Develop Reference

How can I create a plot to visualize the 68–95–99.7 rule?

I've created a plot of normal distribution like this:
fig, ax = plt.subplots()
ax.set_title('Плотнось распределения вероятности')
ax.set_xlabel('x')
ax.set_ylabel('f(x)')
x = np.linspace(148, 200, 100) # X от 148 до 200
y = (1 / (5 * math.sqrt(2*math.pi))) * np.exp((-(x-178)**2) / (2*5**2))
ax.plot(x, y)
plt.show()
But I also need to add vertical lines inside the graph area, color inner segments and add marks like in picture on axis = 0.
How can I do it in python using matplotlib?
I've tried to use plt.axvline, but the vertical lines go outside of my main plot:
plt.axvline(x = 178, color = 'g', label = 'axvline - full height')
plt.axvline(x = 178+5, color = 'b', label = 'axvline - full height')
plt.axvline(x = 178-5, color = 'b', label = 'axvline - full height')
plt.axvline(x = 178+5*2, color = 'r', label = 'axvline - full height')
plt.axvline(x = 178-5*2, color = 'r', label = 'axvline - full height')

The line version can be implemented using vlines, but note that your reference figure can be better reproduced using fill_between.
Line version
Instead of axvline, use vlines which supports ymin and ymax bounds.
Change your y into a lambda f(x, mu, sd) and use that to define the ymax bounds:
# define y as a lambda f(x, mu, sd)
f = lambda x, mu, sd: (1 / (sd * (2*np.pi)**0.5)) * np.exp((-(x-mu)**2) / (2*sd**2))
fig, ax = plt.subplots(figsize=(8, 3))
x = np.linspace(148, 200, 200)
mu = 178
sd = 5
ax.plot(x, f(x, mu, sd))
# define 68/95/99 locations and colors
xs = mu + sd*np.arange(-3, 4)
colors = [*'yrbgbry']
# draw lines at 68/95/99 points from 0 to the curve
ax.vlines(xs, ymin=0, ymax=[f(x, mu, sd) for x in xs], color=colors)
# relabel x ticks
plt.xticks(xs, [f'${n}\sigma$' if n else '0' for n in range(-3, 4)])
Shaded version
Use fill_between to better recreate the sample figure. Define the shaded bounds using the where parameter:
fig, ax = plt.subplots(figsize=(8, 3))
x = np.linspace(148, 200, 200)
mu = 178
sd = 5
y = (1 / (sd * (2*np.pi)**0.5)) * np.exp((-(x-mu)**2) / (2*sd**2))
ax.plot(x, y)
# use `where` condition to shade bounded regions
bounds = mu + sd*np.array([-np.inf] + list(range(-3, 4)) + [np.inf])
alphas = [0.1, 0.2, 0.5, 0.8, 0.8, 0.5, 0.2, 0.1]
for left, right, alpha in zip(bounds, bounds[1:], alphas):
ax.fill_between(x, y, where=(x >= left) & (x < right), color='b', alpha=alpha)
# relabel x ticks
plt.xticks(bounds[1:-1], [f'${n}\sigma$' if n else '0' for n in range(-3, 4)])
To label the region percentages, add text objects at the midpoints of the bounded regions:
midpoints = mu + sd*np.arange(-3.5, 4)
percents = [0.1, 2.1, 13.6, 34.1, 34.1, 13.6, 2.1, 0.1]
colors = [*'kkwwwwkk']
for m, p, c in zip(
midpoints, # midpoints of bounded regions
percents, # percents captured by bounded regions
colors, # colors of text labels
):
ax.text(m, 0.01, f'{p}%', color=c, ha='center', va='bottom')

Matplotlib Title location

i have this several plots and want to correct the title name location. I want to make the Vertical Acceleration (y) on the middle left vertically and the Flare Time (x) on the middle bot horizontally also the Test Title on middle top. Basically I want to be able to move the label location.
Below is the code
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.ticker import NullFormatter
x = ip.RESULTS
y = Vert
xy = np.vstack([x,y])
z = gaussian_kde(xy)(xy)
idx = z.argsort()
x, y, z = x[idx], y[idx], z[idx]
nullfmt = NullFormatter() # no labels
# definitions for the axes
left, width = 0.1, 0.65
bottom, height = 0.1, 0.65
bottom_h = left_h = left + width + 0.02
rect_scatter = [left, bottom, width, height]
rect_histx = [left, bottom_h, width, 0.2]
rect_histy = [left_h, bottom, 0.2, height]
# start with a rectangular Figure
plt.figure(1, figsize=(8, 8))
axScatter = plt.axes(rect_scatter)
#plt.plot(np.unique(x), np.poly1d(np.polyfit(x, y, 1))(np.unique(x)))
#plt.plot(np.unique(x), np.poly1d(np.polyfit(x, y, 1))(np.unique(x)))
axHistx = plt.axes(rect_histx)
axHisty = plt.axes(rect_histy)
# no labels
axHistx.xaxis.set_major_formatter(nullfmt)
axHisty.yaxis.set_major_formatter(nullfmt)
# the scatter plot:
axScatter.scatter(x, y, c=z, s=50, edgecolor='')
# now determine nice limits by hand:
binwidth = 1
xymax = np.max([np.max(np.fabs(x)), np.max(np.fabs(y))])
lim = (int(xymax/binwidth) + 1) * binwidth
bins = np.arange(-lim, lim + binwidth, binwidth)
axHistx.hist(x)
axHisty.hist(y, orientation='horizontal')
plt.title('test title', fontsize=20)
axHisty.set_xlabel("Vertical Acceleration")
axHistx.set_xlabel("Flare Time")
and the results look like this. Any help would be appreciated

You have three Axes objects (plot rectangles to say it sloppy) in your graph: axScatter is your main chart in the bottom left. axHisty is the histogram on the right and axHistx is the histogram on the top. Your axis titles belong on the y- and x-axis of axScatter. So just do:
axScatter.set_ylabel('Vertical Acceleration')
axScatter.set_xlabel('Flare Time')
Based on your vague question I have no idea where you want the "test title", but just figure out which Axes object is best and give it an xlabel, ylabel or title.

How to center the bar plot to show the difference of a certain column?

How to center the bar plot to show the difference of a certain column?
I have the following bar plot, done with matplotlib :
Note how the barplot is really bad. The difference between each bar cant really be seen properly. So what I want, is to use the red bar as the origin in the y-axis. That way, the other bars would show the difference (blue_bar(i) - redbar).
In other words, I want the value of the red bar in the y-axis to be the y-origin of the plot.
Again, in another words, the red bar is the accuracy obtained by my academic work. I want to plot the other article results compared/ IN RELATION to mine.
I made the following picture using paint.net to illustrate what I want.
Any other ideas/suggestions are really appreciated.
Appendix :
I used the following code to produce the first graphic :
import numpy as np
import random
from matplotlib import pyplot as plt
accuracies = [0.9630, 0.9597, 0.9563, 0.9533, 0.9527, 0.9480, 0.9477, 0.9472, 0.9472, 0.9466, 0.9452, 0.9452, 0.9442,
0.9440, 0.9434, 0.9420, 0.9407, 0.9407, 0.9391, 0.9377, 0.9185, 0.9268]
sensitividades = [0.7680, 0.7200, 0.8173, 0.7569, 0.7406, 0.7354, 0.7746, 0.7344, 0.7067, 0.7410, 0.7370, 0.7321,
0.7357]
especificidades = [0.9827, 0.9733, 0.9816, 0.9807, 0.9789, 0.9724, 0.9764, 0.9801, 0.9751, 0.9521, 0.9487, 0.9694]
accuracies = [x * 100 for x in accuracies]
y = accuracies
N = len(y)
x = range(N)
width = 1 / 1.1
fig, ax = plt.subplots(1, 1)
ax.grid(zorder=0)
# Plot other articles
ax.bar(x, y, width, color="blue", zorder=3)
# Plot my work
ax.bar(x[len(x) - 1] + 1, 95.30, width, color="red", zorder=3)
plt.title('Accuracy of each article')
plt.xlabel('Article')
plt.ylabel('Accuracy')
plt.savefig('foo.png')
plt.show()

You could either set the y limits closer to the interesting values:
import numpy as np
import random
from matplotlib import pyplot as plt
accuracies = [0.9630, 0.9597, 0.9563, 0.9533, 0.9527, 0.9480, 0.9477, 0.9472, 0.9472, 0.9466, 0.9452, 0.9452, 0.9442,
0.9440, 0.9434, 0.9420, 0.9407, 0.9407, 0.9391, 0.9377, 0.9185, 0.9268]
sensitividades = [0.7680, 0.7200, 0.8173, 0.7569, 0.7406, 0.7354, 0.7746, 0.7344, 0.7067, 0.7410, 0.7370, 0.7321,
0.7357]
especificidades = [0.9827, 0.9733, 0.9816, 0.9807, 0.9789, 0.9724, 0.9764, 0.9801, 0.9751, 0.9521, 0.9487, 0.9694]
accuracies = [x * 100 for x in accuracies]
my_acc = 95.30
y = accuracies
N = len(y)
x = range(N)
width = 1 / 1.1
fig, ax = plt.subplots(1, 1)
ax.grid(zorder=0)
# Plot other articles
ax.bar(x, y, width, color="blue", zorder=3)
# Plot my work
ax.bar(x[len(x) - 1] + 1, my_acc, width, color="red", zorder=3)
plt.title('Accuracy of each article')
plt.ylim(min(y) - 0.5, max(y) +0.5)
plt.xlabel('Article')
plt.ylabel('Accuracy')
plt.savefig('foo2.png')
plt.show()
Or you could plot it around zero, with your result being the new origin (but you will have to indicate by how much you shifted the origin somewhere in the legend or somewhere else):
import numpy as np
import random
from matplotlib import pyplot as plt
accuracies = [0.9630, 0.9597, 0.9563, 0.9533, 0.9527, 0.9480, 0.9477, 0.9472, 0.9472, 0.9466, 0.9452, 0.9452, 0.9442,
0.9440, 0.9434, 0.9420, 0.9407, 0.9407, 0.9391, 0.9377, 0.9185, 0.9268]
sensitividades = [0.7680, 0.7200, 0.8173, 0.7569, 0.7406, 0.7354, 0.7746, 0.7344, 0.7067, 0.7410, 0.7370, 0.7321,
0.7357]
especificidades = [0.9827, 0.9733, 0.9816, 0.9807, 0.9789, 0.9724, 0.9764, 0.9801, 0.9751, 0.9521, 0.9487, 0.9694]
accuracies = [x * 100 for x in accuracies]
my_acc = 95.30
y = np.asarray(accuracies) - my_acc
N = len(y)
x = range(N)
width = 1 / 1.1
fig, ax = plt.subplots(1, 1)
ax.grid(zorder=0)
# Plot other articles
bars = ax.bar(x, y, width, color="blue", zorder=3)
# Plot my work
# ax.bar(x[len(x) - 1] + 1, my_acc, width, color="red", zorder=3)
plt.title('Accuracy of each article')
plt.yticks([0, -0.3, -1.3, -2.3, -3.3, 0.7, 1.7], [95.30, 95, 94, 93, 92, 96, 97])
plt.xlabel('Article')
plt.ylabel('Accuracy')
plt.ylim(min(y) - 0.5, max(y) + 0.7)
def autolabel(rects):
for i in range(len(rects)):
rect = rects[i]
height = rect.get_height()
if (height >= 0):
ax.text(rect.get_x() + rect.get_width()/2.,
0.3 + height,'[{}]'.format( i), ha='center', va='bottom',
fontsize=7.5)
if (height < 0):
ax.text(rect.get_x() + rect.get_width()/2.,
height - 0.3,'[{}]'.format( i), ha='center', va='bottom',
fontsize=7.5)
autolabel(bars)
plt.savefig('foo.png')
plt.show()
Of course, your own result would not appear in the second plot, since it would have height zero.

I actually think the way you have it represented now is actually best -- meaning there isn't a huge difference in accuracy on a cursory level.
However, if you want to set the value of the red bar as the origin, try this:
...
plt.title('Accuracy of each article')
plt.xlabel('Article')
plt.ylabel('Accuracy')
plt.ylim(95.30) # Sets the value of the red bar as the origin.
plt.savefig('foo.png')
plt.show()
Perhaps setting the minimum value of lowest accuracy of the article might make this graph more digestible.
...
plt.title('Accuracy of each article')
plt.xlabel('Article')
plt.ylabel('Accuracy')
plt.ylim(min(accuracies), 100) # Sets the value of minimum accuracy as the origin and the max value as 100.
plt.savefig('foo.png')
plt.show()

Axis limits for scatter plot - Matplotlib

I'm having the same problem presented here, however, the proposed solution didn't work for me.
I'm plotting a set of data which the main plot have this pattern:
Which is a plot which axis limits varies from (-1, 1) in both x and y, with a margin set with this piece of code:
plt.figure()
plt.show(data)
## Add some margin
l, r, b, t = plt.axis()
dx, dy = r-l, t-b
plt.axis([l-0.1*dx, r+0.1*dx, b-0.1*dy, t+0.1*dy])
The problem is 'cause I have more "complex" plot in which some changes had to me made. This is the code that produces it:
def plot_quiver_singularities(min_points, max_points, vector_field_x, vector_field_y, file_path):
"""
Plot the singularities of vector field
:param file_path : the path to save the data
:param vector_field_x : the vector field x component to be plot
:param vector_field_y : the vector field y component to be plot
:param min_points : a set (x, y) of min points field
:param max_points : a set (x, y) of max points field
"""
fig = plt.figure(figsize=(8, 8))
ax = fig.add_axes([.13, .3, .6, .6])
## Plot quiver
x, y = numpy.mgrid[-1:1:100*1j, -1:1:100*1j]
m = numpy.sqrt(numpy.power(vector_field_x, 2) + numpy.power(vector_field_y, 2))
quiver = ax.quiver(x, y, vector_field_x, vector_field_y, m, zorder=1)
## Plot critical points
x = numpy.linspace(-1, 1, x_steps)
y = numpy.linspace(-1, 1, y_steps)
# Draw the min points
x_indices = numpy.nonzero(min_points)[0]
y_indices = numpy.nonzero(min_points)[1]
ax.scatter(x[x_indices], y[y_indices], marker='$\\circlearrowright$', s=100, zorder=2)
# Draw the max points
x_indices = numpy.nonzero(max_points)[0]
y_indices = numpy.nonzero(max_points)[1]
ax.scatter(x[x_indices], y[y_indices], marker='$\\circlearrowleft$', s=100, zorder=2)
## Put legends
marker_min = plt.Line2D((0, 0), (0, 0), markeredgecolor=(1.0, 0.4, 0.0), linestyle='',
marker='$\\circlearrowright$', markeredgewidth=1, markersize=10)
marker_max = plt.Line2D((0, 0), (0, 0), markeredgecolor=(0.2, 0.2, 1.0), linestyle='',
marker='$\\circlearrowleft$', markeredgewidth=1, markersize=10)
plt.legend([marker_min, marker_max], ['CW rot. center', 'CCW rot. center'], numpoints=1,
loc='center left', bbox_to_anchor=(1, 0.5))
quiver_cax = fig.add_axes([.13, .2, .6, .03])
fig.colorbar(quiver, orientation='horizontal', cax=quiver_cax)
## Set axis limits
plt.xlim(-1, 1)
plt.ylim(-1, 1)
## Add some margin
# l, r, b, t = plt.axis()
# dx, dy = r-l, t-b
# plt.axis([l-0.1*dx, r+0.1*dx, b-0.1*dy, t+0.1*dy])
plt.savefig(file_path + '.png', dpi=dpi)
plt.close()
This produces the following image:
As can be seen, the axis limits do not hold and I didn't found why yet.
Any help would be appreciated.
Thank you in advance.

I was able to solve the problem putting this piece of code
plt.xlim(-1, 1)
plt.ylim(-1, 1)
Right after calling scatter().

You can also set those to the ax object:
ax.set_xlim((-1,1))
ax.set_ylim((-1,1))

Legend combined with Text, how to find the legend width and height

I would like to set legend and text boxes locations and styles exactly same, the latter especially to make text aligned.
import matplotlib.pyplot as plt
x = np.arange(10)
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1)
for i in range(3):
ax.plot(x, i * x ** 2, label = '$y = %i x^2$'%i)
ax.set_title('example plot')
# Shrink the axis by 20% to put legend and text at the bottom
#+ of the figure
vspace = .2
box = ax.get_position()
ax.set_position([box.x0, box.y0 + box.height * vspace,
box.width, box.height * (1 - vspace)])
# Put a legend to the bottom left of the current axis
x, y = 0, 0
# First solution
leg = ax.legend(loc = 'lower left', bbox_to_anchor = (x, y), \
bbox_transform = plt.gcf().transFigure)
# Second solution
#leg = ax.legend(loc = (x, y)) , bbox_transform = plt.gcf().transFigure)
# getting the legend location and size properties using a code line I found
#+ somewhere in SoF
bb = leg.legendPatch.get_bbox().inverse_transformed(ax.transAxes)
ax.text(x + bb.width, y, 'some text', transform = plt.gcf().transFigure, \
bbox = dict(boxstyle = 'square', ec = (0, 0, 0), fc = (1, 1, 1)))
plt.show()
This should place the text at the right of the legend box but that's not what it does. And the two boxes are not vertically aligned.
The second solution does not actually anchoring the legend to the figure, but to the axes instead.

You can use the frame data to get the right width in order to position the Text() object correctly.
In the example below I had to apply a 1.1 factor for the width (this value I haven't found how to get, and if you don't apply the factor the text clashes with the legend).
Note also that you must plt.draw() before getting the right width value.
import matplotlib.pyplot as plt
import numpy as np
x = np.arange(10)
fig = plt.figure(figsize=(3, 2))
ax = fig.add_subplot(1, 1, 1)
for i in range(3):
ax.plot(x, i*x**2, label=r'$y = %i \cdot x^2$'%i)
ax.set_title('example plot')
ax.spines['top'].set_visible(False)
ax.spines['right'].set_visible(False)
ax.xaxis.set_ticks_position('bottom')
ax.yaxis.set_ticks_position('left')
x, y = 0.2, 0.5
leg = ax.legend(loc='lower left', bbox_to_anchor=(x, y),
bbox_transform=fig.transFigure, fontsize=8)
plt.draw()
f = leg.get_frame()
w0, h0 = f.get_width(), f.get_height()
inv = fig.transFigure.inverted()
w, h = inv.transform((w0, h0))
ax.text(x+w*1.1, y+h/2., 'some text', transform=fig.transFigure,
bbox=dict(boxstyle='square', ec=(0, 0, 0), fc=(1, 1, 1)),
fontsize=7)
fig.savefig('test.jpg', bbox_inches='tight')
for x, y = 0.2, 0.5:
for x, y = -0.3, -0.3: