I would like to create a heatmap based on the matrix and bounds below and then plot the data (x1, x2) to see dots falling into the respective classes. The best I could do was use seaborn, but since the classes on both axes are not evenly spaced, it's hard to read the values corresponding to a dot, on both axes. Is there a way (using seaborn or any other library) to have the cell sizes of the heatmap proportional to the numbers of bounds1, bounds2, so that the values on the axis respect the right proportions? Below my example code. Thanks in advance!
import matplotlib.pyplot as plt
import matplotlib
import seaborn as sns
import numpy as np
bounds1 = [ 0. , 3. , 27.25 , 51.5 , 75.75 , 100. ]
bounds2 = [ 0. , 127., 165., 334. , 522. , 837., 1036., 1316., 1396., 3000]
matrix = [[0.3 , 0.5 , 0.7 , 0.9 , 1. , 0.9 , 0.7 , 0.4 , 0.3 , 0.3 ],
[0.22725, 0.37875, 0.53025, 0.68175, 0.7575, 0.68175, 0.53025, 0.303, 0.22725, 0.22725],
[0.1545 , 0.2575 , 0.3605 , 0.4635 , 0.515 , 0.4635 , 0.3605 , 0.206, 0.1545 , 0.1545 ],
[0.08175, 0.13625, 0.19075, 0.24525, 0.2725, 0.24525, 0.19075, 0.109, 0.08175, 0.08175],
[0.009 , 0.015 , 0.021 , 0.027 , 0.03 , 0.027 , 0.021 , 0.012, 0.009 , 0.009 ],
[0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. , 0. ]]
x2 = np.array([1.7765000e+00, 3.9435000e+00, 4.5005002e+00, 4.5005002e+00,
5.0325003e+00, 6.0124998e+00, 7.0035005e+00, 8.5289993e+00,
1.0150000e+01, 1.1111500e+01, 1.2193500e+01, 1.2193500e+01,
1.2193500e+01, 1.3665500e+01, 1.4780001e+01, 1.5908000e+01,
1.7007000e+01, 1.8597000e+01, 2.0439001e+01, 2.2047001e+01,
2.4724501e+01, 2.7719501e+01, 3.0307501e+01, 3.3042500e+01,
3.6326000e+01, 3.8622997e+01, 4.1292500e+01, 4.4293495e+01,
4.7881500e+01, 5.1105499e+01, 5.3708996e+01, 5.6908497e+01,
5.9103497e+01, 6.1926003e+01, 6.6175499e+01, 6.9841499e+01,
7.3534996e+01, 7.8712997e+01, 8.3992500e+01, 8.7227493e+01,
9.1489487e+01, 9.6500992e+01, 1.0068549e+02, 1.0625399e+02,
1.1245149e+02, 1.1828050e+02, 1.2343950e+02, 1.2875299e+02,
1.3531699e+02, 1.4146500e+02, 1.4726399e+02, 1.5307101e+02,
1.5917000e+02, 1.6554350e+02, 1.7167050e+02, 1.7897350e+02,
1.8766650e+02, 1.9705751e+02, 2.0610300e+02, 2.1421350e+02,
2.2146150e+02, 2.2975949e+02, 2.3886848e+02, 2.4766153e+02,
2.5618802e+02, 2.6506250e+02, 2.7528250e+02, 2.8465201e+02,
2.9246451e+02, 3.0088300e+02, 3.1069800e+02, 3.2031000e+02,
3.2950650e+02, 3.3929001e+02, 3.4919598e+02, 3.5904755e+02,
3.6873303e+02, 3.7849451e+02, 3.8831549e+02, 3.9915201e+02,
4.1044501e+02, 4.2201651e+02, 4.3467300e+02, 4.4735904e+02,
4.5926651e+02, 4.7117001e+02, 4.8231406e+02, 4.9426105e+02,
5.0784149e+02, 5.2100049e+02, 5.3492249e+02, 5.4818701e+02,
5.6144202e+02, 5.7350153e+02, 5.8634998e+02, 5.9905096e+02,
6.1240802e+02, 6.2555353e+02, 6.3893542e+02, 6.5263202e+02,
6.6708154e+02, 6.8029950e+02, 6.9236456e+02, 7.0441150e+02,
7.1579163e+02, 7.2795203e+02, 7.4106995e+02, 7.5507953e+02,
7.6881946e+02, 7.8363702e+02, 7.9864905e+02, 8.1473901e+02,
8.3018762e+02, 8.4492249e+02, 8.6007306e+02, 8.7455353e+02,
8.8938556e+02, 9.0509601e+02, 9.2196307e+02, 9.3774091e+02,
9.5391345e+02, 9.7015198e+02, 9.8671466e+02, 1.0042726e+03,
1.0209606e+03, 1.0379355e+03, 1.0547625e+03, 1.0726985e+03,
1.0912705e+03, 1.1100559e+03, 1.1288949e+03, 1.1476450e+03,
1.1654260e+03, 1.1823262e+03, 1.1997356e+03, 1.2171041e+03,
1.2353951e+03, 1.2535184e+03, 1.2718250e+03, 1.2903676e+03,
1.3086545e+03, 1.3270005e+03, 1.3444775e+03, 1.3612805e+03,
1.3784171e+03, 1.3958615e+03, 1.4131825e+03, 1.4311034e+03,
1.4489685e+03, 1.4677334e+03, 1.4869026e+03, 1.5062087e+03,
1.5258719e+03, 1.5452015e+03, 1.5653271e+03, 1.5853635e+03,
1.6053860e+03, 1.6247255e+03, 1.6436824e+03, 1.6632330e+03,
1.6819221e+03, 1.7011276e+03, 1.7198782e+03, 1.7383060e+03,
1.7565670e+03, 1.7749023e+03, 1.7950280e+03, 1.8149988e+03,
1.8360586e+03, 1.8572985e+03, 1.8782219e+03, 1.8991390e+03,
1.9200371e+03, 1.9395586e+03, 1.9595035e+03, 1.9790668e+03,
1.9995455e+03, 2.0203715e+03, 2.0416791e+03, 2.0616587e+03,
2.0819294e+03, 2.1032202e+03, 2.1253989e+03, 2.1470112e+03,
2.1686660e+03, 2.1908926e+03, 2.2129436e+03, 2.2349995e+03,
2.2567026e+03, 2.2784224e+03, 2.2997925e+03, 2.3198750e+03,
2.3393770e+03, 2.3588149e+03, 2.3783970e+03, 2.3988135e+03,
2.4175618e+03, 2.4363840e+03, 2.4572385e+03, 2.4773455e+03,
2.4965142e+03, 2.5157107e+03, 2.5354666e+03, 2.5554331e+03,
2.5757551e+03, 2.5955181e+03, 2.6157085e+03, 2.6348906e+03,
2.6535190e+03, 2.6727512e+03, 2.6923147e+03, 2.7118843e+03])
x1 = np.array([28.427988 , 28.891748 , 30.134018 , 29.833858 , 30.540195 ,
31.762226 , 32.163025 , 31.623648 , 31.964993 , 32.73733 ,
32.562325 , 32.89953 , 33.064743 , 32.76882 , 32.1024 ,
32.171394 , 33.363426 , 34.328148 , 36.24527 , 35.877434 ,
35.29762 , 35.193832 , 35.61119 , 36.50994 , 35.615444 ,
35.2758 , 34.447975 , 34.183205 , 35.781815 , 35.510662 ,
35.277668 , 35.26543 , 34.944313 , 35.301414 , 34.63578 ,
34.36223 , 35.496872 , 35.488243 , 35.494583 , 35.21087 ,
34.275524 , 33.945126 , 33.63986 , 33.904293 , 33.553017 ,
34.348408 , 33.84105 , 32.8437 , 32.19287 , 31.688663 ,
32.035015 , 31.641226 , 31.138266 , 30.629492 , 30.111526 ,
29.571909 , 29.244211 , 28.42031 , 27.908197 , 27.316568 ,
26.909412 , 25.928982 , 25.03047 , 24.354822 , 23.54626 ,
22.88031 , 23.000391 , 22.300774 , 21.988918 , 21.467094 ,
21.730871 , 23.060678 , 22.910374 , 24.45383 , 23.610855 ,
24.594006 , 24.263508 , 25.077124 , 23.9773 , 22.611958 ,
21.88306 , 21.014484 , 19.674965 , 18.745205 , 20.225956 ,
19.433172 , 19.451014 , 18.264421 , 17.588757 , 16.837574 ,
17.252535 , 18.967127 , 19.111462 , 19.90994 , 19.15653 ,
18.49522 , 17.376019 , 17.35794 , 16.200405 , 17.9445 ,
18.545986 , 17.69698 , 20.665318 , 20.90071 , 20.32658 ,
21.27805 , 21.145922 , 19.32898 , 19.160307 , 18.60541 ,
18.902897 , 18.843922 , 17.890692 , 18.197395 , 17.662706 ,
18.578962 , 18.898802 , 18.435923 , 17.644451 , 16.393314 ,
15.570944 , 16.779602 , 15.74104 , 15.041967 , 14.544464 ,
15.014386 , 14.156769 , 13.591232 , 12.386208 , 11.133551 ,
10.472783 , 9.7923355 , 10.571391 , 11.245247 , 10.063455 ,
10.742685 , 8.819294 , 8.141182 , 6.9487176 , 6.3410373 ,
7.033326 , 6.5856943 , 6.0214376 , 6.6087174 , 9.583405 ,
9.4608135 , 9.183213 , 10.673293 , 9.477165 , 8.667246 ,
7.3392615 , 6.2609572 , 5.5752296 , 4.4312773 , 4.0997415 ,
4.127005 , 4.072541 , 3.5704772 , 2.7370691 , 2.3750854 ,
2.0708292 , 3.4086852 , 3.8237891 , 3.9072614 , 3.1760776 ,
2.4963813 , 1.5232614 , 0.931248 , 0.49159998, 0.21676798,
0.874704 , 2.0560641 , 1.5494559 , 3.0944476 , 2.6151357 ,
2.7285278 , 3.4450078 , 3.4614875 , 5.779072 , 8.063728 ,
7.7077436 , 7.8576636 , 7.4494233 , 6.5933595 , 6.1667037 ,
4.9452477 , 5.6894236 , 6.0578876 , 5.9922714 , 5.060448 ,
6.074832 , 6.7870073 , 5.7388477 , 5.8681116 , 4.7604475 ,
4.2740316 , 3.785328 , 4.060576 , 4.9203672 , 5.355184 ,
4.793792 , 3.8007674 , 3.6115997 , 2.7794237 , 2.5385118 ,
5.1410074 , 5.5506234 , 7.638063 , 7.512544 , 6.617264 ,
6.5637918 , 6.452815 ])
# define colormap
N=5 # number of desired color bins
cmap = plt.cm.RdYlGn_r
cmaplist = [cmap(i) for i in range(cmap.N)]
cmap = cmap.from_list('Custom cmap', cmaplist, cmap.N)
# define the bins and normalize
bounds = np.linspace(0, 1, N+1)
norm = matplotlib.colors.BoundaryNorm(bounds, cmap.N)
fig, ax = plt.subplots(figsize=(15,10))
ax = sns.heatmap(matrix, cmap=cmap, norm=norm, ax=ax, linewidths=0.1)
ax.invert_yaxis()
ax.tick_params(axis = 'both', which = 'major')
ax.set_xticklabels(bounds2)
ax.set_yticklabels(bounds1)
cbar = ax.collections[0].colorbar
cbar.set_ticks(bounds)
cbar.set_ticklabels(bounds)
x2_idx = np.interp(x2, bounds2, range(len(bounds2)))+0.5 # +0.5: to shift data start to bin center
x1_idx = np.interp(x1, bounds1, range(len(bounds1)))+0.5 # +0.5: to shift data start to bin center
ax.plot(x2_idx, x1_idx, color='black', marker='o')
plt.show()
plt.close()
