fitbenchmarking.cost_func.hellinger_nlls_cost_func module
Implements the root non-linear least squares cost function
- class fitbenchmarking.cost_func.hellinger_nlls_cost_func.HellingerNLLSCostFunc(problem)
Bases:
fitbenchmarking.cost_func.nlls_base_cost_func.BaseNLLSCostFuncThis defines the Hellinger non-linear least squares cost function where, given a set of \(n\) data points \((x_i,y_i)\), associated errors \(e_i\), and a model function \(f(x,p)\), we find the optimal parameters in the Hellinger least-squares sense by solving:
\[\min_p \sum_{i=1}^n \left(\sqrt{y_i} - \sqrt{f(x_i, p})\right)^2\]where \(p\) is a vector of length \(m\), and we start from a given initial guess for the optimal parameters. More information on non-linear least squares cost functions can be found here and for the Hellinger distance measure see here.
- eval_r(params, **kwargs)
Calculate the residuals, \(\sqrt{y_i} - \sqrt{f(x_i, p)}\)
- Parameters
params (list) – The parameters, \(p\), to calculate residuals for
- Returns
The residuals for the datapoints at the given parameters
- Return type
numpy array
- hes_res(params, **kwargs)
Uses the Hessian of the model to evaluate the Hessian of the cost function residual, \(\nabla_p^2 r(x,y,p)\), at the given parameters.
- Parameters
params (list) – The parameters at which to calculate Hessians
- Returns
evaluated Hessian and Jacobian of the residual at each x, y pair
- Return type
tuple (list of 2D numpy arrays, list of 1D numpy arrays)
- jac_res(params, **kwargs)
Uses the Jacobian of the model to evaluate the Jacobian of the cost function residual, \(\nabla_p r(x,y,p)\), at the given parameters.
- Parameters
params (list) – The parameters at which to calculate Jacobians
- Returns
evaluated Jacobian of the residual at each x, y pair
- Return type
a list of 1D numpy arrays