def test_evaluate_failure(self):
c = [1.0, 1.0]
p = tl.MVP2D(c)
with self.assertRaises(tl.TriangularException):
p.evaluate(0.0, 0.0)
c = [1.0, 1.0, 1.0, 0.0]
p = tl.MVP2D(c)
with self.assertRaises(tl.TriangularException):
p.evaluate(-42.6733, -27.0083)
c = [1.0, 1.0, 1.0, 0.0, 1.0, 1.0, 1.0, 1.0]
p = tl.MVP2D(c)
with self.assertRaises(tl.TriangularException):
p.evaluate(-42.6733, -27.0083)
def test_augmented_line_integral_4(self):
'''MVP2D.augmented_line_integral: parabollic prism with pos and neg integrate to zero'''
for trial in range(100):
# generate coefs of parabolic prism that ensure positve and negative regions
a0 = np.random.uniform(-10, 10)
a3 = np.random.uniform(-10, 10)
a3 = -a3 if np.sign(a3) == np.sign(a0) else a3
# randomly assign prism along x or y axis
if np.random.rand() > 0.5:
coefs = np.array([a0, 0.0, 0.0, a3, 0.0, 0])
else:
coefs = np.array([a0, 0.0, 0.0, a3, 0.0, 0])
mvp = tl.MVP2D(coefs)
# form square region of integration
b = np.sqrt(-3.0 * a0 / a3)
verts = [(-b, -b), (b, -b), (b, b), (-b, b)]
# perform integral and test it is approximately 0
I = 0.0
for i, _ in enumerate(verts[:-1]):
I += mvp.augmented_line_integral(verts[i], verts[i + 1])
I += mvp.augmented_line_integral(verts[-1], verts[0])
self.assertAlmostEqual(I, 0.0)
def test_evaluate_3(self):
# polynomial = 1
c = [1.0]
p = tl.MVP2D(c)
self.assertAlmostEqual(p.evaluate(0.0, 0.0), 1.0)
self.assertAlmostEqual(p.evaluate(1.0, 0.0), 1.0)
self.assertAlmostEqual(p.evaluate(-1.0, 1.0), 1.0)
self.assertAlmostEqual(p.evaluate(0.0, 1.0), 1.0)
self.assertAlmostEqual(p.evaluate(-42.6733, -27.0083), 1.0)
def test_evaluate_2(self):
# polynomial = 1 + x + y + x^2 + x*y + y^2
c = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0]
p = tl.MVP2D(c)
self.assertAlmostEqual(p.evaluate(0.0, 0.0), 1.0)
self.assertAlmostEqual(p.evaluate(1.0, 0.0), 3.0)
self.assertAlmostEqual(p.evaluate(-1.0, 1.0), 2.0)
self.assertAlmostEqual(p.evaluate(0.0, 1.0), 3.0)
self.assertAlmostEqual(p.evaluate(-42.6733, -27.0083),
3634.310490169999)
def test_evaluate_1(self):
# polynomial = x^2 + y^2
c = [0.0, 0.0, 0.0, 1.0, 0.0, 1.0]
p = tl.MVP2D(c)
self.assertAlmostEqual(p.evaluate(0.0, 0.0), 0.0)
self.assertAlmostEqual(p.evaluate(1.0, 0.0), 1.0)
self.assertAlmostEqual(p.evaluate(-1.0, 1.0), 2.0)
self.assertAlmostEqual(p.evaluate(0.0, 1.0), 1.0)
self.assertAlmostEqual(p.evaluate(-42.6733, -27.0083),
2550.4588017799997)
def test_augmented_line_integral_2(self):
'''MVP2D.augmented_line_integral: square region under parabolic dome'''
coefs = np.array([1.0, 0.0, 0.0, -1.0, 0.0, -1.0])
mvp = tl.MVP2D(coefs)
b = np.sqrt(2.0) / 2.0
verts = [(-b, -b), (b, -b), (b, b), (-b, b)]
expected_integral = 4.0 * b**2 - 8.0 / 3.0 * b**4
I = 0.0
for i, _ in enumerate(verts[:-1]):
I += mvp.augmented_line_integral(verts[i], verts[i + 1])
I += mvp.augmented_line_integral(verts[-1], verts[0])
self.assertAlmostEqual(I, expected_integral)
def test_evaluate_4(self):
# polynomial = (randomly generated coefs)
c = [
4.9888785066963, -2.6072258560952, 2.6480911731013,
1.9870246909498, 4.6454780151348, 2.2809308451977,
-9.5205873062464, 0.850583925308, 9.0531745362343, -9.9005566723182
]
p = tl.MVP2D(c)
self.assertAlmostEqual(p.evaluate(0.0, 0.0), 4.9888785066963)
self.assertAlmostEqual(p.evaluate(1.0, 0.0), -5.1519099646955)
self.assertAlmostEqual(p.evaluate(-1.0, 1.0), 1.2841130799074048)
self.assertAlmostEqual(p.evaluate(0.0, 1.0), 0.017343852677100813)
self.assertAlmostEqual(p.evaluate(-42.6733, -27.0083),
621923.6139074472)
def test_convex_hull_integral_2(self):
'''MVP2D.convex_hull_integral: integral over parabolic dome with random internal points'''
coefs = np.array([1.0, 0.0, 0.0, -1.0, 0.0, -1.0])
mvp = tl.MVP2D(coefs)
b = np.sqrt(2.0) / 2.0
ext_verts = np.asarray([(-b, -b), (b, -b), (b, b), (-b, b)])
expected_integral = 4.0 * b**2 - 8.0 / 3.0 * b**4
for trial in range(100):
points = np.concatenate(
(ext_verts, np.random.rand(30, 2) * 2 * b - b))
np.random.shuffle(points)
I = mvp.convex_hull_integral(points)
self.assertAlmostEqual(I, expected_integral)
def test_convex_hull_integral_3(self):
'''MVP2D.convex_hull_integral: integral over degenerate hull with random mvp'''
for trial in range(100):
coefs = np.random.rand(6) * 10.0 - 5.0
mvp = tl.MVP2D(coefs)
rand_vert_0 = tuple(np.random.rand(2) * 20.0 - 10.0)
rand_vert_1 = tuple(np.random.rand(2) * 20.0 - 10.0)
collinear_vert = tuple(
np.random.rand(1) * 10.0 * np.array([
rand_vert_1[0] - rand_vert_0[0], rand_vert_1[1] -
rand_vert_0[1]
]) + rand_vert_0)
points = np.array([rand_vert_0, rand_vert_1, collinear_vert])
np.random.shuffle(points)
I = mvp.convex_hull_integral(points)
self.assertAlmostEqual(I, 0.0)
def test_convex_hull_integral_1(self):
'''MVP2D.convex_hull_integral: integral over unit cube with shuffled vertices'''
points = [(0, 0), (1, 0), (1, 1), (0, 1)]
for trial in range(100):
random.shuffle(points)
# generate random heigh of uniform curce
a0 = np.random.uniform(-10, 10)
# generate random length coefficient mvp
coef_len = random.choice([1, 3, 6, 10, 15, 21])
coefs = np.concatenate(([a0], np.zeros(coef_len - 1)))
mvp = tl.MVP2D(coefs)
I = mvp.convex_hull_integral(points)
self.assertAlmostEqual(I, a0)
def test_augmented_line_integral_3(self):
'''MVP2D.augmented_line_integral: ramp through origin integrates to zero over symmetric bounds'''
for trial in range(100):
# generate coefs of 2D ramp through origin
a1 = np.random.uniform(-10, 10)
a2 = np.random.uniform(-10, 10)
coefs = np.array([0.0, a1, a2])
mvp = tl.MVP2D(coefs)
# form rectangular region centered on zero
xc = np.random.uniform(0, 10)
yc = np.random.uniform(0, 10)
verts = [(-xc, -yc), (xc, -yc), (xc, yc), (-xc, yc)]
# perform integral and test it is approximately 0
I = 0.0
for i, _ in enumerate(verts[:-1]):
I += mvp.augmented_line_integral(verts[i], verts[i + 1])
I += mvp.augmented_line_integral(verts[-1], verts[0])
self.assertAlmostEqual(I, 0.0)
def test_augmented_line_integral_1(self):
'''MVP2D.augmented_line_integral: test integral of unit cube'''
c = [1.0]
mvp = tl.MVP2D(c)
# test full cube
verts = [(0, 0), (1, 0), (1, 1), (0, 1)]
I = 0.0
for i, _ in enumerate(verts[:-1]):
I += mvp.augmented_line_integral(verts[i], verts[i + 1])
I += mvp.augmented_line_integral(verts[-1], verts[0])
self.assertAlmostEqual(I, 1.0)
# test half cube
verts = [(0, 0), (1, 0), (1, 1)]
I = 0.0
for i, _ in enumerate(verts[:-1]):
I += mvp.augmented_line_integral(verts[i], verts[i + 1])
I += mvp.augmented_line_integral(verts[-1], verts[0])
self.assertAlmostEqual(I, 0.5)
def test_augmented_line_integral_5(self):
'''MVP2D.augmented_line_integral: random triangular region under uniform curve with random length coeffs'''
for trial in range(100):
# generate random heigh of uniform curce
a0 = np.random.uniform(-10, 10)
# generate random length coefficient mvp
coef_len = random.choice([1, 3, 6, 10, 15, 21])
coefs = np.concatenate(([a0], np.zeros(coef_len - 1)))
mvp = tl.MVP2D(coefs)
# form random triangular path with positive orientation
p1 = np.random.uniform(-10, 10, 2)
p2 = np.random.uniform(-10, 10, 2)
p3 = np.random.uniform(-10, 10, 2)
verts = [p1, p2, p3]
if tl.vertex_orientation_2d(verts)[0] < 0:
verts = [p1, p3, p2]
# find area of triangle region
v12 = p2 - p1
v13 = p3 - p1
l12 = np.linalg.norm(v12)
l13 = np.linalg.norm(v13)
gamma = np.arccos(np.dot(v12, v13) / (l12 * l13))
height = l13 * np.sin(gamma)
area = 0.5 * l12 * height
# perform integral and test it is approximately area * a0
I = 0.0
for i, _ in enumerate(verts[:-1]):
I += mvp.augmented_line_integral(verts[i], verts[i + 1])
I += mvp.augmented_line_integral(verts[-1], verts[0])
self.assertAlmostEqual(I, a0 * area)