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# -*- Mode: python; tab-width: 4; indent-tabs-mode:nil; coding:utf-8 -*-
# vim: tabstop=4 expandtab shiftwidth=4 softtabstop=4 fileencoding=utf-8
#
# MDAnalysis --- https://www.mdanalysis.org
# Copyright (c) 2006-2017 The MDAnalysis Development Team and contributors
# (see the file AUTHORS for the full list of names)
#
# Released under the Lesser GNU Public Licence, v2.1 or any higher version
#
# Please cite your use of MDAnalysis in published work:
#
# R. J. Gowers, M. Linke, J. Barnoud, T. J. E. Reddy, M. N. Melo, S. L. Seyler,
# D. L. Dotson, J. Domanski, S. Buchoux, I. M. Kenney, and O. Beckstein.
# MDAnalysis: A Python package for the rapid analysis of molecular dynamics
# simulations. In S. Benthall and S. Rostrup editors, Proceedings of the 15th
# Python in Science Conference, pages 102-109, Austin, TX, 2016. SciPy.
# doi: 10.25080/majora-629e541a-00e
#
# N. Michaud-Agrawal, E. J. Denning, T. B. Woolf, and O. Beckstein.
# MDAnalysis: A Toolkit for the Analysis of Molecular Dynamics Simulations.
# J. Comput. Chem. 32 (2011), 2319--2327, doi:10.1002/jcc.21787
#
"""
:Author: Joshua L. Adelman, University of Pittsburgh
:Contact: jla65@pitt.edu
Sample code to use the routine for fast RMSD & rotational matrix calculation.
For the example provided below, the minimum least-squares RMSD for the two
7-atom fragments should be 0.719106 A.
And the corresponding 3x3 rotation matrix is:
[[ 0.72216358 -0.52038257 -0.45572112]
[ 0.69118937 0.51700833 0.50493528]
[-0.0271479 -0.67963547 0.73304748]]
"""
import numpy as np
import MDAnalysis.lib.qcprot as qcp
from numpy.testing import assert_almost_equal, assert_array_almost_equal
import MDAnalysis.analysis.rms as rms
import pytest
@pytest.fixture()
def atoms_a():
return np.array(
[[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], dtype=np.float64
)
@pytest.fixture()
def atoms_b():
return np.array(
[[13, 14, 15], [16, 17, 18], [19, 20, 21], [22, 23, 24]],
dtype=np.float64,
)
# Calculate rmsd after applying rotation
def rmsd(a, b):
"""Returns RMSD between two coordinate sets a and b."""
return np.sqrt(np.sum(np.power(a - b, 2)) / a.shape[1])
def test_CalcRMSDRotationalMatrix():
# Setup coordinates
frag_a = np.zeros((3, 7), dtype=np.float64)
frag_b = np.zeros((3, 7), dtype=np.float64)
N = 7
frag_a[0][0] = -2.803
frag_a[1][0] = -15.373
frag_a[2][0] = 24.556
frag_a[0][1] = 0.893
frag_a[1][1] = -16.062
frag_a[2][1] = 25.147
frag_a[0][2] = 1.368
frag_a[1][2] = -12.371
frag_a[2][2] = 25.885
frag_a[0][3] = -1.651
frag_a[1][3] = -12.153
frag_a[2][3] = 28.177
frag_a[0][4] = -0.440
frag_a[1][4] = -15.218
frag_a[2][4] = 30.068
frag_a[0][5] = 2.551
frag_a[1][5] = -13.273
frag_a[2][5] = 31.372
frag_a[0][6] = 0.105
frag_a[1][6] = -11.330
frag_a[2][6] = 33.567
frag_b[0][0] = -14.739
frag_b[1][0] = -18.673
frag_b[2][0] = 15.040
frag_b[0][1] = -12.473
frag_b[1][1] = -15.810
frag_b[2][1] = 16.074
frag_b[0][2] = -14.802
frag_b[1][2] = -13.307
frag_b[2][2] = 14.408
frag_b[0][3] = -17.782
frag_b[1][3] = -14.852
frag_b[2][3] = 16.171
frag_b[0][4] = -16.124
frag_b[1][4] = -14.617
frag_b[2][4] = 19.584
frag_b[0][5] = -15.029
frag_b[1][5] = -11.037
frag_b[2][5] = 18.902
frag_b[0][6] = -18.577
frag_b[1][6] = -10.001
frag_b[2][6] = 17.996
# Allocate rotation array
rot = np.zeros((9,), dtype=np.float64)
# Calculate center of geometry
comA = np.sum(frag_a, axis=1) / N
comB = np.sum(frag_b, axis=1) / N
# Center each fragment
frag_a = frag_a - comA.reshape(3, 1)
frag_b = frag_b - comB.reshape(3, 1)
# Calculate rmsd and rotation matrix
qcp_rmsd = qcp.CalcRMSDRotationalMatrix(frag_a.T, frag_b.T, N, rot, None)
# print 'qcp rmsd = ',rmsd
# print 'rotation matrix:'
# print rot.reshape((3,3))
# rotate frag_b to obtain optimal alignment
frag_br = np.dot(frag_b.T, rot.reshape((3, 3)))
aligned_rmsd = rmsd(frag_br.T, frag_a)
# print 'rmsd after applying rotation: ',rmsd
assert_almost_equal(
aligned_rmsd,
0.719106,
6,
"RMSD between fragments A and B does not match excpected value.",
)
expected_rot = np.array(
[
[0.72216358, -0.52038257, -0.45572112],
[0.69118937, 0.51700833, 0.50493528],
[-0.0271479, -0.67963547, 0.73304748],
]
)
assert_almost_equal(
rot.reshape((3, 3)),
expected_rot,
6,
"Rotation matrix for aliging B to A does not have expected values.",
)
def test_innerproduct(atoms_a, atoms_b):
a = 2450.0
b = np.array([430, 452, 474, 500, 526, 552, 570, 600, 630])
number_of_atoms = 4
e = np.zeros(9, dtype=np.float64)
g = qcp.InnerProduct(e, atoms_a, atoms_b, number_of_atoms, None)
assert_almost_equal(a, g)
assert_array_almost_equal(b, e)
def test_RMSDmatrix(atoms_a, atoms_b):
number_of_atoms = 4
rotation = np.zeros(9, dtype=np.float64)
rmsd = qcp.CalcRMSDRotationalMatrix(
atoms_a, atoms_b, number_of_atoms, rotation, None
) # no weights
rmsd_ref = 20.73219522556076
assert_almost_equal(rmsd_ref, rmsd)
rotation_ref = np.array(
[
0.9977195,
0.02926979,
0.06082009,
-0.0310942,
0.9990878,
0.02926979,
-0.05990789,
-0.0310942,
0.9977195,
]
)
assert_array_almost_equal(rotation, rotation_ref, 6)
def test_RMSDmatrix_simple(atoms_a, atoms_b):
number_of_atoms = 4
rotation = np.zeros(9, dtype=np.float64)
rmsd = qcp.CalcRMSDRotationalMatrix(
atoms_a, atoms_b, number_of_atoms, rotation, None
) # no weights
rmsd_ref = 20.73219522556076
assert_almost_equal(rmsd_ref, rmsd)
rotation_ref = np.array(
[
0.9977195,
0.02926979,
0.06082009,
-0.0310942,
0.9990878,
0.02926979,
-0.05990789,
-0.0310942,
0.9977195,
]
)
assert_array_almost_equal(rotation, rotation_ref, 6)
def test_rmsd(atoms_a, atoms_b):
rotation_m = np.array(
[
[0.9977195, 0.02926979, 0.06082009],
[-0.0310942, 0.9990878, 0.02926979],
[-0.05990789, -0.0310942, 0.9977195],
]
)
atoms_b_aligned = np.dot(atoms_b, rotation_m)
rmsd = rms.rmsd(atoms_b_aligned, atoms_a)
rmsd_ref = 20.73219522556076
assert_almost_equal(rmsd, rmsd_ref, 6)
def test_weights(atoms_a, atoms_b):
no_of_atoms = 4
weights = np.array([1, 2, 3, 4], dtype=np.float64)
rotation = np.zeros(9, dtype=np.float64)
rmsd = qcp.CalcRMSDRotationalMatrix(
atoms_a, atoms_b, no_of_atoms, rotation, weights
)
assert_almost_equal(rmsd, 32.798779202159416)
rotation_ref = np.array(
[
0.99861395,
0.022982,
0.04735006,
-0.02409085,
0.99944556,
0.022982,
-0.04679564,
-0.02409085,
0.99861395,
]
)
np.testing.assert_almost_equal(rotation_ref, rotation)
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