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#! /usr/bin/env python
#
# Calculate SMART RMSD with or without molecular superposition (FIT or NOFIT) 
# Script distributed under GNU LGPL 3.0 along rDock software.
# 
# This algorithm takes into account molecular automorphism. That is, it identifies
# molecules which are the same but might have atom orders changed and still be able to 
# match the pairs and correctly calculate the RMSD.
#
# Author: Daniel Alvarez-Garcia
# Date: 08-11-2013

import math
import pybel
import numpy as npy
import optparse

def superpose3D(ref, target, weights=None,refmask=None,targetmask=None,returnRotMat=False):
    """superpose3D performs 3d superposition using a weighted Kabsch algorithm : http://dx.doi.org/10.1107%2FS0567739476001873 & doi: 10.1529/biophysj.105.066654
    definition : superpose3D(ref, target, weights,refmask,targetmask)
    @parameter 1 :  ref - xyz coordinates of the reference structure (the ligand for instance)
    @type 1 :       float64 numpy array (nx3)
    ---
    @parameter 2 :  target - theoretical target positions to which we should move (does not need to be physically relevant.
    @type 2 :       float 64 numpy array (nx3)
    ---
    @parameter 3:   weights - numpy array of atom weights (usuallly between 0 and 1)
    @type 3 :       float 64 numpy array (n)
    @parameter 4:   mask - a numpy boolean mask for designating atoms to include
    Note ref and target positions must have the same dimensions -> n*3 numpy arrays where n is the number of points (or atoms)
    Returns a set of new coordinates, aligned to the target state as well as the rmsd
    """
    if weights == None :
        weights=1.0
    if refmask == None :
        refmask=npy.ones(len(ref),"bool")
    if targetmask == None :
        targetmask=npy.ones(len(target),"bool")
    #first get the centroid of both states
    ref_centroid = npy.mean(ref[refmask]*weights,axis=0)
    #print ref_centroid
    refCenteredCoords=ref-ref_centroid
    #print refCenteredCoords
    target_centroid=npy.mean(target[targetmask]*weights,axis=0)
    targetCenteredCoords=target-target_centroid
    #print targetCenteredCoords
    #the following steps come from : http://www.pymolwiki.org/index.php/OptAlign#The_Code and http://en.wikipedia.org/wiki/Kabsch_algorithm
    # Initial residual, see Kabsch.
    E0 = npy.sum( npy.sum(refCenteredCoords[refmask] * refCenteredCoords[refmask]*weights,axis=0),axis=0) + npy.sum( npy.sum(targetCenteredCoords[targetmask] * targetCenteredCoords[targetmask]*weights,axis=0),axis=0)
    reftmp=npy.copy(refCenteredCoords[refmask])
    targettmp=npy.copy(targetCenteredCoords[targetmask])
    #print refCenteredCoords[refmask]
    #single value decomposition of the dotProduct of both position vectors
    try:
        dotProd = npy.dot( npy.transpose(reftmp), targettmp* weights)
        V, S, Wt = npy.linalg.svd(dotProd )
    except Exception:
        try:
            dotProd = npy.dot( npy.transpose(reftmp), targettmp)
            V, S, Wt = npy.linalg.svd(dotProd )
        except Exception:
            print >> sys.stderr,"Couldn't perform the Single Value Decomposition, skipping alignment"
        return ref, 0
    # we already have our solution, in the results from SVD.
    # we just need to check for reflections and then produce
    # the rotation.  V and Wt are orthonormal, so their det's
    # are +/-1.
    reflect = float(str(float(npy.linalg.det(V) * npy.linalg.det(Wt))))
    if reflect == -1.0:
        S[-1] = -S[-1]
        V[:,-1] = -V[:,-1]
    rmsd = E0 - (2.0 * sum(S))
    rmsd = npy.sqrt(abs(rmsd / len(ref[refmask])))   #get the rmsd
    #U is simply V*Wt
    U = npy.dot(V, Wt)  #get the rotation matrix
    # rotate and translate the molecule
    new_coords = npy.dot((refCenteredCoords), U)+ target_centroid  #translate & rotate
    #new_coords=(refCenteredCoords + target_centroid)
    #print U
    if returnRotMat : 
        return new_coords,rmsd, U
    return new_coords,rmsd


def squared_distance(coordsA, coordsB):
    """Find the squared distance between two 3-tuples"""
    sqrdist = sum( (a-b)**2 for a, b in zip(coordsA, coordsB) )
    return sqrdist
    
def rmsd(allcoordsA, allcoordsB):
    """Find the RMSD between two lists of 3-tuples"""
    deviation = sum(squared_distance(atomA, atomB) for
                    (atomA, atomB) in zip(allcoordsA, allcoordsB))
    return math.sqrt(deviation / float(len(allcoordsA)))
    
def mapToCrystal(xtal, pose):
    """Some docking programs might alter the order of the atoms in the output (like Autodock Vina does...)
     this will mess up the rmsd calculation with OpenBabel"""
    query = pybel.ob.CompileMoleculeQuery(xtal.OBMol) 
    mapper=pybel.ob.OBIsomorphismMapper.GetInstance(query)
    mappingpose = pybel.ob.vvpairUIntUInt()
    exit=mapper.MapUnique(pose.OBMol,mappingpose)
    return mappingpose[0]

def parseArguments():
	optparse.OptionParser.format_epilog = lambda self, formatter: self.epilog
	epilog = """Args:
	reference.sdf		SDF file with the reference molecule.
	input.sdf		SDF file with the molecules to be compared to reference.\n"""
	parser = optparse.OptionParser("usage: %prog [options] reference.sdf input.sdf", epilog=epilog)
	parser.add_option("-f", "--fit",dest="fit", action="store_true", default=False,
                  help="Superpose molecules before RMSD calculation")
	parser.add_option("--threshold","-t",dest="threshold", action="store", nargs=1, 
                  help="Discard poses with RMSD < THRESHOLD with respect previous poses which where not rejected based on same principle. A Population SDField will be added to output SD with the population number.", type=float)
	parser.add_option("-o","--out", dest="outfilename", metavar="FILE", default=False,
                  help="If declared, write an output SDF file with the input molecules with a new sdfield <RMSD>. If molecule was fitted, the fitted molecule coordinates will be saved.")
	(options, args) =  parser.parse_args()
	
	#Check we have two arguments
	if len(args) < 2:
		parser.error("Incorrect number of arguments. Use -h or --help options to print help.")

	return options, args

def updateCoords(obmol, newcoords):
    "Update OBMol coordinates. newcoords is a numpy array"
    for i,atom in enumerate(obmol):
        atom.OBAtom.SetVector(*newcoords[i])

def getAutomorphRMSD(target, molec, fit=False):
    """
    Use Automorphism to reorder target coordinates to match ref coordinates atom order
    for correct RMSD comparison. Only the lowest RMSD will be returned.
    
    Returns:
      If fit=False: 	bestRMSD	(float)					RMSD of the best matching mapping.
      If fit=True:	(bestRMSD, molecCoordinates)	(float, npy.array)	RMSD of best match and its molecule fitted coordinates.	
    """
    mappings = pybel.ob.vvpairUIntUInt()
    bitvec = pybel.ob.OBBitVec()
    lookup = []
    for i, atom in enumerate(target):
        lookup.append(i)
    success = pybel.ob.FindAutomorphisms(target.OBMol, mappings)
    targetcoords = [atom.coords for atom in target]
    mappose = npy.array(mapToCrystal(target, molec))
    mappose = mappose[npy.argsort(mappose[:,0])][:,1]
    posecoords = npy.array([atom.coords for atom in molec])[mappose]
    resultrmsd = 999999999999
    for mapping in mappings:
	automorph_coords = [None] * len(targetcoords)
	for x, y in mapping:
	    automorph_coords[lookup.index(x)] = targetcoords[lookup.index(y)]
	mapping_rmsd = rmsd(posecoords, automorph_coords)
	if mapping_rmsd < resultrmsd:
	    resultrmsd = mapping_rmsd
	    fitted_result = False
	if fit: 
	    fitted_pose, fitted_rmsd = superpose3D(npy.array(automorph_coords), npy.array(posecoords))
	    if fitted_rmsd < resultrmsd:
		resultrmsd = fitted_rmsd
		fitted_result = fitted_pose
    
    if fit:
      return (resultrmsd, fitted_pose)
    else:
      return resultrmsd

def saveMolecWithRMSD(outsdf, molec, rmsd, population=False):
    newData = pybel.ob.OBPairData()	
    newData.SetAttribute("RMSD")
    newData.SetValue('%.3f'%rmsd)
    
    if population:
	popData = pybel.ob.OBPairData()
	popData.SetAttribute("Population")
	popData.SetValue('%i'%population)
	molec.OBMol.CloneData(popData)
	
    molec.OBMol.CloneData(newData)           # Add new data
    outsdf.write(molec)
    
if __name__ == "__main__":
    import sys, os
   
    (opts, args) = parseArguments() 
	
    xtal = args[0]
    poses = args[1]

    if not os.path.exists(xtal) or not os.path.exists(poses):
	sys.exit("Input files not found. Please check the path given is correct.")
	
    fit = opts.fit
    outfname = opts.outfilename
    threshold = opts.threshold

    # Read crystal pose
    crystal = next(pybel.readfile("sdf", xtal))
    crystal.removeh()
    crystalnumatoms = len(crystal.atoms)

    #If outfname is defined, prepare an output SDF sink to write molecules
    if outfname:
	outsdf = pybel.Outputfile('sdf', outfname, overwrite=True)

    # Find the RMSD between the crystal pose and each docked pose
    dockedposes = pybel.readfile("sdf", poses)
    if fit: print "POSE\tRMSD_FIT"
    else: print "POSE\tRMSD_NOFIT"
    skipped = []
    moleclist = {}	# Save all poses with their dockid
    population = {}	# Poses to be written
    outlist = {}
    for docki, dockedpose in enumerate(dockedposes):
        dockedpose.removeh()
	natoms = len(dockedpose.atoms)
	if natoms != crystalnumatoms: 
		skipped.append(docki+1)
		continue
	if fit: 
	    resultrmsd, fitted_result = getAutomorphRMSD(crystal, dockedpose, fit=True)
	    updateCoords(dockedpose, fitted_result)
	else:
	    resultrmsd = getAutomorphRMSD(crystal, dockedpose, fit=False)
	
	if threshold:
	    # Calculate RMSD between all previous poses
	    # Discard if rmsd < FILTER threshold
	    if moleclist:
		match = None
		bestmatchrmsd = 999999
		for did,prevmol in moleclist.iteritems():
		    tmprmsd = getAutomorphRMSD(prevmol, dockedpose)
		    if tmprmsd < threshold:
			if tmprmsd < bestmatchrmsd:
			    bestmatchrmsd = tmprmsd
			    match = did
			
		if match != None:
		    # Do not write this one
		    # sum one up to the matching previous molecule id
		    print >> sys.stderr, "Pose %i matches pose %i with %.3f RMSD"%(docki+1, match+1, bestmatchrmsd)
		    population[match] += 1
		else:
		    # There's no match. Print info for this one and write to outsdf if needed
		    # Save this one!
		    if outfname: outlist[docki] = (dockedpose, resultrmsd)
		    print "%d\t%.2f"%((docki+1),resultrmsd)
		    moleclist[docki] = dockedpose
		    population[docki] = 1
	    else:
		# First molecule in list. Append for sure
		moleclist[docki] = dockedpose
		population[docki] = 1
		if outfname: outlist[docki] = (dockedpose, resultrmsd)
	else:
	    # Just write best rmsd found and the molecule to outsdf if demanded
	    if outfname: saveMolecWithRMSD(outsdf, dockedpose, resultrmsd)
	    print "%d\t%.2f"%((docki+1),resultrmsd)

    if outlist:
	# Threshold applied and outlist need to be written
	for docki in sorted(outlist.iterkeys()):
	    molrmsd = outlist[docki]
	    # Get number of matchs in thresholding operation
	    pop = population.get(docki)
	    if not pop: pop = 1
	    # Save molecule
	    saveMolecWithRMSD(outsdf, molrmsd[0], molrmsd[1], pop)
	    
    if skipped: print >> sys.stderr, "SKIPPED input molecules due to number of atom missmatch: %s"%skipped