ConsIndShockSolverNumba

Over the last few weeks I’ve worked on a numba version of ConsIndShockSolver in IndShockNumbaModel.py. For this, I created two numba helper functions, solveConsIndShockCubicNumba for solving using a cubic approximation for the consumption policy function, and addvFuncNumba for calculating the value function during the solution.

solveConsIndShockCubicNumba

In the previous post, I described the process of linearly interpolating the value function using interp from interpolation.py. For the cubic version, I needed to use a similar cubic interpolator that worked with numba, but using tools from interpolation.py did not seem straightforward. However, I had created a basic numba cubic interpolator for my own purposes previously, and added these functions to HARK.numba. A more thorough overview of what these do is presented here, but below I briefly explain.

The function splrep taxes 1-d vectors x and y, where y=f(x) for some function f, and creates interpolating coefficients using a complete cubic spline method. The function returns a 1-d vector of coefficients, which we can call z. The function splevec then takes 1-d vectors x0, x, y, and z, where y=f(x), z are interpolating coefficients, and x0 contains values where we need an approximation for f, and returns an approximation y0=g(x0), where g is the cubic spline approximation. The final code looks like this:

cFuncCoeffs = splrep(sn_cFunc_x_list, sn_cFunc_y_list)
cFuncNext = splevec(mNrmNext.flatten(), sn_cFunc_x_list, sn_cFunc_y_list, cFuncCoeffs)
vPfuncNext = (cFuncNext ** -CRRA).reshape(mNrmNext.shape)

The same process is used to calculate vPPfuncNext.

addvFuncNumba

This section uses the same process above to calculate a cubic approximation of vfuncNext on current resources. The only novel part of this section is the use of @vectorize on the different kind of utility functions. Instead of importing utilities from HARK.utilities, I have created basic numba implementations of utilities by simply adding @vectorize decorators in HARK.numba. In the future, these vectorized functions could be easily adaptable to GPU processing by adding target="cuda" as a parameter. Instead of creating lambda functions with a set CRRA parameter, however, I use the full call f(c,crra) for all f in utilities, which is used to reduce overhead and prevent numba recompiling. The solver appears to work, although there will be numerical differences given different interpolators that need to be explored further.

Alan Lujan
Alan Lujan
PhD Candidate in Economics

My research interests include poverty and inequality, household finance, and computational economics.

Related