fitbenchmarking.cost_func.poisson_cost_func module
Implements a Poisson deviance cost function based on Mantid’s: https://docs.mantidproject.org/nightly/fitting/fitcostfunctions/Poisson.html
- class fitbenchmarking.cost_func.poisson_cost_func.PoissonCostFunc(problem)
Bases:
fitbenchmarking.cost_func.base_cost_func.CostFuncThis defines the Poisson deviance cost-function where, given the set of \(n\) data points \((x_i, y_i)\), and a model function \(f(x,p)\), we find the optimal parameters in the Poisson deviance sense by solving:
\[\min_p \sum_{i=1}^n \left( y_i \left(\log{y_i} - \log{f(x_i, p)} \right) - \left( y_i - f(x_i, p) \right) \right)\]where \(p\) is a vector of length \(m\), and we start from a given initial guess for the optimal parameters.
This cost function is intended for positive values.
This cost function is not a least squares problem and as such will not work with least squares minimizers. Please use algorithm_type to select general solvers. See options docs (Fitting Options) for information on how to do this.
- eval_cost(params, **kwargs)
Evaluate the Poisson deviance cost function
- Parameters
params (list) – The parameters to calculate residuals for
x (np.array (optional)) – The x values to evaluate at. Default is self.problem.data_x
y (np.array (optional)) – The y values to evaluate at. Default is self.problem.data_y
- Returns
evaluated cost function
- Return type
float
- hes_cost(params, **kwargs)
Uses the Hessian of the model to evaluate the Hessian of the cost function, \(\nabla_p^2 F(r(x,y,p))\), at the given parameters.
- Parameters
params (list) – The parameters at which to calculate Hessians
- Returns
evaluated Hessian of the cost function
- Return type
2D 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 :rtype: tuple(list of 2D numpy arrays, list of 1D numpy arrays)
- jac_cost(params, **kwargs)
Uses the Jacobian of the model to evaluate the Jacobian of the cost function, \(\nabla_p F(r(x,y,p))\), at the given parameters. :param params: The parameters at which to calculate Jacobians :type params: list :return: evaluated Jacobian of the cost function :rtype: 1D numpy array
- 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