Linear Solve

NonlinearSolve.LinearSolverCache — Type
LinearSolverCache(alg, linsolve, A, b, u; kwargs...)

Construct a cache for solving linear systems of the form A * u = b. Following cases are handled:

  1. A is Number, then we solve it with u = b / A
  2. A is SMatrix, then we solve it with u = A \ b (using the defaults from base Julia)
  3. A is Diagonal, then we solve it with u = b ./ A.diag
  4. In all other cases, we use alg to solve the linear system using LinearSolve.jl.

Solving the System

(cache::LinearSolverCache)(; A = nothing, b = nothing, linu = nothing,
    du = nothing, p = nothing, weight = nothing, cachedata = nothing,
    reuse_A_if_factorization = false, kwargs...)

Returns the solution of the system u and stores the updated cache in cache.lincache.

Keyword Arguments

  • reuse_A_if_factorization: If true, then the factorization of A is reused if possible. This is useful when solving the same system with different b values. If the algorithm is an iterative solver, then we reset the internal linear solve cache.

One distinct feature of this compared to the cache from LinearSolve is that it respects the aliasing arguments even after cache construction, i.e., if we passed in an A that A is not mutated, we do this by copying over A to a preconstructed cache.