def test_param_shift_2q(pl_op, braket_gate, angle, observable):
"""Tests that the parameter-shift rules of custom operations yield the correct derivatives."""
op = pl_op(angle, wires=[0, 1])
if op.grad_recipe[0]:
shifts = op.grad_recipe[0]
else:
orig_shifts = qml.gradients.generate_shift_rule(
op.parameter_frequencies[0])
shifts = [[c, 1, s] for c, s in orig_shifts]
summands = []
for shift in shifts:
shifted = pl_op.compute_matrix(angle + shift[2])
summands.append(shift[0] * np.matmul(
np.matmul(np.transpose(np.conj(shifted)), observable), shifted))
from_shifts = sum(summands)
def conj_obs_gate(angle):
mat = pl_op.compute_matrix(angle)
return anp.matmul(anp.matmul(anp.transpose(anp.conj(mat)), observable),
mat)
direct_calculation = deriv(conj_obs_gate)(angle)
assert np.allclose(from_shifts, direct_calculation)
def inner(ws):
result = []
for li in range(len(ws)):
ll = ws[li]
result.append([[
deriv(lambda x: f(
replace_ith(
ws, li,
replace_ith(ws[li], ui, replace_ith(ws[li][ui], wi, x))
)))(ws[li][ui][wi]) for wi in range(len(ll[ui]))
] for ui in range(len(ll))])
return result
def test_van_genuchten(theta):
params = {
'Ks': 42,
'alpha': 0.0123,
'l': 0.27,
'm': 0.3142,
'theta_range': (0.123, 0.654)
}
D = fronts.D.van_genuchten(**params)
assert np.all(D(theta, 1)[0] == D(theta))
assert np.all(D(theta, 2)[0] == D(theta))
assert np.all(D(theta, 1)[1] == D(theta, 2)[1])
D_ref = functools.partial(van_genuchten_D, **params)
assert D(theta) == pytest.approx(D_ref(theta))
assert D(theta, 1)[1] == pytest.approx(deriv(D_ref)(theta))
assert D(theta, 2)[2] == pytest.approx(deriv(deriv(D_ref))(theta),
rel=1e-5)
def mrf_ir_fisp_efficient_crb_forward_differentiation(M0, FAs, TEs, TRs,
inversion_delay, T1, T2):
deriv_fn_T1 = deriv(mrf_ir_fisp_real,
get_arg_index(mrf_ir_fisp_real, 'T1'))
deriv_fn_T2 = deriv(mrf_ir_fisp_real,
get_arg_index(mrf_ir_fisp_real, 'T2'))
#deriv_fn_M0 = deriv(mrf_ir_fisp_real, get_arg_index(mrf_ir_fisp_real, 'M0'))
m_echos = mrf_ir_fisp_real(M0, FAs, TEs, TRs, inversion_delay, T1, T2)
fim_T1 = np.transpose(
deriv_fn_T1(M0, FAs, TEs, TRs, inversion_delay, T1, T2))
fim_T2 = np.transpose(
deriv_fn_T2(M0, FAs, TEs, TRs, inversion_delay, T1, T2))
#fim_M0 = np.transpose(deriv_fn_M0(M0, FAs, TEs, TRs, inversion_delay, T1, T2))
# if M0 == 1.0 (which should always be done - you can just weight the W crlb differently)
# then this is true so we can save a bit of computation, for N_TR = 1000, 10 EPG states, this lets us go from
# 22 -> 18.5 +/- 0.845 seconds for calculation of grad (using %%timeit)
fim_M0 = np.transpose(m_echos)
return m_echos, fim_M0, fim_T1, fim_T2
def test_deriv():
def fun(x):
return (x + np.sin(x**2)) * x
assert 3.190948746871 - 1e-6 < deriv(fun)(1.3) < 3.190948746871 + 1e-6
def test_no_jvp_def():
fun = primitive(lambda x: 2. * x)
with pytest.raises(NotImplementedError):
deriv(fun)(1.)
def inner(x):
return [
deriv(lambda xi: f(replace_ith(x, i, xi)))(x[i])
for i in range(len(x))
]
def test_no_jvp_def():
fun = primitive(lambda x: 2. * x)
deriv(fun)(1.)
def test_array_creation_fwd():
def fun(x, N):
arr = [x for i in range(N)]
return np.sum(np.array(arr))
assert_linear_time(lambda N: deriv(fun)(1.0, 400 * N))
def test_list_creation():
def fun(x, N):
return make_list(*[x for _ in range(N)])
assert_linear_time(lambda N: deriv(fun)(0.0, 20 * N))
def test_deriv():
def fun(x): return (x + np.sin(x**2)) * x
assert 3.190948746871 - 1e-6 < deriv(fun)(1.3) < 3.190948746871 + 1e-6
def test_array_creation_fwd():
def fun(x, N):
arr = [x for i in range(N)]
return np.sum(np.array(arr))
assert_linear_time(lambda N: deriv(fun)(1.0, 400*N))
def test_list_creation():
def fun(x, N):
return make_list(*[x for _ in range(N)])
assert_linear_time(lambda N: deriv(fun)(0.0, 20*N))
def test_no_jvp_def():
fun = primitive(lambda x: 2. * x)
deriv(fun)(1.)