def setUp(self):
self.amp, self.mu, self.std, self.mu2 = 1., 0., 1., 3.
self.one_gauss_params = np.array([self.amp, self.mu, self.std], dtype=np.float)
self.two_gauss_params = np.array([self.amp, self.mu, self.std, self.amp, self.mu2, self.std], dtype=np.float)
self.x = np.array(np.linspace(-5, 5, 101), dtype=np.float)
self.one_gauss = peaks.gauss_ndim(self.x, self.one_gauss_params)
self.two_gauss = peaks.gauss_ndim(self.x, self.two_gauss_params)
def setUp(self):
super(FittingTests, self).setUp()
self.amp, self.mu, self.std, self.mu2 = 1., 0., 1., 3.
self.one_gauss_params = np.array([self.amp, self.mu, self.std], dtype=np.float)
self.two_gauss_params = np.array([self.amp, self.mu, self.std, self.amp, self.mu2, self.std], dtype=np.float)
self.x = np.array(np.linspace(-5, 5, 101), dtype=np.float)
self.one_gauss = peaks.gauss_ndim(self.x, self.one_gauss_params)
self.two_gauss = peaks.gauss_ndim(self.x, self.two_gauss_params)
self.std_2, self.std2_2 = 0.5, 0.75
self.one_bigauss_params = np.array([self.amp, self.mu, self.std, self.std_2], dtype=np.float)
self.two_bigauss_params = np.array([self.amp, self.mu, self.std, self.std_2, self.amp, self.mu2, self.std, self.std2_2], dtype=np.float)
self.one_bigauss = peaks.bigauss_ndim(self.x, self.one_bigauss_params)
self.two_bigauss = peaks.bigauss_ndim(self.x, self.two_bigauss_params)
def test_hessians(self):
y, x, a, u, s1, a2, u2, s2, a3, u3, s3 = symbols('y x a u s1 a2 u2 s2 a3 u3 s3')
three_gauss = (y - (
a * exp(-(u - x) ** 2 / (2 * s1 ** 2)) + a2 * exp(-(u2 - x) ** 2 / (2 * s2 ** 2)) + a3 * exp(
-(u3 - x) ** 2 / (2 * s3 ** 2)))) ** 2
hess_store = {}
for _ in xrange(2):
subs = [
('a', random()+0.5),
('u', random()*10),
('s1', random()*3+2),
('a2', random()+0.5),
('u2', random()*10+10),
('s2', random()*3+2),
('a3', random()+0.5),
('u3', random()*10+20),
('s3', random()*3+2),
]
params = np.array([i[1] for i in subs], dtype=float)
noisy_params = params + 2 * np.random.rand(params.shape[0])
gauss_x = np.linspace(-10, 40, 100)
gauss_y = peaks.gauss_ndim(gauss_x, noisy_params)
hessian = peaks.gauss_hess(params, gauss_x, gauss_y)
for var_index, var in enumerate([a, u, s1, a2, u2, s2, a3, u3, s3]):
for var_index2, var2 in enumerate([a, u, s1, a2, u2, s2, a3, u3, s3]):
deriv = hess_store.setdefault((var, var2), diff(three_gauss, var, var2))
sympy_hessian = sum([deriv.subs(dict(subs, **{'x': xi, 'y': yi})) for xi, yi in zip(gauss_x, gauss_y)])
pq_hess = hessian[var_index, var_index2]
np.testing.assert_allclose(pq_hess, np.array(sympy_hessian, dtype=float), err_msg='d{}d{} - pq: {}, sympy: {}'.format(var, var2, pq_hess, sympy_hessian), atol=1e-4)
def test_jacobians(self):
one_gauss_jac = peaks.gauss_jac(self.one_gauss_params, self.x, self.one_gauss, False)
self.assertEqual(one_gauss_jac.tolist(), np.zeros_like(self.one_gauss_params).tolist())
two_gauss_jac = peaks.gauss_jac(self.two_gauss_params, self.x, self.two_gauss, False)
self.assertEqual(two_gauss_jac.tolist(), np.zeros_like(self.two_gauss_params).tolist())
one_bigauss_jac = peaks.bigauss_jac(self.one_bigauss_params, self.x, self.one_bigauss, False)
self.assertEqual(one_bigauss_jac.tolist(), np.zeros_like(self.one_bigauss_params).tolist())
two_bigauss_jac = peaks.bigauss_jac(self.two_bigauss_params, self.x, self.two_bigauss, False)
self.assertEqual(two_bigauss_jac.tolist(), np.zeros_like(self.two_bigauss_params).tolist())
y, x, a, u, s1, s1_2, a2, u2, s2, s2_2, a3, u3, s3, s3_2 = symbols('y x a u s1 s1_2 a2 u2 s2 s2_2 a3 u3 s3 s3_2')
three_gauss = (y - (a * exp(-(u - x) ** 2 / (2 * s1 ** 2)) + a2 * exp(-(u2 - x) ** 2 / (2 * s2 ** 2)) + a3 * exp(-(u3 - x) ** 2 / (2 * s3 ** 2)))) ** 2
three_gauss2 = (y - (a * exp(-(u - x) ** 2 / (2 * s1_2 ** 2)) + a2 * exp(-(u2 - x) ** 2 / (2 * s2_2 ** 2)) + a3 * exp(-(u3 - x) ** 2 / (2 * s3_2 ** 2)))) ** 2
bigauss = Piecewise((three_gauss, x<u))
deriv_store = {}
for i in xrange(2):
subs = [
('a', random()),
('u', randint(1,10)),
('s1', random()),
('a2', random()),
('u2', randint(12, 20)),
('s2', random()),
('a3', random()),
('u3', randint(22, 30)),
('s3', random()),
]
params = np.array([i[1] for i in subs], dtype=float)
noisy_params = params + 2*np.random.rand(params.shape[0])
gauss_x = np.linspace(-10, 40, 100)
gauss_y = peaks.gauss_ndim(gauss_x, noisy_params)
jacobian = peaks.gauss_jac(params, gauss_x, gauss_y, False)
for var_index, var in enumerate([a,u,s1,a2,u2,s2,a3,u3,s3]):
deriv = deriv_store.setdefault(var, diff(three_gauss, var))
pq_jac = jacobian[var_index]
sympy_jacobian = sum([deriv.subs(dict(subs, **{'x': xi, 'y': yi})) for xi, yi in zip(gauss_x, gauss_y)])
np.testing.assert_allclose(pq_jac, np.array(sympy_jacobian, dtype=float),
err_msg='d{} - pq: {}, sympy: {}'.format(var, pq_jac,
sympy_jacobian), atol=1e-4)
def test_jacobians(self):
one_gauss_jac = peaks.gauss_jac(self.one_gauss_params, self.x, self.one_gauss, False)
self.assertEqual(one_gauss_jac.tolist(), np.zeros_like(self.one_gauss_params).tolist())
two_gauss_jac = peaks.gauss_jac(self.two_gauss_params, self.x, self.two_gauss, False)
self.assertEqual(two_gauss_jac.tolist(), np.zeros_like(self.two_gauss_params).tolist())
one_bigauss_jac = peaks.bigauss_jac(self.one_bigauss_params, self.x, self.one_bigauss, False)
self.assertEqual(one_bigauss_jac.tolist(), np.zeros_like(self.one_bigauss_params).tolist())
two_bigauss_jac = peaks.bigauss_jac(self.two_bigauss_params, self.x, self.two_bigauss, False)
self.assertEqual(two_bigauss_jac.tolist(), np.zeros_like(self.two_bigauss_params).tolist())
y, x, a, u, s1, s1_2, a2, u2, s2, s2_2, a3, u3, s3, s3_2 = symbols('y x a u s1 s1_2 a2 u2 s2 s2_2 a3 u3 s3 s3_2')
three_gauss = (y - (a * exp(-(u - x) ** 2 / (2 * s1 ** 2)) + a2 * exp(-(u2 - x) ** 2 / (2 * s2 ** 2)) + a3 * exp(-(u3 - x) ** 2 / (2 * s3 ** 2)))) ** 2
three_gauss2 = (y - (a * exp(-(u - x) ** 2 / (2 * s1_2 ** 2)) + a2 * exp(-(u2 - x) ** 2 / (2 * s2_2 ** 2)) + a3 * exp(-(u3 - x) ** 2 / (2 * s3_2 ** 2)))) ** 2
bigauss = Piecewise((three_gauss, x<u))
deriv_store = {}
for i in xrange(2):
subs = [
('a', random()),
('u', randint(1,10)),
('s1', random()),
('a2', random()),
('u2', randint(12, 20)),
('s2', random()),
('a3', random()),
('u3', randint(22, 30)),
('s3', random()),
]
params = np.array([i[1] for i in subs], dtype=float)
noisy_params = params + 2*np.random.rand(params.shape[0])
gauss_x = np.linspace(-10, 40, 100)
gauss_y = peaks.gauss_ndim(gauss_x, noisy_params)
jacobian = peaks.gauss_jac(params, gauss_x, gauss_y, False)
for var_index, var in enumerate([a,u,s1,a2,u2,s2,a3,u3,s3]):
deriv = deriv_store.setdefault(var, diff(three_gauss, var))
pq_jac = jacobian[var_index]
sympy_jacobian = sum([deriv.subs(dict(subs, **{'x': xi, 'y': yi})) for xi, yi in zip(gauss_x, gauss_y)])
np.testing.assert_allclose(pq_jac, np.array(sympy_jacobian, dtype=float),
err_msg='d{} - pq: {}, sympy: {}'.format(var, pq_jac,
sympy_jacobian), atol=1e-4)