本文整理汇总了Python中symfit.parameters函数的典型用法代码示例。如果您正苦于以下问题:Python parameters函数的具体用法?Python parameters怎么用?Python parameters使用的例子?那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了parameters函数的20个代码示例,这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞,您的评价将有助于我们的系统推荐出更棒的Python代码示例。
示例1: fourier_series
def fourier_series(x, f, n=0):
"""
Returns a symbolic fourier series of order `n`.
:param n: Order of the fourier series.
:param x: Independent variable
:param f: Frequency of the fourier series
"""
# Make the parameter objects for all the terms
a0, *cos_a = parameters(','.join(['a{}'.format(i) for i in range(0, n + 1)]))
sin_b = parameters(','.join(['b{}'.format(i) for i in range(1, n + 1)]))
# Construct the series
series = a0 + sum(ai * cos(i * f * x) + bi * sin(i * f * x)
for i, (ai, bi) in enumerate(zip(cos_a, sin_b), start=1))
return series
开发者ID:tBuLi,项目名称:symfit,代码行数:15,代码来源:fourier_series.py
示例2: test_known_solution
def test_known_solution(self):
p, c1 = parameters('p, c1')
y, t = variables('y, t')
p.value = 3.0
model_dict = {
D(y, t): - p * y,
}
# Lets say we know the exact solution to this problem
sol = Model({y: exp(- p * t)})
# Generate some data
tdata = np.linspace(0, 3, 10001)
ydata = sol(t=tdata, p=3.22)[0]
ydata += np.random.normal(0, 0.005, ydata.shape)
ode_model = ODEModel(model_dict, initial={t: 0.0, y: ydata[0]})
fit = Fit(ode_model, t=tdata, y=ydata)
ode_result = fit.execute()
c1.value = ydata[0]
fit = Fit(sol, t=tdata, y=ydata)
fit_result = fit.execute()
self.assertAlmostEqual(ode_result.value(p) / fit_result.value(p), 1, 2)
self.assertAlmostEqual(ode_result.r_squared / fit_result.r_squared, 1, 4)
self.assertAlmostEqual(ode_result.stdev(p) / fit_result.stdev(p), 1, 3)
开发者ID:tBuLi,项目名称:symfit,代码行数:28,代码来源:test_ode.py
示例3: test_simple_kinetics
def test_simple_kinetics(self):
"""
Simple kinetics data to test fitting
"""
tdata = np.array([10, 26, 44, 70, 120])
adata = 10e-4 * np.array([44, 34, 27, 20, 14])
a, b, t = variables('a, b, t')
k, a0 = parameters('k, a0')
k.value = 0.01
# a0.value, a0.min, a0.max = 54 * 10e-4, 40e-4, 60e-4
a0 = 54 * 10e-4
model_dict = {
D(a, t): - k * a**2,
D(b, t): k * a**2,
}
ode_model = ODEModel(model_dict, initial={t: 0.0, a: a0, b: 0.0})
# Analytical solution
model = GradientModel({a: 1 / (k * t + 1 / a0)})
fit = Fit(model, t=tdata, a=adata)
fit_result = fit.execute()
fit = Fit(ode_model, t=tdata, a=adata, b=None, minimizer=MINPACK)
ode_result = fit.execute()
self.assertAlmostEqual(ode_result.value(k) / fit_result.value(k), 1.0, 4)
self.assertAlmostEqual(ode_result.stdev(k) / fit_result.stdev(k), 1.0, 4)
self.assertAlmostEqual(ode_result.r_squared / fit_result.r_squared, 1, 4)
fit = Fit(ode_model, t=tdata, a=adata, b=None)
ode_result = fit.execute()
self.assertAlmostEqual(ode_result.value(k) / fit_result.value(k), 1.0, 4)
self.assertAlmostEqual(ode_result.stdev(k) / fit_result.stdev(k), 1.0, 4)
self.assertAlmostEqual(ode_result.r_squared / fit_result.r_squared, 1, 4)
开发者ID:tBuLi,项目名称:symfit,代码行数:35,代码来源:test_ode.py
示例4: test_taylor_model
def test_taylor_model(self):
a, b = parameters('a, b')
x, y, z = variables('x, y, z')
model = Model({y: a * x + b})
appr = TaylorModel(model)
self.assertEqual(set([a, b]), set(appr.params))
appr.p0 = {a: 2.0, b: 5.0}
self.assertEqual(set(appr.p0.keys()), set(appr.params_0[p] for p in appr.params))
self.assertTrue(LinearLeastSquares.is_linear(appr))
model = Model({z: a * x**2 + b * y**2})
appr = TaylorModel(model)
appr.p0 = {a: 2, b: 5}
model = Model({z: a * x**2 + b * y**2})
appr_2 = TaylorModel(model)
appr_2.p0 = {a: 1, b: 1}
self.assertTrue(appr == appr_2)
model = Model({y: a * sympy.exp(x * b)})
appr = TaylorModel(model)
appr.p0 = {a: 2.0, b: 5.0}
self.assertTrue(LinearLeastSquares.is_linear(appr))
model = Model({y: sympy.sin(a * x)})
appr = TaylorModel(model)
appr.p0 = {a: 0.0}
self.assertTrue(LinearLeastSquares.is_linear(appr))
开发者ID:Pitje06,项目名称:symfit,代码行数:28,代码来源:test_analytical_fit.py
示例5: test_data_for_constraint
def test_data_for_constraint(self):
"""
Test the signature handling when constraints are at play. Constraints
should take seperate data, but still kwargs that are not found in either
the model nor the constraints should raise an error.
"""
A, mu, sig = parameters('A, mu, sig')
x, y, Y = variables('x, y, Y')
model = Model({y: A * Gaussian(x, mu=mu, sig=sig)})
constraint = Model.as_constraint(Y, model, constraint_type=Eq)
np.random.seed(2)
xdata = np.random.normal(1.2, 2, 10)
ydata, xedges = np.histogram(xdata, bins=int(np.sqrt(len(xdata))),
density=True)
# Allowed
fit = Fit(model, x=xdata, y=ydata, Y=2, constraints=[constraint])
fit = Fit(model, x=xdata, y=ydata)
fit = Fit(model, x=xdata, objective=LogLikelihood)
# Not allowed
with self.assertRaises(TypeError):
fit = Fit(model, x=xdata, y=ydata, Y=2)
with self.assertRaises(TypeError):
fit = Fit(model, x=xdata, y=ydata, Y=2, Z=3, constraints=[constraint])
开发者ID:tBuLi,项目名称:symfit,代码行数:27,代码来源:test_constrained.py
示例6: test_straight_line_analytical
def test_straight_line_analytical(self):
"""
Test symfit against a straight line, for which the parameters and their
uncertainties are known analytically. Assuming equal weights.
"""
data = [[0, 1], [1, 0], [3, 2], [5, 4]]
xdata, ydata = (np.array(i, dtype='float64') for i in zip(*data))
# x = np.arange(0, 100, 0.1)
# np.random.seed(10)
# y = 3.0*x + 105.0 + np.random.normal(size=x.shape)
dx = xdata - xdata.mean()
dy = ydata - ydata.mean()
mean_squared_x = np.mean(xdata**2) - np.mean(xdata)**2
mean_xy = np.mean(xdata * ydata) - np.mean(xdata)*np.mean(ydata)
a = mean_xy/mean_squared_x
b = ydata.mean() - a * xdata.mean()
self.assertAlmostEqual(a, 0.694915, 6) # values from Mathematica
self.assertAlmostEqual(b, 0.186441, 6)
S = np.sum((ydata - (a*xdata + b))**2)
var_a_exact = S/(len(xdata) * (len(xdata) - 2) * mean_squared_x)
var_b_exact = var_a_exact*np.mean(xdata**2)
a_exact = a
b_exact = b
# We will now compare these exact results with values from symfit, numerically
a, b = parameters('a, b')
x, y = variables('x, y')
model = {y: a*x + b}
fit = NumericalLeastSquares(model, x=xdata, y=ydata)#, absolute_sigma=False)
fit_result = fit.execute()
popt, pcov = curve_fit(lambda z, c, d: c * z + d, xdata, ydata,
jac=lambda z, c, d: np.transpose([xdata, np.ones_like(xdata)]))
# jac=lambda p, x, y, func: np.transpose([x, np.ones_like(x)]))
# Dfun=lambda p, x, y, func: print(p, func, x, y))
# curve_fit
self.assertAlmostEqual(a_exact, popt[0], 4)
self.assertAlmostEqual(b_exact, popt[1], 4)
self.assertAlmostEqual(var_a_exact, pcov[0][0], 6)
self.assertAlmostEqual(var_b_exact, pcov[1][1], 6)
self.assertAlmostEqual(a_exact, fit_result.value(a), 4)
self.assertAlmostEqual(b_exact, fit_result.value(b), 4)
self.assertAlmostEqual(var_a_exact, fit_result.variance(a), 6)
self.assertAlmostEqual(var_b_exact, fit_result.variance(b), 6)
# Do the fit with the LinearLeastSquares object
fit = LinearLeastSquares(model, x=xdata, y=ydata)
fit_result = fit.execute()
self.assertAlmostEqual(a_exact, fit_result.value(a), 4)
self.assertAlmostEqual(b_exact, fit_result.value(b), 4)
self.assertAlmostEqual(var_a_exact, fit_result.variance(a), 6)
self.assertAlmostEqual(var_b_exact, fit_result.variance(b), 6)
# Lets also make sure the entire covariance matrix is the same
for cov1, cov2 in zip(fit_result.params.covariance_matrix.flatten(), pcov.flatten()):
self.assertAlmostEqual(cov1, cov2)
开发者ID:Pitje06,项目名称:symfit,代码行数:60,代码来源:test_analytical_fit.py
示例7: test_likelihood_fitting_gaussian
def test_likelihood_fitting_gaussian(self):
"""
Fit using the likelihood method.
"""
mu, sig = parameters('mu, sig')
sig.min = 0.01
sig.value = 3.0
mu.value = 50.
x = Variable()
pdf = Gaussian(x, mu, sig)
np.random.seed(10)
xdata = np.random.normal(51., 3.5, 10000)
# Expected parameter values
mean = np.mean(xdata)
stdev = np.std(xdata)
mean_stdev = stdev/np.sqrt(len(xdata))
fit = Fit(pdf, xdata, objective=LogLikelihood)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(mu) / mean, 1, 6)
self.assertAlmostEqual(fit_result.stdev(mu) / mean_stdev, 1, 3)
self.assertAlmostEqual(fit_result.value(sig) / np.std(xdata), 1, 6)
开发者ID:tBuLi,项目名称:symfit,代码行数:25,代码来源:test_general.py
示例8: test_vector_fitting
def test_vector_fitting(self):
"""
Tests fitting to a 3 component vector valued function, without bounds
or guesses.
"""
a, b, c = parameters('a, b, c')
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = {a_i: a, b_i: b, c_i: c}
xdata = np.array([
[10.1, 9., 10.5, 11.2, 9.5, 9.6, 10.],
[102.1, 101., 100.4, 100.8, 99.2, 100., 100.8],
[71.6, 73.2, 69.5, 70.2, 70.8, 70.6, 70.1],
])
fit = NumericalLeastSquares(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(a), 9.985691, 6)
self.assertAlmostEqual(fit_result.value(b), 1.006143e+02, 4)
self.assertAlmostEqual(fit_result.value(c), 7.085713e+01, 5)
开发者ID:Pitje06,项目名称:symfit,代码行数:27,代码来源:test_general.py
示例9: test_pickle
def test_pickle(self):
"""
Make sure models can be pickled are preserved when pickling
"""
a, b = parameters('a, b')
x, y = variables('x, y')
exact_model = Model({y: a * x ** b})
constraint = Model.as_constraint(Eq(a, b), exact_model)
num_model = CallableNumericalModel(
{y: a * x ** b}, independent_vars=[x], params=[a, b]
)
connected_num_model = CallableNumericalModel(
{y: a * x ** b}, connectivity_mapping={y: {x, a, b}}
)
# Test if lsoda args and kwargs are pickled too
ode_model = ODEModel({D(y, x): a * x + b}, {x: 0.0}, 3, 4, some_kwarg=True)
models = [exact_model, constraint, num_model, ode_model,
connected_num_model]
for model in models:
new_model = pickle.loads(pickle.dumps(model))
# Compare signatures
self.assertEqual(model.__signature__, new_model.__signature__)
# Trigger the cached vars because we compare `__dict__` s
model.vars
new_model.vars
# Explicitly make sure the connectivity mapping is identical.
self.assertEqual(model.connectivity_mapping,
new_model.connectivity_mapping)
if not isinstance(model, ODEModel):
model.function_dict
model.vars_as_functions
new_model.function_dict
new_model.vars_as_functions
self.assertEqual(model.__dict__, new_model.__dict__)
开发者ID:tBuLi,项目名称:symfit,代码行数:35,代码来源:test_model.py
示例10: test_vector_none_fitting
def test_vector_none_fitting(self):
"""
Fit to a 3 component vector valued function with one variables data set
to None, without bounds or guesses.
"""
a, b, c = parameters('a, b, c')
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = {a_i: a, b_i: b, c_i: c}
xdata = np.array([
[10.1, 9., 10.5, 11.2, 9.5, 9.6, 10.],
[102.1, 101., 100.4, 100.8, 99.2, 100., 100.8],
[71.6, 73.2, 69.5, 70.2, 70.8, 70.6, 70.1],
])
fit_none = NumericalLeastSquares(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=None,
)
fit = NumericalLeastSquares(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
fit_none_result = fit_none.execute()
fit_result = fit.execute()
self.assertAlmostEqual(fit_none_result.value(a), fit_result.value(a), 4)
self.assertAlmostEqual(fit_none_result.value(b), fit_result.value(b), 4)
# the parameter without data should be unchanged.
self.assertAlmostEqual(fit_none_result.value(c), 1.0)
开发者ID:Pitje06,项目名称:symfit,代码行数:35,代码来源:test_general.py
示例11: test_global_fitting
def test_global_fitting(self):
"""
In case of shared parameters between the components of the model, `Fit`
should automatically use `ConstrainedLeastSquares`.
:return:
"""
x_1, x_2, y_1, y_2 = variables('x_1, x_2, y_1, y_2')
y0, a_1, a_2, b_1, b_2 = parameters('y0, a_1, a_2, b_1, b_2')
# The following vector valued function links all the equations together
# as stated in the intro.
model = Model({
y_1: a_1 * x_1**2 + b_1 * x_1 + y0,
y_2: a_2 * x_2**2 + b_2 * x_2 + y0,
})
self.assertTrue(model.shared_parameters)
# Generate data from this model
xdata1 = np.linspace(0, 10)
xdata2 = xdata1[::2] # Only every other point.
ydata1, ydata2 = model(x_1=xdata1, x_2=xdata2, a_1=101.3, b_1=0.5, a_2=56.3, b_2=1.1111, y0=10.8)
# Add some noise to make it appear like real data
np.random.seed(1)
ydata1 += np.random.normal(0, 2, size=ydata1.shape)
ydata2 += np.random.normal(0, 2, size=ydata2.shape)
xdata = [xdata1, xdata2]
ydata = [ydata1, ydata2]
# Guesses
a_1.value = 100
a_2.value = 50
b_1.value = 1
b_2.value = 1
y0.value = 10
fit = Fit(
model, x_1=xdata[0], x_2=xdata[1], y_1=ydata[0], y_2=ydata[1]
)
self.assertIsInstance(fit.fit, ConstrainedNumericalLeastSquares)
# The next model does not share parameters, but is still a vector
model = Model({
y_1: a_1 * x_1**2 + b_1 * x_1,
y_2: a_2 * x_2**2 + b_2 * x_2,
})
fit = Fit(
model, x_1=xdata[0], x_2=xdata[1], y_1=ydata[0], y_2=ydata[1]
)
self.assertFalse(model.shared_parameters)
self.assertIsInstance(fit.fit, NumericalLeastSquares)
# Scalar model, so it should use NumericalLeastSquares.
model = Model({
y_1: a_1 * x_1**2 + b_1 * x_1,
})
fit = Fit(model, x_1=xdata[0], y_1=ydata[0])
self.assertFalse(model.shared_parameters)
self.assertIsInstance(fit.fit, NumericalLeastSquares)
开发者ID:Pitje06,项目名称:symfit,代码行数:60,代码来源:test_auto_fit.py
示例12: test_single_eval
def test_single_eval(self):
"""
Eval an ODEModel at a single value rather than a vector.
"""
x, y, t = variables('x, y, t')
k, = parameters('k') # C is the integration constant.
# The harmonic oscillator as a system, >1st order is not supported yet.
harmonic_dict = {
D(x, t): - k * y,
D(y, t): k * x,
}
# Make a second model to prevent caching of integration results.
# This also means harmonic_dict should NOT be a Model object.
harmonic_model_array = ODEModel(harmonic_dict, initial={t: 0.0, x: 1.0, y: 0.0})
harmonic_model_points = ODEModel(harmonic_dict, initial={t: 0.0, x: 1.0, y: 0.0})
tdata = np.linspace(0, 100, 101)
X, Y = harmonic_model_array(t=tdata, k=0.1)
# Shuffle the data to prevent using the result at time t to calculate
# t+dt
random_order = np.random.permutation(len(tdata))
for idx in random_order:
t = tdata[idx]
X_val = X[idx]
Y_val = Y[idx]
X_point, Y_point = harmonic_model_points(t=t, k=0.1)
self.assertAlmostEqual(X_point[0], X_val)
self.assertAlmostEqual(Y_point[0], Y_val)
开发者ID:Pitje06,项目名称:symfit,代码行数:29,代码来源:test_ode.py
示例13: test_simple_kinetics
def test_simple_kinetics(self):
"""
Simple kinetics data to test fitting
"""
tdata = np.array([10, 26, 44, 70, 120])
adata = 10e-4 * np.array([44, 34, 27, 20, 14])
a, b, t = variables('a, b, t')
k, a0 = parameters('k, a0')
k.value = 0.01
# a0.value, a0.min, a0.max = 54 * 10e-4, 40e-4, 60e-4
a0 = 54 * 10e-4
model_dict = {
D(a, t): - k * a**2,
D(b, t): k * a**2,
}
ode_model = ODEModel(model_dict, initial={t: 0.0, a: a0, b: 0.0})
# Generate some data
tvec = np.linspace(0, 500, 1000)
fit = NumericalLeastSquares(ode_model, t=tdata, a=adata, b=None)
fit_result = fit.execute()
# print(fit_result)
self.assertAlmostEqual(fit_result.value(k), 4.302875e-01, 4)
self.assertAlmostEqual(fit_result.stdev(k), 6.447068e-03, 4)
fit = Fit(ode_model, t=tdata, a=adata, b=None)
fit_result = fit.execute()
# print(fit_result)
self.assertAlmostEqual(fit_result.value(k), 4.302875e-01, 4)
self.assertTrue(np.isnan(fit_result.stdev(k)))
开发者ID:Pitje06,项目名称:symfit,代码行数:33,代码来源:test_ode.py
示例14: test_full_eval_range
def test_full_eval_range(self):
"""
Test if ODEModels can be evaluated at t < t_initial.
A bit of a no news is good news test.
"""
tdata = np.array([0, 10, 26, 44, 70, 120])
adata = 10e-4 * np.array([54, 44, 34, 27, 20, 14])
a, b, t = variables('a, b, t')
k, a0 = parameters('k, a0')
k.value = 0.01
t0 = tdata[2]
a0 = adata[2]
b0 = 0.02729855 # Obtained from evaluating from t=0.
model_dict = {
D(a, t): - k * a**2,
D(b, t): k * a**2,
}
ode_model = ODEModel(model_dict, initial={t: t0, a: a0, b: b0})
fit = Fit(ode_model, t=tdata, a=adata, b=None)
ode_result = fit.execute()
self.assertGreater(ode_result.r_squared, 0.95, 4)
# Now start from a timepoint that is not in the t-array such that it
# triggers another pathway to be taken in integrating it.
# Again, no news is good news.
ode_model = ODEModel(model_dict, initial={t: t0 + 1e-5, a: a0, b: b0})
fit = Fit(ode_model, t=tdata, a=adata, b=None)
ode_result = fit.execute()
self.assertGreater(ode_result.r_squared, 0.95, 4)
开发者ID:tBuLi,项目名称:symfit,代码行数:34,代码来源:test_ode.py
示例15: test_vector_fitting_guess
def test_vector_fitting_guess(self):
"""
Tests fitting to a 3 component vector valued function, with guesses.
"""
a, b, c = parameters('a, b, c')
a.value = 10
b.value = 100
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = {a_i: a, b_i: b, c_i: c}
xdata = np.array([
[10.1, 9., 10.5, 11.2, 9.5, 9.6, 10.],
[102.1, 101., 100.4, 100.8, 99.2, 100., 100.8],
[71.6, 73.2, 69.5, 70.2, 70.8, 70.6, 70.1],
])
fit = NumericalLeastSquares(
model=model,
a_i=xdata[0],
b_i=xdata[1],
c_i=xdata[2],
)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(a), np.mean(xdata[0]), 4)
self.assertAlmostEqual(fit_result.value(b), np.mean(xdata[1]), 4)
self.assertAlmostEqual(fit_result.value(c), np.mean(xdata[2]), 4)
开发者ID:Pitje06,项目名称:symfit,代码行数:28,代码来源:test_general.py
示例16: test_interdependency_constrained
def test_interdependency_constrained(self):
"""
Test a model with interdependent components, and with constraints which
depend on the Model's output.
This is done in the MatrixSymbol formalism, using a Tikhonov
regularization as an example. In this, a matrix inverse has to be
calculated and is used multiple times. Therefore we split that term of
into a seperate component, so the inverse only has to be computed once
per model call.
See https://arxiv.org/abs/1901.05348 for a more detailed background.
"""
N = Symbol('N', integer=True)
M = MatrixSymbol('M', N, N)
W = MatrixSymbol('W', N, N)
I = MatrixSymbol('I', N, N)
y = MatrixSymbol('y', N, 1)
c = MatrixSymbol('c', N, 1)
a, = parameters('a')
z, = variables('z')
i = Idx('i')
model_dict = {
W: Inverse(I + M / a ** 2),
c: - W * y,
z: sqrt(c.T * c)
}
# Sympy currently does not support derivatives of matrix expressions,
# so we use CallableModel instead of Model.
model = CallableModel(model_dict)
# Generate data
iden = np.eye(2)
M_mat = np.array([[2, 1], [3, 4]])
y_vec = np.array([[3], [5]])
eval_model = model(I=iden, M=M_mat, y=y_vec, a=0.1)
# Calculate the answers 'manually' so I know it was done properly
W_manual = np.linalg.inv(iden + M_mat / 0.1 ** 2)
c_manual = - np.atleast_2d(W_manual.dot(y_vec))
z_manual = np.atleast_1d(np.sqrt(c_manual.T.dot(c_manual)))
self.assertEqual(y_vec.shape, (2, 1))
self.assertEqual(M_mat.shape, (2, 2))
self.assertEqual(iden.shape, (2, 2))
self.assertEqual(W_manual.shape, (2, 2))
self.assertEqual(c_manual.shape, (2, 1))
self.assertEqual(z_manual.shape, (1, 1))
np.testing.assert_almost_equal(W_manual, eval_model.W)
np.testing.assert_almost_equal(c_manual, eval_model.c)
np.testing.assert_almost_equal(z_manual, eval_model.z)
fit = Fit(model, z=z_manual, I=iden, M=M_mat, y=y_vec)
fit_result = fit.execute()
# See if a == 0.1 was reconstructed properly. Since only a**2 features
# in the equations, we check for the absolute value. Setting a.min = 0.0
# is not appreciated by the Minimizer, it seems.
self.assertAlmostEqual(np.abs(fit_result.value(a)), 0.1)
开发者ID:tBuLi,项目名称:symfit,代码行数:57,代码来源:test_constrained.py
示例17: test_jacobian_matrix
def test_jacobian_matrix(self):
"""
The jacobian matrix of a model should be a 2D list (matrix) containing
all the partial derivatives.
"""
a, b, c = parameters('a, b, c')
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = Model({a_i: 2 * a + 3 * b, b_i: 5 * b, c_i: 7 * c})
self.assertEqual([[2, 3, 0], [0, 5, 0], [0, 0, 7]], model.jacobian)
开发者ID:Pitje06,项目名称:symfit,代码行数:10,代码来源:test_general.py
示例18: test_global_fitting
def test_global_fitting(self):
"""
Test a global fitting scenario with datasets of unequal length. In this
scenario, a quartic equation is fitted where the constant term is shared
between the datasets. (e.g. identical background noise)
"""
x_1, x_2, y_1, y_2 = variables('x_1, x_2, y_1, y_2')
y0, a_1, a_2, b_1, b_2 = parameters('y0, a_1, a_2, b_1, b_2')
# The following vector valued function links all the equations together
# as stated in the intro.
model = Model({
y_1: a_1 * x_1**2 + b_1 * x_1 + y0,
y_2: a_2 * x_2**2 + b_2 * x_2 + y0,
})
# Generate data from this model
# xdata = np.linspace(0, 10)
xdata1 = np.linspace(0, 10)
xdata2 = xdata1[::2] # Make the sets of unequal size
ydata1, ydata2 = model(x_1=xdata1, x_2=xdata2, a_1=101.3, b_1=0.5, a_2=56.3, b_2=1.1111, y0=10.8)
# Add some noise to make it appear like real data
np.random.seed(1)
ydata1 += np.random.normal(0, 2, size=ydata1.shape)
ydata2 += np.random.normal(0, 2, size=ydata2.shape)
xdata = [xdata1, xdata2]
ydata = [ydata1, ydata2]
# Guesses
a_1.value = 100
a_2.value = 50
b_1.value = 1
b_2.value = 1
y0.value = 10
eval_jac = model.eval_jacobian(x_1=xdata1, x_2=xdata2, a_1=101.3,
b_1=0.5, a_2=56.3, b_2=1.1111, y0=10.8)
self.assertEqual(len(eval_jac), 2)
for comp in eval_jac:
self.assertEqual(len(comp), len(model.params))
sigma_y = np.concatenate((np.ones(20), [2., 4., 5, 7, 3]))
fit = Fit(model, x_1=xdata[0], x_2=xdata[1],
y_1=ydata[0], y_2=ydata[1], sigma_y_2=sigma_y)
fit_result = fit.execute()
# fit_curves = model(x_1=xdata[0], x_2=xdata[1], **fit_result.params)
self.assertAlmostEqual(fit_result.value(y0), 1.061892e+01, 3)
self.assertAlmostEqual(fit_result.value(a_1), 1.013269e+02, 3)
self.assertAlmostEqual(fit_result.value(a_2), 5.625694e+01, 3)
self.assertAlmostEqual(fit_result.value(b_1), 3.362240e-01, 3)
self.assertAlmostEqual(fit_result.value(b_2), 1.565253e+00, 3)
开发者ID:tBuLi,项目名称:symfit,代码行数:55,代码来源:test_constrained.py
示例19: test_hessian_matrix
def test_hessian_matrix(self):
"""
The Hessian matrix of a model should be a 3D list (matrix) containing
all the 2nd partial derivatives.
"""
a, b, c = parameters('a, b, c')
a_i, b_i, c_i = variables('a_i, b_i, c_i')
model = Model({a_i: 2 * a**2 + 3 * b, b_i: 5 * b**2, c_i: 7 * c*b})
self.assertEqual([[[4, 0, 0], [0, 0, 0], [0, 0, 0]],
[[0, 0, 0], [0, 10, 0], [0, 0, 0]],
[[0, 0, 0], [0, 0, 7], [0, 7, 0]]], model.hessian)
开发者ID:tBuLi,项目名称:symfit,代码行数:12,代码来源:test_general.py
示例20: test_linear_analytical_fit
def test_linear_analytical_fit(self):
a, b = parameters('a, b')
x, y = variables('x, y')
model = {y: a * x + b}
data = [[0, 1], [1, 0], [3, 2], [5, 4]]
xdata, ydata = (np.array(i, dtype='float64') for i in zip(*data))
fit = LinearLeastSquares(model, x=xdata, y=ydata)
fit_result = fit.execute()
self.assertAlmostEqual(fit_result.value(a), 0.694915, 6) # values from Mathematica
self.assertAlmostEqual(fit_result.value(b), 0.186441, 6)
开发者ID:Pitje06,项目名称:symfit,代码行数:13,代码来源:test_analytical_fit.py
注:本文中的symfit.parameters函数示例由纯净天空整理自Github/MSDocs等源码及文档管理平台,相关代码片段筛选自各路编程大神贡献的开源项目,源码版权归原作者所有,传播和使用请参考对应项目的License;未经允许,请勿转载。 |
请发表评论