def persistent(self):
"""
This method is used to create dionysus persistent homology
implementation of given vectors
:return: dionysus diagrams
"""
vectors = self._get_vectors()
f_lower_star = dn.fill_freudenthal(vectors)
p = dn.homology_persistence(f_lower_star)
dgms = dn.init_diagrams(p, f_lower_star)
return dgms
h1 = np.asarray(h1)
h0 = h0.reshape((-1, 2))
h1 = h1.reshape((-1, 2))
return [h0, h1]
PI_null_images = []
PI_one_images = []
for i in range(images.shape[0]):
print(i)
f_lower_star = d.fill_freudenthal(images[i, :, :, 0].astype(float))
f_upper_star = d.fill_freudenthal(images[i, :, :, 0].astype(float),
reverse=True)
p = d.homology_persistence(f_lower_star)
dgms_temp = d.init_diagrams(p, f_lower_star)
h0_temp = homology_persistent_diagrams(dgms_temp)[0]
h1_temp = homology_persistent_diagrams(dgms_temp)[1]
pim = PersImage(pixels=[20, 20], spread=1)
PI_0_temp = pim.transform(h0_temp[1:, :])
PI_1_temp = pim.transform(h1_temp)
PI_null_images.append(PI_0_temp)
PI_one_images.append(PI_1_temp)
PI_null_images = np.array(PI_null_images, dtype=np.float32)
PI_null_images = PI_null_images.reshape((-1, 20, 20, 1)) # reshape
PI_null_images = PI_null_images / (PI_null_images.max() / 255.0) # normalize
PI_one_images = np.array(PI_one_images, dtype=np.float32)
PI_one_images = PI_one_images.reshape((-1, 20, 20, 1)) # reshape
PI_one_images = PI_one_images / (PI_one_images.max() / 255.0) # normalize
##############################
#Compute Persistence Diagrams#
prime = 23
maxscale = float(sys.argv[3])
#Choose the prime base for the coefficient field that we use to construct the persistence cohomology.
threshold = float(sys.argv[2])
print('Base coefficient field: Z/', prime, 'Z', sep='')
print('Maximal scale:', float(sys.argv[3]))
print('Persistence threshold for selecting significant cocyles:',
threshold, '\n')
vr = dionysus.fill_rips(dataset, 2, float(sys.argv[3]))
#Vietoris-Rips complex
cp = dionysus.cohomology_persistence(vr, prime, True)
#Create the persistent cohomology based on the chosen parameters.
dgms = dionysus.init_diagrams(cp, vr)
#Calculate the persistent diagram using the designated coefficient field and complex.
now = datetime.datetime.now()
print('End Time (VR-computation):', now.strftime("%Y-%m-%d %H:%M:%S"))
###Plot the barcode and diagrams using matplotlib incarnation within Dionysus2. This mechanism is different in Dionysus.
#Plots of persistence barcodes of Vietoris-Rips complex for dimension 0 and 1.
fig = plt.figure(figsize=(5, 5), dpi=100)
plt.title('Persistence Barcode for dim 0')
dionysus.plot.plot_bars(dgms[0], show=True)
pdf.savefig(fig)
fig = plt.figure(figsize=(5, 5), dpi=100)
plt.title('Persistence Barcode for dim 1')
dionysus.plot.plot_bars(dgms[1], show=True)
pdf.savefig(fig)
plt.close('all')
# vim: ft=python foldmethod=marker foldlevel=0
import dionysus as d
#---#
simplices = [([2], 4), ([1, 2], 5), ([0, 2], 6), ([0], 1), ([1], 2), ([0,
1], 3)]
f = d.Filtration()
for vertices, time in simplices:
f.append(d.Simplex(vertices, time))
f.sort()
for s in f:
print(s)
#var> f
#---#
#var> f
m = d.homology_persistence(f)
#chk>
#---#
dgms = d.init_diagrams(m, f)
print(dgms)
#var> dgms
D = 20
#Here is the data insertion part
def sample_spherical(npoints, ndim=D):
vec = np.random.randn(ndim, npoints)
vec /= np.linalg.norm(vec, axis=0)
return vec
dat1 = np.array(sample_spherical(100).T)
vr = dionysus.fill_rips(dat1, 2, 10) #Vietoris-Rips complex
cp = dionysus.cohomology_persistence(vr, prime,
True) #Create the persistent cohomology
dgms = dionysus.init_diagrams(
cp, vr
) #Calculate the persistent diagram using the designated coefficient field.
#record for plottings..
A = np.array([0, 0, 1, 1])
for thres in [0, 0.025, 0.05, 0.1, 0.2]:
#######Thresholding the features on the persistent diagrams describing persistent cohomology of VR complex(CC)
dgms_tmp = denoise_dgm(dgms, thres) #thresholding CC diagrams
dgms_base_0 = dionysus._dionysus.Diagram(
) #take persistent points of dim 0
dgms_base_1 = dionysus._dionysus.Diagram(
) #take persistent points of dim 1
#pybind issue, need to be correct instead of succint.
for itr in range(len(dgms_tmp[0])):
dgms_base_0.append(dgms_tmp[0][itr])
for itr in range(len(dgms_tmp[1])):
ax.set_xlim(dims[0][0],dims[0][1])
ax.set_ylim(dims[1][0],dims[1][1])
ax.set_zlim(dims[2][0],dims[2][1])
ax.scatter(sphere_data[:,0],sphere_data[:,1],sphere_data[:,2])
ax.set_aspect("equal")
plt.show()
"""
computing homology
"""
#VR filtration TDA
test_f = d.fill_rips(TDA_data, 2, 10.)
p = d.homology_persistence(test_f)
dgms = d.init_diagrams(p, test_f)
#scatters
d.plot.plot_diagram(dgms[0])
d.plot.plot_diagram(dgms[1])
plt.show()
#bars
d.plot.plot_bars(dgms[0])
plt.show()
d.plot.plot_bars(dgms[1])
plt.show()
#alpha filtration TDA
ax.scatter(xs=X[:, 0], ys=X[:, 1], zs=X[:, 2], s=10, c='b')
plt.title('Scatter plot of data points')
pdf.savefig(fig)
# The persistent cohomology of $X$ is in the plot. As expected from the dataset, the $1$-dimensional persistent cohomology
# of $X$ has one prominent topological feature.
# In[5]:
prime = 23 #choose the prime base for the coefficient field that we use to construct the persistence cohomology.
vr = dionysus.fill_rips(X, 2, 2.) #Vietoris-Rips complex
cp = dionysus.cohomology_persistence(
vr, prime,
True) #Create the persistent cohomology based on the chosen parameters.
dgms = dionysus.init_diagrams(
cp, vr
) #Calculate the persistent diagram using␣ the designated coefficient field and complex.
# In[6]:
with PdfPages('fig_cc-pca_dataset_ph.pdf') as pdf:
fig = plt.figure(figsize=(4, 4), dpi=100)
plt.xlim([0, 2])
plt.yticks([])
plt.title('Barcode(dim 1) of data points')
dionysus.plot.plot_bars(dgms[1], show=True)
#dionysus.plot.plot_diagram(dgms[1], show=True)
#dionysus.plot.plot_diagram(dgms[0], show=True)
#Plot the barcode and diagrams using matplotlib incarnation within Dionysus2. This mechanism is different in Dionysus.
pdf.savefig(fig)
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from sklearn import manifold, datasets
n_points = 100
Y, color = datasets.make_circles(n_points, random_state=1, factor=0.5, noise=0)
fig, ax = plt.subplots()
ax.scatter(Y[:,0], Y[:,1], c=color, cmap=plt.cm.Spectral)
# plt.show()
import dionysus as d
max_epsilon = 1
k_skeleton = 3
f = d.fill_rips(Y, k_skeleton, max_epsilon)
p = d.homology_persistence(f)
dgms = d.init_diagrams(p, f)
fig, axes = plt.subplots(nrows=2, ncols=2)
d.plot.plot_diagram(dgms[0], ax=axes[0,0], show=False)
d.plot.plot_diagram(dgms[1], ax=axes[0,1], show=False)
d.plot.plot_bars(dgms[0], ax=axes[1,0], show=False)
d.plot.plot_bars(dgms[1], ax=axes[1,1], show=False)
axes[0,0].set_title("Dimension 0")
axes[0,1].set_title("Dimension 1")
plt.show()
for cell in grid:
weight += [max([pw[n] for n in cell])]
dense += [max([pd[n] for n in cell])]
fil_weight = []
for v_f, v_rho in zip(weight, dense):
if v_rho <= 0.4:
fil_weight += [v_f]
else:
fil_weight += [Mf]
f = d.Filtration()
for cell, level in zip(grid, fil_weight):
f.append(d.Simplex(cell, level))
f.sort()
res = d.homology_persistence(f)
dgm = d.init_diagrams(res, f)
for i, dg in enumerate(dgm):
for pt in dg:
if pt.death - pt.birth > 0.1:
print(i, pt.birth, pt.death)
for l in range(2, 3):
rho_0 = mrho + l * rstep
epsilon = 0.3
epsilon0 = 0.4
print("rho_0", rho_0)
estep = epsilon * (1 - epsilon0) / 6
for k in range(7):
print("epsilon:", epsilon)
for n in range(17):
a = mf * (16 - n) / 16 + Mf * n / 16
def compute_layer_mask(self, x, hiddens, subgraph_indices=[0], percentile=0):
f,nm = self.compute_induced_filtration(x[0], hiddens, percentile=percentile)
m = dion.homology_persistence(f)
dgms = dion.init_diagrams(m,f)
subgraphs = {}
dion.plot.plot_diagram(dgms[0],show=False)
plt.savefig('/home/tgebhart/projects/homo_explico/logdir/experiments/alexnet_vis/plt_3.png', format='png')
plt.close()
# compute ones tensors of same hidden dimensions
muls = [torch.zeros(x.reshape((x.shape[0],-1)).shape)]
for h in hiddens:
print('h shape', h.reshape((h.shape[0],-1)).shape)
muls.append(torch.zeros(h.reshape((h.shape[0],-1)).shape))
fac = 1.0
for i,c in enumerate(m):
if len(c) == 2:
if f[c[0].index][0] in subgraphs:
subgraphs[f[c[0].index][0]].add_edge(f[c[0].index][0],f[c[1].index][0], weight=f[i].data)
else:
eaten = False
for k, v in subgraphs.items():
if v.has_node(f[c[0].index][0]):
v.add_edge(f[c[0].index][0], f[c[1].index][0], weight=f[i].data)
eaten = True
break
if not eaten:
g = nx.Graph()
g.add_edge(f[c[0].index][0], f[c[1].index][0], weight=f[i].data)
subgraphs[f[c[0].index][0]] = g
# I don't think we need this composition. Disjoint subgraphs are fine.
# subgraph = nx.compose_all([subgraphs[k] for k in list(subgraphs.keys())[:thru]])
ids = dict((v,k) for k,v in nm.items())
ks = list(subgraphs.keys())
print('KS: ',ks)
ks_sub = [ks[s] for s in subgraph_indices]
# lifetimes = np.empty(thru)
# t = 0
# for pt in dgms[0]:
# if pt.death < float('inf'):
# lifetimes[t] = pt.birth - pt.death
# t += 1
# if t >= thru:
# break
# max_lifetime = max(lifetimes)
# min_lifetime = min(lifetimes)
for k in ks_sub:
for e in subgraphs[k].edges(data=True):
n1 = ids[e[0]]
n2 = ids[e[1]]
# allow the outcoming activation from that node at that channel (idx 1)
if n1[1] > 0:
muls[n1[0]][n1[1],n1[2]] = fac
else:
muls[n1[0]][n1[2]] = fac
if n2[1] > 0:
muls[n2[0]][n2[1],n2[2]] = fac
else:
muls[n2[0]][n2[2]] = fac
return muls
def GCC2(dataset,threshold,maxscale,CEthreshold=1e-5,lp=1,lq=2,Nsteps=1000,lambda_coef=0.5,PLOT=True):
sys.argv = np.asarray(['GCC2_fun.GCC2','dataset',threshold,maxscale,CEthreshold,lp,lq,Nsteps,lambda_coef])
return_list = []
print('Number of arguments:', str(len(sys.argv)), 'arguments.')
if len(sys.argv)!=8 and len(sys.argv)!=9:
print("""
### usage: GCC2(dataset,threshold,maxscale,CEthreshold=1e-5,lp=1,lq=2,Nsteps=1000,lambda_coef=0.5)
###[dataset] The dataset you want to analyze using circular coordinates in numpy array. The cols of the array are dimensions/variables; the rows of the array are samples.
###[threshold] The threhold on persistence which we use to select those significant cocyles from all cocycles constructed from the Vietoris-Rips complex built upon the data. If negative integer M, the 1-cocycles with the 1,2,...,M-th largest persistence will be picked. This option would override the threshold option.
###[CEthreshold] The threshold that we use to determine the constant edges. When the coordinate functions' values changed below this threshold, we consider it as a constant edge and plot it.
###[maxscal] The maximal scale at which we shall construct the Vietoris-Rips complex for circular coordinate computation.
###[lp] [lq] The generalized penalty function is in form of (1-lambda_parameter)*L^[lp]+lambda_parameter*L^[lq].
###[Nsteps] How many iterations you want to run in the tensorflow optimizer to obtain our circular coordinates? If negative number, no optimization would be executed.
###[lambda] This is a float parameter, if supplied, then only that lambda in the genealized coordinate would be calculated.
###Functionality of this code.
####Part1: Construct the Vietoris-Rips complex built upon the data and associated persistence diagrams and barcodes.
#####Scatter plot and associated persistence diagrams and barcodes, with significant topological features selected.
####Part2: Output the circular coordinates with different penalty functions.
####Part3: Output the embeddings with different penalty functions.""")
return return_list
print('Argument List:', str(sys.argv),'\n')
filenam=sys.argv[1]
print('Data file:', filenam)
#From Python_code/utils.py
def coboundary_1(vr, thr):
D = [[],[]]
data = []
indexing = {}
ix = [0]*2
for s in vr:
if s.dimension() != 1:
continue
elif s.data > thr:
#break
continue
indexing.setdefault(s.dimension(),{})
indexing.setdefault(s.dimension()-1,{})
if not s in indexing[s.dimension()]:
indexing[s.dimension()][s] = ix[s.dimension()]
ix[s.dimension()] += 1
for dat, k in enumerate(s.boundary()):
if not k in indexing[s.dimension()-1]:
indexing[k.dimension()][k] = k[0]
ix[k.dimension()] += 1
D[0].append(indexing[s.dimension()][s]) #rows
D[1].append(indexing[k.dimension()][k]) #cols
data.append(1. if dat % 2 == 0 else -1.)
return sp.sparse.csr_matrix((data, (D[0], D[1]))), indexing
def optimizer_inputs(vr, bars, cocycle, init_z, prime, thr):
bdry,indexing = coboundary_1(vr,thr)
n, m = bdry.shape # edges X nodes
#-----------------
l2_cocycle = [0]*len(init_z) #reorganize the coordinates so they fit with the coboundary indices
for i, coeff in enumerate(init_z):
l2_cocycle[i] = coeff
l2_cocycle = np.array(l2_cocycle)
#-----------------
f = np.zeros((n,1)) # cocycle we need to smooth out, reorganize to fit coboundary
for c2 in cocycle:
if c2.element<(prime//2):
f[indexing[1][vr[c2.index]]] += c2.element
else:
f[indexing[1][vr[c2.index]]] += c2.element-prime
return l2_cocycle,f,bdry
#Dionysus2 only.
#This code is composed in such way that it produces the whole thing in a single pdf file.
#dataset = np.loadtxt(filenam)
#from matplotlib.backends.backend_pdf import PdfPages
title_str='Circular Coordinates with Generalized Penalty Functions'
# Create the PdfPages object to which we will save the pages:
# The with statement makes sure that the PdfPages object is closed properly at the end of the block, even if an Exception occurs.
os.environ['TF_CPP_MIN_LOG_LEVEL'] = '2'
filenam = os.path.splitext(filenam)[0]
pdfnam = filenam+'_output.pdf'
print('Output file:', pdfnam,'\n')
now = datetime.datetime.now()
print('>>>>>>Start Time(VR computation):',now.strftime("%Y-%m-%d %H:%M:%S"))
##############################
#Scatter plots for datapoints#
if PLOT:
fig = plt.figure(figsize=(5,5), dpi=100)
plt.xlabel('X')
plt.ylabel('Y')
plt.gca().set_aspect('equal', 'datalim')
plt.scatter(dataset.T[0,:],dataset.T[1,:],s=10, c='b')
plt.axis('equal')
plt.title('Scatter plot of data points')
#pdf.savefig(fig)
# #
##############################
##############################
#Compute Persistence Diagrams#
prime = 23
maxscale = float(sys.argv[3])
#Choose the prime base for the coefficient field that we use to construct the persistence cohomology.
threshold = float(sys.argv[2])
print('Base coefficient field: Z/', prime ,'Z',sep='')
print('Maximal scale:', float(sys.argv[3]))
print('Persistence threshold for selecting significant cocyles:',threshold)
vr = dionysus.fill_rips(dataset, 2, float(sys.argv[3]))
#Vietoris-Rips complex
cp = dionysus.cohomology_persistence(vr, prime, True)
#Create the persistent cohomology based on the chosen parameters.
dgms = dionysus.init_diagrams(cp, vr)
#Calculate the persistent diagram using the designated coefficient field and complex.
now = datetime.datetime.now()
print('>>>>>>End Time (VR-computation):',now.strftime("%Y-%m-%d %H:%M:%S"))
###Plot the barcode and diagrams using matplotlib incarnation within Dionysus2. This mechanism is different in Dionysus.
if PLOT:
#Plots of persistence barcodes of Vietoris-Rips complex for dimension 0 and 1.
fig = plt.figure(figsize=(5,5), dpi=100)
plt.title('Persistence Barcode for dim 0')
dionysus.plot.plot_bars(dgms[0], show=True)
#pdf.savefig(fig)
fig = plt.figure(figsize=(5,5), dpi=100)
plt.title('Persistence Barcode for dim 1')
dionysus.plot.plot_bars(dgms[1], show=True)
#pdf.savefig(fig)
plt.show()
#Plots of persistence diagrams of Vietoris-Rips complex for dimension 0 and 1.
fig = plt.figure(figsize=(5,5), dpi=100)
plt.title('Persistence Diagram for dim 0')
dionysus.plot.plot_diagram(dgms[0], show=True)
#pdf.savefig(fig)
fig = plt.figure(figsize=(5,5), dpi=100)
plt.title('Persistence Diagram for dim 1')
dionysus.plot.plot_diagram(dgms[1], show=True)
#pdf.savefig(fig)
plt.show()
######Select and highlight the features selected.
bars = [bar for bar in dgms[1] ]
#Choose cocycle that persist at least threshold we choose.
cocycles = [cp.cocycle(bar.data) for bar in bars]
#Sort the list 'cocycles' by the persistence corresponding to each bar
cocycles_persistence = [bar.death-bar.birth for bar in bars]
#print(cocycles_persistence)
cocycles_ind = np.argsort(-np.asarray(cocycles_persistence), axis=-1, kind=None, order=None)
cocycles = [cocycles[i] for i in cocycles_ind]
bars = [bars[i] for i in cocycles_ind]
if threshold<0:
leadings = int(np.abs(threshold))
#Override threshold option
threshold = 0
print('\n>>>>>>Threshold overridden, the 1-cocyles with the ',leadings,' largest persistence would be selected for computation.')
cocycles = cocycles[0:leadings]
bars = bars[0:leadings]
else:
bars = [bar for bar in dgms[1] if bar.death-bar.birth > threshold and bar.death-bar.birth < float(sys.argv[3]) ]
cocycles = [cp.cocycle(bar.data) for bar in bars]
print('>>>>>>Selected significant features:')
for B_Lt in bars:
print(B_Lt,'\tpersistence = ',B_Lt.death-B_Lt.birth)
####################
#PersistenceBarcode#
if PLOT:
#Red highlight ***ALL*** cocyles that persist more than threshold value on barcode, when more than one cocyles have persisted over threshold values, this plots the first one.
fig = plt.figure(figsize=(5,5), dpi=100)
dionysus.plot.plot_bars(dgms[1], show=False)
Lt1 = [[bar.birth,bar.death] for bar in bars]
#Lt1 stores the bars with persistence greater than the [threshold].
Lt1_tmp = [[bar.birth,bar.death] for bar in dgms[1] ]
for Lt in Lt1:
loc=0
target=Lt
for g in range(len(Lt1_tmp)):
if Lt1_tmp[g][0] == target[0] and Lt1_tmp[g][1] == target[1]:
loc=g
#Searching correct term
plt.plot([Lt[0],Lt[1]],[loc,loc],'r-')
#print(Lt)
plt.title('Selected cocycles on barcodes (red bars)')
#pdf.savefig(fig)
plt.show()
# #
####################
####################
#PersistenceDiagram#
if PLOT:
#Red highlight ***ALL*** cocyles that persist more than threshold value on diagram.
fig = plt.figure(figsize=(5,5), dpi=100)
dionysus.plot.plot_diagram(dgms[1], show=False)
Lt2 = [[point.birth,point.death] for point in bars ]
#Lt2 stores the (multi-)points with persistence greater than the [threshold].
for Lt in Lt2:
plt.plot(Lt[0],Lt[1],'ro')
plt.title('Selected cocycles on diagram (red points)')
plt.figure(figsize=(5,5), dpi=100)
#pdf.savefig(fig)
plt.show()
# #
####################
# #
##############################
##############################
# Visualization of GCC #
overall_coords = np.zeros(dataset.shape[0], dtype = float)
#from Python_code import utils
toll = float(sys.argv[4])#tolerance for constant edges.
print('\nConstant edges, with coordinates difference <',toll)
print('Optimizer maximal iteration steps=',int(sys.argv[7]))
lp=int(sys.argv[5])
lq=int(sys.argv[6])
now = datetime.datetime.now()
print('>>>>>> Start Time (GCC computation):',now.strftime("%Y-%m-%d %H:%M:%S"))
if len(sys.argv)>=9:
lambda_list = [float(sys.argv[8])]
else:
lambda_list = [0,0.5,1]
for lambda_parameter in lambda_list:
print('>>>>>> lambda = ',lambda_parameter,'. => Analysis of Circular coordinates \n (mod {} - {}*L{} + {}*L{})'.format(prime,1-lambda_parameter,lp,lambda_parameter,lq))
embedding = []
if PLOT:
fig = plt.figure(figsize=(5,5), dpi=100)
plt.text(0.3,0.5,'Analysis of Circular coordinates \n (mod {} - {}*L{} + {}*L{})'.format(prime,1-lambda_parameter,lp,lambda_parameter,lq),transform=plt.gca().transAxes)
#pdf.savefig(fig)
plt.show()
print('Penalty function =>',(1-lambda_parameter),'*L^',lp,"+",lambda_parameter,"*L^",lq,sep='')
for g in range(len(cocycles)):
chosen_cocycle = cocycles[g]
chosen_bar = bars[g]
#print(chosen_cocycle,chosen_bar)
NEW_THRESHOLD = max([vr[c2.index].data for c2 in chosen_cocycle])
vr_L2 = dionysus.Filtration([s for s in vr if s.data <=NEW_THRESHOLD])
coords = dionysus.smooth(vr_L2, chosen_cocycle, prime)
l2_cocycle,f,bdry = optimizer_inputs(vr, bars, chosen_cocycle, coords, prime, NEW_THRESHOLD)
l2_cocycle = l2_cocycle.reshape(-1, 1)
##It does not seem to work to have double invokes here...
B_mat = bdry.todense()
z_init = l2_cocycle
z = tf.Variable(z_init, name='z', trainable=True, dtype=tf.float64)
trainable_variables = [z]
def loss_function():
cost_z = (1-lambda_parameter)*tf.math.pow( tf.math.reduce_sum( tf.math.pow( tf.abs(f - tf.linalg.matmul(B_mat,z) ),lp ) ), 1/lp) + lambda_parameter*tf.math.pow( tf.math.reduce_sum( tf.math.pow( tf.math.abs(f - tf.linalg.matmul(B_mat,z) ),lq ) ), 1/lq)
return cost_z
#print(B_mat.shape)
#l2_cocycle=np.zeros((B_mat.shape[1],1))
tf.random.set_seed(1)
optimizer = tf.optimizers.Adam(learning_rate=1e-4, beta_1=0.9, beta_2=0.999, epsilon=1e-7, amsgrad=False)
#optimizer = tf.keras.optimizers.SGD(learning_rate=1e-4) #Not recommended if you are not using tensorflow-gpu, may result a different result sometimes.
B_mat = tf.Variable(B_mat, name="B_mat", trainable=False, dtype=tf.float64)
f = tf.Variable(f, name="f", trainable=False, dtype=tf.float64)
if int(sys.argv[7])>0:
print('Before optim cost:',loss_function().numpy())
for i in range(int(sys.argv[7])):
train = optimizer.minimize(loss_function, var_list=trainable_variables)
#err = np.sum(np.abs(z.numpy() - z_init))
#print('>>> step',train.numpy(),' err=',err)
print('After optim cost:',loss_function().numpy(),' in ',train.numpy(),' steps')
res_tf=z.numpy()
else:
print('Non-optimized cost:',loss_function().numpy())
res_tf=z_init
#print("Absolute differentiation =>",np.sum(np.abs(res_tf-np.asarray(coords) )))
overall_coords=overall_coords+res_tf.T[0,:]
color = np.mod(res_tf.T[0,:],1)
#print(color)
return_list.append(color)
if PLOT:
fig = plt.figure(figsize=(5,5), dpi=100)
plt.scatter(dataset.T[0,:],dataset.T[1,:],s=10, c=color, cmap="hsv",zorder=10)
plt.clim(0,1)
plt.colorbar()
plt.axis('equal')
plt.title('Circular coordinates {}-th cocyle (mod {} - {}*L{} + {}*L{})'.format(g+1,prime,1-lambda_parameter,lp,lambda_parameter,lq))
plt.show()
edges_constant = []
thr = chosen_bar.birth
#####Constatn edges
#Want to check constant edges in all edges that were there when the cycle was created
for s in vr:
if s.dimension() != 1:
continue
elif s.data > thr:
break
if abs(color[s[0]]-color[s[1]]) <= toll:
edges_constant.append([dataset[s[0],:],dataset[s[1],:]])
edges_constant = np.array(edges_constant)
#pdf.savefig(fig)
#print('Loop End Time:',now.strftime("%Y-%m-%d %H:%M:%S"))
if PLOT:
fig = plt.figure(figsize=(5,5), dpi=100)
if edges_constant.T!=[]:
plt.plot(edges_constant.T[0,:],edges_constant.T[1,:], c='k', alpha=.5)
plt.scatter(dataset.T[0,:],dataset.T[1,:],s=10, c=color, cmap="hsv",zorder=10)
plt.clim(0,1)
plt.colorbar()
plt.axis('equal')
plt.title('Circular coordinates/constant edges, \n {}-th cocyle (mod {} - {}*L{} + {}*L{})'.format(g+1,prime,1-lambda_parameter,lp,lambda_parameter,lq))
#pdf.savefig(fig)
plt.show()
color_filenam = filenam+'_CircularCoordinates_'+str(lambda_parameter)+'_'+str(g)+'.txt'
np.savetxt(color_filenam,color)
print('Penalty function =>',(1-lambda_parameter),'*L^',lp,"+",lambda_parameter,"*L^",lq,' Coordinates=>',color_filenam,sep='')
if PLOT:
fig = plt.figure(figsize=(5,5), dpi=100)
angle = np.arctan(dataset.T[0,:]/dataset.T[1,:])
plt.scatter(angle,color,s=10, c='b',zorder=10)
plt.ylim([0,1])
plt.xlim([-np.pi/2,np.pi/2])
plt.title('Correlation plot against angle, \n {}-th cocyle (mod {} - {}*L{} + {}*L{})'.format(g+1,prime,1-lambda_parameter,lp,lambda_parameter,lq))
#pdf.savefig(fig)
plt.show()
embedding.extend([[np.sin(a) for a in 2*np.pi*color], [np.cos(a) for a in 2*np.pi*color]])
if PLOT:
fig = plt.figure(figsize=(5,5), dpi=100)
dist2 = np.sqrt(np.power(dataset.T[0,:],2)+np.power(dataset.T[1,:],2))
plt.scatter(dist2,color,s=10, c='b',zorder=10)
plt.ylim([0,1])
plt.xlim([0,maxscale])
plt.title('Correlation plot aginst distance, \n {}-th cocyle (mod {} - {}*L{} + {}*L{})'.format(g+1,prime,1-lambda_parameter,lp,lambda_parameter,lq))
#pdf.savefig(fig)
plt.show()
emb_filenam = filenam+'_Embedding_'+str(lambda_parameter)+'.txt'
np.savetxt(emb_filenam, np.array(embedding))
print('Penalty function =>',(1-lambda_parameter),'*L^',lp,"+",lambda_parameter,"*L^",lq,' Embeddings=>',emb_filenam,sep='')
#We plot the final circular coordinates with all co-cycles combined.
overall_edges_constant = []
overall_thr = float(sys.argv[2]) #For the combined coordinates, we choose the global threshold.
for s in vr:
if s.dimension() != 1:
continue
elif s.data > overall_thr:
break
if abs(overall_coords[s[0]]-overall_coords[s[1]]) <= toll:
overall_edges_constant.append([dataset[s[0],:],dataset[s[1],:]])
overall_edges_constant = np.array(overall_edges_constant)
if PLOT:
#fig = plt.figure(figsize=(5,5), dpi=100)
#if overall_edges_constant.T!=[]:
# plt.plot(overall_edges_constant.T[0,:],overall_edges_constant.T[1,:], c='k', alpha=.5)
#plt.scatter(dataset.T[0,:],dataset.T[1,:],s=10, c=overall_coords, cmap="hsv",zorder=10)
#plt.clim(0,1)
#plt.colorbar()
#plt.axis('equal')
#plt.title('Combined circular coordinates/constant edges \n (mod {} - {}*L{} + {}*L{})'.format(prime,1-lambda_parameter,lp,lambda_parameter,lq))
#pdf.savefig(fig)
#plt.show()
fig = plt.figure(figsize=(5,5), dpi=100)
angle = np.arctan(dataset.T[0,:]/dataset.T[1,:])
plt.scatter(angle,overall_coords,s=10, c='b',zorder=10)
plt.ylim([0,1])
plt.xlim([-np.pi/2,np.pi/2])
plt.title('Correlation plot \n (mod {} - {}*L{} + {}*L{})'.format(prime,1-lambda_parameter,lp,lambda_parameter,lq))
#pdf.savefig(fig)
plt.show()
fig = plt.figure(figsize=(5,5), dpi=100)
dist2 = np.sqrt(np.power(dataset.T[0,:],2)+np.power(dataset.T[1,:],2))
#print(color)
plt.scatter(dist2,color,s=10, c='b',zorder=10)
plt.ylim([0,1])
plt.xlim([0,maxscale])
plt.title('Correlation plot aginst distance, \n {}-th cocyle (mod {} - {}*L{} + {}*L{})'.format(g+1,prime,1-lambda_parameter,lp,lambda_parameter,lq))
#pdf.savefig(fig)
plt.show()
now = datetime.datetime.now()
print('>>>>>> End Time (GCC computation):',now.strftime("%Y-%m-%d %H:%M:%S"))
return return_list
def EPH_mask_demo(vertex_values, simplices):
times = []
t0 = time.time()
s2v_lst = [[
sorted(s),
sorted([[vertex_values[v], v] for v in s], key=lambda x: x[0])
] for s in simplices]
f_ord = [dionysus.Simplex(s[0], s[1][-1][0]) for s in s2v_lst] #takes max
f_ext = [dionysus.Simplex([-1] + s[0], s[1][0][0])
for s in s2v_lst] #takes min
ord_dict = {tuple(s[0]): s[1][-1][1] for s in s2v_lst}
ext_dict = {tuple([-1] + s[0]): s[1][0][1] for s in s2v_lst}
t1 = time.time()
times.append(t1 - t0)
t0 = time.time()
f_ord.sort(key=lambda s: (s.data, len(s)))
f_ext.sort(key=lambda s: (-s.data, len(s)))
t1 = time.time()
times.append(t1 - t0)
t0 = time.time()
#computes persistence
f = dionysus.Filtration([dionysus.Simplex([-1], -float('inf'))] + f_ord +
f_ext)
m = dionysus.homology_persistence(f)
t1 = time.time()
times.append(t1 - t0)
t0 = time.time()
dgms = [[[], []], [[], []], [[], []], [[],
[]]] #H0ord, H0ext, H1rel, H1ext
for i in range(len(m)):
dim = f[i].dimension()
if m.pair(i) < i:
continue # skip negative simplices to avoid double counting
if m.pair(
i
) != m.unpaired: #should be no unpaired apart from H0 from fictitious -1 vertex
pos, neg = f[i], f[m.pair(i)]
if pos.data != neg.data: #off diagonal
if -1 in pos and -1 in neg: #rel1
dgms[2][0].append(ext_dict[tuple(neg)])
dgms[2][1].append(ext_dict[tuple(pos)])
elif -1 not in pos and -1 not in neg: #ord0
dgms[1][0].append(ord_dict[tuple(pos)])
dgms[1][1].append(ord_dict[tuple(neg)])
else:
if dim == 0: #H0ext
dgms[0][0].append(ord_dict[tuple(pos)])
dgms[0][1].append(ext_dict[tuple(neg)])
if dim == 1: #H1ext
dgms[3][0].append(ext_dict[tuple(neg)])
dgms[3][1].append(ord_dict[tuple(pos)])
t1 = time.time()
times.append(t1 - t0)
t0 = time.time()
dgms = dionysus.init_diagrams(m, f)
t1 = time.time()
times.append(t1 - t0)
return times
def compute_dropouts(self, x, hiddens, thru=2, p=1, dropout_type='static', percentile=0, muls=None, invert=False, mat=None):
if dropout_type == 'static':
f = self.compute_static_filtration(x, hiddens, percentile=percentile)
if dropout_type == 'induced':
f = self.compute_induced_filtration(x, hiddens, percentile=percentile, mat=mat)
m = dion.homology_persistence(f)
dgms = dion.init_diagrams(m,f)
subgraphs = {}
# compute ones tensors of same hidden dimensions
muls = []
if invert:
for h in hiddens:
muls.append(torch.zeros(h.shape))
else:
for h in hiddens:
muls.append(torch.ones(h.shape))
fac = 1.0 if invert else 0.0
for i,c in enumerate(m):
if len(c) == 2:
if f[c[0].index][0] in subgraphs:
subgraphs[f[c[0].index][0]].add_edge(f[c[0].index][0],f[c[1].index][0],weight=f[i].data)
else:
eaten = False
for k, v in subgraphs.items():
if v.has_node(f[c[0].index][0]):
v.add_edge(f[c[0].index][0], f[c[1].index][0], weight=f[i].data)
eaten = True
break
if not eaten:
g = nx.Graph()
g.add_edge(f[c[0].index][0], f[c[1].index][0], weight=f[i].data)
subgraphs[f[c[0].index][0]] = g
# I don't think we need this composition. Disjoint subgraphs are fine.
# subgraph = nx.compose_all([subgraphs[k] for k in list(subgraphs.keys())[:thru]])
sub_keys = list(subgraphs.keys())[:thru]
lifetimes = np.empty(thru)
t = 0
for pt in dgms[0]:
if pt.death < float('inf'):
lifetimes[t] = pt.birth - pt.death
t += 1
if t >= thru:
break
max_lifetime = max(lifetimes)
min_lifetime = min(lifetimes)
ids = self.layerwise_ids()
layer_types = self.layer_types
for i in range(len(sub_keys)):
k = sub_keys[i]
lifetime = lifetimes[i]
lim = p*lifetime/max_lifetime
for e in subgraphs[k].edges(data=True):
r = np.random.uniform()
if r < lim:
for l in range(len(ids)-1):
if e[0] in ids[l] and e[1] in ids[l+1]:
# drop out this edge connection
# if layer_types[l] == 'convolution':
# num_filters = self.filters
# inp_size = self.input_size
# stride = self.stride
# kernel_size = self.kernel_size
# next_ids = list(ids[l+1])
# # muls[l] = (28-self.kernel_size+1)**2*self.filters
# filt_num = math.floor((e[1]-ids[l][-1])/((inp_size-kernel_size+1)**2))
# print('filtnum', filt_num)
# # filters are 0-indexed, so add 1 and 2 to get ids
# start_id = (inp_size-kernel_size+stride)**2*(filt_num+1)
# end_id = (inp_size-kernel_size+stride)**2*(filt_num+2)
# print('s min end', start_id, end_id, e[0], e[1])
# # find which element of the kernel produced this edge
# index_no = (e[1]-start_id) % (kernel_size*kernel_size)
# image_no = (e[1]-start_id)//(kernel_size*kernel_size)
muls[l][e[1]-ids[l+1][0]] = fac
return muls