def analytic_soln(t, initial_conditions):
c1 = initial_conditions[0]
c2 = initial_conditions[1] - 1
return D.stack([
c2 * D.sin(D.to_float(D.asarray(t))) + c1 * D.cos(D.to_float(D.asarray(t))) + D.asarray(t),
c2 * D.cos(D.to_float(D.asarray(t))) - c1 * D.sin(D.to_float(D.asarray(t))) + 1
])
def analytic_soln(t, initial_conditions):
c1 = initial_conditions[0]
c2 = initial_conditions[1] - 1
return D.array([
c2 * D.sin(t) + c1 * D.cos(t) + t,
c2 * D.cos(t) - c1 * D.sin(t) + 1
])
def true_solution_sho(t, initial_state, k, m):
w2 = D.array(k / m).to(device)
w = D.sqrt(w2)
A = D.sqrt(initial_state[0]**2 + initial_state[1]**2 / w2)
phi = D.atan2(-initial_state[1], w * initial_state[0])
return D.stack([A * D.cos(w * t + phi), -w * A * D.sin(w * t + phi)]).T
def test_sin_within_tolerance(ffmt):
D.set_float_fmt(ffmt)
pi = D.to_float(D.pi)
assert (-2 * D.epsilon() <= D.sin(pi) <= 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()))
