freq_points = side//2
freqs = np.arange( 0,freq_points )
powers = scipy_ndimage_mean(image_fft, np.round(rad), index=freqs)
autoexp, autoc, autopcov = fract.autoseeded_weighted_power_law_fit(freqs[2:-cutoff], powers[2:-cutoff], sigmas=powers[2:-cutoff])
tailexp, tailc, tailpcov = fract.autoseeded_weighted_power_law_fit(freqs[-cutoff:], powers[-cutoff:], sigmas=powers[-cutoff:])
detect_H = fract.freq_exp_to_H(autoexp)
print("expected H", gen_H)
print(" detect_H",detect_H)
det_H_s[i] = detect_H
plt.figure()
plt.scatter(freqs,powers, marker=".", color="deepskyblue")
plt.plot(freqs, fract.power_law(freqs, autoexp, autoc), color="red")
plt.plot(freqs, fract.power_law(freqs, tailexp, tailc), color="green")
# plt.plot(freqs, (10**c)*freqs**expected_freq_exp, color="red")
plt.xscale("log")
plt.yscale("log")
plt.title("detect_H = %g, gen_H = %g, tail exp = %g" % (detect_H, gen_H, tailexp) )
plt.show()
plt.figure()
plt.plot(gen_H_s, gen_H_s)
plt.scatter(gen_H_s, det_H_s)
plt.show()
plt.figure()
plt.imshow(npy_points)
plt.show()
## fourier
fourier_H, freq_exp, f_c, freqs, powers = fract.fourier_H(np.copy(npy_points),
fill_with_mean=True,
images=True,
corr=True)
print("fourier_H", fourier_H)
plt.figure()
plt.scatter(freqs, powers)
plt.plot(freqs,
fract.power_law(freqs, freq_exp, f_c),
color="red",
label="fourier")
plt.xscale("log")
plt.yscale("log")
plt.legend()
plt.show()
#### dfa
dfa_H, dfa_c, scales3, flucts3 = fract.dfa_H(npy_points,
messages=False,
min_nonzero=0.99)
print("dfa_H", dfa_H)
### first branch
dfa_H2, c2, pcov = fract.autoseeded_weighted_power_law_fit(
M, N = z2d.shape
if s_max == "auto":
s_max = min(N, M) // 4
else:
pass # (keep the passed s_max)
scales_flucts = np.zeros((s_max - s_min, 2))
# remove nan values (from linear regression on too few data points)
scales_flucts = scales_flucts[~np.isnan(scales_flucts).any(axis=1)]
# return scales_flucts[:,0], scales_flucts[:,1]
scales, flucts = scales_flucts[:, 0], scales_flucts[:, 1]
dfa_H, dfa_c, pcov = fract.autoseeded_weighted_power_law_fit(scales,
flucts,
sigmas=scales)
plt.figure()
plt.scatter(scales, flucts)
plt.plot(scales,
fract.power_law(scales, dfa_H, dfa_c),
color="springgreen",
label="dfa")
plt.xscale("log")
plt.yscale("log")
plt.legend()
plt.show()
######### else: zero boxes
nbox_s[i] = n_boxes * area
scales[i] = s
num = 1
b_exp, b_c, b_k, pcov = fract.autoseeded_weighted_power_law_fit(
scales[num:], nbox_s[num:])
# det_H = 2 - (-b_exp +1 )
det_H = 3 + b_exp - s_dim
fract_dim = 3 - det_H
print("fractal dimension:", fract_dim)
print("detected H:", det_H)
plt.scatter(scales, nbox_s)
plt.plot(scales, fract.power_law(scales, b_exp, b_c, b_k), color="red")
plt.xscale("log")
plt.yscale("log")
plt.title("Box counting: H = " + str(det_H))
plt.show()
# def to_data(name, inner_func, *args, **kwargs):
# npy_points = np.load("/home/gaboloth/D/fisica/tesi/dati/npysquare/all/"+name+"-2d.npy")
# return inner_func(npy_points, *args, **kwargs)
# def higuchi_H_discard(*args, **kwargs):
# try:
# det_H, _b_c, _scales, _areas = higuchi_H(*args, **kwargs)
# print(det_H)
# return det_H
# except Exception as ex:
# windowing?
image_fft = abs( np.fft.fftshift(np.fft.fft2(z2d*hann)) ) **2
# image_fft = abs( np.fft.fftshift(np.fft.fft2(z2d)) ) **2
corr2d = scipy.signal.fftconvolve(z2d, z2d[::-1,::-1], mode="full")
# plt.figure()
# plt.imshow(z2d, interpolation="None")
# plt.show()
plt.figure()
plt.imshow(corr2d, interpolation="None")
plt.show()
r_points = np.arange(1,max_r)
autocorrs = scipy.ndimage.mean(image_fft, np.round(rad), index=r_points)
exp, c, pcov = fract.autoseeded_weighted_power_law_fit(r_points, autocorrs, sigmas=autocorrs)
plt.scatter(r_points, autocorrs)
plt.plot(r_points, fract.power_law(r_points, exp, c), color="orange")
plt.xscale("log")
plt.yscale("log")
plt.show()
det_H = -exp/2 -1
print("gen_H", H)
print("det_H", det_H)
scales[i] = k**2
h_exp, h_c, pcov = fract.autoseeded_weighted_power_law_fit(scales[30:],
areas[30:],
sigmas=areas[30:])
det_H = 2 - (-h_exp + 1)
# return det_H, h_exp, h_c, scales, areas
# det_H, h_exp, h_c, scales, areas = higuchi_H(z2d)
print("fractal dimension:", -h_exp + 1)
plt.scatter(scales, areas)
plt.plot(scales, fract.power_law(scales, h_exp, h_c), color="red")
plt.xscale("log")
plt.yscale("log")
plt.title("Higuchi: H = " + str(det_H))
plt.show()
# def to_data(name, inner_func, *args, **kwargs):
# npy_points = np.load("/home/gaboloth/D/fisica/tesi/dati/npysquare/all/"+name+"-2d.npy")
# return inner_func(npy_points, *args, **kwargs)
# def higuchi_H_discard(*args, **kwargs):
# try:
# det_H, _h_c, _scales, _areas = higuchi_H(*args, **kwargs)
# print(det_H)
# return det_H
# except Exception as ex:
## fourier
fourier_H, freq_exp, f_c, freqs, powers = fract.fourier_H(np.copy(npy_points),
fill_with_mean=True,
images=True,
corr=True)
print("fourier_H", fourier_H)
freq_exp_2, fc2, pcov = fract.autoseeded_weighted_power_law_fit(
freqs[2:20], powers[2:20], sigmas=powers[2:20])
fourier_H2 = fract.freq_exp_to_H(freq_exp_2)
plt.figure()
plt.scatter(freqs, powers)
plt.plot(freqs,
fract.power_law(freqs, freq_exp, f_c),
color="red",
label="fourier: H =" + str(fourier_H))
plt.plot(freqs,
fract.power_law(freqs, freq_exp_2, fc2),
color="springgreen",
label="fourier: H =" + str(fourier_H2))
plt.xscale("log")
plt.yscale("log")
plt.legend()
plt.show()
#### dfa
dfa_H, dfa_c, scales3, flucts3 = fract.dfa_H(npy_points,
messages=False,
min_nonzero=0.99)
np.min(scales_out)
print("dma_1", dma_1)
# ### branches
# scale_f1 = 17
scale_f2 = 25
# dfa_H2, c2, pcov = fract.autoseeded_weighted_power_law_fit(scales_out[:scale_f1], flucts_out[:scale_f1], flucts_out[:scale_f1])
dfa_H2, c2, pcov = fract.autoseeded_weighted_power_law_fit(
scales_out[scale_f2:], flucts_out[scale_f2:], flucts_out[scale_f2:])
# print("dfa_H2", dfa_H2)
plt.figure()
plt.scatter(scales_out, flucts_out)
plt.plot(scales_out,
fract.power_law(scales_out, dma_1, dma_c),
color="springgreen",
label="dma: H =" + str(dma_1))
plt.plot(scales_out,
fract.power_law(scales_out, dfa_H2, c2),
color="red",
label="dfa: H = " + str(dfa_H2))
# plt.plot(scales_out, fract.power_law(scales_out, fourier_H, c2/0.8), color="purple", label="fourier: H = "+str(fourier_H))
plt.xscale("log")
plt.yscale("log")
plt.legend()
plt.show()