我们如何 label 矩阵 plot 与预定义的标签列表（例如素数列表）？

Question

I have a CSV File with elliptic curve related data which looks as follows (excerpt):

3,19,[(1,4,1),(4,7,44)]
3,13,[(4,1,10)]
5,11,[(4,39,14)]
3,7,[(1,2,1),(1,3622,111),(4,17,10)]
3,5,[(4,1,2),(4,959,124)]
3,23,[(3,5,2)]
5,13,[(2,7,2),(2,8,1),(2,47,70),...]
7,11,[(1,2,1),(1,13,2),(1,53,4),...]
3,29,[(4,13,4)]
5,17,[(2,2,3),(4,6881,498)]
5,19,[(4,71,18)]
3,37,[(4,25,14)]
7,17,[(4,19,30)]
7,19,[(3,66,5)]

The first and second number in each line forms a pair of odd prime numbers and the list after these two primes is used to specify the color of the corresponding matrix cell. I want to generate a matrix plot where the x-axis and y-axis are labeled with the first 200 (odd) primes: 3, 5, 7, 11, 13, 17, 19, 23, ..., 1193, 1201, 1213, 1217, 1223, 1229 . The following code works fine to generate the colorized matrix plot.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.pyplot import figure
from sympy import sieve, prime
import itertools
import pandas as pd

matrix_size = 200
matrix = np.zeros((matrix_size, matrix_size))

with open('C:/Users/esultano/git/elliptic_curves/data/elliptic_curves.csv') as f:
    for line in f.readlines():
        line = line.strip()
        p, q, cases = eval(line)
        idx_p = sieve.search(p)[0]-2
        idx_q = sieve.search(q)[0]-2
        if idx_p < matrix_size and idx_q < matrix_size:
            cases_set = set()
            for case in cases:
                cases_set.add(case[0])
            cases_list = list(cases_set)
            val = sum(i*i for i in cases_list)
            matrix[idx_p,idx_q] = val
            matrix[idx_q,idx_p] = val

max_prime = prime(matrix_size+2)
axis_labels = list(sieve.primerange(3, max_prime))

fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
matrix_plot = ax.matshow(matrix, interpolation='nearest')
ax.set_xticklabels(axis_labels)
ax.set_yticklabels(axis_labels)
plt.show()

The plot looks as follows:

Unfortunatelly the axis labeling is not correct since each axis should span the primes from 3 to 1229 . How can I fix the axis labeling? I am not requiring to place each of these 200 primes as axis label (displaying a few labels would be fine).

Answer 1

As documentation of Axes.set_xticklabels() says, obligatory you have to call Axes.set_xticks() before.

I did necessary modifications to your code, so that it works now. Screenshot of output goes after code.

In my code you can see // 9 , because of this 10 primes (ticks) on axis is shown. If you want eg 20 numbers then do // 19 , etc.

Try it online! and See diffs

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.pyplot import figure
from sympy import sieve, prime
import itertools
import pandas as pd

matrix_size = 200
matrix = np.zeros((matrix_size, matrix_size))

with open('elliptic_curves.csv') as f:
    for line in f.readlines():
        line = line.strip()
        p, q, cases = eval(line)
        idx_p = sieve.search(p)[0]-2
        idx_q = sieve.search(q)[0]-2
        if idx_p < matrix_size and idx_q < matrix_size:
            cases_set = set()
            for case in cases:
                cases_set.add(case[0])
            cases_list = list(cases_set)
            val = sum(i*i for i in cases_list)
            matrix[idx_p,idx_q] = val
            matrix[idx_q,idx_p] = val

max_prime = prime(matrix_size+2)
axis_labels = list(enumerate(sieve.primerange(3, max_prime)))
axis_labels = axis_labels[::len(axis_labels) // 9][:-1] + [axis_labels[-1]]
ticks = [e[0] for e in axis_labels]
ticklabels = [e[1] for e in axis_labels]

fig = plt.figure(figsize=(8, 8))
ax = fig.add_subplot(111)
matrix_plot = ax.matshow(matrix, interpolation='nearest')
ax.set_xticks(ticks); ax.set_xticklabels(ticklabels)
ax.set_yticks(ticks); ax.set_yticklabels(ticklabels)
plt.show()

Output: