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_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_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_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_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_fan_out_grouped(self):
prob = Problem(impl=impl)
prob.root = root = Group()
root.add('p', IndepVarComp('x', 1.0))
root.add('comp1', ExecComp(['y=3.0*x']))
sub = root.add('sub', ParallelGroup())
sub.add('comp2', ExecComp(['y=-2.0*x']))
sub.add('comp3', ExecComp(['y=5.0*x']))
root.add('c2', ExecComp(['y=-x']))
root.add('c3', ExecComp(['y=3.0*x']))
root.connect('sub.comp2.y', 'c2.x')
root.connect('sub.comp3.y', 'c3.x')
root.connect("comp1.y", "sub.comp2.x")
root.connect("comp1.y", "sub.comp3.x")
root.connect("p.x", "comp1.x")
prob.root.ln_solver = LinearGaussSeidel()
prob.root.sub.ln_solver = LinearGaussSeidel()
prob.setup(check=False)
prob.run()
param = '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)
unknown_list = ['c2.y', "c3.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], 45.0, 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], 45.0, 1e-6)
def test_complex_step2(self):
prob = Problem(Group())
comp = prob.root.add('comp', ExecComp('y=x*x + x*2.0'))
prob.root.add('p1', ParamComp('x', 2.0))
prob.root.connect('p1.x', 'comp.x')
comp.fd_options['force_fd'] = False
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'], np.array([6.0]), 0.00001)
J = prob.calc_gradient(['p1.x'], ['comp.y'], mode='rev', return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'], np.array([6.0]), 0.00001)
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_derivatives(self):
meta = MetaModel()
meta.add_param('x', 0.)
meta.add_output('f', 0.)
meta.default_surrogate = FloatKrigingSurrogate()
prob = Problem(Group())
prob.root.add('meta', meta, promotes=['x'])
prob.root.add('p', IndepVarComp('x', 0.), promotes=['x'])
prob.setup(check=False)
prob['meta.train:x'] = [0., .25, .5, .75, 1.]
prob['meta.train:f'] = [1., .75, .5, .25, 0.]
prob['x'] = 0.125
prob.run()
Jf = prob.calc_gradient(['x'], ['meta.f'], mode='fwd')
Jr = prob.calc_gradient(['x'], ['meta.f'], mode='rev')
assert_rel_error(self, Jf[0][0], -1.00011, 1.0e-5)
assert_rel_error(self, Jr[0][0], -1.00011, 1.0e-5)
stream = cStringIO()
prob.check_partial_derivatives(out_stream=stream)
abs_errors = findall('Absolute Error \(.+\) : (.+)', stream.getvalue())
self.assertTrue(len(abs_errors) > 0)
for match in abs_errors:
abs_error = float(match)
self.assertTrue(abs_error < 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_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_linear_system(self):
root = Group()
root.add('lin', LinearSystem(3))
x = np.array([1, 2, -3])
A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])
b = A.dot(x)
root.add('p1', ParamComp('A', A))
root.add('p2', ParamComp('b', b))
root.connect('p1.A', 'lin.A')
root.connect('p2.b', 'lin.b')
prob = Problem(root)
prob.setup(check=False)
prob.run()
# Make sure it gets the right answer
assert_rel_error(self, prob['lin.x'], x, .0001)
assert_rel_error(self, np.linalg.norm(prob.root.resids.vec), 0.0,
1e-10)
# Compare against calculated derivs
Ainv = np.linalg.inv(A)
dx_dA = np.outer(Ainv, -x).reshape(3, 9)
dx_db = Ainv
J = prob.calc_gradient(['p1.A', 'p2.b'], ['lin.x'],
mode='fwd',
return_format='dict')
assert_rel_error(self, J['lin.x']['p1.A'], dx_dA, .0001)
assert_rel_error(self, J['lin.x']['p2.b'], dx_db, .0001)
J = prob.calc_gradient(['p1.A', 'p2.b'], ['lin.x'],
mode='rev',
return_format='dict')
assert_rel_error(self, J['lin.x']['p1.A'], dx_dA, .0001)
assert_rel_error(self, J['lin.x']['p2.b'], dx_db, .0001)
J = prob.calc_gradient(['p1.A', 'p2.b'], ['lin.x'],
mode='fd',
return_format='dict')
assert_rel_error(self, J['lin.x']['p1.A'], dx_dA, .0001)
assert_rel_error(self, J['lin.x']['p2.b'], dx_db, .0001)
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_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_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_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_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_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_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_complex_step2(self):
prob = Problem(Group())
comp = prob.root.add('comp', ExecComp('y=x*x + x*2.0'))
prob.root.add('p1', ParamComp('x', 2.0))
prob.root.connect('p1.x', 'comp.x')
comp.fd_options['force_fd'] = False
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'], np.array([6.0]), 0.00001)
J = prob.calc_gradient(['p1.x'], ['comp.y'],
mode='rev',
return_format='dict')
assert_rel_error(self, J['comp.y']['p1.x'], np.array([6.0]), 0.00001)
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_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_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_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_linear_system(self):
root = Group()
root.add('lin', LinearSystem(3))
x = np.array([1, 2, -3])
A = np.array([[ 5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])
b = A.dot(x)
root.add('p1', IndepVarComp('A', A))
root.add('p2', IndepVarComp('b', b))
root.connect('p1.A', 'lin.A')
root.connect('p2.b', 'lin.b')
prob = Problem(root)
prob.setup(check=False)
prob.run()
# Make sure it gets the right answer
assert_rel_error(self, prob['lin.x'], x, .0001)
assert_rel_error(self, np.linalg.norm(prob.root.resids.vec), 0.0, 1e-10)
# Compare against calculated derivs
Ainv = np.linalg.inv(A)
dx_dA = np.outer(Ainv, -x).reshape(3, 9)
dx_db = Ainv
J = prob.calc_gradient(['p1.A', 'p2.b'], ['lin.x'], mode='fwd', return_format='dict')
assert_rel_error(self, J['lin.x']['p1.A'], dx_dA, .0001)
assert_rel_error(self, J['lin.x']['p2.b'], dx_db, .0001)
J = prob.calc_gradient(['p1.A', 'p2.b'], ['lin.x'], mode='rev', return_format='dict')
assert_rel_error(self, J['lin.x']['p1.A'], dx_dA, .0001)
assert_rel_error(self, J['lin.x']['p2.b'], dx_db, .0001)
J = prob.calc_gradient(['p1.A', 'p2.b'], ['lin.x'], mode='fd', return_format='dict')
assert_rel_error(self, J['lin.x']['p1.A'], dx_dA, .0001)
assert_rel_error(self, J['lin.x']['p2.b'], dx_db, .0001)
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_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_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_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_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_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_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_CADRE_MDP(self):
n = 1500
m = 300
npts = 2
# Instantiate
model = Problem(impl=impl)
root = model.root = CADRE_MDP_Group(n=n, m=m, npts=npts)
# Add parameters and constraints to each CADRE instance.
names = ['pt%s' % i for i in range(npts)]
for i, name in enumerate(names):
# add parameters to driver
model.driver.add_desvar("%s.CP_Isetpt" % name, low=0., high=0.4)
model.driver.add_desvar("%s.CP_gamma" % name, low=0, high=np.pi/2.)
model.driver.add_desvar("%s.CP_P_comm" % name, low=0., high=25.)
model.driver.add_desvar("%s.iSOC" % name, indices=[0], low=0.2, high=1.)
model.driver.add_constraint('%s.ConCh'% name, upper=0.0)
model.driver.add_constraint('%s.ConDs'% name, upper=0.0)
model.driver.add_constraint('%s.ConS0'% name, upper=0.0)
model.driver.add_constraint('%s.ConS1'% name, upper=0.0)
model.driver.add_constraint('%s_con5.val'% name, equals=0.0)
# Add Parameter groups
model.driver.add_desvar("bp1.cellInstd", low=0., high=1.0)
model.driver.add_desvar("bp2.finAngle", low=0., high=np.pi/2.)
model.driver.add_desvar("bp3.antAngle", low=-np.pi/4, high=np.pi/4)
# Add objective
model.driver.add_objective('obj.val')
# For Parallel exeuction, we must use KSP
if MPI:
model.root.ln_solver = PetscKSP()
model.setup()
model.run()
# Read pickle
fpath = os.path.dirname(os.path.realpath(__file__))
data = pickle.load(open(fpath + "/mdp_execute.pkl", 'rb'))
for var in data:
# We changed constraint names
xvar = var
if '_con1' in xvar:
xvar = xvar.replace('_con1.val', '.ConCh')
if '_con2' in xvar:
xvar = xvar.replace('_con2.val', '.ConDs')
if '_con3' in xvar:
xvar = xvar.replace('_con3.val', '.ConS0')
if '_con4' in xvar:
xvar = xvar.replace('_con4.val', '.ConS1')
computed = model[xvar]
actual = data[var]
if isinstance(computed, np.ndarray):
rel = np.linalg.norm(actual - computed)/np.linalg.norm(actual)
else:
rel = np.abs(actual - computed)/np.abs(actual)
print(xvar)
print(computed)
print(actual)
if np.mean(actual) > 1e-3 or np.mean(computed) > 1e-3:
assert rel <= 1e-3
# Now do derivatives
params = model.driver.get_desvars().keys()
unks = model.driver.get_objectives().keys() + model.driver.get_constraints().keys()
Jb = model.calc_gradient(params, unks, mode='rev', return_format='dict')
# Read pickle
fpath = os.path.dirname(os.path.realpath(__file__))
Ja = pickle.load(open(fpath + "/mdp_derivs.pkl", 'rb'))
for key1, value in sorted(Ja.items()):
for key2 in sorted(value.keys()):
# We changed constraint names
xkey1 = key1
if '_con1' in xkey1:
xkey1 = xkey1.replace('_con1.val', '.ConCh')
if '_con2' in xkey1:
xkey1 = xkey1.replace('_con2.val', '.ConDs')
if '_con3' in xkey1:
xkey1 = xkey1.replace('_con3.val', '.ConS0')
if '_con4' in xkey1:
xkey1 = xkey1.replace('_con4.val', '.ConS1')
computed = Jb[xkey1][key2]
actual = Ja[key1][key2]
if isinstance(computed, np.ndarray):
rel = np.linalg.norm(actual - computed)/np.linalg.norm(actual)
else:
rel = np.abs(actual - computed)/np.abs(actual)
print(xkey1, 'wrt', key2)
print(computed)
print(actual)
if np.mean(actual) > 1e-3 or np.mean(computed) > 1e-3:
assert rel <= 1e-3
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])
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])
