def d_target_d_alphas_finite(obs, alphas, eps=1.e-8):
result = []
for i_alpha in xrange(len(alphas)):
alphas_eps = list(alphas)
ts = []
for signed_eps in [eps, -eps]:
alphas_eps[i_alpha] = alphas[i_alpha] + signed_eps
exp_sum = exp_i_alpha_sum(alphas=alphas_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
ts.append(target.f())
result.append((ts[0] - ts[1]) / (2 * eps))
return result
def d_target_d_alphas_finite(obs, alphas, eps=1.0e-8):
result = []
for i_alpha in xrange(len(alphas)):
alphas_eps = list(alphas)
ts = []
for signed_eps in [eps, -eps]:
alphas_eps[i_alpha] = alphas[i_alpha] + signed_eps
exp_sum = exp_i_alpha_sum(alphas=alphas_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
ts.append(target.f())
result.append((ts[0] - ts[1]) / (2 * eps))
return result
def d2_target_d_alphas_finite(obs, alphas, eps=1.e-8):
result = []
for i_alpha in xrange(len(alphas)):
alphas_eps = list(alphas)
gs = []
for signed_eps in [eps, -eps]:
alphas_eps[i_alpha] = alphas[i_alpha] + signed_eps
exp_sum = exp_i_alpha_sum(alphas=alphas_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
dalphas = exp_sum.d_target_d_alphas(target=target)
gs.append(dalphas)
result.append([(gp - gm) / (2 * eps) for gp, gm in zip(gs[0], gs[1])])
return result
def d2_target_d_alphas_finite(obs, alphas, eps=1.0e-8):
result = []
for i_alpha in xrange(len(alphas)):
alphas_eps = list(alphas)
gs = []
for signed_eps in [eps, -eps]:
alphas_eps[i_alpha] = alphas[i_alpha] + signed_eps
exp_sum = exp_i_alpha_sum(alphas=alphas_eps)
target = least_squares(obs=obs, calc=exp_sum.f())
dalphas = exp_sum.d_target_d_alphas(target=target)
gs.append(dalphas)
result.append([(gp - gm) / (2 * eps) for gp, gm in zip(gs[0], gs[1])])
return result
def compare_analytical_and_finite(obs, alphas, out):
grads_fin = d_target_d_alphas_finite(obs=obs, alphas=alphas)
print >> out, "grads_fin:", grads_fin
exp_sum = exp_i_alpha_sum(alphas=alphas)
target = least_squares(obs=obs, calc=exp_sum.f())
grads_ana = exp_sum.d_target_d_alphas(target=target)
print >> out, "grads_ana:", grads_ana
assert approx_equal(grads_ana, grads_fin)
curvs_fin = d2_target_d_alphas_finite(obs=obs, alphas=alphas)
print >> out, "curvs_fin:", curvs_fin
curvs_ana = exp_sum.d2_target_d_alphas(target=target)
print >> out, "curvs_ana:", curvs_ana
assert approx_equal(curvs_ana, curvs_fin)
print >> out
def compare_analytical_and_finite(obs, alphas, out):
grads_fin = d_target_d_alphas_finite(obs=obs, alphas=alphas)
print >> out, "grads_fin:", grads_fin
exp_sum = exp_i_alpha_sum(alphas=alphas)
target = least_squares(obs=obs, calc=exp_sum.f())
grads_ana = exp_sum.d_target_d_alphas(target=target)
print >> out, "grads_ana:", grads_ana
assert approx_equal(grads_ana, grads_fin)
curvs_fin = d2_target_d_alphas_finite(obs=obs, alphas=alphas)
print >> out, "curvs_fin:", curvs_fin
curvs_ana = exp_sum.d2_target_d_alphas(target=target)
print >> out, "curvs_ana:", curvs_ana
assert approx_equal(curvs_ana, curvs_fin)
print >> out
def exercise(args):
verbose = "--verbose" in args
if (not verbose):
out = StringIO()
else:
out = sys.stdout
for n_alphas in xrange(2, 5):
for i_trial in xrange(5):
alphas = [2 * math.pi * random.random() for i in xrange(n_alphas)]
exp_sum = exp_i_alpha_sum(alphas=alphas)
obs = abs(exp_sum.f())
compare_analytical_and_finite(obs=obs, alphas=alphas, out=out)
compare_analytical_and_finite(obs=obs * (random.random() + 0.5),
alphas=alphas,
out=out)
for obs in [0, 0.1]:
for calc in [0j, 1.e-200j]:
target = least_squares(obs=obs, calc=calc)
assert target.f() == obs**2
assert target.da() == 0
assert target.db() == 0
if (obs == 0):
assert target.daa() == 2
assert target.dbb() == 2
assert target.dab() == 0
else:
assert target.daa() == -1.e160
assert target.dbb() == -1.e160
assert target.dab() == 1.e160
calc = 1 + 1j
while (calc != 0):
target = least_squares(obs=obs, calc=calc)
# exercise numerical stability without checking the results
target.f()
target.da()
target.db()
target.daa()
target.dbb()
target.dab()
calc /= 2
print "OK"
def exercise(args):
verbose = "--verbose" in args
if not verbose:
out = StringIO()
else:
out = sys.stdout
for n_alphas in xrange(2, 5):
for i_trial in xrange(5):
alphas = [2 * math.pi * random.random() for i in xrange(n_alphas)]
exp_sum = exp_i_alpha_sum(alphas=alphas)
obs = abs(exp_sum.f())
compare_analytical_and_finite(obs=obs, alphas=alphas, out=out)
compare_analytical_and_finite(obs=obs * (random.random() + 0.5), alphas=alphas, out=out)
for obs in [0, 0.1]:
for calc in [0j, 1.0e-200j]:
target = least_squares(obs=obs, calc=calc)
assert target.f() == obs ** 2
assert target.da() == 0
assert target.db() == 0
if obs == 0:
assert target.daa() == 2
assert target.dbb() == 2
assert target.dab() == 0
else:
assert target.daa() == -1.0e160
assert target.dbb() == -1.0e160
assert target.dab() == 1.0e160
calc = 1 + 1j
while calc != 0:
target = least_squares(obs=obs, calc=calc)
# exercise numerical stability without checking the results
target.f()
target.da()
target.db()
target.daa()
target.dbb()
target.dab()
calc /= 2
print "OK"
