def test_derivative_on_log():
x = np.r_[0.01, 0.1]
for method in ['forward', 'reverse']:
dlog = nd.Derivative(np.log, method=method)
assert_array_almost_equal(dlog(x), 1.0 / x)
def test_derivative_sin():
# Evaluate the indicated (default = first)
# derivative at multiple points
for method in ['forward', 'reverse']:
dsin = nd.Derivative(np.sin, method=method)
x = np.linspace(0, 2. * np.pi, 13)
y = dsin(x)
assert_allclose(y, np.cos(x))
def test_derivative_on_sinh(self, x):
true_val = np.cosh(x)
for method in ['forward', ]: # 'reverse']: # TODO: reverse fails
dsinh = nd.Derivative(np.sinh, method=method)
val = dsinh(x)
if np.isnan(true_val):
assert np.isnan(val) == np.isnan(true_val)
else:
assert_allclose(val, true_val)
def test_high_order_derivative_cos():
true_vals = (-1.0, 0.0, 1.0, 0.0) * 5
x = np.pi / 2 # np.linspace(0, np.pi/2, 15)
for method in ['forward', 'reverse']:
nmax = 15 if method in ['forward'] else 2
for n in range(1, nmax):
d3cos = nd.Derivative(np.cos, n=n, method=method)
y = d3cos(x)
assert_allclose(y, true_vals[n - 1], atol=1e-15)
def test_derivative_on_sinh(self, x):
true_val = np.cosh(x)
for method in [
'forward',
]: # 'reverse']: # TODO: reverse fails
dsinh = nd.Derivative(np.sinh, method=method)
val = dsinh(x)
if np.isnan(true_val):
self.assertEqual(np.isnan(val), np.isnan(true_val))
else:
self.assertAlmostEqual(val, true_val)
def _a_levin(omega, f, g, d_g, x, s, basis, *args, **kwds):
def psi(t, k):
return d_g(t, *args, **kwds) * basis(t, k)
j_w = 1j * omega
nu = np.ones((len(x),), dtype=int)
nu[0] = nu[-1] = s
S = np.cumsum(np.hstack((nu, 0)))
S[-1] = 0
n = int(S[-2])
a_matrix = np.zeros((n, n), dtype=complex)
rhs = np.zeros((n,))
dff = Limit(nda.Derivative(f))
d_psi = Limit(nda.Derivative(psi))
dbasis = basis.derivative
for r, t in enumerate(x):
for j in range(S[r - 1], S[r]):
order = ((j - S[r - 1]) % nu[r]) # derivative order
dff.fun.n = order
rhs[j] = dff(t, *args, **kwds)
d_psi.fun.n = order
for k in range(n):
a_matrix[j, k] = (dbasis(t, k, n=order + 1) +
j_w * d_psi(t, k))
k1 = np.flatnonzero(1 - np.isfinite(rhs))
if k1.size > 0: # Remove singularities
warnings.warn('Singularities detected! ')
a_matrix[k1] = 0
rhs[k1] = 0
solution = linalg.lstsq(a_matrix, rhs)
v = basis.eval([-1, 1], solution[0])
lim_g = Limit(g)
g_b = np.exp(j_w * lim_g(1, *args, **kwds))
if np.isnan(g_b):
g_b = 0
g_a = np.exp(j_w * lim_g(-1, *args, **kwds))
if np.isnan(g_a):
g_a = 0
return v[1] * g_b - v[0] * g_a
def aLevinTQ(omega, ff, gg, dgg, x, s, basis, *args, **kwds):
def Psi(t, k):
return dgg(t, *args, **kwds) * basis(t, k)
j_w = 1j * omega
nu = np.ones((len(x), ), dtype=int)
nu[0] = nu[-1] = s
S = np.cumsum(np.hstack((nu, 0)))
S[-1] = 0
nn = int(S[-2])
A = np.zeros((nn, nn), dtype=complex)
F = np.zeros((nn, ))
dff = Limit(nda.Derivative(ff))
dPsi = Limit(nda.Derivative(Psi))
dbasis = basis.derivative
for r, t in enumerate(x):
for j in range(S[r - 1], S[r]):
order = ((j - S[r - 1]) % nu[r]) # derivative order
dff.f.n = order
F[j] = dff(t, *args, **kwds)
dPsi.f.n = order
for k in range(nn):
A[j, k] = (dbasis(t, k, n=order + 1) + j_w * dPsi(t, k))
k1 = np.flatnonzero(1 - np.isfinite(F))
if k1.size > 0: # Remove singularities
warnings.warn('Singularities detected! ')
A[k1] = 0
F[k1] = 0
LS = linalg.lstsq(A, F)
v = basis.eval([-1, 1], LS[0])
lim_gg = Limit(gg)
gb = np.exp(j_w * lim_gg(1, *args, **kwds))
if np.isnan(gb):
gb = 0
ga = np.exp(j_w * lim_gg(-1, *args, **kwds))
if np.isnan(ga):
ga = 0
NR = (v[1] * gb - v[0] * ga)
return NR
def test_derivative_cube():
"""Test for Issue 7"""
def cube(x):
return x * x * x
shape = (3, 2)
x = np.ones(shape) * 2
for method in ['forward', 'reverse']:
dcube = nd.Derivative(cube, method=method)
dx = dcube(x)
assert_allclose(list(dx.shape), list(shape), err_msg='Shape mismatch')
txt = 'First differing element %d\n value = %g,\n true value = %g'
for i, (val, tval) in enumerate(zip(dx.ravel(),
(3 * x ** 2).ravel())):
assert_allclose(val, tval, err_msg=txt % (i, val, tval))
def test_derivative_on_log(x):
for method in ['forward', 'reverse']:
dlog = nd.Derivative(np.log, method=method)
assert_allclose(dlog(x), 1.0 / x)
def test_derivative_exp(x):
for method in ['forward', 'reverse']:
dexp = nd.Derivative(np.exp, method=method)
assert_allclose(dexp(x), np.exp(x))
]) sys.exit() grad_fct = grad(sphere) print(grad_fct([beta_syntetic[0], beta_syntetic[0], beta_syntetic[0]])) sphere(beta_syntetic + epsilon) print(1) grad_fct = jacobian(mixedSchwefel) print(grad_fct(beta_syntetic)) np.gradient([sphere], beta_syntetic) print(2) import numdifftools.nd_algopy as nda import numdifftools as nd fd = nda.Derivative(sphere) # 1'st derivative fd = nda.Jacobian(sphere) fd(beta_syntetic) np.allclose(fd(1), 2.7182818284590424) True # #bnds = list(zip(np.repeat(-500,Nparam),np.repeat(500,Nparam))) #((0, None), (0, None)) #values=pd.DataFrame(np.zeros((Iter*N+1,N)),columns=np.arange(N),index=np.arange(Iter*N+1)) # #target=TargetClass(dim=Nparam, minf=-500.0, maxf=500.0,target_function=target_function) #x01=np.random.randint(-5,5,size=Nparam) ##print (x0[index])
def test_derivative_on_sinh(self):
for method in ['forward', ]: # 'reverse']: # TODO: reverse fails
dsinh = nd.Derivative(np.sinh, method=method)
self.assertAlmostEqual(dsinh(0.0), np.cosh(0.0))
def test_derivative_exp():
# derivative of exp(x), at x == 0
for method in ['forward', 'reverse']:
dexp = nd.Derivative(np.exp, method=method)
assert_array_almost_equal(dexp(0), np.exp(0), decimal=8)
