If researchers use the result of the derivatives in a part of computer simulation,
researchers should not waste their time taking derivatives by hand. This is especially the case as the
complexity of the problem increases. For example, taking derivatives by hand for heterogeneous agent
model by hand will require an unreasonable man-hour. Of the numerical differentiation methods, symbolic
method is slow and will require a lot of coding (in matlab). Forward/backward-difference is strictly
inferior to automatic differentiation in accuracy. Threrefore, automatic differentiation (by operator
overloading) should be used if applicable. Since there was not an (open-source) automatic derivative
package that used sparse matrix storage for matlab, I updated a pre-existing package from Martin
Fink for our use. Instruction for usage is in <README.pdf> file.
Examples:
This is a collection of codes to solve heterogeneous agent models by perturbation methods. This collection of codes include:
This automates the implementation of adaptive finite volume method for economic applications.
If a standard uniform grid method is used the number of grid points increases as
$O(N^d)$ for a problem with d-dimensional state space and N grid points per dimension. This curse of
dimensionality forces people to make (sometimes arbitrary) assumptions to reduce the dimensionality of
the state space. However, there is a different solution to the curse of dimensionality. Using sparse
grids (Smolyak grid), grid points scale at $O(N \log(N)^{d-1})$, and using adaptive sparse grids will
further reduce the number of necessary grid points. This is still work in progress, but here are some
example of sparse grids in action.
Examples: