def Compute_rhoT(fasta_input,empty_fasta, single_line = False): #fasta file and an empty fasta file
print("Reading FASTA file...")
if not single_line:
single_line_fasta(fasta_input, empty_fasta)
fasta_file = empty_fasta
else:
fasta_file = fasta_input
lines = format_data(fasta_file,'fasta')
print("Computing Hamming distance matrix...")
#print(lines[0:5])
matrix = empty_matrix(lines)
hamm_matrix = populate_matrix(matrix, lines)
print('Computing barcodes ...')
dgms = ripser(hamm_matrix, distance_matrix=True, maxdim=1)['dgms']
Rbarc = dgms
Gbarc = Rips_to_GUDHI(Rbarc)
print('Plotting persistence diagrams')
gd.plot_persistence_diagram(Gbarc, colormap = ('navy','darkmagenta','fuchsia'))
gd.plot_persistence_barcode(Gbarc, colormap = ('navy','darkmagenta','fuchsia'))
print('Computing barcode statistics...')
avg0, var0, b1 = barstats(Rbarc)
print('Computing estimate of rho')
rhoT = TREErho(avg0, var0, b1)
print('$\psi = {}, \Phi = {}, \\beta_1 = {}, \\rho_T = {}$'.format(avg0, var0, b1, rhoT))
return hamm_matrix,Rbarc
def bettiNumbers(self, *args, **kwargs):
from gudhi import RipsComplex, plot_persistence_diagram, plot_persistence_barcode, sparsify_point_set
import random as r
import numpy as np
import matplotlib.pyplot as plt
targetCluster = kwargs.get('targetCluster', [1])
threshold = kwargs.get('threshold', 0.05)
sparsifyThreshold = kwargs.get('sparsifyThreshold', threshold/8)
plot = kwargs.get('plot', False)
pointList = []
for point in self.points:
if point.cluster in targetCluster:
pointList.append(np.array(point.coordinates))
pointList = sparsify_point_set(
points=pointList, min_squared_dist=sparsifyThreshold**2)
point_complex = RipsComplex(
max_edge_length=threshold/2, points=pointList)
simplex_tree = point_complex.create_simplex_tree(
max_dimension=self.dimension)
persistence = simplex_tree.persistence()
if plot:
plot_persistence_barcode(persistence)
plt.plot()
plot_persistence_diagram(persistence)
plt.plot()
return simplex_tree.betti_numbers()
def PH_diag(img, patch_side):
cc = gd.CubicalComplex(dimensions=(patch_side, patch_side, patch_side),
top_dimensional_cells=1 - img.flatten())
diag = cc.persistence()
plt.figure(figsize=(3, 3))
# diag_clean = diag_tidy(diag, 1e-3)
gd.plot_persistence_barcode(diag, max_intervals=0, inf_delta=100)
print(diag)
plt.xlim(0, 1)
plt.ylim(-1, len(diag))
plt.xticks(ticks=np.linspace(0, 1, 6),
labels=np.round(np.linspace(1, 0, 6), 2))
plt.yticks([])
plt.show()
def save_PH_diag(img, patch_side, outdir):
cc = gd.CubicalComplex(dimensions=(patch_side, patch_side, patch_side),
top_dimensional_cells=1 - img.flatten())
diag = cc.persistence()
plt.figure(figsize=(3, 3))
diag_clean = diag_tidy(diag, 1e-3)
print(diag_clean)
# np.savetxt(os.path.join(outdir, 'generalization.csv'), diag_clean, delimiter=",")
with open(os.path.join(outdir, 'generalization.txt'), 'wt') as f:
for ele in diag_clean:
f.write(ele + '\n')
gd.plot_persistence_barcode(diag_clean)
plt.ylim(-1, len(diag_clean))
plt.xticks(ticks=np.linspace(0, 1, 6), labels=np.round(np.linspace(1, 0, 6), 2))
plt.yticks([])
plt.savefig(os.path.join(outdir, "PH_diag.png"))
def PH_diag(img):
z, y, x = img.shape
cc = gd.CubicalComplex(dimensions=(z, y, x),
top_dimensional_cells=1 - img.flatten())
diag = cc.persistence()
plt.figure(figsize=(3, 3))
gd.plot_persistence_barcode(diag, max_intervals=0, inf_delta=100)
plt.xlim(0, 1)
plt.ylim(-1, len(diag))
plt.xticks(ticks=np.linspace(0, 1, 6), labels=np.round(np.linspace(1, 0, 6), 2))
plt.yticks([])
plt.show()
gd.plot_persistence_diagram(diag, legend=True)
plt.show()
gd.plot_persistence_density(diag, legend=True)
plt.show()
def drawPB(data):
z, y, x = data.shape
cpx = init_tri_complex_3d(z, y, x)
layer = LevelSetLayer(cpx, maxdim=2, sublevel=False)
dgminfo = layer(torch.from_numpy(data).float())
diag = []
diag2 = getPB(dgminfo, 2)
diag1 = getPB(dgminfo, 1)
diag0 = getPB(dgminfo, 0)
if diag2 != None: diag += diag2
if diag1 != None: diag += diag1
if diag0 != None: diag += diag0
diag = diag_tidy(diag, 1e-3)
print(diag)
plt.figure(figsize=(3, 3))
gd.plot_persistence_barcode(diag, max_intervals=0, inf_delta=100)
plt.xlim(0, 1)
plt.ylim(-1, len(diag))
plt.xticks(ticks=np.linspace(0, 1, 6), labels=np.round(np.linspace(1, 0, 6), 2))
plt.yticks([])
def get_persistence_from_audio(audio_wave,
sample=22050,
length=5,
graph=False):
simplex_up = gd.SimplexTree() # for the upper level persistence data
simplex_dw = gd.SimplexTree() # for the lower level persistence data
for i in np.arange(len(audio_wave)):
simplex_up.insert([i, i + 1], filtration=audio_wave[i])
simplex_dw.insert([i, i + 1], filtration=-audio_wave[i])
for i in np.arange(len(audio_wave) - 1):
simplex_up.insert([i, i + 1], filtration=audio_wave[i])
simplex_dw.insert([i, i + 1], filtration=-audio_wave[i])
simplex_up.initialize_filtration()
simplex_dw.initialize_filtration()
dig_up = simplex_up.persistence()
dig_dw = simplex_dw.persistence()
if graph:
plt.figure()
lr_disp.waveplot(audio_wave, sr=sample)
plt.title("Audio Wave")
plt.show()
plt.figure()
gd.plot_persistence_barcode(dig_up)
plt.title("Upper Level Persistence Barcode")
plt.show()
plt.figure()
gd.plot_persistence_barcode(dig_dw)
plt.title("Sub Levels Persistence Barcode")
plt.show()
plt.figure()
gd.plot_persistence_diagram(dig_up)
plt.title("Upper Level Persistence Diagram")
plt.show()
plt.figure()
gd.plot_persistence_diagram(dig_dw)
plt.title("Sub Levels Persistence Diagram")
plt.show()
return dig_up, dig_dw # NOTE: this does not filter out infinite values
parser.add_argument(
"--no-barcode",
default=False,
action="store_true",
help="Flag for not to display the barcodes",
)
args = parser.parse_args()
if is_file_perseus(args.file):
print("##################################################################")
print("PeriodicCubicalComplex creation")
periodic_cubical_complex = gudhi.PeriodicCubicalComplex(
perseus_file=args.file)
print("persistence(homology_coeff_field=3, min_persistence=0)=")
diag = periodic_cubical_complex.persistence(
homology_coeff_field=3, min_persistence=0
)
print(diag)
print("betti_numbers()=")
print(periodic_cubical_complex.betti_numbers())
if args.no_barcode == False:
import matplotlib.pyplot as plot
gudhi.plot_persistence_barcode(diag)
plot.show()
else:
raise FileNotFoundError(errno.ENOENT, os.strerror(errno.ENOENT),
args.file)
__copyright__ = "Copyright (C) 2016 Inria"
__license__ = "MIT"
print("#####################################################################")
print("Show barcode persistence example")
persistence = [
(2, (1.0, float("inf"))),
(1, (1.4142135623730951, float("inf"))),
(1, (1.4142135623730951, float("inf"))),
(0, (0.0, float("inf"))),
(0, (0.0, 1.0)),
(0, (0.0, 1.0)),
(0, (0.0, 1.0)),
]
gudhi.plot_persistence_barcode(persistence)
plot.show()
print("#####################################################################")
print("Show diagram persistence example")
gudhi.plot_persistence_diagram(persistence)
plot.show()
print("#####################################################################")
print("Show diagram persistence example with a confidence band")
gudhi.plot_persistence_diagram(persistence, band=0.2)
plot.show()
print("#####################################################################")
__author__ = "Vincent Rouvreau"
__copyright__ = "Copyright (C) 2016 Inria"
__license__ = "MIT"
print("#####################################################################")
print("Show barcode persistence example")
persistence = [
(2, (1.0, float("inf"))),
(1, (1.4142135623730951, float("inf"))),
(1, (1.4142135623730951, float("inf"))),
(0, (0.0, float("inf"))),
(0, (0.0, 1.0)),
(0, (0.0, 1.0)),
(0, (0.0, 1.0)),
]
gudhi.plot_persistence_barcode(persistence)
print("#####################################################################")
print("Show diagram persistence example")
pplot = gudhi.plot_persistence_diagram(persistence)
pplot.show()
print("#####################################################################")
print("Show diagram persistence example with a confidence band")
pplot = gudhi.plot_persistence_diagram(persistence, band=0.2)
pplot.show()
def rstg(n, A):
rp = gudhi.RipsComplex(A)
st = rp.create_simplex_tree(max_dimension=n)
diag = st.persistence()
gudhi.plot_persistence_barcode(diag)
'''计算过滤后的复杂体的持久性图,默认情况下，它停在1维，使用persistence_dim_max = True
计算所有维度的同源性'''
dgm = st.persistence(persistence_dim_max=True)
""" dgm = st.persistence()"""
#print("dgm:",dgm)# 有0，1，2维，0是点 1是线段 2是三角形
#但是只有一个2维 (2, (78.57119751, inf)) 其余的0，1还是正常的 (1, (7.01657343, 29.42458725)) (0, (-117.12751007, inf))
#＃绘制一个持久性图
gd.plot_persistence_diagram([pt for pt in dgm if pt[0] == 0])
"""plot = gd.plot_persistence_diagram(dgm)"""
plt.title('persistence diagram with point')
plt.show()
gd.plot_persistence_diagram(dgm)
plt.title('plot_persistence_diagram')
plt.show()
gd.plot_persistence_barcode(dgm)
plt.title('plot_persistence_barcode')
plt.show()
# 获取所有simplex的列表
# 注意，如果一条边不在顶点中，则插入边会自动插入其顶点
# 与之前的问题相同：手臂在普通持久性图中不生成任何点，并且连接的组件具有无限的持久性。 因此，让我们尝试扩展持久性！
############扩展持久性 extend persistence##########
st.extend_filtration()
'''将持久性同源性扩展到代数拓扑中的其他基本概念，例如同调性和相对同源性/同调性，是很自然的'''
dgms = st.extended_persistence(min_persistence=1e-5)
'''gd.plot_persistence_barcode(dgms)
plt.title('plot_extended_persistence_barcode')
plt.show()'''
#print("dgms:",dgms)# 有0，1，2维，0是点 1是线段 2是三角形
import matplotlib.pyplot as plt from src.datasets.datasets import double_tours data_double, labels = double_tours() rips_complex_double = gd.RipsComplex(points = data_double,max_edge_length=2) rips_simplex_tree_double = rips_complex_double.create_simplex_tree(max_dimension=4) persistence_double = rips_simplex_tree_double.persistence() persistence_double_filtered = [x for x in persistence_double if x[0]>1] gd.plot_persistence_diagram(persistence_double_filtered) plt.show() gd.plot_persistence_barcode(persistence_double_filtered) plt.show() from src.datasets.shapes import torus data_single, label = torus(n=500, c=6, a=4, label=0) rips_complex_single = gd.RipsComplex(points = data_single,max_edge_length=2) rips_simplex_tree_single = rips_complex_single.create_simplex_tree(max_dimension=4) persistence_single = rips_simplex_tree_single.persistence() print(persistence_single) persistence_single_filtered = [x for x in persistence_single if x[0]>1] print(persistence_single_filtered) gd.plot_persistence_diagram(persistence_single_filtered) plt.show() gd.plot_persistence_barcode(persistence_single_filtered) plt.show()
import gudhi as gd
cplx = gd.RipsComplex(points=[[0, 0], [1, 2], [2, 1], [4, 3], [4, -3]])
stree = cplx.create_simplex_tree(max_dimension=5)
for x in stree.get_filtration():
print(x)
diag = stree.persistence(min_persistence=0.01)
plot = gd.plot_persistence_barcode(diag)
plot.show()
return Gbarc
def descriptives(Gbarc):
#finds the number of features, birth times, death times,
#and lifespans for a set of GUDHI barcodes
num = len(Gbarc)
birth, death, length = [], [], []
for i in Gbarc:
b = i[1][0]
d = i[1][1]
birth.append(b)
death.append(d)
length.append(d - b)
return num, birth, death, length
# print(tree_sequence.get_num_mutations())
D = Hamming_mat(tree_sequence)
dgms = ripser(D, distance_matrix=True)['dgms'] #computes PH with ripser
barcode = Rips_to_GUDHI(dgms)
#plot barcode and persistence plot with GUDHI
gd.plot_persistence_diagram(barcode,
colormap=('navy', 'darkmagenta', 'fuchsia'))
gd.plot_persistence_barcode(barcode,
colormap=('navy', 'darkmagenta', 'fuchsia'))
''' Record spiking activity of Layer 1 while showing it a bunch of images '''
print("Recording Spikes")
num_images = 1
time_step = 50
spikes = []
for i in tqdm(range(num_images)):
network.populations[0].set_input(x_train[i])
spikes.append(network.run(time_step, learning=False, record_spikes=True, pop_index=1).get("spikes"))
network.rest()
spikes = np.reshape(spikes, (num_neurons, time_step*num_images))
''' Calculate correlation matrix from spiking activity '''
corr = np.zeros((len(spikes), len(spikes)))
print("Calculating correlation matrix")
for i in tqdm(range(len(spikes)-1)):
for j in range(i+1,len(spikes)):
corr[i,j] = correlation(spikes[i,:], spikes[j,:], len(spikes[j,:])-50)
corr[i,j] = 1/(corr[i,j]+.01)
corr = corr + np.transpose(corr)
''' Compute and plot barcodes based on correlation matrix '''
print("Computing Barcodes")
rips_complex = gudhi.RipsComplex(distance_matrix=corr)
simplex_tree = rips_complex.create_simplex_tree(max_dimension=2)
diag_Rips = simplex_tree.persistence()
plt = gudhi.plot_persistence_barcode(diag_Rips)
plt.show()
