Develop Reference

How to plot pdf at the same graph as the histogram

I wrote a function to plot a histogram of the following data(shortened)
data_1 =
[0.68417915 0.53041328 0.05499373 0.32483917 0.30501979 0.12136537
0.22964997 0.5837272 0.06000122 0.69908738 0.15690346 0.20363323
0.10390346 0.98658757 0.98359924 0.29493355 0.72561782 0.75613625
0.69628136 0.71322217 0.63060554 0.91118187 0.14915375 0.70929528
0.42408604 0.35388851 0.62253336 0.63676291 0.44358184 0.45063505
0.36477958 0.15807182 0.714753 0.96713497 0.4094859 0.56495619
0.57509395 0.9355384 0.46284749 0.67779101 0.92363017 0.05682404
0.89631817 0.52587218 0.79428246 0.14486141 0.31300898 0.10176549
0.21841843 0.25688406 0.55415834 0.84957183 0.76246304 0.98489949
0.3936749 0.51460251 0.50138111 0.36060756 0.44854838 0.3919771
0.05113578 0.23980216 0.96111616 0.05969004 0.63652018 0.77869691
0.74565952 0.53789898 0.8876854 0.02370424 0.75647449 0.1494505
0.56362217 0.84942793 0.75265825 0.43319662 0.1012875 0.09946243
0.69463561 0.46931918 0.12913483 0.22142044 0.77253391 0.1691685
0.41114265 0.011321 0.41941435 0.28070956 0.65810948 0.58770776
0.68763623 0.36828773 0.70466821 0.8332811 0.12652526 0.16867114
0.59106388 0.56926637 0.87954323 0.62176163 7.35566843e-01
1.00146415e-01 6.68137620e-01 4.39246138e-01
3.75875260e-01 2.12544712e-02 3.68062161e-01 5.35692768e-01
6.50231419e-01 7.51573475e-01 1.43792206e-01 3.51057868e-01
1.77127799e-03 9.88480387e-01 8.73988015e-01 3.78791845e-01
5.89179323e-01 4.05978444e-01 6.88178816e-01 8.73515486e-01
3.66033185e-01 7.98291151e-01 2.30921252e-01 8.68201375e-04
4.92515713e-01 4.56100036e-01 5.66357689e-01 1.18801303e-01
8.15197293e-01 1.90998886e-02 4.91136435e-01 4.90613456e-01
1.31219088e-01 8.44170500e-01 1.72284226e-01 9.48296215e-01
7.36638954e-01 2.23674369e-01 7.46383520e-02 1.56815967e-01
6.14167905e-02 9.55175567e-01 1.74517808e-01 6.16529512e-01
7.02704931e-01 2.17204373e-01 6.78545848e-01 8.99756168e-01
5.28857712e-01 8.34009864e-01 5.87747412e-01 9.01901813e-02
9.94429960e-01 8.20847209e-01 3.88627889e-01 7.99302264e-01
1.19291073e-01 3.92748464e-01 4.84674232e-01 6.86047613e-01
9.09811416e-01 4.11619033e-01 5.22738580e-01 7.87679969e-01
8.31886542e-01 5.75564445e-01 7.03306890e-01 4.37121850e-01
2.17908948e-01 9.27734103e-01 1.69151398e-01 1.02815443e-01
8.86529746e-01 9.12471508e-01 3.62394360e-02 5.75760637e-01
9.02910130e-01 9.46808438e-01 5.22324825e-01 7.41599515e-02
1.67554744e-01 9.67044492e-01 6.41305316e-02 2.02375526e-01
7.87664750e-01 4.10928526e-01 3.75066800e-01 1.02825038e-01
7.99960722e-01 5.15931793e-01 6.07891990e-01 4.22650890e-01
2.50692729e-01 4.76696332e-01 3.42881458e-01 4.56350909e-01
2.21493003e-02 9.22045389e-01 4.31748031e-01 3.67451551e-01]
And the following code
def plot_histo(data_list, bin_count):
plt.hist(data_list, bins=bin_count, density= True)
return plt.show()
plot_1 = plot_histo(data_1, 100)
I also want to plot the pdf of this distribution on the same graph, but i don't really know how to do that since I'm new to python! Any tips?

There are several methods to estimate the pdf from the samples.
One way is to use kernel density estimation, which can be done easily with sns.kdeplot.
Another way is to fit parameters of a known distribution, e.g. with scikit-learn GaussianMixture if you have reasons to think your data is gaussian.
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as stats
import seaborn as sns
from sklearn.mixture import GaussianMixture
num_samples = 1_000
mu = 3.14
sigma = 1.27
data = np.random.randn(num_samples) * sigma + mu
fig, ax = plt.subplots()
# Histogram
ax.hist(data, bins=10, density=True, label="Histogram")
# Kernel Density Estimation (KDE)
sns.kdeplot(data, bw_method=0.2, ax=ax, label="KDE")
# Gaussian fitting
gm = GaussianMixture(n_components=1).fit(data.reshape(-1, 1))
mu_ = gm.means_.item()
sigma_ = gm.covariances_.item()
xx = np.linspace(*ax.get_xlim(), num=100)
plt.plot(xx, stats.norm.pdf(xx, mu_, sigma_), label="Gaussian")
ax.legend()
plt.show()

How to plot a wind rose map with depend of color set to gas concentration

speed=[0.129438,0.0366483,0.439946,0.090253,0.19373,0.592419,0.00903306,0.520847,0.513714,1.16971,5.12548,4.37745,3.2362,2.91004,1.60186,0.115595,0.270153,0.19367,0.0865046,0.558443,0.613072,0.648203,0.0770592,0.81772,0.234523,1.04013,0.352675,0.0673293,0.492684,0.109398,0.402816,0.140199,0.998795,0.367604,0.52436,0.0968265,1.59786,2.43149,2.94133,0.940624,0.257224,0,0,0.0199409,0.125302,0,0.367911,0.259797,0.237776,0.45428,0.507738,0.389389,0.388758,0.335398,0.510133,0.180295,0.0738368,0.780367,0.925679,1.93922,1.96569,1.39523,0.824564,0.00833059,0,0.0498536,0.112622,0,0.00843256,0.0269059,0.00816307,0.0582206,0.578959,1.0171,2.24302,1.92721]
direction=[189.538,215.866,264.086,135.325,165.893,44.2853,136.158,350.437,83.2484,277.783,288.064,279.222,267.214,265.913,235.173,181.206,136.14,144.281,134.581,108.16,75.4158,22.2881,328.882,68.3736,129.256,278.097,326.581,35.7096,321.297,338.31,354.109,24.1976,38.1465,39.2318,63.8145,119.817,186.106,182.673,185.475,173.223,139.843,np.nan,np.nan,40.9179,320.081,np.nan,333.054,354.726,357.716,18.1253,355.461,286.084,319.073,324.621,339.681,313.331,346.647,84.9661,86.7814,88.5452,104.456,128.953,87.5388,72.1999,np.nan,345.5,356.68,np.nan,316.586,338.82,334.731,98.3435,85.669,25.9086,42.6986,34.4194]
gas=[1.10986,1.25806,1.50921,1.37323,1.41317,1.15709,1.16005,1.43474,1.43952,1.03368,0.246893,0.139811,0.15603,0.203752,0.177984,0.164834,0.528146,0.602864,0.809435,1.0036,1.05669,1.05348,0.988772,1.0588,1.12066,1.15746,1.23219,1.142,1.21676,1.27093,1.00094,1.16773,1.16163,1.1715,0.999969,0.863695,0.832681,0.92631,1.01416,1.02708,1.0084,1.00666,1.06311,1.32098,1.48134,1.60667,1.60324,1.58663,1.41159,1.3251,1.25114,1.24269,1.16683,1.20762,1.0616,1.21975,1.21312,1.11416,0.981076,0.707948,0.590113,0.515484,0.417111,0.436767,0.644229,0.998097,1.24321,1.45975,1.3905,1.50087,1.63685,1.53855,1.21446,1.09367,0.790929,0.693877]
I know it has to be np.meshgrid(direction,speed) firstly, but the var of 'gas' I don't know to how to matching direction and speed so that I can plot a windrose map. Just like a image from a paper I read as follow.
I really appreciate for any help or suggestion.

You might be interested in the Windrose library for some options to create this kind of plots, for example a polar filled contour plot.
Alternatively, here is an approach with small 2D regions in a polar plot:
import matplotlib.pyplot as plt
import numpy as np
from scipy import interpolate
speed = [0.129438, 0.0366483, 0.439946, 0.090253, 0.19373, 0.592419, 0.00903306, 0.520847, 0.513714, 1.16971, 5.12548, 4.37745, 3.2362, 2.91004, 1.60186, 0.115595, 0.270153, 0.19367, 0.0865046, 0.558443, 0.613072, 0.648203, 0.0770592, 0.81772, 0.234523, 1.04013, 0.352675, 0.0673293, 0.492684, 0.109398, 0.402816, 0.140199, 0.998795, 0.367604, 0.52436, 0.0968265, 1.59786, 2.43149, 2.94133, 0.940624, 0.257224, 0, 0, 0.0199409, 0.125302, 0, 0.367911, 0.259797, 0.237776, 0.45428, 0.507738, 0.389389, 0.388758, 0.335398, 0.510133, 0.180295, 0.0738368, 0.780367, 0.925679, 1.93922, 1.96569, 1.39523, 0.824564, 0.00833059, 0, 0.0498536, 0.112622, 0, 0.00843256, 0.0269059, 0.00816307, 0.0582206, 0.578959, 1.0171, 2.24302, 1.92721]
direction = [189.538, 215.866, 264.086, 135.325, 165.893, 44.2853, 136.158, 350.437, 83.2484, 277.783, 288.064, 279.222, 267.214, 265.913, 235.173, 181.206, 136.14, 144.281, 134.581, 108.16, 75.4158, 22.2881, 328.882, 68.3736, 129.256, 278.097, 326.581, 35.7096, 321.297, 338.31, 354.109, 24.1976, 38.1465, 39.2318, 63.8145, 119.817, 186.106, 182.673, 185.475, 173.223, 139.843, np.nan, np.nan, 40.9179, 320.081, np.nan, 333.054, 354.726, 357.716, 18.1253, 355.461, 286.084, 319.073, 324.621, 339.681, 313.331, 346.647, 84.9661, 86.7814, 88.5452, 104.456, 128.953, 87.5388, 72.1999, np.nan, 345.5, 356.68, np.nan, 316.586, 338.82, 334.731, 98.3435, 85.669, 25.9086, 42.6986, 34.4194]
gas = [1.10986, 1.25806, 1.50921, 1.37323, 1.41317, 1.15709, 1.16005, 1.43474, 1.43952, 1.03368, 0.246893, 0.139811, 0.15603, 0.203752, 0.177984, 0.164834, 0.528146, 0.602864, 0.809435, 1.0036, 1.05669, 1.05348, 0.988772, 1.0588, 1.12066, 1.15746, 1.23219, 1.142, 1.21676, 1.27093, 1.00094, 1.16773, 1.16163, 1.1715, 0.999969, 0.863695, 0.832681, 0.92631, 1.01416, 1.02708, 1.0084, 1.00666, 1.06311, 1.32098, 1.48134, 1.60667, 1.60324, 1.58663, 1.41159, 1.3251, 1.25114, 1.24269, 1.16683, 1.20762, 1.0616, 1.21975, 1.21312, 1.11416, 0.981076, 0.707948, 0.590113, 0.515484, 0.417111, 0.436767, 0.644229, 0.998097, 1.24321, 1.45975, 1.3905, 1.50087, 1.63685, 1.53855, 1.21446, 1.09367, 0.790929, 0.693877]
dir_rad = np.radians(np.array(direction))
speed = np.array(speed)
gas = np.array(gas)
WD, WS = np.meshgrid(np.linspace(0, 2 * np.pi, 37), np.linspace(min(speed), max(speed), 16))
filter = np.isfinite(dir_rad)
Z = interpolate.griddata((dir_rad[filter], speed[filter]), gas[filter], (WD, WS), method='linear')
fig, ax = plt.subplots(subplot_kw={"projection": "polar"})
cmap = plt.get_cmap('inferno')
img = ax.pcolormesh(WD, WS, Z, cmap=cmap)
plt.colorbar(img)
plt.show()
PS: Try to avoid the 'jet' colormap, as it creates a yellow highlight at the wrong spots.
Here is another approach, using hist2d, which doesn't interpolate the values over larger regions:
import matplotlib.pyplot as plt
import numpy as np
speed = [0.129438, 0.0366483, 0.439946, 0.090253, 0.19373, 0.592419, 0.00903306, 0.520847, 0.513714, 1.16971, 5.12548, 4.37745, 3.2362, 2.91004, 1.60186, 0.115595, 0.270153, 0.19367, 0.0865046, 0.558443, 0.613072, 0.648203, 0.0770592, 0.81772, 0.234523, 1.04013, 0.352675, 0.0673293, 0.492684, 0.109398, 0.402816, 0.140199, 0.998795, 0.367604, 0.52436, 0.0968265, 1.59786, 2.43149, 2.94133, 0.940624, 0.257224, 0, 0, 0.0199409, 0.125302, 0, 0.367911, 0.259797, 0.237776, 0.45428, 0.507738, 0.389389, 0.388758, 0.335398, 0.510133, 0.180295, 0.0738368, 0.780367, 0.925679, 1.93922, 1.96569, 1.39523, 0.824564, 0.00833059, 0, 0.0498536, 0.112622, 0, 0.00843256, 0.0269059, 0.00816307, 0.0582206, 0.578959, 1.0171, 2.24302, 1.92721]
direction = [189.538, 215.866, 264.086, 135.325, 165.893, 44.2853, 136.158, 350.437, 83.2484, 277.783, 288.064, 279.222, 267.214, 265.913, 235.173, 181.206, 136.14, 144.281, 134.581, 108.16, 75.4158, 22.2881, 328.882, 68.3736, 129.256, 278.097, 326.581, 35.7096, 321.297, 338.31, 354.109, 24.1976, 38.1465, 39.2318, 63.8145, 119.817, 186.106, 182.673, 185.475, 173.223, 139.843, np.nan, np.nan, 40.9179, 320.081, np.nan, 333.054, 354.726, 357.716, 18.1253, 355.461, 286.084, 319.073, 324.621, 339.681, 313.331, 346.647, 84.9661, 86.7814, 88.5452, 104.456, 128.953, 87.5388, 72.1999, np.nan, 345.5, 356.68, np.nan, 316.586, 338.82, 334.731, 98.3435, 85.669, 25.9086, 42.6986, 34.4194]
gas = [1.10986, 1.25806, 1.50921, 1.37323, 1.41317, 1.15709, 1.16005, 1.43474, 1.43952, 1.03368, 0.246893, 0.139811, 0.15603, 0.203752, 0.177984, 0.164834, 0.528146, 0.602864, 0.809435, 1.0036, 1.05669, 1.05348, 0.988772, 1.0588, 1.12066, 1.15746, 1.23219, 1.142, 1.21676, 1.27093, 1.00094, 1.16773, 1.16163, 1.1715, 0.999969, 0.863695, 0.832681, 0.92631, 1.01416, 1.02708, 1.0084, 1.00666, 1.06311, 1.32098, 1.48134, 1.60667, 1.60324, 1.58663, 1.41159, 1.3251, 1.25114, 1.24269, 1.16683, 1.20762, 1.0616, 1.21975, 1.21312, 1.11416, 0.981076, 0.707948, 0.590113, 0.515484, 0.417111, 0.436767, 0.644229, 0.998097, 1.24321, 1.45975, 1.3905, 1.50087, 1.63685, 1.53855, 1.21446, 1.09367, 0.790929, 0.693877]
dir_rad = np.radians(np.array(direction))
speed = np.array(speed)
gas = np.array(gas)
fig, axes = plt.subplots(ncols=2, figsize=(10, 4), subplot_kw={"projection": "polar"})
cmap = 'inferno_r'
for ax in axes:
if ax == axes[1]:
vals, _, _, img = ax.hist2d(dir_rad, speed,
bins=(np.linspace(0, 2 * np.pi, 37), np.linspace(min(speed), max(speed), 16)),
weights=gas, cmap=cmap, vmin=0, vmax=max(gas) * 1.1, cmin=0.00001)
else:
img = ax.scatter(dir_rad, speed, c=gas, cmap=cmap, vmin=0, vmax=max(gas) * 1.1)
# ax.set_theta_zero_location('N')
# ax.set_theta_direction(-1)
plt.colorbar(img, ax=ax, pad=0.12)
plt.show()

Try polar scatter plot:
import numpy as np
import matplotlib.pyplot as plt
speed=[0.129438,0.0366483,0.439946,0.090253,0.19373,0.592419,0.00903306,0.520847,0.513714,1.16971,5.12548,4.37745,3.2362,2.91004,1.60186,0.115595,0.270153,0.19367,0.0865046,0.558443,0.613072,0.648203,0.0770592,0.81772,0.234523,1.04013,0.352675,0.0673293,0.492684,0.109398,0.402816,0.140199,0.998795,0.367604,0.52436,0.0968265,1.59786,2.43149,2.94133,0.940624,0.257224,0,0,0.0199409,0.125302,0,0.367911,0.259797,0.237776,0.45428,0.507738,0.389389,0.388758,0.335398,0.510133,0.180295,0.0738368,0.780367,0.925679,1.93922,1.96569,1.39523,0.824564,0.00833059,0,0.0498536,0.112622,0,0.00843256,0.0269059,0.00816307,0.0582206,0.578959,1.0171,2.24302,1.92721]
direction=[189.538,215.866,264.086,135.325,165.893,44.2853,136.158,350.437,83.2484,277.783,288.064,279.222,267.214,265.913,235.173,181.206,136.14,144.281,134.581,108.16,75.4158,22.2881,328.882,68.3736,129.256,278.097,326.581,35.7096,321.297,338.31,354.109,24.1976,38.1465,39.2318,63.8145,119.817,186.106,182.673,185.475,173.223,139.843,np.nan,np.nan,40.9179,320.081,np.nan,333.054,354.726,357.716,18.1253,355.461,286.084,319.073,324.621,339.681,313.331,346.647,84.9661,86.7814,88.5452,104.456,128.953,87.5388,72.1999,np.nan,345.5,356.68,np.nan,316.586,338.82,334.731,98.3435,85.669,25.9086,42.6986,34.4194]
gas=[1.10986,1.25806,1.50921,1.37323,1.41317,1.15709,1.16005,1.43474,1.43952,1.03368,0.246893,0.139811,0.15603,0.203752,0.177984,0.164834,0.528146,0.602864,0.809435,1.0036,1.05669,1.05348,0.988772,1.0588,1.12066,1.15746,1.23219,1.142,1.21676,1.27093,1.00094,1.16773,1.16163,1.1715,0.999969,0.863695,0.832681,0.92631,1.01416,1.02708,1.0084,1.00666,1.06311,1.32098,1.48134,1.60667,1.60324,1.58663,1.41159,1.3251,1.25114,1.24269,1.16683,1.20762,1.0616,1.21975,1.21312,1.11416,0.981076,0.707948,0.590113,0.515484,0.417111,0.436767,0.644229,0.998097,1.24321,1.45975,1.3905,1.50087,1.63685,1.53855,1.21446,1.09367,0.790929,0.693877]
gas = [g * 100 for g in gas]
fig = plt.figure()
ax = fig.add_subplot(111, projection='polar')
c = ax.scatter(direction, speed, c=direction, s=gas, cmap='hsv', alpha=0.25)
result:
I multiplied gas by 10 to make points bigger, but you may adjust it as You need,
as well as lists/variables to axis assigment and rotation of coordinate system.

Colormap/color problems with bar3d plot

I have written some code to plot the longitude and latitude of towns/cities in the UK with the 3D bar height representing the population of these places. I am trying to also colour code the bars using a colormap so that the variation in population can be more easily seen. However, my code doesnt seem to follow the colormap and instead all the bars have very similar colours - I am not sure where I have gone wrong
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import numpy as np
pop = [189120, 91297, 107123, 107355, 94782, 87590, 142968, 1085810, 117963, 147663, 194189, 187503, 349561, 229700, 535907, 145818, 335145, 110507, 116447, 86011, 88483, 119441, 325949, 106943, 92363, 255394, 109805, 144170, 109185, 468720, 113507, 120046, 104157, 589900, 136362, 88243, 88134, 88855, 91053, 94932, 120256, 162949, 284321, 144957, 474632, 443760, 100160, 552267, 8173941, 211228, 107627, 510746, 174700, 171750, 268064, 128060, 215173, 186682, 289301, 86552, 96555, 159994, 161707, 234982, 154718, 238137, 97886, 95580, 218705, 107926, 109691, 134022, 103886, 518090, 155298, 123187, 253651, 175547, 91703, 102885, 89663, 105878, 270726, 174286, 109015, 179485, 182441, 142723, 99251, 165456, 131982, 91930, 218791, 83641, 103608, 105367, 265178, 100153, 109120, 152841]
lat = [57.14369, 53.55, 51.56844, 51.26249, 51.37795, 52.13459, 53.39337, 52.48142, 53.75, 53.81667, 53.58333, 50.72048, 53.79391, 50.82838, 51.45523, 52.2, 51.48, 51.73575, 51.9, 53.1905, 53.25, 51.88921, 52.40656, 51.11303, 54.52429, 52.92277, 53.52327, 56.5, 50.76871, 55.95206, 50.7236, 54.96209, 51.38914, 55.86515, 51.86568, 53.56539, 53.71667, 54.68611, 50.85519, 51.75369, 51.62907, 53.64904, 53.7446, 52.05917, 53.79648, 52.6386, 53.22683, 53.41058, 51.50853, 51.87967, 51.26667, 53.48095, 54.57623, 52.04172, 54.97328, 51.58774, 52.25, 52.62783, 52.9536, 52.52323, 53.54051, 51.75222, 52.57364, 50.37153, 50.71667, 50.79899, 53.76667, 51.58571, 51.45625, 53.61766, 53.43012, 53.42519, 53.48771, 53.38297, 51.50949, 52.41426, 50.90395, 51.53782, 53.64779, 53.45, 51.90224, 53.40979, 53.00415, 54.90465, 52.56667, 51.62079, 51.55797, 52.67659, 53.68331, 53.39254, 51.65531, 52.51868, 51.50853, 51.34603, 53.53333, 51.31903, 52.58547, 52.18935, 50.81448, 53.95763]
long = [-2.09814, -1.48333, 0.45782, -1.08708, -2.35907, -0.46632, -3.01479, -1.89983, -2.48333, -3.05, -2.43333, -1.8795, -1.75206, -0.13947, -2.59665, 0.11667, -3.18, 0.46958, -2.08333, -2.89189, -1.41667, 0.90421, -1.51217, -0.18312, -1.55039, -1.47663, -1.13691, -2.96667, 0.28453, -3.19648, -3.52751, -1.60168, 0.54863, -4.25763, -2.2431, -0.07553, -1.85, -1.2125, 0.57292, -0.47517, -0.74934, -1.78416, -0.33525, 1.15545, -1.54785, -1.13169, -0.53792, -2.97794, -0.12574, -0.41748, 0.51667, -2.23743, -1.23483, -0.75583, -1.61396, -2.99835, -0.88333, 1.29834, -1.15047, -1.46523, -2.1183, -1.25596, -0.24777, -4.14305, -2.0, -1.09125, -2.71667, 0.60459, -0.97113, -2.1552, -1.35678, -2.32443, -2.29042, -1.4659, -0.59541, -1.78094, -1.40428, 0.71433, -3.00648, -2.73333, -0.20256, -2.15761, -2.18538, -1.38222, -1.81667, -3.94323, -1.78116, -2.44926, -1.49768, -2.58024, -0.39602, -1.9945, -0.12574, -2.97665, -2.61667, -0.55893, -2.12296, -2.22001, -0.37126, -1.08271]
fig = plt.figure()
ax = Axes3D(fig)
X,Y,Z = np.array(long),np.array(lat),np.log10(np.array(pop))
colours = plt.cm.rainbow_r(Z/np.log10(max(pop)))
plot1 = ax.bar3d(X,Y,Z,dx=0.2,dy=0.2,dz=Z/3,color=colours)
ax.set_xlabel('\nLongitude (\u00B0)')
ax.set_ylabel('\nLatitude (\u00B0)')
ax.set_zlabel('\nlog\u2081\u2080(Population)')
ax.set_zlim3d(4,7)
ax.view_init(elev=70,azim=280)
colourMap = plt.cm.ScalarMappable(cmap=plt.cm.rainbow_r)
colourMap.set_array(Z)
colBar = plt.colorbar(colourMap).set_label('log\u2081\u2080(Population)')
plt.show()
The code produces this plot:
I think that the majority of the bars should be red/orange in colour, with only the major cities being yellow/green/blue...

(Z/np.log10(max(pop))).min() is 0.7. So all values are indeed in the upper range of the colormap.
You probably want to normalize your data before giving it to the colormap:
norm = plt.Normalize((Z/np.log10(max(pop))).min(), (Z/np.log10(max(pop))).max())
colours = plt.cm.rainbow_r(norm(Z/np.log10(max(pop))))

2d density contour plot with matplotlib

I'm attempting to plot my dataset, x and y (generated from a csv file via numpy.genfromtxt('/Users/.../somedata.csv', delimiter=',', unpack=True)) as a simple density plot. To ensure this is self containing I will define them here:
x = [ 0.2933215 0.2336305 0.2898058 0.2563835 0.1539951 0.1790058
0.1957057 0.5048573 0.3302402 0.2896122 0.4154893 0.4948401
0.4688092 0.4404935 0.2901995 0.3793949 0.6343423 0.6786809
0.5126349 0.4326627 0.2318232 0.538646 0.1351541 0.2044524
0.3063099 0.2760263 0.1577156 0.2980986 0.2507897 0.1445099
0.2279241 0.4229934 0.1657194 0.321832 0.2290785 0.2676585
0.2478505 0.3810182 0.2535708 0.157562 0.1618909 0.2194217
0.1888698 0.2614876 0.1894155 0.4802076 0.1059326 0.3837571
0.3609228 0.2827142 0.2705508 0.6498625 0.2392224 0.1541462
0.4540277 0.1624592 0.160438 0.109423 0.146836 0.4896905
0.2052707 0.2668798 0.2506224 0.5041728 0.201774 0.14907
0.21835 0.1609169 0.1609169 0.205676 0.4500787 0.2504743
0.1906289 0.3447547 0.1223678 0.112275 0.2269951 0.1616036
0.1532181 0.1940938 0.1457424 0.1094261 0.1636615 0.1622345
0.705272 0.3158471 0.1416916 0.1290324 0.3139713 0.2422002
0.1593835 0.08493619 0.08358301 0.09691083 0.2580497 0.1805554 ]
y = [ 1.395807 1.31553 1.333902 1.253527 1.292779 1.10401 1.42933
1.525589 1.274508 1.16183 1.403394 1.588711 1.346775 1.606438
1.296017 1.767366 1.460237 1.401834 1.172348 1.341594 1.3845
1.479691 1.484053 1.468544 1.405156 1.653604 1.648146 1.417261
1.311939 1.200763 1.647532 1.610222 1.355913 1.538724 1.319192
1.265142 1.494068 1.268721 1.411822 1.580606 1.622305 1.40986
1.529142 1.33644 1.37585 1.589704 1.563133 1.753167 1.382264
1.771445 1.425574 1.374936 1.147079 1.626975 1.351203 1.356176
1.534271 1.405485 1.266821 1.647927 1.28254 1.529214 1.586097
1.357731 1.530607 1.307063 1.432288 1.525117 1.525117 1.510123
1.653006 1.37388 1.247077 1.752948 1.396821 1.578571 1.546904
1.483029 1.441626 1.750374 1.498266 1.571477 1.659957 1.640285
1.599326 1.743292 1.225557 1.664379 1.787492 1.364079 1.53362
1.294213 1.831521 1.19443 1.726312 1.84324 ]
Now, I have used many attempts to plot my contours using variations on:
delta = 0.025
OII_OIII_sAGN_sorted = numpy.arange(numpy.min(OII_OIII_sAGN), numpy.max(OII_OIII_sAGN), delta)
Dn4000_sAGN_sorted = numpy.arange(numpy.min(Dn4000_sAGN), numpy.max(Dn4000_sAGN), delta)
OII_OIII_sAGN_X, Dn4000_sAGN_Y = np.meshgrid(OII_OIII_sAGN_sorted, Dn4000_sAGN_sorted)
Z1 = matplotlib.mlab.bivariate_normal(OII_OIII_sAGN_X, Dn4000_sAGN_Y, 1.0, 1.0, 0.0, 0.0)
Z2 = matplotlib.mlab.bivariate_normal(OII_OIII_sAGN_X, Dn4000_sAGN_Y, 0.5, 1.5, 1, 1)
# difference of Gaussians
Z = 0.2 * (Z2 - Z1)
pyplot_middle.contour(OII_OIII_sAGN_X, Dn4000_sAGN_Y, Z, 12, colors='k')
This doesn't seem to give the desired output.I have also tried:
H, xedges, yedges = np.histogram2d(OII_OIII_sAGN,Dn4000_sAGN)
extent = [xedges[0],xedges[-1],yedges[0],yedges[-1]]
ax.contour(H, extent=extent)
Not quite working as I wanted either. Essentially, I am looking for something similar to this:
If anyone could help me with this I would be very grateful, either by suggesting a totally new method or modifying my existing code. Please also attach images of your output if you have some useful techniques or ideas.

seaborn does density plots right out of the box:
import seaborn as sns
import matplotlib.pyplot as plt
sns.kdeplot(x, y)
plt.show()

It seems that histogram2d takes some fiddling to plot the contour in the right place. I took the transpose of the histogram matrix and also took the mean values of the elements in xedges and yedges instead of just removing one from the end.
from matplotlib import pyplot as plt
import numpy as np
fig = plt.figure()
h, xedges, yedges = np.histogram2d(x, y, bins=9)
xbins = xedges[:-1] + (xedges[1] - xedges[0]) / 2
ybins = yedges[:-1] + (yedges[1] - yedges[0]) / 2
h = h.T
CS = plt.contour(xbins, ybins, h)
plt.scatter(x, y)
plt.show()

Scipy curve_fit does not seem to change the initial parameters

I know that there are several similar questions such as Use of curve_fit to fit data but the answer there (specific float type) does not seem to work for me. I am wondering if anyone is able to explain to me why the following code (which is an adaptation from an answer -> https://stackoverflow.com/a/11507723/1093485) does not work.
sample code:
#! /usr/bin/env python
import numpy
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt
def gaussFunction(x, A, mu, sigma):
return A*numpy.exp(-(x-mu)**2/(2.*sigma**2))
x_points = [4245.428, 4245.4378, 4245.4477, 4245.4575, 4245.4673, 4245.4772, 4245.487, 4245.4968, 4245.5066, 4245.5165, 4245.5263, 4245.5361, 4245.546, 4245.5558, 4245.5656, 4245.5755, 4245.5853, 4245.5951, 4245.605, 4245.6148, 4245.6246, 4245.6345, 4245.6443, 4245.6541, 4245.6639, 4245.6738, 4245.6836, 4245.6934, 4245.7033, 4245.7131, 4245.7229, 4245.7328, 4245.7426, 4245.7524, 4245.7623, 4245.7721, 4245.7819, 4245.7918, 4245.8016, 4245.8114, 4245.8213, 4245.8311, 4245.8409, 4245.8508, 4245.8606, 4245.8704, 4245.8803, 4245.8901, 4245.8999, 4245.9097, 4245.9196, 4245.9294, 4245.9392, 4245.9491, 4245.9589, 4245.9687, 4245.9786, 4245.9884, 4245.9982, 4246.0081, 4246.0179, 4246.0277, 4246.0376, 4246.0474, 4246.0572, 4246.0671, 4246.0769, 4246.0867, 4246.0966, 4246.1064, 4246.1162, 4246.1261, 4246.1359, 4246.1457, 4246.1556, 4246.1654, 4246.1752, 4246.1851, 4246.1949, 4246.2047, 4246.2146]
y_points = [978845.0, 1165115.0, 1255368.0, 1253901.0, 1199857.0, 1134135.0, 1065403.0, 977347.0, 866444.0, 759457.0, 693284.0, 679772.0, 696896.0, 706494.0, 668272.0, 555221.0, 374547.0, 189968.0, 161754.0, 216483.0, 181937.0, 73967.0, 146627.0, 263495.0, 284992.0, 240291.0, 327541.0, 555690.0, 758847.0, 848035.0, 800159.0, 645769.0, 444412.0, 249627.0, 125078.0, 254856.0, 498501.0, 757049.0, 977861.0, 1125316.0, 1202892.0, 1263220.0, 1366361.0, 1497071.0, 1559804.0, 1464012.0, 1196896.0, 848736.0, 584363.0, 478640.0, 392943.0, 312466.0, 355540.0, 320666.0, 114711.0, 690948.0, 1409389.0, 1825921.0, 1636486.0, 1730980.0, 4081179.0, 7754166.0, 11747734.0, 15158681.0, 17197366.0, 17388832.0, 15710571.0, 12593935.0, 8784968.0, 5115720.0, 2277684.0, 769734.0, 674437.0, 647250.0, 708156.0, 882759.0, 833756.0, 504655.0, 317790.0, 711106.0, 1011705.0]
# Try to fit the gaussian
trialX = numpy.linspace(x_points[0],x_points[-1],1000)
coeff, var_matrix = curve_fit(gaussFunction, x_points, y_points)
yEXP = gaussFunction(trialX, *coeff)
# Plot the data (just for visualization)
fig = plt.figure()
ax = fig.add_subplot(111)
plt.plot(x_points, y_points, 'b*')
plt.plot(trialX,yEXP, '--')
plt.show()
The output that it generates:

Without starting parameters they default to 1. Putting in
reasonable p0, it works:
p0 = [np.max(y_points), x_points[np.argmax(y_points)], 0.1]
coeff, var_matrix = curve_fit(gaussFunction, x_points, y_points, p0)
Leads to: