def test_gradients_complex(ffmt, integrator, use_richardson_extrapolation,
device):
if use_richardson_extrapolation and integrator.__implicit__:
pytest.skip(
"Richardson Extrapolation is too slow with implicit methods")
D.set_float_fmt(ffmt)
print("Testing {} float format".format(D.float_fmt()))
import torch
torch.set_printoptions(precision=17)
device = torch.device(device)
torch.autograd.set_detect_anomaly(False) # Enable if a test fails
class NNController(torch.nn.Module):
def __init__(self,
in_dim=2,
out_dim=2,
inter_dim=50,
append_time=False):
super().__init__()
self.append_time = append_time
self.net = torch.nn.Sequential(
torch.nn.Linear(in_dim + (1 if append_time else 0), inter_dim),
torch.nn.Softplus(), torch.nn.Linear(inter_dim, out_dim),
torch.nn.Sigmoid())
for idx, m in enumerate(self.net.modules()):
if isinstance(m, torch.nn.Linear):
torch.nn.init.xavier_normal_(m.weight, gain=1.0)
torch.nn.init.constant_(m.bias, 0.0)
def forward(self, t, y, dy):
if self.append_time:
return self.net(
torch.cat([y.view(-1), dy.view(-1),
t.view(-1)]))
else:
return self.net(torch.cat([y, dy]))
class SimpleODE(torch.nn.Module):
def __init__(self, inter_dim=10, k=1.0):
super().__init__()
self.nn_controller = NNController(in_dim=4,
out_dim=1,
inter_dim=inter_dim)
self.A = torch.nn.Parameter(
torch.tensor([[0.0, 1.0], [-k, -1.0]], requires_grad=False))
def forward(self, t, y, params=None):
if not isinstance(t, torch.Tensor):
torch_t = torch.tensor(t)
else:
torch_t = t
if not isinstance(y, torch.Tensor):
torch_y = torch.tensor(y)
else:
torch_y = y
if params is not None:
if not isinstance(params, torch.Tensor):
torch_params = torch.tensor(params)
else:
torch_params = params
dy = torch.matmul(self.A, torch_y)
controller_effect = self.nn_controller(
torch_t, torch_y, dy) if params is None else params
return dy + torch.cat(
[torch.tensor([0.0]).to(dy), (controller_effect * 2.0 - 1.0)])
method = integrator
if use_richardson_extrapolation:
method = de.integrators.generate_richardson_integrator(method)
with de.utilities.BlockTimer(section_label="Integrator Tests"):
yi1 = D.array([1.0, 0.0], requires_grad=True).to(device)
df = SimpleODE(k=1.0)
a = de.OdeSystem(df,
yi1,
t=(0, 0.1),
dt=1e-3,
rtol=D.epsilon()**0.5,
atol=D.epsilon()**0.5)
a.set_method(method)
print("Testing {} with dt = {:.4e}".format(a.integrator, a.dt))
a.integrate(eta=True)
dyfdyi = D.jacobian(a.y[-1], a.y[0])
dyi = D.array([0.0, 1.0]).to(device) * D.epsilon()**0.5
dyf = D.einsum("nk,k->n", dyfdyi, dyi)
yi2 = yi1 + dyi
print(a.y[-1].device)
b = de.OdeSystem(df,
yi2,
t=(0, a.t[-1]),
dt=a.dt,
rtol=a.rtol,
atol=a.atol)
b.set_method(method)
b.integrate(eta=True)
true_diff = b.y[-1] - a.y[-1]
print(D.norm(true_diff - dyf), D.epsilon()**0.5)
assert (D.allclose(true_diff, dyf, rtol=4 * a.rtol, atol=4 * a.atol))
print("{} method test succeeded!".format(a.integrator))
print("")
print("{} backend test passed successfully!".format(D.backend()))
def test_gradients():
for ffmt in D.available_float_fmt():
D.set_float_fmt(ffmt)
print("Testing {} float format".format(D.float_fmt()))
import torch
torch.set_printoptions(precision=17)
torch.set_num_threads(1)
torch.autograd.set_detect_anomaly(True)
class NNController(torch.nn.Module):
def __init__(self,
in_dim=2,
out_dim=2,
inter_dim=50,
append_time=False):
super().__init__()
self.append_time = append_time
self.net = torch.nn.Sequential(
torch.nn.Linear(in_dim + (1 if append_time else 0),
inter_dim), torch.nn.Softplus(),
torch.nn.Linear(inter_dim, out_dim), torch.nn.Sigmoid())
for idx, m in enumerate(self.net.modules()):
if isinstance(m, torch.nn.Linear):
torch.nn.init.xavier_normal_(m.weight, gain=1.0)
torch.nn.init.constant_(m.bias, 0.0)
def forward(self, t, y, dy):
if self.append_time:
return self.net(
torch.cat([y.view(-1),
dy.view(-1),
t.view(-1)]))
else:
return self.net(torch.cat([y, dy]))
class SimpleODE(torch.nn.Module):
def __init__(self, inter_dim=10, k=1.0):
super().__init__()
self.nn_controller = NNController(in_dim=4,
out_dim=1,
inter_dim=inter_dim)
self.A = torch.tensor([[0.0, 1.0], [-k, -1.0]],
requires_grad=True)
def forward(self, t, y, params=None):
if not isinstance(t, torch.Tensor):
torch_t = torch.tensor(t)
else:
torch_t = t
if not isinstance(y, torch.Tensor):
torch_y = torch.tensor(y)
else:
torch_y = y
if params is not None:
if not isinstance(params, torch.Tensor):
torch_params = torch.tensor(params)
else:
torch_params = params
dy = torch.matmul(self.A, torch_y)
controller_effect = self.nn_controller(
torch_t, torch_y, dy) if params is None else params
return dy + torch.cat(
[torch.tensor([0.0]), (controller_effect * 2.0 - 1.0)])
with de.utilities.BlockTimer(section_label="Integrator Tests"):
for i in sorted(set(de.available_methods(False).values()),
key=lambda x: x.__name__):
try:
yi1 = D.array([1.0, 0.0], requires_grad=True)
df = SimpleODE(k=1.0)
a = de.OdeSystem(df,
yi1,
t=(0, 1.),
dt=0.0675,
rtol=D.epsilon()**0.5,
atol=D.epsilon()**0.5)
a.set_method(i)
a.integrate(eta=True)
dyfdyi = D.jacobian(a.y[-1], a.y[0])
dyi = D.array([0.0, 1.0]) * D.epsilon()**0.5
dyf = D.einsum("nk,k->n", dyfdyi, dyi)
yi2 = yi1 + dyi
b = de.OdeSystem(df,
yi2,
t=(0, 1.),
dt=0.0675,
rtol=D.epsilon()**0.5,
atol=D.epsilon()**0.5)
b.set_method(i)
b.integrate(eta=True)
true_diff = b.y[-1] - a.y[-1]
print(D.norm(true_diff - dyf), D.epsilon()**0.5)
assert (D.allclose(true_diff,
dyf,
rtol=4 * D.epsilon()**0.5,
atol=4 * D.epsilon()**0.5))
print("{} method test succeeded!".format(a.integrator))
except:
raise RuntimeError(
"Test failed for integration method: {}".format(
a.integrator))
print("")
print("{} backend test passed successfully!".format(D.backend()))
def test_einsum_within_tolerance(ffmt):
D.set_float_fmt(ffmt)
assert (-2 * D.epsilon() <= D.einsum(
"nm->", D.array([[1.0, 2.0], [-2.0, -1.0]])) <= 2 * D.epsilon())
def test_backend():
try:
import desolver as de
import desolver.backend as D
import numpy as np
import scipy
if "DES_BACKEND" in os.environ:
assert(D.backend() == os.environ['DES_BACKEND'])
if D.backend() not in ['torch']:
# Default datatype test
for i in D.available_float_fmt():
D.set_float_fmt(i)
assert(D.array(1.0).dtype == D.float_fmts[D.float_fmt()])
expected_eps = {'float16': 5e-3, 'float32': 5e-7, 'float64': 5e-16, 'gdual_double': 5e-16, 'gdual_vdouble': 5e-16, 'gdual_real128': 5e-16}
test_array = np.array([1], dtype=np.int64)
# Test Function Evals
for i in D.available_float_fmt():
D.set_float_fmt(i)
assert(D.float_fmt() == str(i))
assert(D.epsilon() == expected_eps[str(i)])
assert(isinstance(D.available_float_fmt(), list))
if not i.startswith('gdual'):
assert(D.cast_to_float_fmt(test_array).dtype == str(i))
arr1 = D.array([[2.0, 1.0],[1.0, 0.0]])
arr2 = D.array([[1.0, 1.0],[-1.0, 1.0]])
if not i.startswith('gdual'):
arr3 = D.contract_first_ndims(arr1, arr2, 1)
arr4 = D.contract_first_ndims(arr1, arr2, 2)
true_arr3 = D.array([1.0, 1.0])
true_arr4 = D.array(2.)
assert(D.norm(arr3 - true_arr3) <= 2 * D.epsilon())
assert(D.norm(arr4 - true_arr4) <= 2 * D.epsilon())
de.utilities.warning("Testing float format {}".format(D.float_fmt()))
pi = D.to_float(D.pi)
assert(np.pi - 2*D.epsilon() <= pi <= np.pi + 2*D.epsilon())
assert(np.e - 2*D.epsilon() <= D.to_float(D.e) <= np.e + 2*D.epsilon())
assert(np.euler_gamma - 2*D.epsilon() <= D.to_float(D.euler_gamma) <= np.euler_gamma + 2*D.epsilon())
assert(-2*D.epsilon() <= D.sin(pi) <= 2*D.epsilon())
assert(-2*D.epsilon() <= D.cos(pi)+1 <= 2*D.epsilon())
assert(-2*D.epsilon() <= D.tan(pi) <= 2*D.epsilon())
assert(D.asin(D.to_float(1)) == pi/2)
assert(D.acos(D.to_float(1)) == 0)
assert(D.atan(D.to_float(1)) == pi/4)
assert(D.atan2(D.to_float(1), D.to_float(1)) == pi/4)
assert(D.sinh(pi) == np.sinh(pi))
assert(D.cosh(pi) == np.cosh(pi))
assert(D.tanh(pi) == np.tanh(pi))
assert(-3.141592653589793 - 2*D.epsilon() <= D.neg(pi) <= -3.141592653589793 + 2*D.epsilon())
assert(31.00627668029982 - 10*D.epsilon() <= D.pow(pi,3) <= 31.00627668029982 + 10*D.epsilon())
assert(3.141592653589793 - 2*D.epsilon() <= D.abs(pi) <= 3.141592653589793 + 2*D.epsilon())
assert(1.77245385090551603 - 2*D.epsilon() <= D.sqrt(pi) <= 1.77245385090551603 + 2*D.epsilon())
assert(23.1406926327792690 - 10*D.epsilon()<= D.exp(pi) <= 23.1406926327792690 + 10*D.epsilon())
assert(22.1406926327792690 - 10*D.epsilon()<= D.expm1(pi) <= 22.1406926327792690 + 10*D.epsilon())
assert(1.14472988584940017 - 2*D.epsilon() <= D.log(pi) <= 1.14472988584940017 + 2*D.epsilon())
assert(1.14472988584940017 - 2*D.epsilon() <= D.log(pi) <= 1.14472988584940017 + 2*D.epsilon())
assert(0.49714987269413385 - 2*D.epsilon() <= D.log10(pi) <= 0.49714987269413385 + 2*D.epsilon())
assert(1.42108041279429263 - 2*D.epsilon() <= D.log1p(pi) <= 1.42108041279429263 + 2*D.epsilon())
assert(1.65149612947231880 - 2*D.epsilon() <= D.log2(pi) <= 1.65149612947231880 + 2*D.epsilon())
assert(4.14159265358979324 - 2*D.epsilon() <= D.add(pi,1) <= 4.14159265358979324 + 2*D.epsilon())
assert(2.14159265358979324 - 2*D.epsilon() <= D.sub(pi,1) <= 2.14159265358979324 + 2*D.epsilon())
assert(D.div(pi,1) == pi)
assert(D.mul(pi,1) == pi)
assert(0.31830988618379067 - 2*D.epsilon() <= D.reciprocal(pi) <= 0.31830988618379067 + 2*D.epsilon())
if not i.startswith('gdual'):
assert(0.14159265358979324 - 2*D.epsilon() <= D.remainder(pi,3) <= 0.14159265358979324 + 2*D.epsilon())
assert(D.ceil(pi) == 4)
assert(D.floor(pi) == 3)
assert(D.round(pi) == 3)
assert(1.1415926535897931 - 2*D.epsilon() <= D.fmod(pi,2) <= 1.1415926535897931 + 2*D.epsilon())
assert(D.clip(pi,1,2) == 2)
assert(D.sign(pi) == 1)
assert(D.trunc(pi) == 3)
assert(0.9772133079420067 - 2*D.epsilon() <= D.digamma(pi) <= 0.9772133079420067 + 2*D.epsilon())
assert(0.4769362762044699 - 2*D.epsilon() <= D.erfinv(D.to_float(0.5)) <= 0.4769362762044699 + 2*D.epsilon())
assert(1.7891115385869942 - 2*D.epsilon() <= D.mvlgamma(pi, 2) <= 1.7891115385869942 + 2*D.epsilon())
assert(D.frac(pi) == pi - 3)
assert(0.9999911238536324 - 2*D.epsilon() <= D.erf(pi) <= 0.9999911238536324 + 2*D.epsilon())
assert(8.8761463676416054e-6 - 2*D.epsilon() <= D.erfc(pi) <= 8.8761463676416054e-6 + 2*D.epsilon())
assert(0.9585761678336372 - 2*D.epsilon() <= D.sigmoid(pi) <= 0.9585761678336372 + 2*D.epsilon())
assert(0.5641895835477563 - 2*D.epsilon() <= D.rsqrt(pi) <= 0.5641895835477563 + 2*D.epsilon())
assert(pi + 0.5 - 2*D.epsilon() <= D.lerp(pi,pi+1,0.5) <= pi + 0.5 + 2*D.epsilon())
assert(D.addcdiv(pi,1,D.to_float(3),D.to_float(2)) == pi + (1 * (3 / 2)))
assert(D.addcmul(pi,1,D.to_float(3),D.to_float(2)) == pi + (1 * (3 * 2)))
if not i.startswith('gdual'):
assert(-2*D.epsilon() <= D.einsum("nm->", D.array([[1.0, 2.0], [-2.0, -1.0]])) <= 2*D.epsilon())
except:
print("{} Backend Test Failed".format(D.backend()))
raise
print("{} Backend Test Succeeded".format(D.backend()))