I'm doing a research involving linear differential equations with complex coefficients in 4-dimensional phase space. To be able to check some hypothesis about the root of the solutions, I need to be able to solve these equations numerically with arbitrary precision. I used to use mpmath Python module, but it works slowsly, so I prefer to rewrite my program in C/C++ to achieve maximum perfomance. So I have a question:
Are there any C/C++ linear algebra library exists which support both arbitrary precision arithmetic and complex numbers? I need some basic functionality like dot-products and so on. (Actually, I need matrix exponential too, but I can implement it by myself if necessary).
I tried to use Eigen with MPFR C++, but failed due to the fact that it doesn't support complex numbers (and construction like complex <mpreal> doesn't work as it assumes that the base type is a standard float).
Finally, it seems that zkcm did what I want. I'm not sure if it is good from performance viewpoint (didn't do any benchmarks), but at least it works and provides all necessary features.