def test_double_arraycomp(self):
# Mainly testing a bug in the array return for multiple arrays
group = Group()
group.add('x_param1', ParamComp('x1', np.ones((2))), promotes=['*'])
group.add('x_param2', ParamComp('x2', np.ones((2))), promotes=['*'])
group.add('mycomp', DoubleArrayComp(), promotes=['*'])
prob = Problem(impl=impl)
prob.root = group
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
Jbase = group.mycomp.JJ
J = prob.calc_gradient(['x1', 'x2'], ['y1', 'y2'],
mode='fwd',
return_format='array')
diff = np.linalg.norm(J - Jbase)
assert_rel_error(self, diff, 0.0, 1e-8)
J = prob.calc_gradient(['x1', 'x2'], ['y1', 'y2'],
mode='fd',
return_format='array')
diff = np.linalg.norm(J - Jbase)
assert_rel_error(self, diff, 0.0, 1e-8)
J = prob.calc_gradient(['x1', 'x2'], ['y1', 'y2'],
mode='rev',
return_format='array')
diff = np.linalg.norm(J - Jbase)
assert_rel_error(self, diff, 0.0, 1e-8)
def test_double_arraycomp(self):
# Mainly testing a bug in the array return for multiple arrays
group = Group()
group.add('x_param1', IndepVarComp('x1', np.ones((2))), promotes=['*'])
group.add('x_param2', IndepVarComp('x2', np.ones((2))), promotes=['*'])
group.add('mycomp', DoubleArrayComp(), promotes=['*'])
prob = Problem(impl=impl)
prob.root = group
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
Jbase = group.mycomp.JJ
J = prob.calc_gradient(['x1', 'x2'], ['y1', 'y2'], mode='fwd',
return_format='array')
diff = np.linalg.norm(J - Jbase)
assert_rel_error(self, diff, 0.0, 1e-8)
J = prob.calc_gradient(['x1', 'x2'], ['y1', 'y2'], mode='fd',
return_format='array')
diff = np.linalg.norm(J - Jbase)
assert_rel_error(self, diff, 0.0, 1e-8)
J = prob.calc_gradient(['x1', 'x2'], ['y1', 'y2'], mode='rev',
return_format='array')
diff = np.linalg.norm(J - Jbase)
assert_rel_error(self, diff, 0.0, 1e-8)
def test_simple_array_model(self):
prob = Problem()
prob.root = Group()
prob.root.add(
'comp',
ExecComp(['y[0]=2.0*x[0]+7.0*x[1]', 'y[1]=5.0*x[0]-3.0*x[1]'],
x=np.zeros([2]),
y=np.zeros([2])))
prob.root.add('p1', ParamComp('x', np.ones([2])))
prob.root.connect('p1.x', 'comp.x')
prob.setup(check=False)
prob.run()
data = prob.check_partial_derivatives(out_stream=None)
assert_rel_error(self, data['comp'][('y', 'x')]['abs error'][0], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['abs error'][1], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['abs error'][2], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['rel error'][0], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['rel error'][1], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['rel error'][2], 0.0,
1e-5)
def test_single_diamond_grouped(self):
prob = Problem()
prob.root = SingleDiamondGrouped()
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
param_list = ['p.x']
unknown_list = ['comp4.y1', 'comp4.y2']
J = prob.calc_gradient(param_list,
unknown_list,
mode='fwd',
return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='rev',
return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='fd',
return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
def test_fan_in_grouped(self):
prob = Problem(impl=impl)
prob.root = FanInGrouped()
prob.root.ln_solver = PetscKSP()
param_list = ['p1.x1', 'p2.x2']
unknown_list = ['comp3.y']
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(param_list,
unknown_list,
mode='fwd',
return_format='dict')
assert_rel_error(self, J['comp3.y']['p1.x1'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p2.x2'][0][0], 35.0, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='rev',
return_format='dict')
assert_rel_error(self, J['comp3.y']['p1.x1'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p2.x2'][0][0], 35.0, 1e-6)
def test_converge_diverge_compfd(self):
prob = Problem(impl=impl)
prob.root = ConvergeDivergePar()
prob.root.ln_solver = PetscKSP()
# fd comp2 and comp5. each is under a par group
prob.root.par1.comp2.fd_options['force_fd'] = True
prob.root.par2.comp5.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
# Make sure value is fine.
assert_rel_error(self, prob['comp7.y1'], -102.7, 1e-6)
indep_list = ['p.x']
unknown_list = ['comp7.y1']
J = prob.calc_gradient(indep_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='fd', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
def test_converge_diverge_groups(self):
prob = Problem()
prob.root = ConvergeDivergeGroups()
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
# Make sure value is fine.
assert_rel_error(self, prob['comp7.y1'], -102.7, 1e-6)
param_list = ['p.x']
unknown_list = ['comp7.y1']
J = prob.calc_gradient(param_list,
unknown_list,
mode='fwd',
return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='rev',
return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='fd',
return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
def test_fan_out_grouped(self):
prob = Problem(impl=impl)
prob.root = FanOutGrouped()
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
param = 'sub.pgroup.p.x'
unknown_list = ['sub.comp2.y', "sub.comp3.y"]
J = prob.calc_gradient([param],
unknown_list,
mode='fwd',
return_format='dict')
assert_rel_error(self, J[unknown_list[0]][param][0][0], -6.0, 1e-6)
assert_rel_error(self, J[unknown_list[1]][param][0][0], 15.0, 1e-6)
J = prob.calc_gradient([param],
unknown_list,
mode='rev',
return_format='dict')
assert_rel_error(self, J[unknown_list[0]][param][0][0], -6.0, 1e-6)
assert_rel_error(self, J[unknown_list[1]][param][0][0], 15.0, 1e-6)
def test_simple_deriv_xfer(self):
prob = Problem(impl=impl)
prob.root = FanInGrouped()
prob.setup(check=False)
prob.root.comp3.dpmat[None]['x1'] = 7.
prob.root.comp3.dpmat[None]['x2'] = 11.
prob.root._transfer_data(mode='rev', deriv=True)
if not MPI or self.comm.rank == 0:
self.assertEqual(prob.root.sub.comp1.dumat[None]['y'], 7.)
if not MPI or self.comm.rank == 1:
self.assertEqual(prob.root.sub.comp2.dumat[None]['y'], 11.)
prob.root.comp3.dpmat[None]['x1'] = 0.
prob.root.comp3.dpmat[None]['x2'] = 0.
self.assertEqual(prob.root.comp3.dpmat[None]['x1'], 0.)
self.assertEqual(prob.root.comp3.dpmat[None]['x2'], 0.)
prob.root._transfer_data(mode='fwd', deriv=True)
self.assertEqual(prob.root.comp3.dpmat[None]['x1'], 7.)
self.assertEqual(prob.root.comp3.dpmat[None]['x2'], 11.)
def test_simple_array_model2(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add(
'comp',
ExecComp('y = mat.dot(x)',
x=np.zeros((2, )),
y=np.zeros((2, )),
mat=np.array([[2., 7.], [5., -3.]])))
p1 = prob.root.add('p1', ParamComp('x', np.ones([2])))
prob.root.connect('p1.x', 'comp.x')
prob.setup(check=False)
prob.run()
data = prob.check_partial_derivatives(out_stream=None)
assert_rel_error(self, data['comp'][('y', 'x')]['abs error'][0], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['abs error'][1], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['abs error'][2], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['rel error'][0], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['rel error'][1], 0.0,
1e-5)
assert_rel_error(self, data['comp'][('y', 'x')]['rel error'][2], 0.0,
1e-5)
def test_simple_deriv_xfer(self):
prob = Problem(impl=impl)
prob.root = FanInGrouped()
prob.setup(check=False)
prob.root.comp3.dpmat[None]['x1'] = 7.
prob.root.comp3.dpmat[None]['x2'] = 11.
prob.root._transfer_data(mode='rev', deriv=True)
if not MPI or self.comm.rank == 0:
self.assertEqual(prob.root.sub.comp1.dumat[None]['y'], 7.)
if not MPI or self.comm.rank == 1:
self.assertEqual(prob.root.sub.comp2.dumat[None]['y'], 11.)
prob.root.comp3.dpmat[None]['x1'] = 0.
prob.root.comp3.dpmat[None]['x2'] = 0.
self.assertEqual(prob.root.comp3.dpmat[None]['x1'], 0.)
self.assertEqual(prob.root.comp3.dpmat[None]['x2'], 0.)
prob.root._transfer_data(mode='fwd', deriv=True)
self.assertEqual(prob.root.comp3.dpmat[None]['x1'], 7.)
self.assertEqual(prob.root.comp3.dpmat[None]['x2'], 11.)
def test_fd_options_meta_step_size(self):
class MetaParaboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(MetaParaboloid, self).__init__()
# Params
self.add_param('x', 1.0, fd_step_size = 1.0e5)
self.add_param('y', 1.0, fd_step_size = 1.0e5)
# Unknowns
self.add_output('f_xy', 0.0)
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x = params['x']
y = params['y']
f_xy = ((x-3.0)**2 + x*y + (y+4.0)**2 - 3.0)
unknowns['f_xy'] = f_xy
def jacobian(self, params, unknowns, resids):
"""Analytical derivatives"""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = (2.0*x - 6.0 + y)
J['f_xy', 'y'] = (2.0*y + 8.0 + x)
return J
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', MetaParaboloid())
prob.root.add('p1', ParamComp('x', 15.0))
prob.root.add('p2', ParamComp('y', 15.0))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
# Make sure bad meta step_size is used
# Derivative should be way high with this.
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertGreater(J['comp.f_xy']['p1.x'][0][0], 1000.0)
def test_fd_options_meta_step_size(self):
class MetaParaboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(MetaParaboloid, self).__init__()
# Params
self.add_param('x', 1.0, fd_step_size=1.0e5)
self.add_param('y', 1.0, fd_step_size=1.0e5)
# Unknowns
self.add_output('f_xy', 0.0)
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x = params['x']
y = params['y']
f_xy = ((x - 3.0)**2 + x * y + (y + 4.0)**2 - 3.0)
unknowns['f_xy'] = f_xy
def jacobian(self, params, unknowns, resids):
"""Analytical derivatives"""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = (2.0 * x - 6.0 + y)
J['f_xy', 'y'] = (2.0 * y + 8.0 + x)
return J
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', MetaParaboloid())
prob.root.add('p1', ParamComp('x', 15.0))
prob.root.add('p2', ParamComp('y', 15.0))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
# Make sure bad meta step_size is used
# Derivative should be way high with this.
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertGreater(J['comp.f_xy']['p1.x'][0][0], 1000.0)
def test_sellar_derivs_grouped(self):
prob = Problem(impl=impl)
prob.root = SellarDerivativesGrouped()
prob.root.ln_solver = PetscKSP()
prob.root.mda.nl_solver.options['atol'] = 1e-12
prob.setup(check=False)
prob.run()
# Just make sure we are at the right answer
assert_rel_error(self, prob['y1'], 25.58830273, .00001)
assert_rel_error(self, prob['y2'], 12.05848819, .00001)
param_list = ['x', 'z']
unknown_list = ['obj', 'con1', 'con2']
Jbase = {}
Jbase['con1'] = {}
Jbase['con1']['x'] = -0.98061433
Jbase['con1']['z'] = np.array([-9.61002285, -0.78449158])
Jbase['con2'] = {}
Jbase['con2']['x'] = 0.09692762
Jbase['con2']['z'] = np.array([1.94989079, 1.0775421])
Jbase['obj'] = {}
Jbase['obj']['x'] = 2.98061392
Jbase['obj']['z'] = np.array([9.61001155, 1.78448534])
J = prob.calc_gradient(param_list,
unknown_list,
mode='fwd',
return_format='dict')
for key1, val1 in Jbase.items():
for key2, val2 in val1.items():
assert_rel_error(self, J[key1][key2], val2, .00001)
J = prob.calc_gradient(param_list,
unknown_list,
mode='rev',
return_format='dict')
for key1, val1 in Jbase.items():
for key2, val2 in val1.items():
assert_rel_error(self, J[key1][key2], val2, .00001)
prob.root.fd_options['form'] = 'central'
J = prob.calc_gradient(param_list,
unknown_list,
mode='fd',
return_format='dict')
for key1, val1 in Jbase.items():
for key2, val2 in val1.items():
assert_rel_error(self, J[key1][key2], val2, .00001)
def test_simple(self):
group = Group()
group.add('x_param', IndepVarComp('x', 1.0), promotes=['*'])
group.add('mycomp', SimpleCompDerivMatVec(), promotes=['x', 'y'])
prob = Problem(impl=impl)
prob.root = group
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['x'], ['y'], mode='fwd', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
J = prob.calc_gradient(['x'], ['y'], mode='rev', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
def test_simple(self):
group = Group()
group.add('x_param', ParamComp('x', 1.0), promotes=['*'])
group.add('mycomp', SimpleCompDerivMatVec(), promotes=['x', 'y'])
prob = Problem(impl=impl)
prob.root = group
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['x'], ['y'], mode='fwd', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
J = prob.calc_gradient(['x'], ['y'], mode='rev', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
def test_simple_jac(self):
group = Group()
group.add('x_param', ParamComp('x', 1.0), promotes=['*'])
group.add('mycomp', ExecComp(['y=2.0*x']), promotes=['x', 'y'])
prob = Problem()
prob.root = group
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['x'], ['y'], mode='fwd', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
J = prob.calc_gradient(['x'], ['y'], mode='rev', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
def test_simple_jac(self):
group = Group()
group.add('x_param', IndepVarComp('x', 1.0), promotes=['*'])
group.add('mycomp', ExecComp(['y=2.0*x']), promotes=['x', 'y'])
prob = Problem()
prob.root = group
prob.root.ln_solver = DirectSolver()
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['x'], ['y'], mode='fwd', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
J = prob.calc_gradient(['x'], ['y'], mode='rev', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
def test_fd_options_form(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', Paraboloid())
prob.root.add('p1', ParamComp('x', 15.0))
prob.root.add('p2', ParamComp('y', 15.0))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
comp.fd_options['form'] = 'forward'
param_list = ['p1.x']
unknowns_list = ['comp.f_xy']
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(param_list, unknowns_list, return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Make sure it gives good result with small stepsize
comp.fd_options['form'] = 'backward'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Make sure it gives good result with small stepsize
comp.fd_options['form'] = 'central'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Now, Make sure we really are going foward and backward
comp.fd_options['form'] = 'forward'
comp.fd_options['step_size'] = 1e3
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertGreater(J['comp.f_xy']['p1.x'][0][0], 0.0)
comp.fd_options['form'] = 'backward'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertLess(J['comp.f_xy']['p1.x'][0][0], 0.0)
# Central should get pretty close even for the bad stepsize
comp.fd_options['form'] = 'central'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-1)
def test_fd_options_form(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', Paraboloid())
prob.root.add('p1', ParamComp('x', 15.0))
prob.root.add('p2', ParamComp('y', 15.0))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
comp.fd_options['form'] = 'forward'
param_list = ['p1.x']
unknowns_list = ['comp.f_xy']
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(param_list, unknowns_list, return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Make sure it gives good result with small stepsize
comp.fd_options['form'] = 'backward'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Make sure it gives good result with small stepsize
comp.fd_options['form'] = 'central'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Now, Make sure we really are going foward and backward
comp.fd_options['form'] = 'forward'
comp.fd_options['step_size'] = 1e3
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertGreater(J['comp.f_xy']['p1.x'][0][0], 0.0)
comp.fd_options['form'] = 'backward'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertLess(J['comp.f_xy']['p1.x'][0][0], 0.0)
# Central should get pretty close even for the bad stepsize
comp.fd_options['form'] = 'central'
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-1)
def test_simple_in_group_matvec(self):
group = Group()
sub = group.add('sub', Group(), promotes=['x', 'y'])
group.add('x_param', ParamComp('x', 1.0), promotes=['*'])
sub.add('mycomp', SimpleCompDerivMatVec(), promotes=['x', 'y'])
prob = Problem()
prob.root = group
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['x'], ['y'], mode='fwd', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
J = prob.calc_gradient(['x'], ['y'], mode='rev', return_format='dict')
assert_rel_error(self, J['y']['x'][0][0], 2.0, 1e-6)
def test_single_diamond(self):
prob = Problem(impl=impl)
prob.root = SingleDiamond()
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
indep_list = ['p.x']
unknown_list = ['comp4.y1', 'comp4.y2']
J = prob.calc_gradient(indep_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
def test_fan_out(self):
prob = Problem()
prob.root = FanOut()
prob.root.ln_solver = DirectSolver()
prob.setup(check=False)
prob.run()
indep_list = ['p.x']
unknown_list = ['comp2.y', "comp3.y"]
J = prob.calc_gradient(indep_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p.x'][0][0], 15.0, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p.x'][0][0], 15.0, 1e-6)
def test_fan_in_grouped(self):
prob = Problem()
prob.root = FanInGrouped()
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
param_list = ['p1.x1', 'p2.x2']
unknown_list = ['comp3.y']
J = prob.calc_gradient(param_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp3.y']['p1.x1'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p2.x2'][0][0], 35.0, 1e-6)
J = prob.calc_gradient(param_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp3.y']['p1.x1'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p2.x2'][0][0], 35.0, 1e-6)
def test_fan_in(self):
prob = Problem(impl=impl)
prob.root = FanIn()
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
indep_list = ['p1.x1', 'p2.x2']
unknown_list = ['comp3.y']
J = prob.calc_gradient(indep_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp3.y']['p1.x1'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p2.x2'][0][0], 35.0, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp3.y']['p1.x1'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p2.x2'][0][0], 35.0, 1e-6)
def test_no_derivatives(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', ExecComp('y=x*2.0'))
prob.root.add('p1', ParamComp('x', 2.0))
prob.root.connect('p1.x', 'comp.x')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['p1.x'], ['comp.y'], mode='fwd', return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'][0][0], 2.0, 1e-6)
J = prob.calc_gradient(['p1.x'], ['comp.y'], mode='rev', return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'][0][0], 2.0, 1e-6)
def test_fan_out_grouped(self):
prob = Problem(impl=impl)
prob.root = FanOutGrouped()
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
indep_list = ['p.x']
unknown_list = ['sub.comp2.y', "sub.comp3.y"]
J = prob.calc_gradient(indep_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['sub.comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['sub.comp3.y']['p.x'][0][0], 15.0, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['sub.comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['sub.comp3.y']['p.x'][0][0], 15.0, 1e-6)
def test_array2D(self):
group = Group()
group.add('x_param', IndepVarComp('x', np.ones((2, 2))), promotes=['*'])
group.add('mycomp', ArrayComp2D(), promotes=['x', 'y'])
prob = Problem(impl=impl)
prob.root = group
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['x'], ['y'], mode='fwd', return_format='dict')
Jbase = prob.root.mycomp._jacobian_cache
diff = np.linalg.norm(J['y']['x'] - Jbase['y', 'x'])
assert_rel_error(self, diff, 0.0, 1e-8)
J = prob.calc_gradient(['x'], ['y'], mode='rev', return_format='dict')
diff = np.linalg.norm(J['y']['x'] - Jbase['y', 'x'])
assert_rel_error(self, diff, 0.0, 1e-8)
def test_sellar_derivs_grouped(self):
prob = Problem(impl=impl)
prob.root = SellarDerivativesGrouped()
prob.root.ln_solver = PetscKSP()
prob.root.mda.nl_solver.options['atol'] = 1e-12
prob.setup(check=False)
prob.run()
# Just make sure we are at the right answer
assert_rel_error(self, prob['y1'], 25.58830273, .00001)
assert_rel_error(self, prob['y2'], 12.05848819, .00001)
indep_list = ['x', 'z']
unknown_list = ['obj', 'con1', 'con2']
Jbase = {}
Jbase['con1'] = {}
Jbase['con1']['x'] = -0.98061433
Jbase['con1']['z'] = np.array([-9.61002285, -0.78449158])
Jbase['con2'] = {}
Jbase['con2']['x'] = 0.09692762
Jbase['con2']['z'] = np.array([1.94989079, 1.0775421 ])
Jbase['obj'] = {}
Jbase['obj']['x'] = 2.98061392
Jbase['obj']['z'] = np.array([9.61001155, 1.78448534])
J = prob.calc_gradient(indep_list, unknown_list, mode='fwd', return_format='dict')
for key1, val1 in Jbase.items():
for key2, val2 in val1.items():
assert_rel_error(self, J[key1][key2], val2, .00001)
J = prob.calc_gradient(indep_list, unknown_list, mode='rev', return_format='dict')
for key1, val1 in Jbase.items():
for key2, val2 in val1.items():
assert_rel_error(self, J[key1][key2], val2, .00001)
prob.root.fd_options['form'] = 'central'
J = prob.calc_gradient(indep_list, unknown_list, mode='fd', return_format='dict')
for key1, val1 in Jbase.items():
for key2, val2 in val1.items():
assert_rel_error(self, J[key1][key2], val2, .00001)
def test_array2D(self):
group = Group()
group.add('x_param', ParamComp('x', np.ones((2, 2))), promotes=['*'])
group.add('mycomp', ArrayComp2D(), promotes=['x', 'y'])
prob = Problem()
prob.root = group
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['x'], ['y'], mode='fwd', return_format='dict')
Jbase = prob.root.mycomp._jacobian_cache
diff = np.linalg.norm(J['y']['x'] - Jbase['y', 'x'])
assert_rel_error(self, diff, 0.0, 1e-8)
J = prob.calc_gradient(['x'], ['y'], mode='rev', return_format='dict')
diff = np.linalg.norm(J['y']['x'] - Jbase['y', 'x'])
assert_rel_error(self, diff, 0.0, 1e-8)
def test_overrides(self):
class OverrideComp(Component):
def __init__(self):
super(OverrideComp, self).__init__()
# Params
self.add_param('x', 3.0)
# Unknowns
self.add_output('y', 5.5)
def solve_nonlinear(self, params, unknowns, resids):
""" Doesn't do much. """
unknowns['y'] = 7.0 * params['x']
def apply_linear(self, params, unknowns, dparams, dunknowns,
dresids, mode):
"""Never Call."""
raise RuntimeError(
"This should have been overridden by force_fd.")
def jacobian(self, params, unknowns, resids):
"""Never Call."""
raise RuntimeError(
"This should have been overridden by force_fd.")
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', OverrideComp())
prob.root.add('p1', ParamComp('x', 2.0))
prob.root.connect('p1.x', 'comp.x')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['p1.x'], ['comp.y'],
mode='fwd',
return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'][0][0], 7.0, 1e-6)
def test_simple_array_model2(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', ExecComp('y = mat.dot(x)',
x=np.zeros((2,)), y=np.zeros((2,)),
mat=np.array([[2.,7.],[5.,-3.]])))
p1 = prob.root.add('p1', ParamComp('x', np.ones([2])))
prob.root.connect('p1.x', 'comp.x')
prob.setup(check=False)
prob.run()
data = prob.check_partial_derivatives(out_stream=None)
assert_rel_error(self, data['comp'][('y','x')]['abs error'][0], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['abs error'][1], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['abs error'][2], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['rel error'][0], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['rel error'][1], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['rel error'][2], 0.0, 1e-5)
def test_overrides(self):
class OverrideComp(Component):
def __init__(self):
super(OverrideComp, self).__init__()
# Params
self.add_param('x', 3.0)
# Unknowns
self.add_output('y', 5.5)
def solve_nonlinear(self, params, unknowns, resids):
""" Doesn't do much. """
unknowns['y'] = 7.0*params['x']
def apply_linear(self, params, unknowns, dparams, dunknowns, dresids,
mode):
"""Never Call."""
raise RuntimeError("This should have been overridden by force_fd.")
def jacobian(self, params, unknowns, resids):
"""Never Call."""
raise RuntimeError("This should have been overridden by force_fd.")
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', OverrideComp())
prob.root.add('p1', ParamComp('x', 2.0))
prob.root.connect('p1.x', 'comp.x')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['p1.x'], ['comp.y'], mode='fwd', return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'][0][0], 7.0, 1e-6)
def test_single_diamond_grouped(self):
prob = Problem()
prob.root = SingleDiamondGrouped()
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
param_list = ['p.x']
unknown_list = ['comp4.y1', 'comp4.y2']
J = prob.calc_gradient(param_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
J = prob.calc_gradient(param_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
J = prob.calc_gradient(param_list, unknown_list, mode='fd', return_format='dict')
assert_rel_error(self, J['comp4.y1']['p.x'][0][0], 25, 1e-6)
assert_rel_error(self, J['comp4.y2']['p.x'][0][0], -40.5, 1e-6)
def test_no_derivatives(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', ExecComp('y=x*2.0'))
prob.root.add('p1', ParamComp('x', 2.0))
prob.root.connect('p1.x', 'comp.x')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['p1.x'], ['comp.y'],
mode='fwd',
return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'][0][0], 2.0, 1e-6)
J = prob.calc_gradient(['p1.x'], ['comp.y'],
mode='rev',
return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'][0][0], 2.0, 1e-6)
def test_converge_diverge_groups(self):
prob = Problem(impl=impl)
prob.root = ConvergeDivergeGroups()
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
# Make sure value is fine.
assert_rel_error(self, prob['comp7.y1'], -102.7, 1e-6)
indep_list = ['p.x']
unknown_list = ['comp7.y1']
J = prob.calc_gradient(indep_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(indep_list, unknown_list, mode='fd', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
def test_simple_array_model(self):
prob = Problem()
prob.root = Group()
prob.root.add('comp', ExecComp(['y[0]=2.0*x[0]+7.0*x[1]',
'y[1]=5.0*x[0]-3.0*x[1]'],
x=np.zeros([2]), y=np.zeros([2])))
prob.root.add('p1', ParamComp('x', np.ones([2])))
prob.root.connect('p1.x', 'comp.x')
prob.setup(check=False)
prob.run()
data = prob.check_partial_derivatives(out_stream=None)
assert_rel_error(self, data['comp'][('y','x')]['abs error'][0], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['abs error'][1], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['abs error'][2], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['rel error'][0], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['rel error'][1], 0.0, 1e-5)
assert_rel_error(self, data['comp'][('y','x')]['rel error'][2], 0.0, 1e-5)
def openmdao_sellar_converged():
from openmdao.core import Problem
from openmdao.drivers import ScipyOptimizer
top = Problem()
top.root = SellarDerivatives()
top.driver = ScipyOptimizer()
top.driver.options['optimizer'] = 'SLSQP'
top.driver.options['tol'] = 1.0e-8
top.driver.options['disp'] = False
top.driver.add_desvar('z', low=np.array([-10.0, 0.0]),
high=np.array([10.0, 10.0]))
top.driver.add_desvar('x', low=0.0, high=10.0)
top.driver.add_objective('obj')
top.driver.add_constraint('con1', upper=0.0)
top.driver.add_constraint('con2', upper=0.0)
top.setup(check=False)
top.run()
return top
def test_fd_options_step_size(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', Paraboloid())
prob.root.add('p1', ParamComp([('x', 15.0), ('y', 15.0)]))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p1.y', 'comp.y')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Make sure step_size is used
# Derivative should be way high with this.
comp.fd_options['step_size'] = 1e5
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertGreater(J['comp.f_xy']['p1.x'][0][0], 1000.0)
def test_fd_options_step_size(self):
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', Paraboloid())
prob.root.add('p1', ParamComp([('x', 15.0), ('y', 15.0)]))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p1.y', 'comp.y')
comp.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
assert_rel_error(self, J['comp.f_xy']['p1.x'][0][0], 39.0, 1e-6)
# Make sure step_size is used
# Derivative should be way high with this.
comp.fd_options['step_size'] = 1e5
J = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
self.assertGreater(J['comp.f_xy']['p1.x'][0][0], 1000.0)
def test_fan_out(self):
prob = Problem(impl=impl)
prob.root = FanOut()
prob.root.ln_solver = PetscKSP()
prob.setup(check=False)
prob.run()
param_list = ['p.x']
unknown_list = ['comp2.y', "comp3.y"]
J = prob.calc_gradient(param_list,
unknown_list,
mode='fwd',
return_format='dict')
assert_rel_error(self, J['comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p.x'][0][0], 15.0, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='rev',
return_format='dict')
assert_rel_error(self, J['comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['comp3.y']['p.x'][0][0], 15.0, 1e-6)
def test_converge_diverge(self):
prob = Problem()
prob.root = ConvergeDiverge()
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
param_list = ['p.x']
unknown_list = ['comp7.y1']
prob.run()
# Make sure value is fine.
assert_rel_error(self, prob['comp7.y1'], -102.7, 1e-6)
J = prob.calc_gradient(param_list, unknown_list, mode='fwd', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(param_list, unknown_list, mode='rev', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(param_list, unknown_list, mode='fd', return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
def test_converge_diverge_compfd(self):
prob = Problem(impl=impl)
prob.root = ConvergeDivergePar()
prob.root.ln_solver = PetscKSP()
# fd comp2 and comp5. each is under a par group
prob.root.par1.comp2.fd_options['force_fd'] = True
prob.root.par2.comp5.fd_options['force_fd'] = True
prob.setup(check=False)
prob.run()
# Make sure value is fine.
assert_rel_error(self, prob['comp7.y1'], -102.7, 1e-6)
param_list = ['p.x']
unknown_list = ['comp7.y1']
J = prob.calc_gradient(param_list,
unknown_list,
mode='fwd',
return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='rev',
return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='fd',
return_format='dict')
assert_rel_error(self, J['comp7.y1']['p.x'][0][0], -40.75, 1e-6)
def test_fan_out_grouped(self):
prob = Problem()
prob.root = FanOutGrouped()
prob.root.ln_solver = ExplicitSolver()
prob.setup(check=False)
prob.run()
param_list = ['p.x']
unknown_list = ['sub.comp2.y', "sub.comp3.y"]
J = prob.calc_gradient(param_list,
unknown_list,
mode='fwd',
return_format='dict')
assert_rel_error(self, J['sub.comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['sub.comp3.y']['p.x'][0][0], 15.0, 1e-6)
J = prob.calc_gradient(param_list,
unknown_list,
mode='rev',
return_format='dict')
assert_rel_error(self, J['sub.comp2.y']['p.x'][0][0], -6.0, 1e-6)
assert_rel_error(self, J['sub.comp3.y']['p.x'][0][0], 15.0, 1e-6)
def test_fd_options_meta_form(self):
class MetaParaboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(MetaParaboloid, self).__init__()
# Params
self.add_param('x1', 1.0, fd_form='forward')
self.add_param('x2', 1.0, fd_form='backward')
self.add_param('y', 1.0)
# Unknowns
self.add_output('f_xy', 0.0)
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x1 = params['x1']
x2 = params['x2']
y = params['y']
f_xy = ((x1 - 3.0)**2 + (x2 - 3.0)**2 + (x2 + x2) * y +
(y + 4.0)**2 - 3.0)
unknowns['f_xy'] = f_xy
def jacobian(self, params, unknowns, resids):
"""Analytical derivatives"""
x1 = params['x1']
x2 = params['x2']
y = params['y']
J = {}
J['f_xy', 'x1'] = (2.0 * x1 - 6.0 + x2 * y)
J['f_xy', 'x2'] = (2.0 * x2 - 6.0 + x1 * y)
J['f_xy', 'y'] = (2.0 * y + 8.0 + x1 + x2)
return J
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', MetaParaboloid())
prob.root.add('p11', ParamComp('x1', 15.0))
prob.root.add('p12', ParamComp('x2', 15.0))
prob.root.add('p2', ParamComp('y', 15.0))
prob.root.connect('p11.x1', 'comp.x1')
prob.root.connect('p12.x2', 'comp.x2')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
comp.fd_options['step_size'] = 1e3
params_list = ['p11.x1']
unknowns_list = ['comp.f_xy']
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(params_list,
unknowns_list,
return_format='dict')
self.assertGreater(J['comp.f_xy']['p11.x1'][0][0], 0.0)
J = prob.calc_gradient(['p12.x2'], unknowns_list, return_format='dict')
self.assertLess(J['comp.f_xy']['p12.x2'][0][0], 0.0)
def test_fd_options_meta_form(self):
class MetaParaboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(MetaParaboloid, self).__init__()
# Params
self.add_param('x1', 1.0, fd_form = 'forward')
self.add_param('x2', 1.0, fd_form = 'backward')
self.add_param('y', 1.0)
# Unknowns
self.add_output('f_xy', 0.0)
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x1 = params['x1']
x2 = params['x2']
y = params['y']
f_xy = ((x1-3.0)**2 + (x2-3.0)**2 + (x2+x2)*y + (y+4.0)**2 - 3.0)
unknowns['f_xy'] = f_xy
def jacobian(self, params, unknowns, resids):
"""Analytical derivatives"""
x1 = params['x1']
x2 = params['x2']
y = params['y']
J = {}
J['f_xy', 'x1'] = (2.0*x1 - 6.0 + x2*y)
J['f_xy', 'x2'] = (2.0*x2 - 6.0 + x1*y)
J['f_xy', 'y'] = (2.0*y + 8.0 + x1 + x2)
return J
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', MetaParaboloid())
prob.root.add('p11', ParamComp('x1', 15.0))
prob.root.add('p12', ParamComp('x2', 15.0))
prob.root.add('p2', ParamComp('y', 15.0))
prob.root.connect('p11.x1', 'comp.x1')
prob.root.connect('p12.x2', 'comp.x2')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
comp.fd_options['step_size'] = 1e3
params_list = ['p11.x1']
unknowns_list = ['comp.f_xy']
prob.setup(check=False)
prob.run()
J = prob.calc_gradient(params_list, unknowns_list, return_format='dict')
self.assertGreater(J['comp.f_xy']['p11.x1'][0][0], 0.0)
J = prob.calc_gradient(['p12.x2'], unknowns_list, return_format='dict')
self.assertLess(J['comp.f_xy']['p12.x2'][0][0], 0.0)
def test_fd_options_step_type(self):
class ScaledParaboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(ScaledParaboloid, self).__init__()
# Params
self.add_param('x', 1.0)
self.add_param('y', 1.0)
# Unknowns
self.add_output('f_xy', 0.0)
self.scale = 1.0e-6
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x = params['x']
y = params['y']
f_xy = ((x - 3.0)**2 + x * y + (y + 4.0)**2 - 3.0)
unknowns['f_xy'] = self.scale * f_xy
def jacobian(self, params, unknowns, resids):
"""Analytical derivatives"""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = (2.0 * x - 6.0 + y) * self.scale
J['f_xy', 'y'] = (2.0 * y + 8.0 + x) * self.scale
return J
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', ScaledParaboloid())
prob.root.add('p1', ParamComp('x', 8.0 * comp.scale))
prob.root.add('p2', ParamComp('y', 8.0 * comp.scale))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
comp.fd_options['step_type'] = 'absolute'
prob.setup(check=False)
prob.run()
J1 = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
comp.fd_options['step_type'] = 'relative'
J2 = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
# Couldnt put together a case where one is much worse, so just make sure they
# are not equal.
self.assertNotEqual(self, J1['comp.f_xy']['p1.x'][0][0],
J2['comp.f_xy']['p1.x'][0][0])
class TrigMM(Group):
''' FloatKriging gives responses as floats '''
def __init__(self):
super(TrigMM, self).__init__()
# Create meta_model for f_x as the response
sin_mm = self.add("sin_mm", MetaModel())
sin_mm.add_param('x', val=0.)
sin_mm.add_output('f_x:float', val=0., surrogate=FloatKrigingSurrogate())
sin_mm.add_output('f_x:norm_dist', val=(0.,0.), surrogate=KrigingSurrogate())
from openmdao.core import Problem
prob = Problem()
prob.root = TrigMM()
prob.setup()
#traning data is just set manually. No connected input needed, since
# we're assuming the data is pre-existing
prob['sin_mm.train:x'] = np.linspace(0,10,20)
prob['sin_mm.train:f_x:float'] = np.sin(prob['sin_mm.train:x'])
prob['sin_mm.train:f_x:norm_dist'] = np.cos(prob['sin_mm.train:x'])
prob['sin_mm.x'] = 2.1 #prediction happens at this value
prob.run()
print('float predicted:', '%3.4f'%prob['sin_mm.f_x:float']) #predicted value
print('float actual: ', '%3.4f'%np.sin(2.1))
print('norm_dist predicted:', '%3.4f,'%prob['sin_mm.f_x:norm_dist'][0], '%3.4e'%prob['sin_mm.f_x:norm_dist'][1]) #predicted value
print('norm_dist actual: ', '%3.4f'%np.cos(2.1))
def test_fd_options_step_type(self):
class ScaledParaboloid(Component):
""" Evaluates the equation f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3 """
def __init__(self):
super(ScaledParaboloid, self).__init__()
# Params
self.add_param('x', 1.0)
self.add_param('y', 1.0)
# Unknowns
self.add_output('f_xy', 0.0)
self.scale = 1.0e-6
def solve_nonlinear(self, params, unknowns, resids):
"""f(x,y) = (x-3)^2 + xy + (y+4)^2 - 3
Optimal solution (minimum): x = 6.6667; y = -7.3333
"""
x = params['x']
y = params['y']
f_xy = ((x-3.0)**2 + x*y + (y+4.0)**2 - 3.0)
unknowns['f_xy'] = self.scale*f_xy
def jacobian(self, params, unknowns, resids):
"""Analytical derivatives"""
x = params['x']
y = params['y']
J = {}
J['f_xy', 'x'] = (2.0*x - 6.0 + y) * self.scale
J['f_xy', 'y'] = (2.0*y + 8.0 + x) * self.scale
return J
prob = Problem()
prob.root = Group()
comp = prob.root.add('comp', ScaledParaboloid())
prob.root.add('p1', ParamComp('x', 8.0*comp.scale))
prob.root.add('p2', ParamComp('y', 8.0*comp.scale))
prob.root.connect('p1.x', 'comp.x')
prob.root.connect('p2.y', 'comp.y')
comp.fd_options['force_fd'] = True
comp.fd_options['step_type'] = 'absolute'
prob.setup(check=False)
prob.run()
J1 = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
comp.fd_options['step_type'] = 'relative'
J2 = prob.calc_gradient(['p1.x'], ['comp.f_xy'], return_format='dict')
# Couldnt put together a case where one is much worse, so just make sure they
# are not equal.
self.assertNotEqual(self, J1['comp.f_xy']['p1.x'][0][0],
J2['comp.f_xy']['p1.x'][0][0])
