Computing Total Derivatives

Problem has a method, compute_totals, that allows you to compute the unscaled total derivative values for a model.

If the model approximated its Jacobian, the method uses an approximation method.

Problem.compute_totals(of=None, wrt=None, return_format='flat_dict', debug_print=False, driver_scaling=False, use_abs_names=False, get_remote=True, coloring_info=None)

Compute derivatives of desired quantities with respect to desired inputs.

Parameters:

oflist of variable name str or None

Variables whose derivatives will be computed. Default is None, which uses the driver’s objectives and constraints.

wrtlist of variable name str or None

Variables with respect to which the derivatives will be computed. Default is None, which uses the driver’s desvars.

return_formatstr

Format to return the derivatives. Can be ‘dict’, ‘flat_dict’, or ‘array’. Default is a ‘flat_dict’, which returns them in a dictionary whose keys are tuples of form (of, wrt).

debug_printbool

Set to True to print out some debug information during linear solve.

driver_scalingbool

When True, return derivatives that are scaled according to either the adder and scaler or the ref and ref0 values that were specified when add_design_var, add_objective, and add_constraint were called on the model. Default is False, which is unscaled.

use_abs_namesbool

This is deprecated and has no effect.

get_remotebool

If True, the default, the full distributed total jacobian will be retrieved.

coloring_infoColoringMeta, None, or False

If False, do no coloring. If None, use driver coloring info to compute the coloring. Otherwise use the given coloring info object to provide the coloring, if it exists.

Returns:

object

Derivatives in form requested by ‘return_format’.

Usage

Here is a simple example of using compute_totals:

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())

model.set_input_defaults('comp.x', 3.0)
model.set_input_defaults('comp.y', -4.0)

prob.setup()

prob.run_model()

totals = prob.compute_totals(of=['comp.f_xy'], wrt=['comp.x', 'comp.y'])
print(totals[('comp.f_xy', 'comp.x')][0][0])

-4.0

print(totals[('comp.f_xy', 'comp.y')][0][0])

3.0

totals = prob.compute_totals(of=['comp.f_xy'], wrt=['comp.x', 'comp.y'], return_format='dict')
print(totals['comp.f_xy']['comp.x'][0][0])

-4.0

print(totals['comp.f_xy']['comp.y'][0][0])

3.0

By default, compute_totals returns the derivatives unscaled, but you can also request that they be scaled by the driver scale values declared when the des_vars, objectives, or constraints are added:

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

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

model.add_subsystem('comp', Paraboloid())

model.set_input_defaults('comp.x', 3.0)
model.set_input_defaults('comp.y', -4.0)

model.add_design_var('comp.x', 3.0, ref0=50.0)
model.add_design_var('comp.y', -4.0)
model.add_objective('comp.f_xy')

prob.setup()

prob.run_model()

totals = prob.compute_totals(of=['comp.f_xy'], wrt=['comp.x', 'comp.y'], driver_scaling=True)
print(totals[('comp.f_xy', 'comp.x')][0][0])

196.00000000000003

print(totals[('comp.f_xy', 'comp.y')][0][0])

3.0