#include <IPDesignVariableParameterization.hh>
Inheritance diagram for pism::inverse::IPDesignVariableParameterization:Public Member Functions | |
| IPDesignVariableParameterization () | |
| virtual | ~IPDesignVariableParameterization () |
| virtual void | set_scales (const Config &config, const std::string &design_var_name) |
| Initializes the scale parameters of the parameterization. More... | |
| virtual void | toDesignVariable (double zeta, double *value, double *derivative)=0 |
| Converts from parameterization value \(\zeta\) to \(d=g(\zeta)\). More... | |
| virtual void | fromDesignVariable (double d, double *OUTPUT)=0 |
| Converts from \(d\) to a parameterization value \(\zeta\) such that \(d=g(\zeta)\). More... | |
| virtual void | convertToDesignVariable (array::Scalar &zeta, array::Scalar &d, bool communicate=true) |
| Transforms a vector of \(\zeta\) values to a vector of \(d\) values. More... | |
| virtual void | convertFromDesignVariable (array::Scalar &d, array::Scalar &zeta, bool communicate=true) |
| Transforms a vector of \(d\) values to a vector of \(\zeta\) values. More... | |
Protected Attributes | |
| double | m_d_scale |
| Value of \(d\) in PISM units that equals 1 for IPDesignVariableParameterization's units. More... | |
Detailed Description
Encapsulates a parameterization of a design variable (e.g. \(\tau_c\) for SSA inversions) as a function of a different parameter \(\zeta\).
When solving an inverse problem for a design variable \(d\) (think of \(\tau_c\) or hardness for SSA inversions), one frequently does not work with \(d\) directly but with a different variable \(\zeta\), and a relationship \(d=g(\zeta)\). A common choice in the glaciology literature for \(\tau_c\) is \(\tau_c=g(\zeta)=\zeta^2\), which ensures that \(\tau_c\) is non-negative, but has the disadvantage that it is a 2-1 parameterization. A potentially more satisfactory choice is \(g(\zeta)=e^\zeta\), which ensures positivitiy, is 1-1, and respects the wide scale variations of \(\tau_c\).
An IPDesignVariableParameterization implements such a parameterization map.
This method of encoding mathematical expressions is flexible and convenient, but is also slow; it has the overhead that many virtual function calls are needed if the expression is being called over and over again. If this proves to be a significant source of slowness, we could look at using the Expression Template idiom, http://drdobbs.com/184401627.
For certain Tikhonov inversions, it is important to mainain well-scaled variables. If the design parameter name is 'foo', internally the parameterizations use units of \(d\) such that the config parameter design_param_foo_scale equals one. I.e. if 'foo' is 'tauc', then for a conversion function \(g(\zeta)=\zeta^2\),
\[ \frac{d} = d_{\rm scale}g(\zeta^2). \]
where \(d_{\rm scale}={\tt design_param_tauc_scale}\).
Definition at line 62 of file IPDesignVariableParameterization.hh.
The documentation for this class was generated from the following files:
- src/inverse/IPDesignVariableParameterization.hh
- src/inverse/IPDesignVariableParameterization.cc
