def test_vectorized(self):
"""Check against the scipy solver."""
model = om.Group()
x = np.array([[1, 2, -3], [2, -1, 4]])
A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])
b = np.einsum('jk,ik->ij', A, x)
model.add_subsystem('p1', om.IndepVarComp('A', A))
model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', om.LinearSystemComp(size=3, vec_size=2))
model.connect('p1.A', 'lin.A')
model.connect('p2.b', 'lin.b')
prob = om.Problem(model)
prob.setup()
lingrp.linear_solver = om.ScipyKrylov()
prob.set_solver_print(level=0)
prob.run_model()
assert_near_equal(prob['lin.x'], x, .0001)
assert_near_equal(prob.model._residuals.get_norm(), 0.0, 1e-10)
model.run_apply_nonlinear()
with model._scaled_context_all():
val = model.lingrp.lin._residuals['x']
assert_near_equal(val, np.zeros((2, 3)), tolerance=1e-8)
def test_feature_vectorized(self):
import numpy as np
import openmdao.api as om
model = om.Group()
A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])
b = np.array([[2.0, -3.0, 4.0], [1.0, 0.0, -1.0]])
model.add_subsystem('p1', om.IndepVarComp('A', A))
model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', om.LinearSystemComp(size=3, vec_size=2))
model.connect('p1.A', 'lin.A')
model.connect('p2.b', 'lin.b')
prob = om.Problem(model)
prob.setup()
lingrp.linear_solver = om.ScipyKrylov()
prob.run_model()
assert_near_equal(
prob['lin.x'],
np.array([[0.10596026, -0.16556291, 0.48675497],
[0.19205298, -0.11258278, -0.14900662]]), .0001)
def test_feature_vectorized_A(self):
import numpy as np
import openmdao.api as om
model = om.Group()
A = np.array([[[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]],
[[2.0, 3.0, 4.0], [1.0, -1.0, -2.0], [3.0, 2.0, -2.0]]])
b = np.array([[-5.0, 2.0, 3.0], [-1.0, 1.0, -3.0]])
model.add_subsystem('p1', om.IndepVarComp('A', A))
model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem(
'lin', om.LinearSystemComp(size=3, vec_size=2, vectorize_A=True))
model.connect('p1.A', 'lin.A')
model.connect('p2.b', 'lin.b')
prob = om.Problem(model)
prob.setup()
lingrp.linear_solver = om.ScipyKrylov()
prob.run_model()
assert_near_equal(
prob['lin.x'],
np.array([[-0.78807947, 0.66887417, 0.47350993], [0.7, -1.8,
0.75]]), .0001)
def test_feature_vectorized_A(self):
model = om.Group()
A = np.array([[[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]],
[[2.0, 3.0, 4.0], [1.0, -1.0, -2.0], [3.0, 2.0, -2.0]]])
b = np.array([[-5.0, 2.0, 3.0], [-1.0, 1.0, -3.0]])
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem(
'lin', om.LinearSystemComp(size=3, vec_size=2, vectorize_A=True))
prob = om.Problem(model)
prob.setup()
prob.set_val('lin.A', A)
prob.set_val('lin.b', b)
lingrp.linear_solver = om.ScipyKrylov()
prob.run_model()
assert_near_equal(
prob.get_val('lin.x'),
np.array([[-0.78807947, 0.66887417, 0.47350993], [0.7, -1.8,
0.75]]), .0001)
def test_feature_basic(self):
import numpy as np
import openmdao.api as om
model = om.Group()
A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])
b = np.array([1.0, 2.0, -3.0])
model.add_subsystem('p1', om.IndepVarComp('A', A))
model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', om.LinearSystemComp(size=3))
model.connect('p1.A', 'lin.A')
model.connect('p2.b', 'lin.b')
prob = om.Problem(model)
prob.setup()
lingrp.linear_solver = om.ScipyKrylov()
prob.run_model()
assert_near_equal(prob['lin.x'],
np.array([0.36423841, -0.00662252, -0.4205298]),
.0001)
def test_solve_linear_vectorized(self):
"""Check against solve_linear."""
x = np.array([[1, 2, -3], [2, -1, 4]])
A = np.array([[1., 1., 1.], [1., 2., 3.], [0., 1., 3.]])
b = np.einsum('jk,ik->ij', A, x)
b_T = np.einsum('jk,ik->ij', A.T, x)
lin_sys_comp = om.LinearSystemComp(size=3, vec_size=2)
prob = om.Problem()
prob.model.add_subsystem('p1', om.IndepVarComp('A', A))
prob.model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = prob.model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', lin_sys_comp)
prob.model.connect('p1.A', 'lin.A')
prob.model.connect('p2.b', 'lin.b')
prob.setup()
prob.set_solver_print(level=0)
prob.run_model()
prob.model.run_linearize()
# Compare against calculated derivs
Ainv = np.array([[3., -2., 1.], [-3., 3., -2.], [1., -1., 1.]])
dx_dA0 = np.outer(Ainv, -x[0]).reshape(3, 9)
dx_dA1 = np.outer(Ainv, -x[1]).reshape(3, 9)
dx_dA = np.vstack((dx_dA0, dx_dA1))
dx_db = np.kron(np.eye(2), Ainv)
d_inputs, d_outputs, d_residuals = lingrp.get_linear_vectors()
# Forward mode with RHS of self.b
d_residuals['lin.x'] = b
lingrp.run_solve_linear(['linear'], 'fwd')
sol = d_outputs['lin.x']
assert_near_equal(sol, x, .0001)
# Reverse mode with RHS of self.b_T
d_outputs['lin.x'] = b_T
lingrp.run_solve_linear(['linear'], 'rev')
sol = d_residuals['lin.x']
assert_near_equal(sol, x, .0001)
J = prob.compute_totals(['lin.x'], ['p1.A', 'p2.b'],
return_format='flat_dict')
assert_near_equal(J['lin.x', 'p1.A'], dx_dA, .0001)
assert_near_equal(J['lin.x', 'p2.b'], dx_db, .0001)
data = prob.check_partials(out_stream=None)
abs_errors = data['lingrp.lin'][('x', 'x')]['abs error']
self.assertTrue(len(abs_errors) > 0)
for match in abs_errors:
abs_error = float(match)
def test_solve_linear(self):
"""Check against solve_linear."""
x = np.array([1, 2, -3])
A = np.array([[1., 1., 1.], [1., 2., 3.], [0., 1., 3.]])
b = A.dot(x)
b_T = A.T.dot(x)
lin_sys_comp = om.LinearSystemComp(size=3)
prob = om.Problem()
prob.model.add_subsystem('p1', om.IndepVarComp('A', A))
prob.model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = prob.model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', lin_sys_comp)
prob.model.connect('p1.A', 'lin.A')
prob.model.connect('p2.b', 'lin.b')
prob.setup()
prob.set_solver_print(level=0)
prob.run_model()
prob.model.run_linearize()
# Compare against calculated derivs
Ainv = np.array([[3., -2., 1.], [-3., 3., -2.], [1., -1., 1.]])
dx_dA = np.outer(Ainv, -x).reshape(3, 9)
dx_db = Ainv
d_inputs, d_outputs, d_residuals = lingrp.get_linear_vectors()
# Forward mode with RHS of self.b
d_residuals['lin.x'] = b
lingrp.run_solve_linear(['linear'], 'fwd')
sol = d_outputs['lin.x']
assert_near_equal(sol, x, .0001)
# Reverse mode with RHS of self.b_T
d_outputs['lin.x'] = b_T
lingrp.run_solve_linear(['linear'], 'rev')
sol = d_residuals['lin.x']
assert_near_equal(sol, x, .0001)
prob.model.lingrp.lin._no_check_partials = False # override skipping of check_partials
J = prob.compute_totals(['lin.x'], ['p1.A', 'p2.b', 'lin.x'],
return_format='flat_dict')
assert_near_equal(J['lin.x', 'p1.A'], dx_dA, .0001)
assert_near_equal(J['lin.x', 'p2.b'], dx_db, .0001)
data = prob.check_partials(out_stream=None)
abs_errors = data['lingrp.lin'][('x', 'x')]['abs error']
self.assertTrue(len(abs_errors) > 0)
self.assertTrue(abs_errors[0] < 1.e-6)
def setup(self):
thermo = self.options['thermo']
num_element = thermo.num_element
self.add_subsystem('TP2ls', PropsRHS(thermo), promotes_inputs=('T', 'n', 'n_moles', 'b0'))
ne1 = num_element+1
self.add_subsystem('ls2t', om.LinearSystemComp(size=ne1))
self.add_subsystem('ls2p', om.LinearSystemComp(size=ne1))
self.add_subsystem('tp2props', PropsCalcs(thermo=thermo),
promotes_inputs=['n', 'n_moles', 'T', 'P'],
promotes_outputs=['h', 'S', 'gamma', 'Cp', 'Cv', 'rho', 'R']
)
self.connect('TP2ls.lhs_TP', ['ls2t.A', 'ls2p.A'])
self.connect('TP2ls.rhs_T', 'ls2t.b')
self.connect('TP2ls.rhs_P', 'ls2p.b')
self.connect('ls2t.x', 'tp2props.result_T')
self.connect('ls2p.x', 'tp2props.result_P')
def test_feature_basic(self):
model = om.Group()
A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])
b = np.array([1.0, 2.0, -3.0])
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', om.LinearSystemComp(size=3))
prob = om.Problem(model)
prob.setup()
prob.set_val('lin.A', A)
prob.set_val('lin.b', b)
lingrp.linear_solver = om.ScipyKrylov()
prob.run_model()
assert_near_equal(prob.get_val('lin.x'),
np.array([0.36423841, -0.00662252, -0.4205298]),
.0001)
def test_feature_vectorized(self):
model = om.Group()
A = np.array([[5.0, -3.0, 2.0], [1.0, 7.0, -4.0], [1.0, 0.0, 8.0]])
b = np.array([[2.0, -3.0, 4.0], [1.0, 0.0, -1.0]])
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', om.LinearSystemComp(size=3, vec_size=2))
prob = om.Problem(model)
prob.setup()
prob.set_val('lin.A', A)
prob.set_val('lin.b', b)
lingrp.linear_solver = om.ScipyKrylov()
prob.run_model()
assert_near_equal(
prob.get_val('lin.x'),
np.array([[0.10596026, -0.16556291, 0.48675497],
[0.19205298, -0.11258278, -0.14900662]]), .0001)
def test_solve_linear_vectorized_A(self):
"""Check against solve_linear."""
x = np.array([[1, 2, -3], [2, -1, 4]])
A = np.array([[[1., 1., 1.], [1., 2., 3.], [0., 1., 3.]],
[[2.0, 3.0, 4.0], [1.0, -1.0, -2.0], [3.0, 2.0, -2.0]]])
b = np.einsum('ijk,ik->ij', A, x)
b_T = np.einsum('ijk,ik->ij', A.transpose(0, 2, 1), x)
lin_sys_comp = om.LinearSystemComp(size=3,
vec_size=2,
vectorize_A=True)
prob = om.Problem()
prob.model.add_subsystem('p1', om.IndepVarComp('A', A))
prob.model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = prob.model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', lin_sys_comp)
prob.model.connect('p1.A', 'lin.A')
prob.model.connect('p2.b', 'lin.b')
prob.setup()
prob.set_solver_print(level=0)
prob.run_model()
prob.model.run_linearize()
# Compare against calculated derivs
Ainv1 = np.array([[3., -2., 1.], [-3., 3., -2.], [1., -1., 1.]])
Ainv2 = np.array([[0.3, 0.7, -0.1], [-0.2, -0.8, 0.4],
[0.25, 0.25, -0.25]])
dx_dA0 = np.outer(Ainv1, -x[0]).reshape(3, 9)
dx_dA1 = np.outer(Ainv2, -x[1]).reshape(3, 9)
dx_dA = np.zeros((6, 18))
dx_dA[:3, :9] = dx_dA0
dx_dA[3:, 9:] = dx_dA1
dx_db = np.zeros((6, 6))
dx_db[:3, :3] = Ainv1
dx_db[3:, 3:] = Ainv2
d_inputs, d_outputs, d_residuals = lingrp.get_linear_vectors()
# Forward mode with RHS of self.b
d_residuals['lin.x'] = b
lingrp.run_solve_linear(['linear'], 'fwd')
sol = d_outputs['lin.x']
assert_near_equal(sol, x, .0001)
# Reverse mode with RHS of self.b_T
d_outputs['lin.x'] = b_T
lingrp.run_solve_linear(['linear'], 'rev')
sol = d_residuals['lin.x']
assert_near_equal(sol, x, .0001)
J = prob.compute_totals(['lin.x'], ['p1.A', 'p2.b'],
return_format='flat_dict')
assert_near_equal(J['lin.x', 'p1.A'], dx_dA, .0001)
assert_near_equal(J['lin.x', 'p2.b'], dx_db, .0001)
data = prob.check_partials(out_stream=None)
abs_errors = data['lingrp.lin'][('x', 'x')]['abs error']
self.assertTrue(len(abs_errors) > 0)
for match in abs_errors:
abs_error = float(match)
import numpy as np
import openmdao.api as om
# from openmdao.visualization.n2_viewer.n2_viewer import n2
# Whether to pop up a browser window for each N2
DEBUG_BROWSER = False
# set DEBUG_FILES to True if you want to view the generated HTML file(s)
DEBUG_FILES = False
"""Check against the scipy solver."""
SIZE = 10
model = om.Group()
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]])
x = np.random.rand(SIZE) * 1e20
A = np.random.rand(SIZE, SIZE)
b = A.dot(x)
model.add_subsystem('p1', om.IndepVarComp('A', A))
model.add_subsystem('p2', om.IndepVarComp('b', b))
lingrp = model.add_subsystem('lingrp', om.Group(), promotes=['*'])
lingrp.add_subsystem('lin', om.LinearSystemComp(size=SIZE))
model.connect('p1.A', 'lin.A')
model.connect('p2.b', 'lin.b')
prob = om.Problem(model)
prob.setup()
prob.final_setup()
lingrp.linear_solver = om.ScipyKrylov()
prob.setup()