Ncpol2sdpa-Cpp is a C++ library to convert a noncommutative polynomial optimization problem to a sparse semidefinite programming (SDP) problem that can be processed by the SDPA family of solvers. The optimization problem can be unconstrained or constrained by equalities and inequalities.
The objective is to be able to solve very large scale optimization problems. For example, a convergent series of lower bounds can be obtained for ground state problems with arbitrary Hamiltonians.
The implementation has an intuitive syntax for entering Hamiltonians and it scales for a larger number of noncommutative variables using a sparse representation of the SDP problem.
The code requires SymbolicC++ to compile and it relies on the C++11 standard. GCC 4.8.1 is known to compile the code. If Ncpol2sdpa-Cpp is compiled with OpenMP support, SymbolicC++ needs a patch to ensure thread-safety.
A simple usage example is included in examplencpol.cpp. A more sophisticated application is given in benchmarkCase.cpp, which implements the Hamiltonian of a bosonic system on a 1D line.
The implementation installs as a library. Subsequent use must specify the include directory of the header files and the library for compilation.
Compilation & Installation
From GIT repository first run
Then follow the standard procedure:
$ ./configure [options] $ make $ make install
Options for configure
--enable-openmp Enable OpenMP support (experimental)
OpenMP support is still experimental and deadlocks occur in larger problems.
--with-symbolicc++-incdir=DIR SymbolicC++ include directory [default /usr/include] --with-symbolicc++-libdir=DIR SymbolicC++ library directory [default /usr/lib]
Specify these directories if the compiler cannot see them in the include and library paths.
Hermicity of noncommuting variables is not handled correctly.
The fast submonomial substitution does not handle some rare cases.
This work is supported by the European Commission Seventh Framework Programme under Grant Agreement Number FP7-601138 PERICLES, by the Red Española de Supercomputación grants number FI-2013-1-0008 and FI-2013-3-0004, and by the Swedish National Infrastructure for Computing project number SNIC 2014/2-7.
For more information refer to the following manuscript: