rom: Steady LSPG

todo: write this better

The pressio4py steady LSPG ROMs are designed to involve two main steps:

1. Create

You instantiate a "steady LSPG problem", e.g.:

problem = pressio4py.rom.lspg.steady.Problem(...)

We currently support two variants:

Basic Problem: link
Masked: link

Refer to each problem page for details on each specific variant.

The returned problem object is an instantiation of a class exposing the following interface:

class Problem

  def fomStateReconstructor()
    return # reference to object for reconstructing FOM state

  def createResidual()
    return # a residual instance

  def createJacobian()
    return # a Jacobian instance

  def residual(state, R)
    # evaluates the residual for the given state

  def jacobian(state, J)
    # evaluates the Jacobian for the given state
};

2. Solve

you use a nonlinear least-squares solvers to solve the problem

solver = pressio4py.solvers.create_gauss_newton(problem, ...)
solver.solve(problem, ...)

note, in fact, that the problem's API conforms to the one required by the nonlinear solvers
for this solve stage, you don't have to use the pressio4py solvers. Once you have the problem object, you can also use your own nonlinear least-squares solver. As shown above, the problem exposes all the operators that you need to solve.