Ripser.py 0.6.4 Representative Cocycles ( Matplotlib 3.6.2)

See https://ripser.scikit-tda.org/en/latest/notebooks/Representative%20Cocycles.html

Версия  risperCohomology.py для Matplotlib 3.6.2.  

Fixed code lines highlited blue

(.env) boris@UbuntuLTS:~/RIPSER$ cat risperCohomology642.py

import numpy as np

import matplotlib.pyplot as plt

from ripser import ripser

from persim import plot_diagrams

import tadasets

def drawLineColored(X, C):

    for i in range(X.shape[0]-1):

        lines=plt.plot(X[i:i+2, 0], X[i:i+2, 1], c=C[i, :])

        plt.setp(lines, color='black', linewidth=2.0)

def plotCocycle2D(D, X, cocycle, thresh):

    """

    Given a 2D point cloud X, display a cocycle projected

    onto edges under a given threshold "thresh"

    """

    #Plot all edges under the threshold

    N = X.shape[0]

    t = np.linspace(0, 1, 10)

    c = plt.get_cmap('Greys')

    C = c(np.array(np.round(np.linspace(0, 255, len(t))), dtype=np.int32))

    C = C[:, 0:3]

    for i in range(N):

        for j in range(N):

            if D[i, j] <= thresh:

                Y = np.zeros((len(t), 2))

                Y[:, 0] = X[i, 0] + t*(X[j, 0] - X[i, 0])

                Y[:, 1] = X[i, 1] + t*(X[j, 1] - X[i, 1])

                drawLineColored(Y, C)

    #Plot cocycle projected to edges under the chosen threshold

    for k in range(cocycle.shape[0]):

        [i, j, val] = cocycle[k, :]

        if D[i, j] <= thresh:

            [i, j] = [min(i, j), max(i, j)]

            a = 0.5*(X[i, :] + X[j, :])

            plt.text(a[0], a[1], '%g'%val, color='b')

    #Plot vertex labels

    for i in range(N):

        plt.text(X[i, 0], X[i, 1], '%i'%i, color='r')

    plt.axis('equal')

np.random.seed(9)

x = tadasets.dsphere(n=12, d=1, noise=0.1)

plt.scatter(x[:, 0], x[:, 1])

plt.axis('equal')

plt.show()

result = ripser(x, coeff=17, do_cocycles=True)

diagrams = result['dgms']

cocycles = result['cocycles']

D = result['dperm2all']

dgm1 = diagrams[1]

idx = np.argmax(dgm1[:, 1] - dgm1[:, 0])

plot_diagrams(diagrams, show = False)

plt.scatter(dgm1[idx, 0], dgm1[idx, 1], 20, 'k', 'x')

plt.title("Max 1D birth = %.3g, death = %.3g"%(dgm1[idx, 0], dgm1[idx, 1]))

plt.show()

cocycle = cocycles[1][idx]

thresh = dgm1[idx, 1] #Project cocycle onto edges less than or equal to death time

plotCocycle2D(D, x, cocycle, thresh)

plt.title("1-Form Thresh=%g"%thresh)

plt.show()

thresh = dgm1[idx, 1]-0.00001 #Project cocycle onto edges less slightly less than the death time

plotCocycle2D(D, x, cocycle, thresh)

plt.title("1-Form Thresh=%g"%thresh)

plt.show()

thresh = dgm1[idx, 0] #Project cocycle onto edges that have lengths less than or equal to the birth time

plotCocycle2D(D, x, cocycle, thresh)

plt.title("1-Form Thresh=%g"%thresh)

plt.show()

REFRENCES

1. https://informatics-ege.blogspot.com/2022/11/ripser-demonstration.html