/usr/lib/python3/dist-packages/csb/test/cases/numeric/__init__.py is in python3-csb 1.2.2+dfsg-2ubuntu1.
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import numpy as np
@test.regression
class MathRegressions(test.Case):
def testDihedralAngles(self):
"""
r526
"""
from csb.numeric import dihedral_angle
a = np.array([2, 0., 0.])
b = np.array([0, 0., 0.])
c = np.array([0, 2., 0.])
d = np.array([0, 4., -4.])
self.assertEqual(dihedral_angle(a, b, c, d), 90.0)
self.assertEqual(dihedral_angle(a, b, c, a), 0.0)
self.assertEqual(dihedral_angle(a, b, c, -d), -90.0)
@test.unit
class TestMath(test.Case):
def testDihedralAngles(self):
from csb.numeric import dihedral_angle
a = np.array([1, 0., 0.])
b = np.array([0, 0., 0.])
c = np.array([0, 1., 0.])
d = np.array([0, 1., -1.])
self.assertEqual(dihedral_angle(a, b, c, d), 90.0)
self.assertEqual(dihedral_angle(a, b, c, d + a), 45.0)
self.assertEqual(dihedral_angle(a, b, c, a), 0.0)
self.assertEqual(dihedral_angle(a, b, c, -d), -90.0)
def testLog(self):
from csb.numeric import log, LOG_MAX, LOG_MIN
from numpy import log as ref_log
x = np.linspace(LOG_MIN, LOG_MAX, 1000000)
self.assertTrue((log(x) == ref_log(x)).all())
self.assertEqual(log(10 * LOG_MAX), log(LOG_MAX))
self.assertEqual(log(0.1 * LOG_MIN), log(LOG_MIN))
def testExp(self):
from csb.numeric import exp, EXP_MAX, EXP_MIN
from numpy import exp as ref_exp
x = np.linspace(EXP_MIN,
EXP_MAX, 100000)
self.assertTrue((exp(x) == ref_exp(x)).all())
self.assertEqual(exp(EXP_MAX + 10.), exp(EXP_MAX))
self.assertEqual(exp(10. * EXP_MIN), exp(EXP_MIN))
def testPolar(self):
from csb.numeric import polar, from_polar
rand = np.random.random((10000, 3))
result = np.array(list(map(polar, map(from_polar, rand))))
eps = 1e-8
self.assertTrue((np.abs(rand - result) < eps).all())
self.assertTrue((np.abs(polar(np.array([0., 1.0])) - \
np.array([1., np.pi * 0.5])) < eps).all())
def testFromPolar(self):
from csb.numeric import polar, from_polar
rand = np.random.random((10000, 3))
result = np.array(list(map(from_polar, map(polar, rand))))
eps = 1e-8
self.assertTrue((np.abs(rand - result) < eps).all())
self.assertTrue((np.abs(from_polar(np.array([1., np.pi * 0.5])) - \
np.array([0., 1.0])) < eps).all())
def testRadian2Degree(self):
from csb.numeric import degree2radian, radian2degree
rand = np.random.random(10000) * 2 * np.pi
eps = 1e-8
self.assertTrue((np.abs(rand -
degree2radian(radian2degree(rand)))\
< eps).all())
def testDegree2Radian(self):
from csb.numeric import degree2radian, radian2degree
rand = np.random.random(10000) * 2 * np.pi
eps = 1e-8
self.assertTrue((np.abs(rand -
degree2radian(radian2degree(rand)))\
< eps).all())
def testRotationMatrix(self):
from csb.numeric import rotation_matrix, axis_and_angle
R1 = [[0, 1, 0], [-1, 0, 0], [0, 0, 1]]
R2 = rotation_matrix([0, 0, 1], np.pi / 2.0)
axis, angle = axis_and_angle(R2)
R3 = rotation_matrix(axis, angle)
self.assertAlmostEqual(angle, np.pi / 2.0)
self.assertTrue(np.allclose(R1, R2))
self.assertTrue(np.allclose(R1, R3))
@test.unit
class TestNumeric(test.Case):
def testTrapezoidal(self):
from csb.numeric import trapezoidal, exp
x = np.linspace(-10., 10, 1000)
y = exp(-0.5 * x * x) / np.sqrt(2 * np.pi)
self.assertAlmostEqual(trapezoidal(x, y), 1.0, 10)
def testLogTrapezoidal(self):
from csb.numeric import log_trapezoidal, log
x = np.linspace(-100., 100, 1000)
y = -0.5 * x * x - log(np.sqrt(2 * np.pi))
self.assertTrue(abs(log_trapezoidal(y, x)) <= 1e-8)
def testTrapezoidal2D(self):
from csb.numeric import trapezoidal_2d, exp
from numpy import pi
xx = np.linspace(-10., 10, 500)
yy = np.linspace(-10., 10, 500)
X, Y = np.meshgrid(xx, yy)
x = np.array(list(zip(np.ravel(X), np.ravel(Y))))
# mean = np.zeros((2,))
cov = np.eye(2)
mu = np.ones(2)
# D = 2
q = np.sqrt(np.clip(np.sum((x - mu) * np.dot(x - mu, np.linalg.inv(cov).T), -1), 0., 1e308))
f = exp(-0.5 * q ** 2) / ((2 * pi) * np.sqrt(np.abs(np.linalg.det(cov))))
f = f.reshape((len(xx), len(yy)))
I = trapezoidal_2d(f) * (xx[1] - xx[0]) * (yy[1] - yy[0])
self.assertTrue(abs(I - 1.) <= 1e-8)
def testSimpson2D(self):
from csb.numeric import simpson_2d, exp
from numpy import pi
xx = np.linspace(-10., 10, 500)
yy = np.linspace(-10., 10, 500)
X, Y = np.meshgrid(xx, yy)
x = np.array(list(zip(np.ravel(X), np.ravel(Y))))
# mean = np.zeros((2,))
cov = np.eye(2)
mu = np.ones(2)
# D = 2
q = np.sqrt(np.clip(np.sum((x - mu) * np.dot(x - mu, np.linalg.inv(cov).T), -1), 0., 1e308))
f = exp(-0.5 * q ** 2) / ((2 * pi) * np.sqrt(np.abs(np.linalg.det(cov))))
f = f.reshape((len(xx), len(yy)))
I = simpson_2d(f) * (xx[1] - xx[0]) * (yy[1] - yy[0])
self.assertTrue(abs(I - 1.) <= 1e-8)
def testLogTrapezoidal2D(self):
from csb.numeric import log_trapezoidal_2d, log
from numpy import pi
xx = np.linspace(-10., 10, 500)
yy = np.linspace(-10., 10, 500)
X, Y = np.meshgrid(xx, yy)
x = np.array(list(zip(np.ravel(X), np.ravel(Y))))
# mean = np.zeros((2,))
cov = np.eye(2)
mu = np.ones(2)
# D = 2
q = np.sqrt(np.clip(np.sum((x - mu) * np.dot(x - mu, np.linalg.inv(cov).T), -1), 0., 1e308))
f = -0.5 * q ** 2 - log((2 * pi) * np.sqrt(np.abs(np.linalg.det(cov))))
f = f.reshape((len(xx), len(yy)))
logI = log_trapezoidal_2d(f, xx, yy)
self.assertTrue(abs(logI) <= 1e-8)
@test.functional
class InvertibleMatrixTest(test.Case):
d = 100
# Find some random invertible matrix
m_general = np.random.uniform(low=-2, high=2, size=(d, d))
while np.linalg.det(m_general) == 0:
m_general = np.random.uniform(low=-2, high=2, size=(d, d))
m_general_inv = np.linalg.inv(m_general)
m_diagonal = np.diag(np.random.uniform(low=-2, high=2, size=d))
m_diagonal_inv = np.linalg.inv(m_diagonal)
m_2unity = np.eye(d) * 2.
m_2unity_inv = np.linalg.inv(m_2unity)
def invertMatrix(self, matrix):
from csb.numeric import InvertibleMatrix
for i in range(1000):
testmatrix = InvertibleMatrix(matrix)
dummy = testmatrix.inverse
@test.skip("machine-specific")
def testDiagonalTweak(self):
self.assertFasterThan(0.75, self.invertMatrix, self.m_diagonal)
@test.skip("machine-specific")
def testUnityMultipleTweak(self):
self.assertFasterThan(0.5, self.invertMatrix, self.m_2unity)
def testCaching(self):
from csb.numeric import InvertibleMatrix
# Initialize with matrix
testmatrix = InvertibleMatrix(self.m_general)
# Check if it worked
self.assertListAlmostEqual(testmatrix._matrix.flatten().tolist(),
self.m_general.flatten().tolist())
# Because the testmatrix.inverse hasn't been accessed yet, testmatrix._inverse should be None
self.assertEqual(testmatrix._inverse_matrix, None)
# Now we access testmatrix.inverse, which onyl now actually calculates the inverse
self.assertListAlmostEqual(testmatrix.inverse.flatten().tolist(),
self.m_general_inv.flatten().tolist())
# Let's change testmatrix via testmatrix.__imul__
testmatrix *= 2.
# Check if that worked
self.assertListAlmostEqual(testmatrix._matrix.flatten().tolist(),
(2.0 * self.m_general.flatten()).tolist())
# This operation should not have changed the testmatrix._inverse_matrix field, as
# we didn't access testmatrix.inverse again
self.assertListAlmostEqual(testmatrix._inverse_matrix.flatten().tolist(),
self.m_general_inv.flatten().tolist())
# New we access testmatrix.inverse, which calculates the inverse and updates the field
self.assertListAlmostEqual(testmatrix.inverse.flatten().tolist(),
(self.m_general_inv / 2.0).flatten().tolist())
# The same again for testmatrix.__idiv__
testmatrix /= 2.
# Check if that worked
self.assertListAlmostEqual(testmatrix._matrix.flatten().tolist(),
(self.m_general.flatten()).tolist())
# This operation should not have changed the testmatrix._inverse_matrix field, as
# we didn't access testmatrix.inverse again
self.assertListAlmostEqual(testmatrix._inverse_matrix.flatten().tolist(),
(self.m_general_inv / 2.0).flatten().tolist())
# New we access testmatrix.inverse, which calculates the inverse and updates the field
self.assertListAlmostEqual(testmatrix.inverse.flatten().tolist(),
self.m_general_inv.flatten().tolist())
# Initialize with inverse matrix
testmatrix = InvertibleMatrix(inverse_matrix=self.m_general_inv)
# Let's see if that worked, e.g. if the testmatrix._inverse_matrix field has been
# set correctly
self.assertListAlmostEqual(testmatrix._inverse_matrix.flatten().tolist(),
self.m_general_inv.flatten().tolist())
# Check if the property returns what it's supposed to be
self.assertListAlmostEqual(testmatrix.inverse.flatten().tolist(),
self.m_general_inv.flatten().tolist())
# We didn't call testmatrix.__getitem__() yet, so testmatrix._matrix should be None
self.assertEqual(testmatrix._matrix, None)
# To include the numerical error
invinv = np.linalg.inv(self.m_general_inv)
# Now we access testmatrix by its __getitem__ method, which calculates the
# testmatrix._matrix field from the testmatrix._inverse_matrix by inversion
for i in range(len(testmatrix)):
self.assertListAlmostEqual(testmatrix[i].tolist(), invinv[i].tolist())
testmatrix = InvertibleMatrix(inverse_matrix=self.m_general_inv)
# Let's change testmatrix via testmatrix.__imul__
testmatrix *= 2.
# That shouldn't have changed the testmatrix._matrix field (which currently
# should be None), but the testmatrix._inverse_matrix field by a factor of 1/2.0 = 0.5
self.assertEqual(testmatrix._matrix, None)
self.assertListAlmostEqual(testmatrix._inverse_matrix.flatten().tolist(),
(self.m_general_inv / 2.0).flatten().tolist())
# Now we access testmatrix by __getitem__, which calculates the matrix
# from the inverse and updates the field testmatrix._matrix
invinv *= 2.0
for i in range(len(testmatrix)):
self.assertListAlmostEqual(testmatrix[i].tolist(), invinv[i].tolist())
# The same again for testmatrix.__idiv__
testmatrix = InvertibleMatrix(inverse_matrix=self.m_general_inv)
testmatrix /= 2.
# Check if testmatrix._matrix is None and if the testmatrix._inverse field
# has been multiplied by a factor of 2.0
self.assertEqual(testmatrix._matrix, None)
self.assertListAlmostEqual(testmatrix.inverse.flatten().tolist(),
(self.m_general_inv * 2.0).flatten().tolist())
# All that is supposed to leave testmatrix._matrix with None:
self.assertEqual(testmatrix._matrix, None)
# Now we access testmatrix by __getitem__ again, which calculates the matrix from
# its inverse and updates the field
invinv /= 4.0
for i in range(len(testmatrix)):
self.assertListAlmostEqual(testmatrix[i].tolist(), invinv[i].tolist())
def assertListAlmostEqual(self, first, second, places=None, msg=None, delta=0.00000001):
for i, j in zip(first, second):
self.assertAlmostEqual(i, j, places=places, msg=msg, delta=delta)
if __name__ == '__main__':
test.Console()
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