Add Herings-Peeters homotopy method - #1113
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…thods (#973) Implementation of algorithm equation system and termination condition at t=1. Passes several simple tests; more robust test suite to come.
Refactors the HP system of equations to the class-based equation pattern.
This updates `path.cc ` so that the tracer always follows the curve in the direction chosen by the programmer. It has been proven useful in the new `HP`algorithm to avoid a random direction in `t=0`. `logit` has also been affected by the modifications: the headers have been updated. The mechanism implemented is the following: -In `path.h` an enum type named **`TraceDirection`** has been declared. It can be `Positive` associated to the number 1, and `Negative`, (-1). Positive means that the tracer will move forward; negative backwards. -To control whether the tracer is headed into the right direction in the first iteration, it is required to know which is the index of the variable that we are following (`lambda`in `logit`, `t` in `HP`). Another parameter has been added to `TracePath` named **`tracking_index`** that stores the position of that variable in the vector `x`. Note that in `HP` it is the first position and in `logit` is the last one. The check that we are heading the right way is as discussed: if the first step goes as expected (equivalent to the tangent being positive), the internal omega does not change. Otherwise, it is multiplied by -1. Tracing returns with an error result if the tangent in the first step is 0 (up to numerical tolerance)
# Conflicts: # Makefile.am # src/pygambit/nash.h # src/pygambit/nash.pxi # src/solvers/logit/efglogit.cc # src/solvers/logit/logit.h # src/solvers/logit/nfglogit.cc # src/solvers/logit/path.cc # src/tools/logit/logit.cc
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@AndresFerCervell In this branch we've added in all of the instrumentation to be able to use this as an equilibrium solver (callbacks, ability to cancel in a multi-threaded computation), and hooked this up to a command-line driver and added it to the GUI. There are two last things to do:
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