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SVDSuperimposer.py
# Copyright (C) 2002, Thomas Hamelryck (thamelry@vub.ac.be)
# This code is part of the Biopython distribution and governed by its
# license.  Please see the LICENSE file that should have been included
# as part of this package.

from numpy import dot, transpose, sqrt, array
from numpy.linalg import svd, det

00009 class SVDSuperimposer(object):
    """
    SVDSuperimposer 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.  

    SVD stands for Singular Value Decomposition, which is used to calculate
    the superposition.

    Reference:

    Matrix computations, 2nd ed. Golub, G. & Van Loan, CF., The Johns 
    Hopkins University Press, Baltimore, 1989
    """
    def __init__(self):
        self._clear()

    # Private methods

    def _clear(self):
        self.reference_coords=None
        self.coords=None
        self.transformed_coords=None
        self.rot=None
        self.tran=None
        self.rms=None
        self.init_rms=None

    def _rms(self, coords1, coords2):
        "Return rms deviations between coords1 and coords2."
        diff=coords1-coords2
        l=coords1.shape[0]
        return sqrt(sum(sum(diff*diff))/l)

    # Public methods
    
00045     def set(self, reference_coords, coords):
        """
        Set the coordinates to be superimposed.
        coords will be put on top of reference_coords.

        o reference_coords: an NxDIM array
        o coords: an NxDIM array

        DIM is the dimension of the points, N is the number
        of points to be superimposed.
        """
        # clear everything from previous runs
        self._clear()
        # store cordinates
        self.reference_coords=reference_coords
        self.coords=coords
        n=reference_coords.shape
        m=coords.shape
        if n!=m or not(n[1]==m[1]==3):
            raise Exception("Coordinate number/dimension mismatch.")
        self.n=n[0]

    def run(self):
        "Superimpose the coordinate sets."
        if self.coords is None or self.reference_coords is None:
            raise Exception("No coordinates set.")
        coords=self.coords
        reference_coords=self.reference_coords
        # center on centroid
        av1=sum(coords)/self.n  
        av2=sum(reference_coords)/self.n    
        coords=coords-av1
        reference_coords=reference_coords-av2
        # correlation matrix
        a=dot(transpose(coords), reference_coords)
        u, d, vt=svd(a)
        self.rot=transpose(dot(transpose(vt), transpose(u)))
        # check if we have found a reflection
        if det(self.rot)<0:
            vt[2]=-vt[2]
            self.rot=transpose(dot(transpose(vt), transpose(u)))
        self.tran=av2-dot(av1, self.rot)

    def get_transformed(self):
        "Get the transformed coordinate set."
        if self.coords is None or self.reference_coords is None:
            raise Exception("No coordinates set.")
        if self.rot is None:
            raise Exception("Nothing superimposed yet.")
        if self.transformed_coords is None:
            self.transformed_coords=dot(self.coords, self.rot)+self.tran
        return self.transformed_coords

    def get_rotran(self):
        "Right multiplying rotation matrix and translation."
        if self.rot is None:
            raise Exception("Nothing superimposed yet.")
        return self.rot, self.tran

    def get_init_rms(self):
        "Root mean square deviation of untransformed coordinates."
        if self.coords is None:
            raise Exception("No coordinates set yet.")
        if self.init_rms is None:
            self.init_rms=self._rms(self.coords, self.reference_coords)
        return self.init_rms

    def get_rms(self):
        "Root mean square deviation of superimposed coordinates."
        if self.rms is None:
            transformed_coords=self.get_transformed()
            self.rms=self._rms(transformed_coords, self.reference_coords)
        return self.rms


if __name__=="__main__":

    # start with two coordinate sets (Nx3 arrays - float)

    x=array([[51.65, -1.90, 50.07],
         [50.40, -1.23, 50.65],
         [50.68, -0.04, 51.54],
         [50.22, -0.02, 52.85]], 'f')

    y=array([[51.30, -2.99, 46.54],
         [51.09, -1.88, 47.58],
         [52.36, -1.20, 48.03],
         [52.71, -1.18, 49.38]], 'f')

    # start!
    sup=SVDSuperimposer()

    # set the coords
    # y will be rotated and translated on x
    sup.set(x, y)

    # do the lsq fit
    sup.run()

    # get the rmsd
    rms=sup.get_rms()

    # get rotation (right multiplying!) and the translation
    rot, tran=sup.get_rotran()

    # rotate y on x
    y_on_x1=dot(y, rot)+tran

    # same thing
    y_on_x2=sup.get_transformed()

    print y_on_x1
    print
    print y_on_x2
    print
    print "%.2f" % rms

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