def _print_summary(method, order, x_values, scales):
print(scales)
header = 'method="{}", order={}, x_values={}:'.format(
method, order, str(x_values))
print(header)
for n in scales:
print('n={}, mean scale={:.2f}, median scale={:.2f}'.format(
n, np.mean(scales[n]), np.median(scales[n])))
print('Default scale with ' + header)
for n in scales:
print('n={}, scale={:.2f}'.format(n, default_scale(method, n, order)))
def benchmark(x=0.0001,
dfun=None,
fd=None,
name='',
scales=None,
show_plot=True):
if scales is None:
scales = np.arange(1.0, 35, 0.25)
n, method, order = fd.n, fd.method, fd.order
if dfun is None:
return dict(n=n,
order=order,
method=method,
fun=name,
error=np.nan,
scale=np.nan,
x=np.nan)
relativ_errors = _compute_relative_errors(x, dfun, fd, scales)
if not np.isfinite(relativ_errors).any():
return dict(n=n,
order=order,
method=method,
fun=name,
error=np.nan,
scale=np.nan)
if show_plot:
txt = ['', "1'st", "2'nd", "3'rd", "4'th", "5'th", "6'th", "7th"
] + ["%d'th" % i for i in range(8, 25)]
title = "The %s derivative using %s, order=%d" % (txt[n], method,
order)
scale0 = default_scale(method, n, order)
plot_error(scales, relativ_errors, scale0, title, label=name)
i = np.nanargmin(relativ_errors)
error = float('{:.3g}'.format(relativ_errors[i]))
return dict(n=n,
order=order,
method=method,
fun=name,
error=error,
scale=scales[i],
x=x)
def test_default_scale():
for method, scale in zip(
['complex', 'central', 'forward', 'backward', 'multicomplex'],
[1.35, 2.5, 2.5, 2.5, 1.35]):
assert_allclose(scale, default_scale(method, n=1))
def _example3(x=0.0001,
fun_name='cos',
epsilon=None,
method='central',
scale=None,
n=1,
order=2):
fun0, dfun = get_function(fun_name, n)
if dfun is None:
return dict(n=n,
order=order,
method=method,
fun=fun_name,
error=np.nan,
scale=np.nan)
fd = Derivative(fun0, step=epsilon, method=method, n=n, order=order)
t = []
scales = np.arange(1.0, 35, 0.25)
for scale in scales:
fd.step.scale = scale
try:
val = fd(x)
except Exception:
val = np.nan
t.append(val)
t = np.array(t)
tt = dfun(x)
relativ_error = np.abs(t - tt) / (np.maximum(np.abs(tt), 1)) + 1e-16
# weights = np.ones((3,))/3
# relativ_error = convolve1d(relativ_error, weights) # smooth curve
if np.isnan(relativ_error).all():
return dict(n=n,
order=order,
method=method,
fun=fun_name,
error=np.nan,
scale=np.nan)
if True: # False: #
plt.semilogy(scales, relativ_error, label=fun_name)
plt.vlines(default_scale(fd.method, n, order),
np.nanmin(relativ_error), 1)
plt.xlabel('scales')
plt.ylabel('Relative error')
txt = ['', "1'st", "2'nd", "3'rd", "4'th", "5'th", "6'th", "7th"
] + ["%d'th" % i for i in range(8, 25)]
plt.title("The %s derivative using %s, order=%d" %
(txt[n], method, order))
plt.legend(frameon=False, framealpha=0.5)
plt.axis([min(scales), max(scales), np.nanmin(relativ_error), 1])
# plt.figure()
# plt.show('hold')
i = np.nanargmin(relativ_error)
return dict(n=n,
order=order,
method=method,
fun=fun_name,
error=relativ_error[i],
scale=scales[i])
order=order)
print(r)
scale_n = scales.setdefault(n, [])
scale = r['scale']
if np.isfinite(scale):
scale_n.append(scale)
plt.vlines(np.mean(scale_n), 1e-12, 1, 'r', linewidth=3)
print(scales)
print('method={}, order={}'.format(method, order))
for n in scales:
print('n={}, scale={}'.format(n, np.mean(scales[n])))
print('Default scale')
for n in scales:
print('n={}, scale={}'.format(n, default_scale(method, n, order)))
plt.show('hold')
# method=complex, order=2
# n=1, scale=1.05188679245
# n=2, scale=5.55424528302
# n=3, scale=8.34669811321
# n=4, scale=9.08072916667
# n=5, scale=10.1958333333
# n=6, scale=9.13020833333
# n=7, scale=13.859375
# n=8, scale=14.125
# n=9, scale=12.8385416667
# n=10, scale=14.5416666667
def test_default_scale():
for method, scale in zip(['complex', 'central', 'forward', 'backward',
'multicomplex'],
[1.35, 2.5, 2.5, 2.5, 1.35]):
np.testing.assert_allclose(scale, default_scale(method, n=1))