Source code for openmdao.test_suite.components.sellar

"""
Test objects for the sellar two discipline problem.

From Sellar's analytic problem.

    Sellar, R. S., Batill, S. M., and Renaud, J. E., "Response Surface Based, Concurrent Subspace
    Optimization for Multidisciplinary System Design," Proceedings References 79 of the 34th AIAA
    Aerospace Sciences Meeting and Exhibit, Reno, NV, January 1996.
"""
import inspect

import numpy as np

import openmdao.api as om


[docs]class SellarDis1(om.ExplicitComponent): """ Component containing Discipline 1 -- no derivatives version. """
[docs] def __init__(self, units=None, scaling=None): super(SellarDis1, self).__init__() self.execution_count = 0 self._units = units self._do_scaling = scaling
[docs] def setup(self): if self._units: units = 'ft' else: units = None if self._do_scaling: ref = .1 else: ref = 1. # Global Design Variable self.add_input('z', val=np.zeros(2), units=units) # Local Design Variable self.add_input('x', val=0., units=units) # Coupling parameter self.add_input('y2', val=1.0, units=units) # Coupling output self.add_output('y1', val=1.0, lower=0.1, upper=1000., units=units, ref=ref) self._do_declares()
def _do_declares(self): # Finite difference everything self.declare_partials('*', '*', method='fd')
[docs] def compute(self, inputs, outputs): """ Evaluates the equation y1 = z1**2 + z2 + x1 - 0.2*y2 """ z1 = inputs['z'][0] z2 = inputs['z'][1] x1 = inputs['x'] y2 = inputs['y2'] outputs['y1'] = z1**2 + z2 + x1 - 0.2*y2 self.execution_count += 1
[docs]class SellarDis1withDerivatives(SellarDis1): """ Component containing Discipline 1 -- derivatives version. """ def _do_declares(self): # Analytic Derivs self.declare_partials(of='*', wrt='*')
[docs] def compute_partials(self, inputs, partials): """ Jacobian for Sellar discipline 1. """ partials['y1', 'y2'] = -0.2 partials['y1', 'z'] = np.array([[2.0 * inputs['z'][0], 1.0]]) partials['y1', 'x'] = 1.0
[docs]class SellarDis1CS(SellarDis1): """ Component containing Discipline 1 -- complex step version. """ def _do_declares(self): # Analytic Derivs self.declare_partials(of='*', wrt='*', method='cs')
[docs]class SellarDis2(om.ExplicitComponent): """ Component containing Discipline 2 -- no derivatives version. """
[docs] def __init__(self, units=None, scaling=None): super(SellarDis2, self).__init__() self.execution_count = 0 self._units = units self._do_scaling = scaling
[docs] def setup(self): if self._units: units = 'inch' else: units = None if self._do_scaling: ref = .18 else: ref = 1. # Global Design Variable self.add_input('z', val=np.zeros(2), units=units) # Coupling parameter self.add_input('y1', val=1.0, units=units) # Coupling output self.add_output('y2', val=1.0, lower=0.1, upper=1000., units=units, ref=ref) self._do_declares()
def _do_declares(self): # Finite difference everything self.declare_partials('*', '*', method='fd')
[docs] def compute(self, inputs, outputs): """ Evaluates the equation y2 = y1**(.5) + z1 + z2 """ z1 = inputs['z'][0] z2 = inputs['z'][1] y1 = inputs['y1'] # Note: this may cause some issues. However, y1 is constrained to be # above 3.16, so lets just let it converge, and the optimizer will # throw it out if y1.real < 0.0: y1 *= -1 outputs['y2'] = y1**.5 + z1 + z2 self.execution_count += 1
[docs]class SellarDis2withDerivatives(SellarDis2): """ Component containing Discipline 2 -- derivatives version. """ def _do_declares(self): # Analytic Derivs self.declare_partials(of='*', wrt='*')
[docs] def compute_partials(self, inputs, J): """ Jacobian for Sellar discipline 2. """ y1 = inputs['y1'] if y1.real < 0.0: y1 *= -1 if y1.real < 1e-8: y1 = 1e-8 J['y2', 'y1'] = .5*y1**-.5 J['y2', 'z'] = np.array([[1.0, 1.0]])
[docs]class SellarDis2CS(SellarDis2): """ Component containing Discipline 2 -- complex step version. """ def _do_declares(self): # Analytic Derivs self.declare_partials(of='*', wrt='*', method='cs')
[docs]class SellarNoDerivatives(om.Group): """ Group containing the Sellar MDA. This version uses the disciplines without derivatives. """
[docs] def initialize(self): self.options.declare('nonlinear_solver', default=om.NonlinearBlockGS, desc='Nonlinear solver for Sellar MDA') self.options.declare('nl_atol', default=None, desc='User-specified atol for nonlinear solver.') self.options.declare('nl_maxiter', default=None, desc='Iteration limit for nonlinear solver.') self.options.declare('linear_solver', default=om.ScipyKrylov, desc='Linear solver') self.options.declare('ln_atol', default=None, desc='User-specified atol for linear solver.') self.options.declare('ln_maxiter', default=None, desc='Iteration limit for linear solver.')
[docs] def setup(self): self.add_subsystem('px', om.IndepVarComp('x', 1.0), promotes=['x']) self.add_subsystem('pz', om.IndepVarComp('z', np.array([5.0, 2.0])), promotes=['z']) cycle = self.add_subsystem('cycle', om.Group(), promotes=['x', 'z', 'y1', 'y2']) cycle.add_subsystem('d1', SellarDis1(), promotes=['x', 'z', 'y1', 'y2']) cycle.add_subsystem('d2', SellarDis2(), promotes=['z', 'y1', 'y2']) self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', z=np.array([0.0, 0.0]), x=0.0), promotes=['x', 'z', 'y1', 'y2', 'obj']) self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1'), promotes=['con1', 'y1']) self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0'), promotes=['con2', 'y2']) nl = self.options['nonlinear_solver'] self.nonlinear_solver = nl() if inspect.isclass(nl) else nl if self.options['nl_atol']: self.nonlinear_solver.options['atol'] = self.options['nl_atol'] if self.options['nl_maxiter']: self.nonlinear_solver.options['maxiter'] = self.options['nl_maxiter']
[docs] def configure(self): ln = self.options['linear_solver'] self.cycle.linear_solver = ln() if inspect.isclass(ln) else ln if self.options['ln_atol']: self.cycle.linear_solver.options['atol'] = self.options['ln_atol'] if self.options['ln_maxiter']: self.cycle.linear_solver.options['maxiter'] = self.options['ln_maxiter']
[docs]class SellarDerivatives(om.Group): """ Group containing the Sellar MDA. This version uses the disciplines with derivatives. """
[docs] def initialize(self): self.options.declare('nonlinear_solver', default=om.NonlinearBlockGS, desc='Nonlinear solver (class or instance) for Sellar MDA') self.options.declare('nl_atol', default=None, desc='User-specified atol for nonlinear solver.') self.options.declare('nl_maxiter', default=None, desc='Iteration limit for nonlinear solver.') self.options.declare('linear_solver', default=om.ScipyKrylov, desc='Linear solver (class or instance)') self.options.declare('ln_atol', default=None, desc='User-specified atol for linear solver.') self.options.declare('ln_maxiter', default=None, desc='Iteration limit for linear solver.')
[docs] def setup(self): self.add_subsystem('px', om.IndepVarComp('x', 1.0), promotes=['x']) self.add_subsystem('pz', om.IndepVarComp('z', np.array([5.0, 2.0])), promotes=['z']) self.add_subsystem('d1', SellarDis1withDerivatives(), promotes=['x', 'z', 'y1', 'y2']) self.add_subsystem('d2', SellarDis2withDerivatives(), promotes=['z', 'y1', 'y2']) self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', obj=0.0, x=0.0, z=np.array([0.0, 0.0]), y1=0.0, y2=0.0), promotes=['obj', 'x', 'z', 'y1', 'y2']) self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1', con1=0.0, y1=0.0), promotes=['con1', 'y1']) self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0', con2=0.0, y2=0.0), promotes=['con2', 'y2']) nl = self.options['nonlinear_solver'] self.nonlinear_solver = nl() if inspect.isclass(nl) else nl if self.options['nl_atol']: self.nonlinear_solver.options['atol'] = self.options['nl_atol'] if self.options['nl_maxiter']: self.nonlinear_solver.options['maxiter'] = self.options['nl_maxiter'] ln = self.options['linear_solver'] self.linear_solver = ln() if inspect.isclass(ln) else ln if self.options['ln_atol']: self.linear_solver.options['atol'] = self.options['ln_atol'] if self.options['ln_maxiter']: self.linear_solver.options['maxiter'] = self.options['ln_maxiter']
[docs]class SellarDerivativesConnected(om.Group): """ Group containing the Sellar MDA. This version uses the disciplines with derivatives. """
[docs] def setup(self): self.add_subsystem('px', om.IndepVarComp('x', 1.0)) self.add_subsystem('pz', om.IndepVarComp('z', np.array([5.0, 2.0]))) self.add_subsystem('d1', SellarDis1withDerivatives()) self.add_subsystem('d2', SellarDis2withDerivatives()) self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', z=np.array([0.0, 0.0]), x=0.0)) self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1')) self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0')) self.connect('px.x', ['d1.x', 'obj_cmp.x']) self.connect('pz.z', ['d1.z', 'd2.z', 'obj_cmp.z']) self.connect('d1.y1', ['d2.y1', 'obj_cmp.y1', 'con_cmp1.y1']) self.connect('d2.y2', ['d1.y2', 'obj_cmp.y2', 'con_cmp2.y2']) self.nonlinear_solver = om.NonlinearBlockGS() self.linear_solver = om.ScipyKrylov()
[docs]class SellarDerivativesGrouped(om.Group): """ Group containing the Sellar MDA. This version uses the disciplines with derivatives. """
[docs] def initialize(self): self.options.declare('nonlinear_solver', default=om.NonlinearBlockGS, desc='Nonlinear solver (class or instance) for Sellar MDA') self.options.declare('nl_atol', default=None, desc='User-specified atol for nonlinear solver.') self.options.declare('nl_maxiter', default=None, desc='Iteration limit for nonlinear solver.') self.options.declare('linear_solver', default=om.ScipyKrylov, desc='Linear solver (class or instance)') self.options.declare('ln_atol', default=None, desc='User-specified atol for linear solver.') self.options.declare('ln_maxiter', default=None, desc='Iteration limit for linear solver.')
[docs] def setup(self): self.add_subsystem('px', om.IndepVarComp('x', 1.0), promotes=['x']) self.add_subsystem('pz', om.IndepVarComp('z', np.array([5.0, 2.0])), promotes=['z']) self.mda = mda = self.add_subsystem('mda', om.Group(), promotes=['x', 'z', 'y1', 'y2']) mda.add_subsystem('d1', SellarDis1withDerivatives(), promotes=['x', 'z', 'y1', 'y2']) mda.add_subsystem('d2', SellarDis2withDerivatives(), promotes=['z', 'y1', 'y2']) self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', z=np.array([0.0, 0.0]), x=0.0, y1=0.0, y2=0.0), promotes=['obj', 'x', 'z', 'y1', 'y2']) self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1'), promotes=['con1', 'y1']) self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0'), promotes=['con2', 'y2']) nl = self.options['nonlinear_solver'] self.nonlinear_solver = nl() if inspect.isclass(nl) else nl if self.options['nl_atol']: self.nonlinear_solver.options['atol'] = self.options['nl_atol'] if self.options['nl_maxiter']: self.nonlinear_solver.options['maxiter'] = self.options['nl_maxiter'] ln = self.options['linear_solver'] self.linear_solver = ln() if inspect.isclass(ln) else ln if self.options['ln_atol']: self.linear_solver.options['atol'] = self.options['ln_atol'] if self.options['ln_maxiter']: self.linear_solver.options['maxiter'] = self.options['ln_maxiter']
[docs] def configure(self): self.mda.linear_solver = om.ScipyKrylov() self.mda.nonlinear_solver = om.NonlinearBlockGS()
[docs]class StateConnection(om.ImplicitComponent): """ Define connection with an explicit equation. """
[docs] def setup(self): # Inputs self.add_input('y2_actual', 1.0) # States self.add_output('y2_command', val=1.0) # Declare derivatives self.declare_partials(of='*', wrt='*')
[docs] def apply_nonlinear(self, inputs, outputs, residuals): """ Don't solve; just calculate the residual. """ y2_actual = inputs['y2_actual'] y2_command = outputs['y2_command'] residuals['y2_command'] = y2_actual - y2_command
[docs] def compute(self, inputs, outputs): """ This is a dummy comp that doesn't modify its state. """ pass
[docs] def linearize(self, inputs, outputs, J): """ Analytical derivatives. """ # State equation J[('y2_command', 'y2_command')] = -1.0 J[('y2_command', 'y2_actual')] = 1.0
[docs]class SellarStateConnection(om.Group): """ Group containing the Sellar MDA. This version uses the disciplines with derivatives. """
[docs] def initialize(self): self.options.declare('nonlinear_solver', default=om.NewtonSolver, desc='Nonlinear solver (class or instance) for Sellar MDA') self.options.declare('nl_atol', default=None, desc='User-specified atol for nonlinear solver.') self.options.declare('nl_maxiter', default=None, desc='Iteration limit for nonlinear solver.') self.options.declare('linear_solver', default=om.ScipyKrylov, desc='Linear solver (class or instance)') self.options.declare('ln_atol', default=None, desc='User-specified atol for linear solver.') self.options.declare('ln_maxiter', default=None, desc='Iteration limit for linear solver.')
[docs] def setup(self): self.add_subsystem('px', om.IndepVarComp('x', 1.0), promotes=['x']) self.add_subsystem('pz', om.IndepVarComp('z', np.array([5.0, 2.0])), promotes=['z']) sub = self.add_subsystem('sub', om.Group(), promotes=['x', 'z', 'y1', 'state_eq.y2_actual', 'state_eq.y2_command', 'd1.y2', 'd2.y2']) subgrp = sub.add_subsystem('state_eq_group', om.Group(), promotes=['state_eq.y2_actual', 'state_eq.y2_command']) subgrp.add_subsystem('state_eq', StateConnection()) sub.add_subsystem('d1', SellarDis1withDerivatives(), promotes=['x', 'z', 'y1']) sub.add_subsystem('d2', SellarDis2withDerivatives(), promotes=['z', 'y1']) self.connect('state_eq.y2_command', 'd1.y2') self.connect('d2.y2', 'state_eq.y2_actual') self.add_subsystem('obj_cmp', om.ExecComp('obj = x**2 + z[1] + y1 + exp(-y2)', z=np.array([0.0, 0.0]), x=0.0, y1=0.0, y2=0.0), promotes=['x', 'z', 'y1', 'obj']) self.connect('d2.y2', 'obj_cmp.y2') self.add_subsystem('con_cmp1', om.ExecComp('con1 = 3.16 - y1'), promotes=['con1', 'y1']) self.add_subsystem('con_cmp2', om.ExecComp('con2 = y2 - 24.0'), promotes=['con2']) self.connect('d2.y2', 'con_cmp2.y2') nl = self.options['nonlinear_solver'] self.nonlinear_solver = nl() if inspect.isclass(nl) else nl if self.options['nl_atol']: self.nonlinear_solver.options['atol'] = self.options['nl_atol'] if self.options['nl_maxiter']: self.nonlinear_solver.options['maxiter'] = self.options['nl_maxiter'] ln = self.options['linear_solver'] self.linear_solver = ln() if inspect.isclass(ln) else ln if self.options['ln_atol']: self.linear_solver.options['atol'] = self.options['ln_atol'] if self.options['ln_maxiter']: self.linear_solver.options['maxiter'] = self.options['ln_maxiter']
[docs] def configure(self): self.sub.linear_solver = om.ScipyKrylov() self.sub.state_eq_group.linear_solver = om.ScipyKrylov()
[docs]class SellarImplicitDis1(om.ImplicitComponent): """ Component containing Discipline 1 -- no derivatives version. """
[docs] def __init__(self, units=None, scaling=None): super(SellarImplicitDis1, self).__init__() self.execution_count = 0 self._units = units self._do_scaling = scaling
[docs] def setup(self): if self._units: units = 'ft' else: units = None if self._do_scaling is None: ref = 1. else: ref = .1 # Global Design Variable self.add_input('z', val=np.zeros(2), units=units) # Local Design Variable self.add_input('x', val=0., units=units) # Coupling parameter self.add_input('y2', val=1.0, units=units) # Coupling output self.add_output('y1', val=1.0, lower=-0.1, upper=1000, units=units, ref=ref) # Derivatives self.declare_partials('*', '*')
[docs] def apply_nonlinear(self, inputs, outputs, resids): """ Evaluates the equation y1 = z1**2 + z2 + x1 - 0.2*y2 """ z1 = inputs['z'][0] z2 = inputs['z'][1] x1 = inputs['x'] y2 = inputs['y2'] y1 = outputs['y1'] resids['y1'] = -(z1**2 + z2 + x1 - 0.2*y2 - y1)
[docs] def linearize(self, inputs, outputs, J): """ Jacobian for Sellar discipline 1. """ J['y1', 'y2'] = 0.2 J['y1', 'z'] = -np.array([[2.0 * inputs['z'][0], 1.0]]) J['y1', 'x'] = -1.0 J['y1', 'y1'] = 1.0
[docs]class SellarImplicitDis2(om.ImplicitComponent): """ Component containing Discipline 2 -- implicit version. """
[docs] def __init__(self, units=None, scaling=None): super(SellarImplicitDis2, self).__init__() self.execution_count = 0 self._units = units self._do_scaling = scaling
[docs] def setup(self): if self._units: units = 'inch' else: units = None if self._do_scaling is None: ref = 1.0 else: ref = .18 # Global Design Variable self.add_input('z', val=np.zeros(2), units=units) # Coupling parameter self.add_input('y1', val=1.0, units=units) # Coupling output self.add_output('y2', val=1.0, lower=0.1, upper=1000., units=units, ref=ref) # Derivatives self.declare_partials('*', '*')
[docs] def apply_nonlinear(self, inputs, outputs, resids): """ Evaluates the equation y2 = y1**(.5) + z1 + z2 """ z1 = inputs['z'][0] z2 = inputs['z'][1] y1 = inputs['y1'] y2 = outputs['y2'] # Note: this may cause some issues. However, y1 is constrained to be # above 3.16, so lets just let it converge, and the optimizer will # throw it out if y1.real < 0.0: y1 *= -1 resids['y2'] = -(y1**.5 + z1 + z2 - y2)
[docs] def linearize(self, inputs, outputs, J): """ Jacobian for Sellar discipline 2. """ y1 = inputs['y1'] if y1.real < 0.0: y1 *= -1 if y1.real < 1e-8: y1 = 1e-8 J['y2', 'y1'] = -.5*y1**-.5 J['y2', 'z'] = -np.array([[1.0, 1.0]]) J['y2', 'y2'] = 1.0
[docs]class SellarProblem(om.Problem): """ The Sellar problem with configurable model class. """
[docs] def __init__(self, model_class=SellarDerivatives, **kwargs): super(SellarProblem, self).__init__(model_class(**kwargs)) model = self.model model.add_design_var('z', lower=np.array([-10.0, 0.0]), upper=np.array([10.0, 10.0])) model.add_design_var('x', lower=0.0, upper=10.0) model.add_objective('obj') model.add_constraint('con1', upper=0.0) model.add_constraint('con2', upper=0.0) # default to non-verbose self.set_solver_print(0)
[docs]class SellarProblemWithArrays(om.Problem): """ The Sellar problem with ndarray variable options """
[docs] def __init__(self, model_class=SellarDerivatives, **kwargs): super(SellarProblemWithArrays, self).__init__(model_class(**kwargs)) model = self.model model.add_design_var('z', lower=np.array([-10.0, 0.0]), upper=np.array([10.0, 10.0]), indices=np.arange(2, dtype=int)) model.add_design_var('x', lower=0.0, upper=10.0) model.add_objective('obj') model.add_constraint('con1', equals=np.zeros(1)) model.add_constraint('con2', upper=0.0) # default to non-verbose self.set_solver_print(0)