def test_expm(self):
def f(x):
x = x.reshape((2,2))
return sum(expm(x))
x = numpy.random.random(2*2)
# forward mode
ax = UTPM.init_jacobian(x)
ay = f(ax)
g1 = UTPM.extract_jacobian(ay)
# reverse mode
cg = CGraph()
ax = Function(x)
ay = f(ax)
cg.independentFunctionList = [ax]
cg.dependentFunctionList = [ay]
g2 = cg.gradient(x)
assert_array_almost_equal(g1, g2)
def test_tracer_on_mixed_utpm_ndarray_mul(self):
D, P = 1, 1
A = numpy.arange(2 * 2, dtype=float).reshape(2, 2)
x = UTPM(numpy.zeros((D, P, 2, 2)))
def f(x):
return sum(A * x)
cg = CGraph()
ax = Function(x)
ay = f(ax)
cg.independentFunctionList = [ax]
cg.dependentFunctionList = [ay]
assert_array_almost_equal(A, cg.gradient(x))
def test_tracer_on_mixed_utpm_ndarray_mul(self):
D, P = 1, 1
A = numpy.arange(2 * 2, dtype=float).reshape(2, 2)
x = UTPM(numpy.zeros((D, P, 2, 2)))
def f(x):
return sum(A * x)
cg = CGraph()
ax = Function(x)
ay = f(ax)
cg.independentFunctionList = [ax]
cg.dependentFunctionList = [ay]
assert_array_almost_equal(A, cg.gradient(x))
def test_expm(self):
def f(x):
x = x.reshape((2, 2))
return sum(expm(x))
x = numpy.random.random(2 * 2)
# forward mode
ax = UTPM.init_jacobian(x)
ay = f(ax)
g1 = UTPM.extract_jacobian(ay)
# reverse mode
cg = CGraph()
ax = Function(x)
ay = f(ax)
cg.independentFunctionList = [ax]
cg.dependentFunctionList = [ay]
g2 = cg.gradient(x)
assert_array_almost_equal(g1, g2)
cg1.independentFunctionList = [J1, J2]
cg1.dependentFunctionList = [y]
print('covariance matrix: C =\n', C)
# trace the function evaluation of METHOD 2: naive method (potentially numerically unstable)
cg2 = CGraph()
J1 = Function(J1.x)
J2 = Function(J2.x)
C2 = eval_covariance_matrix_naive(J1, J2)
y = C2[0, 0]
cg2.trace_off()
cg2.independentFunctionList = [J1, J2]
cg2.dependentFunctionList = [y]
print('covariance matrix: C =\n', C2)
# check that both algorithms returns the same result
print('difference between naive and nullspace method:\n', C - C2)
# compute the gradient for another value of J1 and J2
J1 = numpy.random.rand(*(M, N))
J2 = numpy.random.rand(*(K, N))
g1 = cg1.gradient([J1, J2])
g2 = cg2.gradient([J1, J2])
print('naive approach: dy/dJ1 = ', g1[0])
print('naive approach: dy/dJ2 = ', g1[1])
print('nullspace approach: dy/dJ1 = ', g2[0])
print('nullspace approach: dy/dJ2 = ', g2[1])
cg2 = CGraph()
J1 = Function(J1.x)
J2 = Function(J2.x)
C2 = eval_covariance_matrix_naive(J1, J2)
y = C2[0,0]
cg2.trace_off()
cg2.independentFunctionList = [J1, J2]
cg2.dependentFunctionList = [y]
print('covariance matrix: C =\n',C2)
# check that both algorithms returns the same result
print('difference between naive and nullspace method:\n',C - C2)
# compute the gradient for another value of J1 and J2
J1 = numpy.random.rand(*(M,N))
J2 = numpy.random.rand(*(K,N))
g1 = cg1.gradient([J1,J2])
g2 = cg2.gradient([J1,J2])
print('naive approach: dy/dJ1 = ', g1[0])
print('naive approach: dy/dJ2 = ', g1[1])
print('nullspace approach: dy/dJ1 = ', g2[0])
print('nullspace approach: dy/dJ2 = ', g2[1])
n_p = 512 # Datenpunkte pro Periode
t = np.arange(n * n_p) / (n_p * f) # Zeitvektor
current = i_hat * (np.sin(2 * np.pi * f * t) +
0.7 * np.sin(6 * np.pi * f * t + 1)) # Stromvorgabe
H = current / (2 * np.pi * r) # Resultierende Feldvorgabe
graph = CGraph()
graph.trace_on()
x = Function([alpha, a, k, c, Msat])
# Parametervektor
p = {'alpha': x[0], 'a': x[1], 'k': x[2], 'c': x[3], 'm_sat': x[4]}
model = JilesAthertonModel.from_dict(p)
M = model.integrate_rk4(t, H)
H = H[::2]
t = t[::2]
B = mu_0 * (H + M)
dB_dt = np.zeros(np.size(B))
new = np.append([0.0], (B[1:] - B[0:-1]) / (t[1:] - t[0:-1]))
P = np.sum(0.5 * H * new)
graph.trace_off()
graph.independentFunctionList = [x]
graph.dependentFunctionList = [P]
a = graph.gradient([alpha, a, k, c, Msat])
print(a)
