodic boundary conditions. Parameters ---------- a1, a2, a3 : Atom or collection of 3 coordinates The three atoms between whom the angle should be calculated (with a2 being the central atoms) Returns ------- ang : float The angle between the vectors a1-a2 and a2-a3 in degrees Notes ----- This is done in pure Python, so it should not be used for large numbers of distance calculations. For that, use numpy-vectorized routines and the numpy coordinate arrays Raises ------ TypeError if a1, a2, or a3 are not Atom or iterable ValueError if a1, a2, or a3 are iterable, but do not have exactly 3 items )r)r'arrayr dotrarccos)r*r+a3r,r-r.r/r0r1Zx3Zy3Zz3v1v2l1l2cosarrr anglesr<c Cstt|t|t|t|g}|d|d}|d|d}|d|d}t||}t||} tt||} tt| | } t|| | | } t||dkrtt| Stt|  SdS)a Computes the angle between three vectors made up of four points (all three vectors share one point with one other vector) Parameters ---------- a1, a2, a3, a4 : Atom or collection of 4 coordinates The four atoms between whom the torsion angle should be calculated (with a1 and a4 being the two end-point atoms not shared between two vectors) Returns ------- dihed : float The measured dihedral between the 4 points in degrees rrrr%gN)r'r3r)_crossr r4rr5) r*r+r6Za4pr7r8Zv3Zv1xv2Zv2xv3r9r:r;rrr dihedrals    r?cCsdt|d|d|d|d|d|d|d|d|d|d|d|dgS)z Computes the cross-product rrr)r'r3)r7r8rrr r=6s"r=cCs*ddlm}t||r&|j|j|jfS|S)Nr)Atom)Zparmed.topologyobjectsr@ isinstanceZxxZxyZxz)rr@rrr r)>s  r)g?g?rcCstS)N)_DEFAULT_CUTOFFrrrr IrCgGz?gp= ף?g333333?gGz?gGz@gffffff@gq= ףp?g)\(?gQ?g ףp= ?gq= ףp?gQ?gzG?g?gq= ףp?gQ?gRQ?g ףp= ?gffffff?g(\?g\(\?gzG?g?gQ?gGz?g(\?g(\?g= ףp=@g(\@)8)rr)rE)rF)rG)rH)rI)rrE)rEr)rrF)rFr)rrG)rGr)rrH)rHr)rrI)rIr)rErF)rFrE)rErG)rGrE)rE )rJrE)rErH)rHrE)rErI)rIrE)rE)rKrE)rE#)rLrE)rFrG)rGrF)rFrJ)rJrF)rFrH)rHrF)rFrI)rIrF)rFrK)rKrF)rGrJ)rJrG)rGrH)rHrG)rGrI)rIrG)rJrH)rHrJ)rJrI)rIrJ)rHrI)rIrH)rHrK)rKrH)rIrK)rKrI)$__doc__Z __future__r collectionsrZparmedrrZparmed.constantsrrrZ parmed.vec3rZmathr r r r r Znumpyr'rr!r"r$r(r2r<r?r=r)Z_OFFSETrBZSTANDARD_BOND_LENGTHS_SQUAREDupdaterrrr sh    ?,+##