LinearRunOnce

The simplest linear solver in OpenMDAO is LinearRunOnce, which sequentially calls apply_linear and solve_linear once on each subsystem. It is directly analogous to applying a single pass of the chain rule to the whole system without any iteration at the top level. This linear solver can only be used in systems where the following conditions are satisfied:

1. System does not contain a cycle, though subsystems may.

2. System does not contain any implicit states, though subsystems may.

However, subsystems can contain cycles or implicit states, provided that they are using the appropriate solver such as ScipyKrylov.

Here is an example of using LinearRunOnce to calculate the derivatives across a simple model with the Paraboloid component.

Paraboloid class definition

class Paraboloid(om.ExplicitComponent):
    """
    Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3.
    """

    def setup(self):
        self.add_input('x', val=0.0)
        self.add_input('y', val=0.0)

        self.add_output('f_xy', val=0.0)

    def setup_partials(self):
        self.declare_partials('*', '*')

    def compute(self, inputs, outputs):
        """
        f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3

        Optimal solution (minimum): x = 6.6667; y = -7.3333
        """
        x = inputs['x']
        y = inputs['y']

        outputs['f_xy'] = (x-3.0)**2 + x*y + (y+4.0)**2 - 3.0

    def compute_partials(self, inputs, partials):
        """
        Jacobian for our paraboloid.
        """
        x = inputs['x']
        y = inputs['y']

        partials['f_xy', 'x'] = 2.0*x - 6.0 + y
        partials['f_xy', 'y'] = 2.0*y + 8.0 + x

import openmdao.api as om
from openmdao.test_suite.components.paraboloid import Paraboloid

prob = om.Problem()
model = prob.model

model.add_subsystem('comp', Paraboloid(), promotes=['x', 'y', 'f_xy'])

model.linear_solver = om.LinearRunOnce()

prob.setup(check=False, mode='fwd')

prob.set_val('x', 0.0)
prob.set_val('y', 0.0)

prob.run_model()

of = ['f_xy']
wrt = ['x', 'y']
derivs = prob.compute_totals(of=of, wrt=wrt, return_format='dict')

print(derivs['f_xy']['x'], [[-6.0]])
print(derivs['f_xy']['y'], [[8.0]])

[[-6.]] [[-6.0]]
[[8.]] [[8.0]]

LinearRunOnce Options

Option	Default	Acceptable Values	Acceptable Types	Description
aitken_initial_factor	1.0	N/A	N/A	initial value for Aitken relaxation factor
aitken_max_factor	1.5	N/A	N/A	upper limit for Aitken relaxation factor
aitken_min_factor	0.1	N/A	N/A	lower limit for Aitken relaxation factor
assemble_jac	False	[True, False]	['bool']	Activates use of assembled jacobian by this solver.
iprint	1	N/A	['int']	whether to print output
use_aitken	False	[True, False]	['bool']	set to True to use Aitken relaxation

LinearRunOnce Constructor

The call signature for the LinearRunOnce constructor is:

LinearRunOnce.__init__(**kwargs)

Initialize all attributes.