What is the theory behind the odeintw package for complex matrix differential equations?

问题

In most of the below answers for complex matrix differential equations, the odeintw package has been suggested. https://stackoverflow.com/a/45970853/7952027

https://stackoverflow.com/a/26320130/7952027

https://stackoverflow.com/a/26747232/7952027

https://stackoverflow.com/a/26582411/7952027

I want to know the theory behind the manipulations done in the code of odeintw. Like why one has to build that banded jacobian, the idea behind the functions _complex_to_real_jac, _transform_banded_jac, etc.

来源：https://stackoverflow.com/questions/65880726/what-is-the-theory-behind-the-odeintw-package-for-complex-matrix-differential-eq