P = 2 * N
x = UTPM(numpy.zeros((D, P, 2 * N, 1)))
x.data[0, :] = numpy.random.rand(2 * N, 1)
x.data[1, :, :, 0] = numpy.eye(P)
y = x[N:]
x = x[:N]
# wrap the UTPM instance in a Function instance to trace all operations
# that have x as an argument
# create a CGraph instance that to store the computational trace
cg = CGraph().trace_on()
x = Function(x)
y = Function(y)
z = f(x, y)
cg.trace_off()
# define dependent and independent variables in the computational procedure
cg.independentFunctionList = [x, y]
cg.dependentFunctionList = [z]
# Since the UTPM instrance is wrapped in a Function instance we have to access it
# by y.x. That means the Jacobian is
grad1 = z.x.data[1, :, 0]
print('forward gradient g(x) = \n', grad1)
# Now we want to compute the same Jacobian in the reverse mode of AD
# before we do that we have a look what the computational graph looks like:
# print 'Computational graph is', cg
J1_tilde = dot(J1, Q2.T)
Q, R = qr(J1_tilde)
V = solve(R.T, Q2)
return dot(V.T, V)
# dimensions of the involved matrices
D, P, M, N, K, Nx = 2, 1, 5, 3, 1, 1
# trace the function evaluation of METHOD 1: nullspace method
cg1 = CGraph()
J1 = Function(UTPM(numpy.random.rand(*(D, P, M, N))))
J2 = Function(UTPM(numpy.random.rand(*(D, P, K, N))))
C = eval_covariance_matrix_qr(J1, J2)
y = C[0, 0]
cg1.trace_off()
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)
from algopy import CGraph, Function
cg = CGraph()
cg.trace_on()
x = Function(1)
y = Function(3)
z = x * y + x
cg.trace_off()
cg.independentFunctionList = [x,y]
cg.dependentFunctionList = [z]
print cg
cg.plot('example_tracer_cgraph.png')
J1_tilde = dot(J1,Q2.T)
Q,R = qr(J1_tilde)
V = solve(R.T, Q2)
return dot(V.T,V)
# dimensions of the involved matrices
D,P,M,N,K,Nx = 2,1,5,3,1,1
# trace the function evaluation of METHOD 1: nullspace method
cg1 = CGraph()
J1 = Function(UTPM(numpy.random.rand(*(D,P,M,N))))
J2 = Function(UTPM(numpy.random.rand(*(D,P,K,N))))
C = eval_covariance_matrix_qr(J1, J2)
y = C[0,0]
cg1.trace_off()
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)
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)
