Python Fit.execute方法代码示例

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    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)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_chained_min_signature(self):
        """
        Test the automatic generation of the signature for ChainedMinimizer
        """
        minimizers = [
            BFGS, DifferentialEvolution, BFGS, DifferentialEvolution, BFGS
        ]

        fit = Fit(self.model, self.xx, self.yy, self.ydata,
                  minimizer=minimizers)

        names = [
            'BFGS', 'DifferentialEvolution', 'BFGS_2',
            'DifferentialEvolution_2', 'BFGS_3'
        ]
        for name, param_name in zip(names, fit.minimizer.__signature__.parameters):
            self.assertEqual(name, param_name)
        # Check for equal lengths because zip is slippery that way
        self.assertEqual(len(names), len(fit.minimizer.__signature__.parameters))

        for param in fit.minimizer.__signature__.parameters.values():
            self.assertEqual(param.kind, inspect_sig.Parameter.KEYWORD_ONLY)
        # Make sure keywords end up at the right minimizer.
        with self.assertRaises(TypeError):
            # This is not a valid kwarg to DiffEvo, but it is to BFGS. Check if
            # we really go by name of the Minimizer, not by order.
            fit.execute(DifferentialEvolution={'return_all': False})

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    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)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    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)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_minimize(self):
        """
        Tests maximizing a function with and without constraints, taken from the
        scipy `minimize` tutorial. Compare the symfit result with the scipy
        result.
        https://docs.scipy.org/doc/scipy-0.18.1/reference/tutorial/optimize.html#constrained-minimization-of-multivariate-scalar-functions-minimize
        """
        x = Parameter(value=-1.0)
        y = Parameter(value=1.0)
        # Use an  unnamed Variable on purpose to test the auto-generation of names.
        model = Model(2 * x * y + 2 * x - x ** 2 - 2 * y ** 2)

        constraints = [
            Ge(y - 1, 0),  # y - 1 >= 0,
            Eq(x**3 - y, 0),  # x**3 - y == 0,
        ]

        def func(x, sign=1.0):
            """ Objective function """
            return sign*(2*x[0]*x[1] + 2*x[0] - x[0]**2 - 2*x[1]**2)

        def func_deriv(x, sign=1.0):
            """ Derivative of objective function """
            dfdx0 = sign*(-2*x[0] + 2*x[1] + 2)
            dfdx1 = sign*(2*x[0] - 4*x[1])
            return np.array([ dfdx0, dfdx1 ])

        cons = (
            {'type': 'eq',
             'fun' : lambda x: np.array([x[0]**3 - x[1]]),
             'jac' : lambda x: np.array([3.0*(x[0]**2.0), -1.0])},
            {'type': 'ineq',
             'fun' : lambda x: np.array([x[1] - 1]),
             'jac' : lambda x: np.array([0.0, 1.0])})

        # Unconstrained fit
        res = minimize(func, [-1.0,1.0], args=(-1.0,), jac=func_deriv,
               method='BFGS', options={'disp': False})
        fit = Fit(model=- model)
        self.assertIsInstance(fit.objective, MinimizeModel)
        self.assertIsInstance(fit.minimizer, BFGS)

        fit_result = fit.execute()

        self.assertAlmostEqual(fit_result.value(x) / res.x[0], 1.0, 6)
        self.assertAlmostEqual(fit_result.value(y) / res.x[1], 1.0, 6)

        # Same test, but with constraints in place.
        res = minimize(func, [-1.0,1.0], args=(-1.0,), jac=func_deriv,
               constraints=cons, method='SLSQP', options={'disp': False})

        from symfit.core.minimizers import SLSQP
        fit = Fit(- model, constraints=constraints)
        self.assertEqual(fit.constraints[0].constraint_type, Ge)
        self.assertEqual(fit.constraints[1].constraint_type, Eq)
        fit_result = fit.execute()
        self.assertAlmostEqual(fit_result.value(x), res.x[0], 6)
        self.assertAlmostEqual(fit_result.value(y), res.x[1], 6)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_simple_sigma(self):
        """
        Make sure we produce the same results as scipy's curve_fit, with and
        without sigmas, and compare the results of both to a known value.
        """
        t_data = np.array([1.4, 2.1, 2.6, 3.0, 3.3])
        y_data = np.array([10, 20, 30, 40, 50])

        sigma = 0.2
        n = np.array([5, 3, 8, 15, 30])
        sigma_t = sigma / np.sqrt(n)

        # We now define our model
        y = Variable()
        g = Parameter()
        t_model = (2 * y / g)**0.5

        fit = Fit(t_model, y_data, t_data)  # , sigma=sigma_t)
        fit_result = fit.execute()

        # h_smooth = np.linspace(0,60,100)
        # t_smooth = t_model(y=h_smooth, **fit_result.params)

        # Lets with the results from curve_fit, no weights
        popt_noweights, pcov_noweights = curve_fit(lambda y, p: (2 * y / p)**0.5, y_data, t_data)

        self.assertAlmostEqual(fit_result.value(g), popt_noweights[0])
        self.assertAlmostEqual(fit_result.stdev(g), np.sqrt(pcov_noweights[0, 0]))

        # Same sigma everywere
        fit = Fit(t_model, y_data, t_data, 0.0031, absolute_sigma=False)
        fit_result = fit.execute()
        popt_sameweights, pcov_sameweights = curve_fit(lambda y, p: (2 * y / p)**0.5, y_data, t_data, sigma=0.0031, absolute_sigma=False)
        self.assertAlmostEqual(fit_result.value(g), popt_sameweights[0], 4)
        self.assertAlmostEqual(fit_result.stdev(g), np.sqrt(pcov_sameweights[0, 0]), 4)
        # Same weight everywere should be the same as no weight when absolute_sigma=False
        self.assertAlmostEqual(fit_result.value(g), popt_noweights[0], 4)
        self.assertAlmostEqual(fit_result.stdev(g), np.sqrt(pcov_noweights[0, 0]), 4)

        # Different sigma for every point
        fit = Fit(t_model, y_data, t_data, 0.1*sigma_t, absolute_sigma=False)
        fit_result = fit.execute()
        popt, pcov = curve_fit(lambda y, p: (2 * y / p)**0.5, y_data, t_data, sigma=.1*sigma_t)

        self.assertAlmostEqual(fit_result.value(g), popt[0])
        self.assertAlmostEqual(fit_result.stdev(g), np.sqrt(pcov[0, 0]))

        # according to Mathematica
        self.assertAlmostEqual(fit_result.value(g), 9.095, 3)
        self.assertAlmostEqual(fit_result.stdev(g), 0.102, 3)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_gaussian_2d_fitting(self):
        """
        Tests fitting to a scalar gaussian function with 2 independent
        variables. Very sensitive to initial guesses, and if they are chosen too
        restrictive Fit actually throws a tantrum.
        It therefore appears to be more sensitive than NumericalLeastSquares.
        """
        mean = (0.6, 0.4)  # x, y mean 0.6, 0.4
        cov = [[0.2**2, 0], [0, 0.1**2]]

        np.random.seed(0)
        data = np.random.multivariate_normal(mean, cov, 100000)

        # Insert them as y,x here as np fucks up cartesian conventions.
        ydata, xedges, yedges = np.histogram2d(data[:, 0], data[:, 1], bins=100,
                                               range=[[0.0, 1.0], [0.0, 1.0]])
        xcentres = (xedges[:-1] + xedges[1:]) / 2
        ycentres = (yedges[:-1] + yedges[1:]) / 2

        # Make a valid grid to match ydata
        xx, yy = np.meshgrid(xcentres, ycentres, sparse=False, indexing='ij')

        x0 = Parameter(value=mean[0], min=0.0, max=1.0)
        sig_x = Parameter(value=0.2, min=0.0, max=0.3)
        y0 = Parameter(value=mean[1], min=0.0, max=1.0)
        sig_y = Parameter(value=0.1, min=0.0, max=0.3)
        A = Parameter(value=np.mean(ydata), min=0.0)
        x = Variable('x')
        y = Variable('y')
        g = Variable('g')
        model = Model({g: A * Gaussian(x, x0, sig_x) * Gaussian(y, y0, sig_y)})
        fit = Fit(model, x=xx, y=yy, g=ydata)
        fit_result = fit.execute()

        self.assertAlmostEqual(fit_result.value(x0), np.mean(data[:, 0]), 3)
        self.assertAlmostEqual(fit_result.value(y0), np.mean(data[:, 1]), 3)
        self.assertAlmostEqual(np.abs(fit_result.value(sig_x)), np.std(data[:, 0]), 2)
        self.assertAlmostEqual(np.abs(fit_result.value(sig_y)), np.std(data[:, 1]), 2)
        self.assertGreaterEqual(fit_result.r_squared, 0.96)

        # Compare with industry standard MINPACK
        fit_std = Fit(model, x=xx, y=yy, g=ydata, minimizer=MINPACK)
        fit_std_result = fit_std.execute()

        self.assertAlmostEqual(fit_std_result.value(x0), fit_result.value(x0), 4)
        self.assertAlmostEqual(fit_std_result.value(y0), fit_result.value(y0), 4)
        self.assertAlmostEqual(fit_std_result.value(sig_x), fit_result.value(sig_x), 4)
        self.assertAlmostEqual(fit_std_result.value(sig_y), fit_result.value(sig_y), 4)
        self.assertAlmostEqual(fit_std_result.r_squared, fit_result.r_squared, 4)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_fitting(self):
        xdata = np.linspace(1,10,10)
        ydata = 3*xdata**2

        a = Parameter() #3.1, min=2.5, max=3.5
        b = Parameter()
        x = Variable()
        new = a*x**b

        fit = Fit(new, xdata, ydata, minimizer=MINPACK)
        fit_result = fit.execute()
        self.assertIsInstance(fit_result, FitResults)
        self.assertAlmostEqual(fit_result.value(a), 3.0)
        self.assertAlmostEqual(fit_result.value(b), 2.0)

        self.assertIsInstance(fit_result.stdev(a), float)
        self.assertIsInstance(fit_result.stdev(b), float)

        self.assertIsInstance(fit_result.r_squared, float)
        self.assertEqual(fit_result.r_squared, 1.0)  # by definition since there's no fuzzyness

        # Test several illegal ways to access the data.
        self.assertRaises(AttributeError, getattr, *[fit_result.params, 'a_fdska'])
        self.assertRaises(AttributeError, getattr, *[fit_result.params, 'c'])
        self.assertRaises(AttributeError, getattr, *[fit_result.params, 'a_stdev_stdev'])
        self.assertRaises(AttributeError, getattr, *[fit_result.params, 'a_stdev_'])
        self.assertRaises(AttributeError, getattr, *[fit_result.params, 'a__stdev'])

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_fitting(self):
        """
        Tests fitting with NumericalLeastSquares. Makes sure that the resulting
        objects and values are of the right type, and that the fit_result does
        not have unexpected members.
        """
        xdata = np.linspace(1, 10, 10)
        ydata = 3*xdata**2

        a = Parameter()  # 3.1, min=2.5, max=3.5
        b = Parameter()
        x = Variable()
        new = a*x**b

        fit = Fit(new, xdata, ydata, minimizer=MINPACK)

        fit_result = fit.execute()
        self.assertIsInstance(fit_result, FitResults)
        self.assertAlmostEqual(fit_result.value(a), 3.0)
        self.assertAlmostEqual(fit_result.value(b), 2.0)

        self.assertIsInstance(fit_result.stdev(a), float)
        self.assertIsInstance(fit_result.stdev(b), float)

        self.assertIsInstance(fit_result.r_squared, float)
        self.assertEqual(fit_result.r_squared, 1.0)  # by definition since there's no fuzzyness

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_gaussian_fitting(self):
        """
        Tests fitting to a gaussian function and fit_result.params unpacking.
        """
        xdata = 2*np.random.rand(10000) - 1  # random betwen [-1, 1]
        ydata = 5.0 * scipy.stats.norm.pdf(xdata, loc=0.0, scale=1.0)

        x0 = Parameter()
        sig = Parameter()
        A = Parameter()
        x = Variable()
        g = A * Gaussian(x, x0, sig)

        fit = Fit(g, xdata, ydata)
        fit_result = fit.execute()

        self.assertAlmostEqual(fit_result.value(A), 5.0)
        self.assertAlmostEqual(np.abs(fit_result.value(sig)), 1.0)
        self.assertAlmostEqual(fit_result.value(x0), 0.0)
        # raise Exception([i for i in fit_result.params])
        sexy = g(x=2.0, **fit_result.params)
        ugly = g(
            x=2.0,
            x0=fit_result.value(x0),
            A=fit_result.value(A),
            sig=fit_result.value(sig),
        )
        self.assertEqual(sexy, ugly)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    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 = Fit(
            model=model,
            a_i=xdata[0],
            b_i=xdata[1],
            c_i=xdata[2],
            minimizer = MINPACK
        )
        fit_result = fit.execute()

        self.assertAlmostEqual(fit_result.value(a) / 9.985691, 1.0, 5)
        self.assertAlmostEqual(fit_result.value(b) / 1.006143e+02, 1.0, 4)
        self.assertAlmostEqual(fit_result.value(c) / 7.085713e+01, 1.0, 5)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_vector_fitting_bounds(self):
        """
        Tests fitting to a 3 component vector valued function, with bounds.
        """
        a, b, c = parameters('a, b, c')
        a.min = 0
        a.max = 25
        b.min = 0
        b.max = 500
        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 = Fit(
            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)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_likelihood_fitting_exponential(self):
        """
        Fit using the likelihood method.
        """
        b = Parameter(value=4, min=3.0)
        x, y = variables('x, y')
        pdf = {y: Exp(x, 1/b)}

        # Draw points from an Exp(5) exponential distribution.
        np.random.seed(100)
        xdata = np.random.exponential(5, 1000000)

        # Expected parameter values
        mean = np.mean(xdata)
        stdev = np.std(xdata)
        mean_stdev = stdev / np.sqrt(len(xdata))

        with self.assertRaises(NotImplementedError):
            fit = Fit(pdf, x=xdata, sigma_y=2.0, objective=LogLikelihood)
        fit = Fit(pdf, xdata, objective=LogLikelihood)
        fit_result = fit.execute()

        self.assertAlmostEqual(fit_result.value(b) / mean, 1, 3)
        self.assertAlmostEqual(fit_result.value(b) / stdev, 1, 3)
        self.assertAlmostEqual(fit_result.stdev(b) / mean_stdev, 1, 3)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    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)

# 需要导入模块: from symfit import Fit [as 别名]
# 或者: from symfit.Fit import execute [as 别名]
    def test_constraint_types(self):
        x = Parameter(value=-1.0)
        y = Parameter(value=1.0)
        z = Variable()
        model = Model({z: 2*x*y + 2*x - x**2 - 2*y**2})

        # These types are not allowed constraints.
        for relation in [Lt, Gt, Ne]:
            with self.assertRaises(ModelError):
                Fit(model, constraints=[relation(x, y)])

        # Should execute without problems.
        for relation in [Eq, Ge, Le]:
            Fit(model, constraints=[relation(x, y)])

        fit = Fit(model, constraints=[Le(x, y)])
        # Le should be transformed to Ge
        self.assertIs(fit.constraints[0].constraint_type, Ge)

        # Redo the standard test as a Le
        constraints = [
            Le(- y + 1, 0),  # y - 1 >= 0,
            Eq(x**3 - y, 0),  # x**3 - y == 0,
        ]
        std_constraints = [
            Ge(y - 1, 0),  # y - 1 >= 0,
            Eq(x**3 - y, 0),  # x**3 - y == 0,
        ]

        fit = Fit(- model, constraints=constraints)
        std_fit = Fit(- model, constraints=std_constraints)
        self.assertEqual(fit.constraints[0].constraint_type, Ge)
        self.assertEqual(fit.constraints[1].constraint_type, Eq)
        self.assertEqual(fit.constraints[0].params, [x, y])
        self.assertEqual(fit.constraints[1].params, [x, y])
        self.assertEqual(fit.constraints[0].jacobian_model.params, [x, y])
        self.assertEqual(fit.constraints[1].jacobian_model.params, [x, y])
        self.assertEqual(fit.constraints[0].hessian_model.params, [x, y])
        self.assertEqual(fit.constraints[1].hessian_model.params, [x, y])
        self.assertEqual(fit.constraints[0].__signature__,
                         fit.constraints[1].__signature__)
        fit_result = fit.execute()
        std_result = std_fit.execute()
        self.assertAlmostEqual(fit_result.value(x), std_result.value(x))
        self.assertAlmostEqual(fit_result.value(y), std_result.value(y))