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# Copyright (C) 2002, Thomas Hamelryck ([email protected])
#
# This file is part of the Biopython distribution and governed by your
# choice of the "Biopython License Agreement" or the "BSD 3-Clause License".
# Please see the LICENSE file that should have been included as part of this
# package.
"""Align on protein structure onto another using SVD alignment.
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 in the algorithm.
"""
try:
from numpy import dot, transpose, sqrt
from numpy.linalg import svd, det
except ImportError:
from Bio import MissingPythonDependencyError
raise MissingPythonDependencyError(
"Install NumPy if you want to use Bio.SVDSuperimposer."
)
class SVDSuperimposer:
"""Class to run SVD alignment.
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
start with two coordinate sets (Nx3 arrays - float)
>>> from Bio.SVDSuperimposer import SVDSuperimposer
>>> from numpy import array, dot, set_printoptions
>>>
>>> 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()
>>> set_printoptions(precision=2)
>>> print(y_on_x1)
[[ 5.17e+01 -1.90e+00 5.01e+01]
[ 5.04e+01 -1.23e+00 5.06e+01]
[ 5.07e+01 -4.16e-02 5.15e+01]
[ 5.02e+01 -1.94e-02 5.29e+01]]
>>> print(y_on_x2)
[[ 5.17e+01 -1.90e+00 5.01e+01]
[ 5.04e+01 -1.23e+00 5.06e+01]
[ 5.07e+01 -4.16e-02 5.15e+01]
[ 5.02e+01 -1.94e-02 5.29e+01]]
>>> print("%.2f" % rms)
0.00
"""
def __init__(self):
"""Initialize the class."""
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 (PRIVATE)."""
diff = coords1 - coords2
return sqrt(sum(sum(diff * diff)) / coords1.shape[0])
# Public methods
def set(self, reference_coords, coords):
"""Set 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.
"""
# clear everything from previous runs
self._clear()
# store coordinates
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__":
from Bio._utils import run_doctest
run_doctest(verbose=0)
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