def test_expression_with_string_and_replacements(self):
fit = Fit(model=self.get_model())
fit.expression = 'exp'
a, k, t, tau = fit.model.get_symbols('a', 'k', 't', 'τ')
fit.replacements = (k, 1 / tau)
expression = a * sympy.functions.exp(-t / tau)
eq_(fit.expression, expression)
def test_expression_with_replacements(self):
fit = Fit(model=self.get_model())
fit.replacements = 'tau'
fit.expression = fit.model.expressions['exp']
a, t, tau = fit.model.get_symbols('a', 't', 'τ')
expression = a * sympy.functions.exp(-t / tau)
eq_(fit.expression, expression)
def test_lmfit_parameters_with_options(self):
fit = Fit()
fit.options['fit_function'] = 'lmfit'
fit.parameters = self.get_parameters()
fit.parameters[2]['lmfit'] = {'min': 0, 'max': 20}
eq_(fit.lmfit_parameters['p_00000'].value, 10)
eq_(fit.lmfit_parameters['p_00000'].min, 0)
eq_(fit.lmfit_parameters['p_00000'].max, 20)
def test_lmfit_parameters_with_scale(self):
fit = Fit()
fit.options['fit_function'] = 'lmfit'
fit.parameters = [
{'symbol': 'k', 'guess': 2, 'prefix': 'kilo',
'lmfit': {'min': 0.5, 'max': 4}
},
]
eq_(fit.lmfit_parameters['p_00000'].value, 2000.0)
eq_(fit.lmfit_parameters['p_00000'].min, 500)
eq_(fit.lmfit_parameters['p_00000'].max, 4000.0)
def get_fit_for_fitting(self):
fit = Fit('exponential_fit',
data=self.get_data(),
model=self.get_model())
fit.expression = 'exp'
fit.independent = {'symbol': 't'}
fit.parameters = [
{'symbol': 'a', 'guess': 10},
{'symbol': 'k', 'guess': 20},
]
return fit
def test_fixed_values(self):
fit = Fit(model=Model())
fit.parameters = [
{'symbol': 'D', 'guess': 2},
{'symbol': 'k', 'value': 3, 'prefix': 'kilo'},
{'symbol': 'm', 'value': 4},
]
fit.constants = [
{'symbol': 'a', 'value': 10},
{'symbol': 'b', 'value': 5, 'prefix': 'milli'},
{'symbol': 'c', 'value': 'Avogadro constant'},
]
eq_(fit.fixed_values, (3000, 4, 10, 0.005, 6.022140857e+23))
def test_all_variables(self):
fit = Fit(model=Model())
symbols = ('t', 'u', 'x', 'm', 'D', 'k', 'τ', 'a', 'b')
fit.model.add_symbols(*symbols)
fit.free_variables = ['t', 'u']
fit.independent = {'symbol': 'x'}
fit.parameters = [
{'symbol': 'm', 'guess': 2},
{'symbol': 'D', 'guess': 2},
{'symbol': fit.model.symbol('k'), 'value': 3},
{'symbol': 'τ', 'value': 4},
]
fit.constants = [
{'symbol': 'a'},
{'symbol': 'b'},
]
eq_(fit.all_variables, tuple( fit.model.symbol(s) for s in symbols ))
def test_function_with_more_symbols(self):
fit = Fit()
fit.model = Model()
symbols = ('x', 'a', 'b', 'c', 'd', 'e', 'f')
fit.model.add_symbols(*symbols)
x, a, b, c, d, e, f = fit.model.get_symbols(*symbols)
fit.model.expressions['exp'] = a * f + b * e + x * c + d
fit.expression = 'exp'
fit.independent = {'symbol': 'x'}
fit.parameters = [
{'symbol': 'a', 'guess': 2},
{'symbol': 'b', 'guess': 3},
{'symbol': 'c', 'value': 4, 'prefix': 'kilo'},
{'symbol': 'd', 'value': 5},
]
fit.constants = [
{'symbol': 'e', 'value': 10},
{'symbol': 'f', 'value': 12, 'prefix': 'milli'},
]
eq_(fit.function(2, 4, 7), 8075.048)
def test_expression_with_string(self):
fit = Fit(model=self.get_model())
expression = fit.model.expressions['exp']
fit.expression = 'exp'
eq_(fit.expression, expression)
def test_expression(self):
fit = Fit(model=self.get_model())
expression = fit.model.expressions['exp']
fit.expression = expression
eq_(fit.expression, expression)
def test_fixed_parameters(self):
fit = Fit()
fit.parameters = self.get_parameters()
eq_(fit.fixed_parameters, [{'symbol': 'a', 'value': 2}, {'symbol': 'b', 'value': 5}])
def test_fitting_parameters(self):
fit = Fit()
fit.parameters = self.get_parameters()
eq_(fit.fitting_parameters, [{'symbol': 'k', 'guess': 10}, {'symbol': 'm', 'guess': 20}])
#
# Example of a basic linear fit with error bars.
#
name = 'linear'
# Load data from a csv file.
data = Data(name)
data.path = os.path.join('examples', 'data', 'linear.csv')
data.genfromtxt_args['skip_header'] = 1
data.error_columns = (2, 3)
# Create a linear model.
model = Model(name)
model.add_symbols('t', 'v', 'x_0')
t, v, x_0 = model.get_symbols('t', 'v', 'x_0')
model.expressions['line'] = v * t + x_0
# Create the fit using the data and model.
fit = Fit(name, data=data, model=model)
fit.expression = 'line'
fit.independent = {'symbol': 't', 'name': 'Time', 'units': 's'}
fit.dependent = {'name': 'Distance', 'units': 'm'}
fit.parameters = [
{'symbol': 'v', 'guess': 1, 'units': 'm/s'},
{'symbol': 'x_0', 'value': 1, 'units': 'm'},
]
# Save the fit to disk.
save_example_fit(fit)
def test_lmfit_parameter_values(self):
fit = Fit()
params = lmfit.Parameters()
params.add('a', 1)
params.add('b', 2)
eq_(fit.lmfit_parameter_values(params), (1, 2))
def test_lmfit_parameters(self):
fit = Fit()
fit.options['fit_function'] = 'lmfit'
fit.parameters = self.get_parameters()
eq_(fit.lmfit_parameters['p_00000'].value, 10)
eq_(fit.lmfit_parameters['p_00001'].value, 20)
# Load data from a csv file.
data = Data(name)
data.path = os.path.join('examples','data', 'wave.csv')
data.genfromtxt_args['skip_header'] = 1
data.error = (0.1, 0.05)
# Create a wave model.
model = Model(name)
model.add_symbols('t', 'A', 'ω', 'δ')
A, t, ω, δ = model.get_symbols('A', 't', 'ω', 'δ')
model.expressions['wave'] = A * sympy.functions.sin(ω * t + δ)
model.expressions['frequency'] = ω / (2 * sympy.pi)
# Create the fit using the data and model.
fit = Fit(name, data=data, model=model)
fit.expression = 'wave'
fit.independent = {'symbol': 't', 'name': 'Time', 'units': 's'}
fit.dependent = {'name': 'Voltage', 'prefix': 'kilo', 'units': 'kV'}
fit.parameters = [
{'symbol': 'A', 'value': 0.3, 'prefix': 'kilo', 'units': 'kV'},
{'symbol': 'ω', 'guess': 1, 'units': 'Hz'},
{'symbol': 'δ', 'guess': 1},
]
fit.quantities = [
{'expression': 'frequency', 'name': 'Frequency', 'units': 'Hz'},
{'expression': 1 / model.expressions['frequency'] , 'name': 'Period', 'units': 's'},
]
# Save the fit to disk.
save_example_fit(fit)
#
name = 'linear_polyfit'
# Load data from a csv file.
data = Data(name)
data.path = os.path.join('examples', 'data', 'linear.csv')
data.genfromtxt_args['skip_header'] = 1
# Create a linear model.
model = Model(name)
model.add_symbols('t', 'v', 'x_0')
t, v, x_0 = model.get_symbols('t', 'v', 'x_0')
model.expressions['line'] = v * t + x_0
# Create the fit using the data and model.
fit = Fit(name, data=data, model=model)
fit.expression = 'line'
fit.independent = {'symbol': 't', 'name': 'Time', 'units': 's'}
fit.dependent = {'name': 'Distance', 'units': 'm'}
fit.parameters = [
{'symbol': 'v', 'guess': 1, 'units': 'm/s'},
{'symbol': 'x_0', 'guess': 1, 'units': 'm'},
]
# Use `numpy.polyfit` to do the fit.
fit.options['fit_function'] = lambda f, x, y, p0, **op: (numpy.polyfit(x, y, 1), )
# Save the fit to disk.
save_example_fit(fit)
#
name = 'linear_scaled'
# Load data from a csv file.
data = Data(name)
data.path = os.path.join('examples', 'data', 'linear.csv')
data.genfromtxt_args['skip_header'] = 1
# Assume the data was not saved in SI base units.
data.scale = ('micro', 'kilo')
# Create a linear model.
model = Model(name)
model.add_symbols('t', 'v', 'x_0')
t, v, x_0 = model.get_symbols('t', 'v', 'x_0')
model.expressions['line'] = v * t + x_0
# Create the fit using the data and model.
fit = Fit(name, data=data, model=model)
fit.expression = 'line'
fit.independent = {'symbol': 't', 'name': 'Time', 'prefix': 'micro', 'units': 'µs'}
fit.dependent = {'name': 'Distance', 'prefix': 'kilo', 'units': 'km'}
fit.parameters = [
{'symbol': 'v', 'guess': 1, 'prefix': 10**9, 'units': 'km/µs'},
{'symbol': 'x_0', 'value': 1, 'prefix': 'kilo', 'units': 'km'},
]
# Save the fit to disk.
save_example_fit(fit)
