def test_accuracy_comparison_illcond(target_conds=None):
if target_conds is None:
target_conds = [10 ** k for k in range(1, 2)]
kernels = [
sum,
numpy.sum,
accupy.kahan_sum,
lambda p: accupy.ksum(p, K=2),
lambda p: accupy.ksum(p, K=3),
accupy.fsum,
]
labels = [
"sum",
"numpy.sum",
"accupy.kahan_sum",
"accupy.ksum[2]",
"accupy.ksum[3]",
"accupy.fsum",
]
colors = plt.rcParams["axes.prop_cycle"].by_key()["color"][: len(labels)]
data = numpy.empty((len(target_conds), len(kernels)))
condition_numbers = numpy.empty(len(target_conds))
numpy.random.seed(0)
for k, target_cond in enumerate(target_conds):
p, ref, C = accupy.generate_ill_conditioned_sum(1000, target_cond)
condition_numbers[k] = C
data[k] = [abs(kernel(p) - ref) / abs(ref) for kernel in kernels]
# sort
s = numpy.argsort(condition_numbers)
condition_numbers = condition_numbers[s]
data = data[s]
for label, color, d in zip(labels, colors, data.T):
plt.loglog(condition_numbers, d, label=label, color=color)
lgd = plt.legend(bbox_to_anchor=(1.05, 1), loc=2, borderaxespad=0.0)
plt.grid()
plt.ylim(5.0e-18, 1.0)
plt.xlabel("condition number")
plt.ylabel("relative error")
plt.gca().set_aspect(1.3)
# plt.show()
# <https://stackoverflow.com/a/10154763/353337>
plt.savefig(
"accuracy-sums.png",
transparent=True,
bbox_extra_artists=(lgd,),
bbox_inches="tight",
)
return
def test_accuracy_comparison_illcond(filename=None, target_conds=None):
plt.style.use(dufte.style)
if target_conds is None:
target_conds = [10 ** k for k in range(1, 2)]
kernels = [
sum,
numpy.sum,
accupy.kahan_sum,
lambda p: accupy.ksum(p, K=2),
lambda p: accupy.ksum(p, K=3),
accupy.fsum,
]
labels = [
"sum",
"numpy.sum",
"accupy.kahan_sum",
"accupy.ksum[2]",
"accupy.ksum[3]",
"accupy.fsum",
]
colors = plt.rcParams["axes.prop_cycle"].by_key()["color"][: len(labels)]
data = numpy.empty((len(target_conds), len(kernels)))
condition_numbers = numpy.empty(len(target_conds))
numpy.random.seed(0)
for k, target_cond in enumerate(target_conds):
p, ref, C = accupy.generate_ill_conditioned_sum(1000, target_cond)
condition_numbers[k] = C
data[k] = [abs(kernel(p) - ref) / abs(ref) for kernel in kernels]
# sort
s = numpy.argsort(condition_numbers)
condition_numbers = condition_numbers[s]
data = data[s]
for label, color, d in zip(labels, colors, data.T):
plt.loglog(condition_numbers, d, label=label, color=color)
dufte.legend()
plt.xlabel("condition number")
plt.ylabel("relative error")
# plt.gca().set_aspect(1.3)
# plt.show()
# <https://stackoverflow.com/a/10154763/353337>
if filename:
plt.savefig(filename, transparent=True, bbox_inches="tight")
def test_fsum(cond):
p, ref, _ = accupy.generate_ill_conditioned_sum(100, cond)
assert abs(accupy.fsum(p) - ref) < 1.0e-15 * abs(ref)
return
def test_ksum3(cond):
p, ref, _ = accupy.generate_ill_conditioned_sum(100, cond)
assert abs(accupy.ksum(p, K=3) - ref) < 1.0e-15 * abs(ref)