Using DIIS

This guide shows you how to use and customize :py:class:DIIS. This is an implementation of algorithms from Ref. [1].

Truncating history

Like other quasi-Newton methods, DIIS uses the history of previous guesses for the vector \(x\) that minimizes the loss/root function \(f(x)\). If your system requires many iteraions to find a solution this history can become computationally expensive. Sometimes the history also includes old and bad guesses that have too much influence on new gusses for \(x\).

To specify how big the history should be

from risb.optimize import DIIS

optimize = DIIS(history_size = ...)

If you want to reset the entire history after \(n\) iterations

optimize = DIIS(n_restart = ...)

Linear mixing step

Our implementation takes a single linear mixing step every n_period iterations.

To change how frequently a linear mixing step is taken

optimize = DIIS(n_period = ...)

The size of the linear mixing step \(\alpha\) is specified in the solve() method as

optimize.solve(alpha = ...)

Only linear mixing

If you just want to use linear mixing with nothing special

from risb.optimize import LinearMixing

optimize = LinearMixing()
optimize.solve(alpha = ...)

Arguments to solve()

optimize.solve(fun = function to minimize,
               x0 = initial guess for x,
               args = args for fun,
               tol = stop solver when the error is less than this,
               maxiter = maxium number of iterations,
               alpha = step size in linear mixing,
)

Using with LatticeSolver

See also

Using LatticeSolver.

If you want to use your customized DIIS solver

from risb import LatticeSolver

S = LatticeSolver(...,
                  root = optimize.solve
)

To pass keyword arguments to optimize.solve()

S.solve(...,
        tol = ...,
        maxiter = ...,
        alpha = ...,
)

If you want to access the default DIIS instance that is used it is stored in S.optimize.