Develop Reference

Plotting histogram of probability function and results of inverse transform sampling

Here I tried to plot the probability function P(s)=C/s and then plot a histogram showing real probability function and then show the results of sampling:
import numpy as np
s_min = 1
s_max = 1000
# calculate the normalization constant
C = 1 / (np.log(s_max) - np.log(s_min))
u = np.random.rand(int(1000000))
s = s_min * np.exp(u * (np.log(s_max) - np.log(s_min)))
a = np.log10(min(s))
b = np.log10(max(s))
mybins = np.logspace(a, b, num=17)
plt.hist(s, bins=mybins, density=True, histtype='step', log=True, label='Random Numbers')
x = np.logspace(a, b, num=100)
y = C / x
plt.plot(x, y, 'r', label='Expected Distribution')
plt.xlabel('s')
plt.ylabel('P(s)')
plt.xscale('log')
plt.yscale('log')
plt.legend()
plt.show()
but the code is generating an empty plot with labels.
Tried to add %matplotlib inline and nothing changed

Plot 2 images side by side for each for loop

I'm training a KNN model and I want to plot 2 images per for loop, as shown in the imagen below:
What I need
At the left, I plot the boundary visualization of my model for a certain amoung of neighbours. At the right, I plot the confusion matrix.
To accomplish something along those lines I've written the following code:
fig = plt.figure()
for i in range(1,3):
neigh = KNeighborsClassifier(n_neighbors=i)
neigh.fit(X, y)
y_pred = neigh.predict(X)
acc = accuracy_score(y_pred,y)
# Boundary
ax1 = fig.add_subplot(1,2,1)
visualize_classifier(neigh, X, y, ax=ax1) # Defined by me
# Plot confusion matrix. Defined by sklearn.metrics
ax2 = fig.add_subplot(1,2,2)
plot_confusion_matrix(neigh, X, y, cmap=plt.cm.Blues, values_format = '.0f',ax=ax2)
ax1.set_title(f'Neighbors = {i}.\nAccuracy = {acc:.4f}',
fontsize = 14)
ax2.set_title(f'Neighbors = {i}.\nAccuracy = {acc:.4f}',
fontsize = 14)
plt.tight_layout()
plt.figure(i)
plt.show()
The visualize_classifier() function:
def visualize_classifier(model, X, y, ax=None, cmap='Dark2'):
ax = ax or plt.gca()
# Plot the training points
ax.scatter(X.iloc[:, 0], X.iloc[:, 1], c=y, s=30, cmap=cmap, # Changed to iloc.
clim=(y.min(), y.max()), zorder=3, alpha = 0.5)
ax.axis('tight')
ax.set_xlabel('x1')
ax.set_ylabel('x2')
# ax.axis('off')
xlim = ax.get_xlim()
ylim = ax.get_ylim()
xx, yy = np.meshgrid(np.linspace(*xlim, num=200),
np.linspace(*ylim, num=200))
Z = model.predict(np.c_[xx.ravel(), yy.ravel()]).reshape(xx.shape)
# Create a color plot with the results
n_classes = len(np.unique(y))
contours = ax.contourf(xx, yy, Z, alpha=0.3,
levels=np.arange(n_classes + 1) - 0.5,
cmap=cmap, clim=(y.min(), y.max()),
zorder=1)
ax.set(xlim=xlim, ylim=ylim)
What I get
What I get. Continues...
As you can see, only the first loop is plotted. the second one is not plotted and I can't figure out why.
Furthermore, I have the same title for the plot at the right and at the left. I would like to have only one on top of both, how can this be accomplished?
Now, you might be wondering why do I need to do this and the answer is that I would like to see how the boundaries change depending on the number of neighbors. It's just to get a visual sense of KNN algorithm.
Any suggestion would be pretty much appreciated.

I was able to make it work. What I had wrong was the first line inside the for loop. I assigned plt.figure(i, figsize=(18, 8)) to the variable fig.
for i in range(1,30):
fig = plt.figure(i, figsize=(18, 8))
sns.set(font_scale=2.0) # Adjust to fit
neigh = KNeighborsClassifier(n_neighbors=i)
neigh.fit(X, y)
y_pred = neigh.predict(X)
acc = accuracy_score(y_pred,y)
# Boundary
ax1 = fig.add_subplot(1,2,1)
visualize_classifier(neigh, X, y, ax=ax1) # Defined by me
# Plot confusion matrix. Defined by sklearn.metrics
ax2 = fig.add_subplot(1,2,2)
plot_confusion_matrix(neigh, X, y, cmap=plt.cm.Blues, values_format = '.0f',ax=ax2)
fig.suptitle(f'Neighbors = {i}. Accuracy = {acc:.4f}',y=1)
plt.show()
For the title I used: fig.suptitle(f'Neighbors = {i}. Accuracy = {acc:.4f}',y=1)

Draw lines connecting points between two separate one-D plots

As title, I am working on time-series alignment, and a visualization of the alignment result is desired.
To this end, I want to draw lines connecting "anchor points" generated by the alignment algorithm.
np.random.seed(5)
x = np.random.rand(10) # time-series 1
y = np.random.rand(20) # time-series 2
ap = np.array(([0, 4, 9], # the anchor points
[0, 9, 19]))
fig = plt.figure(figsize=(10,5))
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
ax1.plot(x, 'r')
ax2.plot(y, 'g')
the anchor points ap in the example specify the one-to-one "mapping" between the indices of two time series x and y, i.e., x[0] is corresponding to y[0]; x[4] to y[9]; and x[9] to y[19]. The goal is to draw lines between two separate plot to show the result of the alignment.

To connect two subplots in matplotlib you may use a ConnectionPatch.
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.patches import ConnectionPatch
np.random.seed(5)
x = np.random.rand(21) # time-series 1
y = np.random.rand(21) # time-series 2
ap = np.array(([0, 5, 10], # the anchor points
[0,10, 20]))
fig = plt.figure(figsize=(10,5))
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212)
ax1.plot(x, 'r')
ax2.plot(y, 'g')
ls = ["-","--"]
c = ["gold", "blue"]
for i, row in enumerate(ap):
for j, ind in enumerate(row):
px = (ind, x[ind])
py = (ind, y[ind])
con = ConnectionPatch(py,px, coordsA="data", coordsB="data",
axesA=ax2, axesB=ax1, linestyle=ls[i], color=c[i])
ax2.add_artist(con)
plt.show()

Thanks to #ImportanceOfBeingErnest, I identified the typo in the OP and achieved connecting indices between two series of different length:
np.random.seed(5)
x = np.random.rand(10)
y = np.random.rand(20)
ap = np.array(([0, 4, 9],
[0,9, 19]))
fig = plt.figure(figsize=(10,5))
ax1 = fig.add_subplot(211)
ax2 = fig.add_subplot(212, sharex=ax1)
ax1.plot(x, 'r')
ax2.plot(y, 'g')
plt.setp(ax1.get_xticklabels(), visible=False)
for j in ap.T:
ax1.axvline(x=j[0], linestyle='--', color='k')
ax2.axvline(x=j[1], linestyle='--', color='k')
x_ind = (j[0], ax1.get_ylim()[0])
y_ind = (j[1], ax2.get_ylim()[1])
con = ConnectionPatch(y_ind, x_ind, coordsA="data", coordsB="data",
axesA=ax2, axesB=ax1, linewidth='1.5')
ax2.add_artist(con)
I know it is off the topic, but how to further truncate the blank part in order to make the range of x-axis fit the signal length, while maintain the actual ratio of the length of the two signals? Though sharex=ax1 shows the ratio of signal length, the blank part on the right of the top figure is annoying.

Get coordinates from points density with KDE

I have a set of points (> 1k) in this form:
y,x
173.549,308.176
173.549,313.328
213.26,419.588
Using KDE, i can plot points density with pcolormesh and contourf. This is an example result, plotting points too:
This is the code i used to have the plot:
import matplotlib.pyplot as plt
import matplotlib
import numpy as np
from scipy.stats.kde import gaussian_kde
x, y = np.genfromtxt('terzinoSX.csv', delimiter=',', unpack=True)
y = y[np.logical_not(np.isnan(y))]
x = x[np.logical_not(np.isnan(x))]
k = gaussian_kde(np.vstack([x, y]))
xi, yi = np.mgrid[x.min():x.max():x.size**0.5*1j,y.min():y.max():y.size**0.5*1j]
zi = k(np.vstack([xi.flatten(), yi.flatten()]))
fig = plt.figure(figsize=(7,4))
ax2 = fig.add_subplot(111)
#alpha=0.5 will make the plots semitransparent
#ax1.pcolormesh(yi, xi, zi.reshape(xi.shape), alpha=0.5)
ax2.contourf(yi, xi, zi.reshape(xi.shape), alpha=0.5)
plt.axis('off')
ax2.plot(y,x, "o")
ax2.set_xlim(0, 740)
ax2.set_ylim(515, 0)
#overlay soccer field
im = plt.imread('statszone_football_pitch.png')
ax2.imshow(im, extent=[0, 740, 0, 515], aspect='auto')
fig.savefig('test.png', bbox_inches='tight')
I would like to have one point representing coordinates of most populated zone (middle point for example), like a middle point over the "red" zone. Is it possible in some way?

I solved this by adding these lines that calculate the point in the most populated area:
xy = np.vstack([x,y])
kde = stats.gaussian_kde(xy)
density = kde(xy)
pts = xy.T[np.argmax(density)]

You can use np.argmax to get the coordinates of the maximum. For example:
kde = compute_my_kde() # Returns a two-dimensional array
y, x = np.argmax(kde) # x and y are swapped because matplotlib displays images as a matrix (first index is rows, second index is colums)
plt.imshow(kde) # Show the kde
plt.scatter(x, y) # Show the maximum point

Pandas plotting linear regression on scatter graph

I'm trying to plot a linear regression on a scatter graph.
def chart1(df, yr, listcols):
temp = df[(df['YEAR']==yr)]
fig, axes = plt.subplots(nrows=2, ncols=2, figsize = (12,12))
for e in [['WD','pk_h',0,0],['WD','of_h',0,1],['SAT','of_h',1,0],['SUN','of_h',1,1]]:
temp.ix[(temp['daytype']==e[0])&(temp['hourtype']==e[1]),listcols].plot(kind='scatter', title=str(yr)+' '+e[0]+' '+e[1], x=listcols[0], y=listcols[1], ax=axes[e[2],e[3]])
fig.tight_layout()
return temp
chartd = chart1(o2, 2017,['PROD', 'option_exercise'])
I can't figure out how to make it possible in my loop.

It should work this way:
In your for loop run a regression and store the results in 'res'. Manually caclulate the predicted y ('yhat') using the stored coefficients. Then chart both x vs. y and x vs. yhat:
import pandas.stats.api
def chart4(df, yr, day, Y, sensi):
temp = df[(df['YEAR']==yr)]
temp = temp[(temp['daytype']==day)]
fig = plt.figure(figsize=(15,13))
for i, var in enumerate(sensi):
res = ols(y=temp[Y], x=temp[var])
label = 'R2: ' + str(res.r2)
temp['yhat'] = temp[var]*res.beta[0] + res.beta[1]
axis=fig.add_subplot(4,3,i+1)
temp.plot(ax=axis,kind='scatter', x=var, y=Y, title=var)
temp.plot(ax=axis, kind='scatter', x=var, y='yhat', color='grey', s=1, label=label)
axis.set_xlabel(r'alpha', fontsize=18)
fig.tight_layout()
return