def test_linear2(self):
U = (1, 2, 3, 4, 5)
d1 = 2
d2 = 2
fractal = [at.w(U, d1, d2, 3)(i) for i in [1, 3]]
self.assertAlmostEqual(U[1], fractal[0](0.5))
self.assertAlmostEqual(U[3], fractal[1](0.5))
def test_constant(self):
U = (1, 1, 1, 1, 1)
d1 = 2
d2 = 2
fractal = [at.w(U, d1, d2, 1)(i) for i in [1, 2]]
self.assertAlmostEqual(U[1], fractal[0](0.5))
self.assertAlmostEqual(U[1], fractal[1](0.5))
def draw_interpolation_scheme():
d1 = 2**(-1 / 3)
d2 = -2**(-1 / 3)
d1_1 = 2**(-1 / 5)
d2_1 = -2**(-1 / 5)
d1_2 = 2**(-1 / 11)
d2_2 = -2**(-1 / 11)
w3_13 = fractal_interpolation(at.w(UFX_SHORT, d1, d2, 3), len(UFX_SHORT))
w3_17 = fractal_interpolation(at.w(UFX_SHORT, d1_2, d2_2, 3),
len(UFX_SHORT))
w3_15 = fractal_interpolation(at.w(UFX_SHORT, d1_1, d2_1, 3),
len(UFX_SHORT))
label = {
0: '$|d_{i}| = 2^{-1/3}$',
1: '$|d_{i}| = 2^{-1/5}$',
2: '$|d_{i}| = 2^{-1/11}$'
}
draw_fractal('stretching_factors.pdf', w3_13, w3_15, w3_17, label=label)
def run_project(args):
opt = options.Options()
parsed_args = opt.parse(args[1:])
y = parsed_args.slice_yplus
d1 = 2**(-1 / 3)
d2 = -2**(-1 / 3)
w3_LES = fractal_interpolation(at.w(Ufx, d1, d2, 3), len(Ufx))
w3_from_resampled = fractal_interpolation(at.w(Ux_resampled, d1, d2, 3),
len(Ufx))
label = {0: '$W^{3}$: filtered DNS', 1: '$W^{3}$: resampled DNS'}
draw_fractal('LES_and_resampled.pdf',
w3_LES,
w3_from_resampled,
label=label)
draw_fractal('LES_and_DNS.pdf')
ek = kinetic_energy(Ux, Ufx, Ux_resampled, w3_LES['y'],
w3_from_resampled['y'])
fft = fourier_transform(Ux, Ufx, Ux_resampled, w3_LES['y'],
w3_from_resampled['y'])
plt.figure(figsize=(8, 4))
sns.violinplot(data=list(fft.values())[:3])
plt.xticks(plt.xticks()[0], fft.keys())
plt.tight_layout()
plt.savefig("fractal_violinplot_ftt.pdf")
for_box = {
'DNS': Ux,
'filtered DNS': Ufx,
'$W^{3}$: filtered': w3_LES['y'],
'resampled DNS': Ux_resampled,
'$W^{3}$: resampled': w3_from_resampled['y']
}
colors = {
i: v
for i, v in enumerate(
['lightgrey', 'lightgrey', 'darkorange', 'lightgrey', 'slateblue'])
}
plt.figure(figsize=(8, 4))
sns.violinplot(data=list(for_box.values()),
orient='v',
palette=colors,
inner='quartile',
bw='silverman')
plt.xticks(plt.xticks()[0], for_box.keys())
plt.tight_layout()
plt.savefig("fractal_violinplot.pdf")
plt.figure(figsize=(8, 4))
sns.boxplot(data=list(for_box.values()))
plt.xticks(plt.xticks()[0], for_box.keys())
plt.tight_layout()
plt.savefig("fractal_boxplot.pdf")
def test_w1_u0_1(self):
U = (1, 4, 3)
d1 = 2
d2 = 2
fractal = at.w(U, d1, d2, 1)(1)
self.assertAlmostEqual(fractal(0.5), 4)
def test_u0(self):
U = (1, 4, 3)
d1 = 1
d2 = 1
fractal = at.w(U, d1, d2, 0)(1)
self.assertAlmostEqual(fractal(0.5), 2)
def test_constant(self):
U = (1, 1, 1)
d1 = 1
d2 = 1
fractal = at.w(U, d1, d2, 1)(1)
self.assertAlmostEqual(U[1], fractal(0.5))