@@ -121,9 +121,28 @@ As an example, if :math:`A`, :math:`B` and :math:`C` are of type :py:class:`Line
...
@@ -121,9 +121,28 @@ As an example, if :math:`A`, :math:`B` and :math:`C` are of type :py:class:`Line
f2 = X(f1)
f2 = X(f1)
will perform the operation suggested intuitively by the notation, checking domain compatibility while building the composed operator.
will perform the operation suggested intuitively by the notation, checking domain compatibility while building the composed operator.
The combined operator infers its domain and target from its constituents, as well as the set of operations it can support.
.. _minimization:
.. _minimization:
Minimization
Minimization
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Most problems in IFT are solved by (possibly nested) minimizations of high-dimensional functions, which are often nonlinear.
In NIFTy4 such functions are represented by objects of type :py:class:`Energy`.
These hold the prescription how to calculate the function's value, gradient and (optionally) curvature at any given position.
Function values are floating-point scalars, gradients have the form of fields living on the energy's position domain, and curvatures are represented by linear operator objects.
Some examples of concrete energy classes delivered with NIFTy4 are :py:class:`QuadraticEnergy` (with position-independent curvature, mainly used with conjugate gradient minimization) and :py:class:`WienerFilterEnergy`.
Energies are classes that typically have to be provided by the user when tackling new IFT problems.
The minmization procedure can be carried out by one of several algorithms; NIFTy4 currently ships solvers based on
- the conjugate gradient method (for quadratic energies)
