def test_jacobian_wrapper_no_adaptive(ffmt): D.set_float_fmt(ffmt) rhs = lambda x: D.exp(-x) drhs_exact = lambda x: -D.exp(-x) jac_rhs = de.utilities.JacobianWrapper(rhs, richardson_iter=4, adaptive=False, rtol=D.epsilon() ** 0.5, atol=D.epsilon() ** 0.5) x = D.array(0.0) assert (D.allclose(D.to_float(drhs_exact(x)), D.to_float(jac_rhs(x)), rtol=4 * D.epsilon() ** 0.5, atol=4 * D.epsilon() ** 0.5))
def test_exp_within_tolerance(ffmt): D.set_float_fmt(ffmt) pi = D.to_float(D.pi) assert (23.1406926327792690 - 10 * D.epsilon() <= D.exp(pi) <= 23.1406926327792690 + 10 * D.epsilon())
def true_solution_decay(t, initial_state, k): return initial_state * D.exp(-k * t)
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()))