def test_supply_attribute(self):
"""
Test that we can supply an attribute instead of a function.
"""
iden = Identity()
lst = LeastSquaresTerm(Target(iden, 'x'), 3, weight=0.1)
self.assertEqual(lst.goal, 3)
self.assertAlmostEqual(lst.weight, 0.1, places=13)
iden.set_dofs([17])
self.assertEqual(lst.f_in(), 17)
correct_value = 0.1 * ((17 - 3) ** 2)
self.assertAlmostEqual(lst.f_out(), correct_value, places=13)
def test_supply_property(self):
"""
Test that we can supply a property instead of a function.
"""
iden = Identity()
lst = LeastSquaresTerm.from_sigma(Target(iden, 'f'), 3, sigma=0.1)
self.assertEqual(lst.goal, 3)
self.assertAlmostEqual(lst.weight, 100, places=13)
iden.set_dofs([17])
self.assertEqual(lst.f_in(), 17)
correct_value = ((17 - 3) / 0.1) ** 2
self.assertAlmostEqual(lst.f_out(), correct_value, places=11)
def test_supply_object(self):
"""
Test that we can supply an object with a J function instead of a function.
"""
iden = Identity()
# Note here we supply iden instead of iden.J
lst = LeastSquaresTerm.from_sigma(iden, 3, sigma=0.1)
self.assertEqual(lst.f_in, iden.J)
self.assertEqual(lst.goal, 3)
self.assertAlmostEqual(lst.weight, 100, places=13)
iden.set_dofs([17])
self.assertEqual(lst.f_in(), 17)
correct_value = ((17 - 3) / 0.1) ** 2
self.assertAlmostEqual(lst.f_out(), correct_value, places=11)
def test_supply_tuples(self):
"""
Test basic usage
"""
# Objective function f(x) = ((x - 3) / 2) ** 2
iden1 = Identity()
term1 = (iden1.J, 3, 0.25)
prob = LeastSquaresProblem([term1])
self.assertAlmostEqual(prob.objective(), 2.25)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertEqual(len(prob.dofs.f()), 1)
self.assertAlmostEqual(prob.dofs.f()[0], 0)
self.assertEqual(len(prob.f()), 1)
self.assertAlmostEqual(prob.f()[0], -1.5)
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 2.25)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 2.25)
iden1.set_dofs([10])
self.assertAlmostEqual(prob.objective(), 12.25)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 12.25)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 12.25)
self.assertAlmostEqual(prob.objective([0]), 2.25)
self.assertAlmostEqual(prob.objective([10]), 12.25)
self.assertEqual(prob.dofs.all_owners, [iden1])
self.assertEqual(prob.dofs.dof_owners, [iden1])
# Objective function
# f(x,y) = ((x - 3) / 2) ** 2 + ((y + 4) / 5) ** 2
iden2 = Identity()
term2 = (iden2.J, -4, 0.04)
prob = LeastSquaresProblem([term1, term2])
self.assertAlmostEqual(prob.objective(), 12.89)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertEqual(len(prob.f()), 2)
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 12.89)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 12.89)
iden1.set_dofs([5])
iden2.set_dofs([-7])
self.assertAlmostEqual(prob.objective(), 1.36)
self.assertAlmostEqual(prob.objective(), sum(t.f_out() for t in prob.terms))
self.assertEqual(len(prob.f()), 2)
self.assertAlmostEqual(prob.objective_from_shifted_f(prob.f()), 1.36)
self.assertAlmostEqual(prob.objective_from_unshifted_f(prob.dofs.f()), 1.36)
self.assertAlmostEqual(prob.objective([10, 0]), 12.89)
self.assertAlmostEqual(prob.objective([5, -7]), 1.36)
self.assertEqual(prob.dofs.dof_owners, [iden1, iden2])
self.assertEqual(prob.dofs.all_owners, [iden1, iden2])
def test_no_dependents(self):
"""
For an object that does not depend on anything, just return the
original object.
"""
obj = object()
self.assertEqual(get_owners(obj), [obj])
iden = Identity()
self.assertEqual(get_owners(iden), [iden])
def test_circular2(self):
"""
Verify that a circular dependency among 2 objects is detected.
"""
o1 = Identity()
o2 = Identity()
o1.depends_on = ["o2"]
o2.depends_on = ["o1"]
o1.o2 = o2
o2.o1 = o1
with self.assertRaises(RuntimeError):
get_owners(o1)
def test_basic(self):
"""
Test basic usage
"""
iden = Identity()
lst = LeastSquaresTerm(iden.J, 3, weight=0.1)
self.assertEqual(lst.f_in, iden.J)
self.assertEqual(lst.goal, 3)
self.assertAlmostEqual(lst.weight, 0.1, places=13)
lst = LeastSquaresTerm.from_sigma(iden.J, 3, sigma=0.1)
self.assertEqual(lst.f_in, iden.J)
self.assertEqual(lst.goal, 3)
self.assertAlmostEqual(lst.weight, 100.0, places=13)
iden.set_dofs([17])
self.assertEqual(lst.f_in(), 17)
correct_value = ((17 - 3) / 0.1) ** 2
self.assertAlmostEqual(lst.f_out(), correct_value, places=11)
def test_depth_2(self):
"""
Check cases in which the original object depends on another, which
depends on another.
"""
o1 = Identity()
o2 = Identity()
o3 = object()
o1.depends_on = ["o2"]
o2.depends_on = ["o3"]
o1.o2 = o2
o2.o3 = o3
self.assertEqual(get_owners(o1), [o1, o2, o3])
def test_solve_quadratic(self):
"""
Minimize f(x,y,z) = 1 * (x - 1) ^ 2 + 2 * (y - 2) ^ 2 + 3 * (z - 3) ^ 2.
The optimum is at (x,y,z)=(1,2,3), and f=0 at this point.
"""
for solver in solvers:
iden1 = Identity()
iden2 = Identity()
iden3 = Identity()
term1 = (iden1.J, 1, 1)
term2 = (iden2.J, 2, 2)
term3 = (iden3.J, 3, 3)
prob = LeastSquaresProblem([term1, term2, term3])
if solver == serial_solve:
solver(prob, tol=1e-12)
else:
solver(prob)
self.assertAlmostEqual(prob.objective(), 0)
self.assertAlmostEqual(iden1.x, 1)
self.assertAlmostEqual(iden2.x, 2)
self.assertAlmostEqual(iden3.x, 3)
def test_depth_1(self):
"""
Check cases in which the original object depends on 1 or more others.
"""
o1 = Identity()
o2 = Identity()
o1.o2 = o2
o1.depends_on = ["o2"]
self.assertEqual(get_owners(o1), [o1, o2])
o3 = object()
o1.depends_on = ["o3", "o2"]
o1.o3 = o3
self.assertEqual(get_owners(o1), [o1, o3, o2])
def test_gradient(self):
iden = Identity()
for n in range(1, 10):
iden.set_dofs([np.random.rand() * 4 - 2])
# Supply an object to finite_difference():
fd_grad = Dofs([iden]).fd_jac().flatten()
np.testing.assert_allclose(fd_grad, iden.df)
np.testing.assert_allclose(fd_grad, iden.dJ())
# Supply a function to finite_difference():
fd_grad = Dofs([iden.J]).fd_jac().flatten()
np.testing.assert_allclose(fd_grad, iden.df)
np.testing.assert_allclose(fd_grad, iden.dJ())
# Supply an attribute to finite_difference():
fd_grad = Dofs([Target(iden, "f")]).fd_jac().flatten()
np.testing.assert_allclose(fd_grad, iden.df)
np.testing.assert_allclose(fd_grad, iden.dJ())
def test_exceptions(self):
"""
Test that exceptions are thrown when invalid inputs are
provided.
"""
# First argument must be callable
with self.assertRaises(TypeError):
lst = LeastSquaresTerm(2, 3, 0.1)
# Second and third arguments must be real numbers
iden = Identity()
#with self.assertRaises(TypeError):
# lst = LeastSquaresTerm(iden.J, "hello", sigma=0.1)
with self.assertRaises(TypeError):
lst = LeastSquaresTerm.from_sigma(iden.J, 3, sigma=iden)
#with self.assertRaises(TypeError):
# lst = LeastSquaresTerm(iden.J, "hello", weight=0.1)
with self.assertRaises(TypeError):
lst = LeastSquaresTerm(iden.J, 3, weight=iden)
# sigma cannot be zero
with self.assertRaises(ValueError):
lst = LeastSquaresTerm.from_sigma(iden.J, 3, sigma=0)
with self.assertRaises(ValueError):
lst = LeastSquaresTerm.from_sigma(iden.J, 3, sigma=0.0)
# Cannot specify both weight and sigma
with self.assertRaises(TypeError):
lst = LeastSquaresTerm(iden.J, 3, sigma=1.2, weight=3.4)
# Must specify either weight or sigma
with self.assertRaises(TypeError):
lst = LeastSquaresTerm(iden.J, 3)
# Weight cannot be negative
with self.assertRaises(ValueError):
lst = LeastSquaresTerm(iden.J, 3, weight=-1.0)
def test_solve_quadratic_fixed_supplying_attributes(self):
"""
Same as test_solve_quadratic_fixed, except supplying attributes
rather than functions as targets.
"""
for solver in solvers:
iden1 = Identity()
iden2 = Identity()
iden3 = Identity()
iden1.x = 4
iden2.x = 5
iden3.x = 6
iden1.names = ['x1']
iden2.names = ['x2']
iden3.names = ['x3']
iden1.fixed = [True]
iden3.fixed = [True]
# Try a mix of explicit LeastSquaresTerms and tuples
term1 = LeastSquaresTerm(Target(iden1, 'x'), 1, 1)
term2 = (iden2, 'x', 2, 1 / 4.)
term3 = (iden3, 'x', 3, 1 / 9.)
prob = LeastSquaresProblem([term1, term2, term3])
solver(prob)
self.assertAlmostEqual(prob.objective(), 10)
self.assertAlmostEqual(iden1.x, 4)
self.assertAlmostEqual(iden2.x, 2)
self.assertAlmostEqual(iden3.x, 6)
def test_basic(self):
iden = Identity()
self.assertAlmostEqual(iden.J(), 0, places=13)
np.testing.assert_allclose(iden.get_dofs(), np.array([0.0]))
np.testing.assert_allclose(iden.fixed, np.array([False]))
x = 3.5
iden = Identity(x)
self.assertAlmostEqual(iden.J(), x, places=13)
np.testing.assert_allclose(iden.get_dofs(), np.array([x]))
np.testing.assert_allclose(iden.fixed, np.array([False]))
y = -2
iden.set_dofs([y])
self.assertAlmostEqual(iden.J(), y, places=13)
np.testing.assert_allclose(iden.get_dofs(), np.array([y]))
np.testing.assert_allclose(iden.fixed, np.array([False]))
def test_solve_quadratic_fixed_supplying_objects(self):
"""
Same as test_solve_quadratic_fixed, except supplying objects
rather than functions as targets.
"""
for solver in solvers:
iden1 = Identity()
iden2 = Identity()
iden3 = Identity()
iden1.x = 4
iden2.x = 5
iden3.x = 6
iden1.names = ['x1']
iden2.names = ['x2']
iden3.names = ['x3']
iden1.fixed = [True]
iden3.fixed = [True]
term1 = [iden1, 1, 1]
term2 = [iden2, 2, 1 / 4.]
term3 = [iden3, 3, 1 / 9.]
prob = LeastSquaresProblem([term1, term2, term3])
solver(prob)
self.assertAlmostEqual(prob.objective(), 10)
self.assertAlmostEqual(iden1.x, 4)
self.assertAlmostEqual(iden2.x, 2)
self.assertAlmostEqual(iden3.x, 6)
def test_solve_quadratic_fixed_supplying_properties(self):
"""
Same as test_solve_quadratic_fixed, except supplying @properties
rather than functions as targets.
"""
for solver in solvers:
iden1 = Identity()
iden2 = Identity()
iden3 = Identity()
iden1.x = 4
iden2.x = 5
iden3.x = 6
iden1.names = ['x1']
iden2.names = ['x2']
iden3.names = ['x3']
iden1.fixed = [True]
iden3.fixed = [True]
# Try a mix of explicit LeastSquaresTerms and lists
term1 = [iden1, 'f', 1, 1]
term2 = [iden2, 'f', 2, 1 / 4.]
term3 = LeastSquaresTerm.from_sigma(Target(iden3, 'f'), 3, sigma=3)
prob = LeastSquaresProblem([term1, term2, term3])
solver(prob)
self.assertAlmostEqual(prob.objective(), 10)
self.assertAlmostEqual(iden1.x, 4)
self.assertAlmostEqual(iden2.x, 2)
self.assertAlmostEqual(iden3.x, 6)
def test_solve_quadratic_fixed(self):
"""
Same as test_solve_quadratic, except with different weights and x
and z are fixed, so only y is optimized.
"""
for solver in solvers:
iden1 = Identity()
iden2 = Identity()
iden3 = Identity()
iden1.x = 4
iden2.x = 5
iden3.x = 6
iden1.names = ['x1']
iden2.names = ['x2']
iden3.names = ['x3']
iden1.fixed = [True]
iden3.fixed = [True]
term1 = (iden1.J, 1, 1)
term2 = (iden2.J, 2, 1 / 4.)
term3 = (iden3.J, 3, 1 / 9.)
prob = LeastSquaresProblem([term1, term2, term3])
solver(prob)
self.assertAlmostEqual(prob.objective(), 10)
self.assertAlmostEqual(iden1.x, 4)
self.assertAlmostEqual(iden2.x, 2)
self.assertAlmostEqual(iden3.x, 6)
def test_circular4(self):
"""
Verify that a circular dependency among 4 objects is detected.
"""
o1 = Identity()
o2 = Identity()
o3 = Identity()
o4 = Identity()
o1.depends_on = ["o2"]
o2.depends_on = ["o3"]
o3.depends_on = ["o4"]
o4.depends_on = ["o1"]
o1.o2 = o2
o2.o3 = o3
o3.o4 = o4
o4.o1 = o1
with self.assertRaises(RuntimeError):
get_owners(o1)
from simsopt.objectives.functions import Identity from simsopt.objectives.least_squares import LeastSquaresProblem from simsopt.solve.serial import least_squares_serial_solve """ Minimize f(x,y,z) = ((x-1)/1)^2 + ((y-2)/2)^2 + ((z-3)/3)^2. The optimum is at (x,y,z)=(1,2,3), and f=0 at this point. """ # To print out diagnostic information along the way, uncomment this # next line: #logging.basicConfig(level=logging.INFO) # Define some Target objects that depend on Parameter objects. In the # future these functions would involve codes like VMEC, but for now we # just use the functions f(x) = x. iden1 = Identity() iden2 = Identity() iden3 = Identity() # Parameters are all not fixed by default, meaning they will not be # optimized. You can choose to exclude any subset of the parameters # from the space of independent variables by setting their 'fixed' # property to True. #iden1.fixed[0] = True #iden2.fixed[0] = True #iden3.fixed[0] = True # Each Target is then equipped with a shift and weight, to become a # term in a least-squares objective function term1 = (iden1, 1, 1) term2 = (iden2, 2, 2)