def test_dchi2(self):
"""Unit test for the chi-squared gradient created by the dchi2 function.
The chi-squared gradient is [0, 10] for the following data::
data = | 1.0 1.5 2.0 2.5 3.0 |,
back_calc = | 0.9 1.45 2.0 2.55 3.1 |,
back_calc_grad = | 0.1 0.2 0.3 0.2 0.1 |
| -0.2 -0.1 0.0 0.1 0.2 |,
errors = | 0.1 0.1 0.1 0.1 0.1 |.
"""
# Calculate the gradient elements.
grad = zeros(2, float64)
dchi2(grad, 2, self.data, self.back_calc, self.back_calc_grad, self.errors)
# Assert, to a precision of 13 decimal places, that the gradient is [0, 10].
self.assertAlmostEqual(grad[0], 0.0, places=13)
self.assertAlmostEqual(grad[1], 10.0, places=13)
# Delete the gradient data.
del grad
def test_dchi2(self):
"""Unit test for the chi-squared gradient created by the dchi2 function.
The chi-squared gradient is [0, 10] for the following data::
data = | 1.0 1.5 2.0 2.5 3.0 |,
back_calc = | 0.9 1.45 2.0 2.55 3.1 |,
back_calc_grad = | 0.1 0.2 0.3 0.2 0.1 |
| -0.2 -0.1 0.0 0.1 0.2 |,
errors = | 0.1 0.1 0.1 0.1 0.1 |.
"""
# Calculate the gradient elements.
grad = zeros(2, float64)
dchi2(grad, 2, self.data, self.back_calc, self.back_calc_grad,
self.errors)
# Assert, to a precision of 13 decimal places, that the gradient is [0, 10].
self.assertAlmostEqual(grad[0], 0.0, places=13)
self.assertAlmostEqual(grad[1], 10.0, places=13)
# Delete the gradient data.
del grad
def func_exp_chi2_grad(self, params=None, times=None, values=None, errors=None):
"""Target function for the gradient (Jacobian matrix) to minfx, for exponential fit .
@param params: The vector of parameter values.
@type params: numpy rank-1 float array
@keyword times: The time points.
@type times: numpy array
@param values: The measured values.
@type values: numpy array
@param errors: The standard deviation of the measured intensity values per time point.
@type errors: numpy array
@return: The Jacobian matrix with 'm' rows of function derivatives per 'n' columns of parameters, which have been summed together.
@rtype: numpy array
"""
# Get the back calc.
back_calc = self.func_exp(params=params, times=times)
# Get the Jacobian, with partial derivative, with respect to r2eff and i0.
exp_grad = self.func_exp_grad(params=params, times=times)
# Transpose back, to get rows.
exp_grad_t = transpose(exp_grad)
# n is number of fitted parameters.
n = len(params)
# Define array to update parameters in.
jacobian_chi2_minfx = zeros([n])
# Update value elements.
dchi2(dchi2=jacobian_chi2_minfx, M=n, data=values, back_calc_vals=back_calc, back_calc_grad=exp_grad_t, errors=errors)
# Return Jacobian matrix.
return jacobian_chi2_minfx
def func_exp_chi2_grad(self,
params=None,
times=None,
values=None,
errors=None):
"""Target function for the gradient (Jacobian matrix) to minfx, for exponential fit .
@param params: The vector of parameter values.
@type params: numpy rank-1 float array
@keyword times: The time points.
@type times: numpy array
@param values: The measured values.
@type values: numpy array
@param errors: The standard deviation of the measured intensity values per time point.
@type errors: numpy array
@return: The Jacobian matrix with 'm' rows of function derivatives per 'n' columns of parameters, which have been summed together.
@rtype: numpy array
"""
# Get the back calc.
back_calc = self.func_exp(params=params, times=times)
# Get the Jacobian, with partial derivative, with respect to r2eff and i0.
exp_grad = self.func_exp_grad(params=params, times=times)
# Transpose back, to get rows.
exp_grad_t = transpose(exp_grad)
# n is number of fitted parameters.
n = len(params)
# Define array to update parameters in.
jacobian_chi2_minfx = zeros([n])
# Update value elements.
dchi2(dchi2=jacobian_chi2_minfx,
M=n,
data=values,
back_calc_vals=back_calc,
back_calc_grad=exp_grad_t,
errors=errors)
# Return Jacobian matrix.
return jacobian_chi2_minfx