x0 = array([v[0], 1., 0.]) x = explicit_euler(x0,f1,ts,p,q) h = measurement_model(x[:,0],p,q) etas = h + numpy.random.normal(size=Nm) p[0]-= 3.; p[1] -= 2. # taping F av = array([adolc.adouble(0) for i in range(Nv)]) y = zeros(Nm) adolc.trace_on(1) av[0].is_independent(p[0]) av[1].is_independent(p[1]) av[2].is_independent(q[0]) ay = F(av[:Np],av[Np:],ts,Sigma,etas) for m in range(Nm): y[m] = adolc.depends_on(ay[m]) adolc.trace_off() # taping dFdp av = array([adolc.adouble(0) for i in range(Nv)]) adolc.trace_on(1) av[0].is_independent(p[0]) av[1].is_independent(p[1]) av[2].is_independent(q[0]) ay = dFdp(av[:Np],av[Np:],ts,Sigma,etas) for m in range(Nm): for n in range(Np): adolc.dependent(ay[m,n]) adolc.trace_off() # tape the objective function with Algopy
return 0.5*array( [[(x[0]-17.)*(x[0]-17.), (x[0]-17.)*(x[0]-17.)], [ x[1]-19. , x[1]-19.]]) # TAPING THE FUNCTIONS # -------------------- # taping function ffcn u = 3.; v = 7. ax = array([adolc.adouble(u), adolc.adouble(v)]) adolc.trace_on(1) ax[0].is_independent(u) ax[1].is_independent(v) ay = ffcn(ax) for n in range(2): for m in range(2): adolc.depends_on(ay[n,m]) adolc.trace_off() # taping matrix functions with algopy x = array([u,v]) F = ffcn(x) Fdot = zeros((2,2)) cg = CGraph() FF = Function(Mtc(F)) Fy = Phi(FF) cg.independentFunctionList = [FF] cg.dependentFunctionList = [Fy] # COMPUTING THE HESSIAN H = d^2 Phi/ dx^2 # --------------------------------------- # need for that to propagate two directions
tape_eval_times.append(end_time - start_time)
## reverse evaluation
start_time = time()
g_reverse2 = rm.gradient_from_graph(cg)
end_time = time()
rev_eval_times.append(end_time - start_time)
## PyADOLC taping
start_time = time()
ax = numpy.array([adolc.adouble(0.) for i in range(N)])
adolc.trace_on(0)
for n in range(N):
ax[n].is_independent(x[n])
ay = f(ax)
adolc.depends_on(ay)
adolc.trace_off()
end_time = time()
adolc_tape_times.append(end_time - start_time)
## PyADOLC gradient
start_time = time()
adolc_g = adolc.gradient(0, x)
end_time = time()
adolc_gradient_times.append(end_time - start_time)
### check that both derivatives give the same result
#print 'difference between forward and reverse gradient computation', numpy.linalg.norm(g_forward - g_reverse)
#print 'difference between forward and reverse gradient2 computation', numpy.linalg.norm(g_forward - g_reverse2)
#print 'difference between Algopy and PyAdolc', numpy.linalg.norm(adolc_g - g_reverse2)
tape_eval_times.append(end_time - start_time)
## reverse evaluation
start_time = time()
g_reverse2 = rm.gradient_from_graph(cg)
end_time = time()
rev_eval_times.append(end_time - start_time)
## PyADOLC taping
start_time = time()
ax = numpy.array([adolc.adouble(0.0) for i in range(N)])
adolc.trace_on(0)
for n in range(N):
ax[n].is_independent(x[n])
ay = f(ax)
adolc.depends_on(ay)
adolc.trace_off()
end_time = time()
adolc_tape_times.append(end_time - start_time)
## PyADOLC gradient
start_time = time()
adolc_g = adolc.gradient(0, x)
end_time = time()
adolc_gradient_times.append(end_time - start_time)
### check that both derivatives give the same result
# print 'difference between forward and reverse gradient computation', numpy.linalg.norm(g_forward - g_reverse)
# print 'difference between forward and reverse gradient2 computation', numpy.linalg.norm(g_forward - g_reverse2)
# print 'difference between Algopy and PyAdolc', numpy.linalg.norm(adolc_g - g_reverse2)
