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# Copyright 2017 by Peter Cock. All rights reserved.
# 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.
"""Tests for the vector code in Bio.PDB."""
import unittest
try:
import numpy as np
from numpy.random import random
except ImportError:
from Bio import MissingPythonDependencyError
raise MissingPythonDependencyError(
"Install NumPy if you want to use Bio.PDB."
) from None
from Bio.PDB import calc_angle
from Bio.PDB import calc_dihedral
from Bio.PDB import m2rotaxis
from Bio.PDB import refmat
from Bio.PDB import rotaxis
from Bio.PDB import rotmat
from Bio.PDB.vectors import coord_space
from Bio.PDB.vectors import get_spherical_coordinates
from Bio.PDB.vectors import homog_trans_mtx
from Bio.PDB.vectors import multi_coord_space
from Bio.PDB.vectors import Vector
class VectorTests(unittest.TestCase):
"""Tests for the Vector class."""
def test_division(self):
"""Confirm division works."""
v = Vector(1, 1, 1) / 2
self.assertEqual(repr(v), "<Vector 0.50, 0.50, 0.50>")
def test_Vector(self):
"""Test Vector object."""
v1 = Vector(0, 0, 1)
v2 = Vector(0, 0, 0)
v3 = Vector(0, 1, 0)
v4 = Vector(1, 1, 0)
self.assertEqual(calc_angle(v1, v2, v3), 1.5707963267948966)
self.assertEqual(calc_dihedral(v1, v2, v3, v4), 1.5707963267948966)
self.assertTrue(
np.array_equal((v1 - v2).get_array(), np.array([0.0, 0.0, 1.0]))
)
self.assertTrue(
np.array_equal((v1 - 1).get_array(), np.array([-1.0, -1.0, 0.0]))
)
self.assertTrue(
np.array_equal((v1 - (1, 2, 3)).get_array(), np.array([-1.0, -2.0, -2.0]))
)
self.assertTrue(
np.array_equal((v1 + v2).get_array(), np.array([0.0, 0.0, 1.0]))
)
self.assertTrue(np.array_equal((v1 + 3).get_array(), np.array([3.0, 3.0, 4.0])))
self.assertTrue(
np.array_equal((v1 + (1, 2, 3)).get_array(), np.array([1.0, 2.0, 4.0]))
)
self.assertTrue(np.array_equal(v1.get_array() / 2, np.array([0, 0, 0.5])))
self.assertTrue(np.array_equal(v1.get_array() / 2, np.array([0, 0, 0.5])))
self.assertEqual(v1 * v2, 0.0)
self.assertTrue(
np.array_equal((v1**v2).get_array(), np.array([0.0, -0.0, 0.0]))
)
self.assertTrue(np.array_equal((v1**2).get_array(), np.array([0.0, 0.0, 2.0])))
self.assertTrue(
np.array_equal((v1 ** (1, 2, 3)).get_array(), np.array([0.0, 0.0, 3.0]))
)
self.assertEqual(v1.norm(), 1.0)
self.assertEqual(v1.normsq(), 1.0)
v1[2] = 10
self.assertEqual(v1.__getitem__(2), 10)
def test_normalization(self):
"""Test Vector normalization."""
v1 = Vector([2, 0, 0])
self.assertTrue(
np.array_equal(v1.normalized().get_array(), np.array([1, 0, 0]))
)
# State of v1 should not be affected by `normalized`
self.assertTrue(np.array_equal(v1.get_array(), np.array([2, 0, 0])))
v1.normalize()
# State of v1 should be affected by `normalize`
self.assertTrue(np.array_equal(v1.get_array(), np.array([1, 0, 0])))
def test_refmat(self):
"""Test refmat can mirror one matrix to another."""
v1 = Vector(0, 0, 1)
v2 = Vector(0, 1, 0)
ref = refmat(v1, v2)
self.assertTrue(np.allclose(ref[0], [1.0, 0.0, 0.0]))
self.assertTrue(np.allclose(ref[1], [0.0, 0.0, 1.0]))
self.assertTrue(np.allclose(ref[2], [0.0, 1.0, 0.0]))
self.assertTrue(np.allclose(v1.left_multiply(ref).get_array(), [0.0, 1.0, 0.0]))
def test_rotmat_90(self):
"""Test regular 90 deg rotation."""
v1 = Vector(0, 0, 1)
v2 = Vector(0, 1, 0)
rot = rotmat(v1, v2)
self.assertTrue(np.allclose(rot[0], np.array([1.0, 0.0, 0.0])))
self.assertTrue(np.allclose(rot[1], np.array([0.0, 0.0, 1.0])))
self.assertTrue(np.allclose(rot[2], np.array([0.0, -1.0, 0.0])))
self.assertTrue(np.allclose(v1.left_multiply(rot).get_array(), [0.0, 1.0, 0.0]))
self.assertTrue(
np.allclose(
v1.right_multiply(np.transpose(rot)).get_array(),
[0.0, 1.0, 0.0],
)
)
def test_rotmat_180(self):
"""Test rotmat when the rotation is 180 deg (singularity)."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([-1.0, -0.8, 0])
rot = rotmat(v1, v2)
v3 = v1.left_multiply(rot)
self.assertTrue(np.allclose(v2.get_array(), v3.get_array()))
def test_rotmat_0(self):
"""Test rotmat when the rotation is 0 deg (singularity)."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([1.0, 0.8, 0])
rot = rotmat(v1, v2)
v3 = v1.left_multiply(rot)
self.assertTrue(np.allclose(v1.get_array(), v3.get_array()))
def test_m2rotaxis_90(self):
"""Test 90 deg rotation."""
v1 = Vector(0, 0, 1)
v2 = Vector(0, 1, 0)
rot = rotmat(v1, v2)
angle, axis = m2rotaxis(rot)
self.assertTrue(np.allclose(axis.get_array(), [-1.0, 0.0, 0.0]))
self.assertLess(abs(angle - np.pi / 2), 1e-5)
def test_m2rotaxis_180(self):
"""Test 180 deg rotation."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([-1.0, -0.8, 0])
rot = rotmat(v1, v2)
angle, axis = m2rotaxis(rot)
self.assertLess(abs(axis * v1), 1e-5) # axis orthogonal to v1
self.assertLess(abs(angle - np.pi), 1e-5)
def test_m2rotaxis_0(self):
"""Test 0 deg rotation. Axis must be [1, 0, 0] as per Vector docs."""
v1 = Vector([1.0, 0.8, 0])
v2 = Vector([1.0, 0.8, 0])
rot = rotmat(v1, v2)
angle, axis = m2rotaxis(rot)
self.assertTrue(np.allclose(axis.get_array(), [1, 0, 0]))
self.assertLess(abs(angle), 1e-5)
def test_Vector_angles(self):
"""Test Vector angles."""
angle = random() * np.pi
axis = Vector(random(3) - random(3))
axis.normalize()
m = rotaxis(angle, axis)
cangle, caxis = m2rotaxis(m)
self.assertAlmostEqual(angle, cangle, places=3)
self.assertTrue(
np.allclose(list(map(int, (axis - caxis).get_array())), [0, 0, 0]),
f"Want {axis.get_array()!r} and {caxis.get_array()!r}"
" to be almost equal",
)
def test_get_spherical_coordinates(self):
"""Test spherical coordinates."""
srt22 = np.sqrt(2.0) / 2
r45 = np.radians(45)
# r90 = np.radians(90)
r135 = np.radians(135)
for i in range(2):
for j in range(2):
for k in range(2):
sc = get_spherical_coordinates(
[
(0.5 if i else -0.5),
0.5 if j else -0.5,
(1 if k else -1) * srt22,
]
)
# print(sc[0], np.degrees(sc[1]), np.degrees(sc[2]))
self.assertEqual(1.0, sc[0]) # r
self.assertEqual(
(1 if j else -1) * (r45 if i else r135), sc[1]
) # azimuth
self.assertEqual((r45 if k else r135), sc[2]) # polar angle
def test_coord_space(self):
"""Confirm can generate coordinate space transform for 3 points."""
# start with 3 points already aligned to axes
point_set = (
np.array([[2.0], [0.0], [2.0], [1.0]]),
np.array([[0.0], [0.0], [0.0], [1.0]]),
np.array([[0.0], [0.0], [2.0], [1.0]]),
)
# confirm get id matrix to transform to/from coord space
homog_id = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
mtxs = coord_space(point_set[0], point_set[1], point_set[2], True)
for i in range(2):
self.assertTrue(np.array_equal(mtxs[i], homog_id))
# test in every quadrant
for i in range(2):
for j in range(2):
for k in range(2):
# translate point_set arbitrary amount in each axis
tm = homog_trans_mtx(
(3 if i else -3), (3 if j else -3), (3 if k else -3)
)
ps2 = [1, 2, 3]
for i in range(3):
ps2[i] = tm.dot(point_set[i])
# confirm coord_space puts points back to axis alignment
mtxs = coord_space(ps2[0], ps2[1], ps2[2], True)
rslt = [1, 2, 3]
for i in range(3):
rslt[i] = mtxs[0].dot(ps2[i])
self.assertTrue(np.array_equal(rslt, point_set))
# confirm reverse transform returns translated points
for i in range(3):
rslt[i] = mtxs[1].dot(rslt[i])
self.assertTrue(np.array_equal(rslt, ps2))
def test_multi_coord_space(self):
"""Confirm multi_coord_space computes forward, reverse transforms."""
# start with 3 points already aligned to axes
point_set = np.array(
[
[
[2.0, 0.0, 2.0, 1.0],
[0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, 2.0, 1.0],
]
]
)
# confirm get id matrix to transform to/from coord space
homog_id = np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 0, 1]])
mtxs = multi_coord_space(point_set, 1, True)
for i in range(2):
self.assertTrue(np.array_equal(mtxs[i][0], homog_id))
# test in every quadrant
test_set = np.empty([8, 3, 4], dtype=np.float64)
m = 0
for i in range(2):
for j in range(2):
for k in range(2):
# translate point_set arbitrary amount in each axis
tm = homog_trans_mtx(
(3 if i else -3), (3 if j else -3), (3 if k else -3)
)
for i in range(3):
test_set[m, i] = tm.dot(point_set[0][i])
m += 1
# confirm coord_space puts points back to axis alignment
mtxs = multi_coord_space(test_set, 8, True)
for m in range(8):
rslt = [1, 2, 3]
for i in range(3):
rslt[i] = mtxs[0][m].dot(test_set[m][i])
self.assertTrue(np.array_equal(rslt, point_set[0]))
# confirm reverse transform returns translated points
for i in range(3):
rslt[i] = mtxs[1][m].dot(rslt[i])
self.assertTrue(np.array_equal(rslt, test_set[m]))
if __name__ == "__main__":
runner = unittest.TextTestRunner(verbosity=2)
unittest.main(testRunner=runner)
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