Develop Reference

Python matplotlib, adding single custom tickmark on axis

I am trying to label the intersection of two lines in a plot I have made. The code/MWE is:
import matplotlib.pyplot as plt
import numpy as np
#ignore my gross code, first time ever using Python :-)
#parameters
d = 0.02
s = 0.50 #absurd, but dynamics robust to 1>s>0
A = 0.90
u = 0.90
#variables
kt = np.arange(0, 50, 1)
invest = (1 - np.exp(-d*kt))*kt
output = A*u*kt
saving = s*output
#plot
plt.plot(kt, invest, 'r', label='Investment')
plt.plot(kt, output, 'b', label='Output')
plt.plot(kt, saving, label='Saving')
plt.xlabel('$K_t$')
plt.ylabel('$Y_t$, $S_t$, $I_t$')
plt.legend(loc="upper left")
#Steady State; changes with parameters
Kbar = np.log(1-s*A*u)/-d
x, y = [Kbar, Kbar], [0, s*A*u*Kbar]
plt.plot(x, y, 'k--')
#custom axes (no top and right)
ax = plt.gca()
right_side = ax.spines["right"]
right_side.set_visible(False)
top_side = ax.spines["top"]
top_side.set_visible(False)
#ax.grid(True) #uncomment for gridlines
plt.xlim(xmin=0) #no margins; preference
plt.ylim(ymin=0)
plt.show()
which creates:
I am trying to create a little label at the bottom of the dotted black line that says "$K^*$". I want it to coincide with Kbar so that, like the black line, it moves along with the parameters. Any tips or suggestions here?

I don't quite understand what you mean by "under the black dotted line", but you can already use the coordinate data of the dotted line to annotate it. I put it above the intersection point, but if you want to put it near the x-axis, you can set y=0.
plt.text(max(x), max(y)+1.5, '$K^*$', transform=ax.transData)

baseTicks=list(plt.xticks()[0]) #for better control, replace with a range or arange
ax.set_xticks(baseTicks+[np.log(1-A*u*s)/(-d)])
ax.set_xticklabels(baseTicks+['$K^*$'])

How to make standard deviation and percentile bands in a python scatter plot

I have data for a scatter plot (for reference, x values are labelled sm, y values are labelled bhm) and my three goals are to find the medians of binned data, create standard deviation bands, and create bands at the 90th and 10th percentiles. I've managed to do the first, and while I've been able to make vertical bars indicating the standard deviation, I can't figure out how to make filled-in bands since every time I try to set parameters with the fill_between function, it says operators with sm/bhm are incompatible since they're datasets and I'm comparing them to singular values (the mean line). I copied all of my code down below and there's a comment pointing out the relevant stuff - I just kept all of it since the variable names are a bit important and also because some parts of the plot don't show up properly without the seemingly extraneous code
To create the bands at 90/10 percent, I tried this bit of code by trying to bin the mean as I did for the median, and then filling the top and bottom of the line +-90% of the data but I keep getting
patsy.PatsyError: model is missing required outcome variables
#stuff that really doesn't work
model = smf.quantreg(bhm, sm)
quantiles = [0.1, 0.9]
fits = [model.fit(q=q) for q in quantiles]
figure, axes = plt.subplots()
_sm = np.linspace(min(sm), max(sm))
for index, quantile in enumerate(quantiles):
_bhm = fits[index].params['world'] * _sm +
fits[index].params['Intercept']
axes.plot(_sm, _bhm, label = quantile)
axes.plot(_sm, _sm, 'g--', label = 'i guess this line is the mean')
#stuff that also doesn't really work
import matplotlib.pyplot as plt
import numpy as np
import matplotlib.patches as mpatches
import h5py
import statistics as stat
import pandas as pd
import statsmodels.formula.api as smf
#my files and labels for things
f=h5py.File(r'C:\Users\hanna\Downloads\CatalogueGalsz0p0.hdf5', 'r')
sm = f['StellarMass']
bhm = f['BHMass']
bt = f['BtoT']
dt = f['DtoT']
nbins = 125
#titles and scaling for the plot
plt.title('Relationships Between Stellar Mass, Black Hole Mass, and Bulge
to Total Ratios')
plt.xlabel('Stellar Mass')
plt.ylabel('Black Hole Mass')
plt.xscale('log')
plt.yscale('log')
axes = plt.gca()
axes.set_ylim([500000,max(bhm)])
axes.set_xlim([min(sm),max(sm)])
#labels for the legend and how I colored the points in the plot
DtoT = np.copy(f['DtoT'].value)
colour = np.zeros(len(DtoT),dtype=str)
for i in np.arange(0, len(bt)):
if bt[i]>=0.5:
colour[i]='green'
else:
colour[i]='red'
redbt = mpatches.Patch(color = 'red', label = 'Bulge to Total Ratios Below 0.5')
greenbt = mpatches.Patch(color = 'green', label = 'Bulge to Total Ratios Above 0.5')
plt.legend(handles = [(redbt), (greenbt)])
#the important part - this is how I binned my data to make the median line, and this part works but not the standard deviation bands
bins = np.linspace(0, max(sm), nbins)
delta = bins[1]-bins[0]
idx = np.digitize(sm, bins)
runningmedian = [np.median(bhm[idx==k]) for k in range(nbins)]
runningstd = [bhm[idx==k].std() for k in range(nbins)]
plt.plot(bins-delta/2, runningmedian, c = 'b', lw=1)
plt.scatter(sm, bhm, c=colour, s=.2)
plt.show()

How to smooth the curve?

I am using the following code to draw a curve from my two column Raw data ( x=time , y=|float data|).The graph it is plotting is a rough edge graph. Is it possible to have a smooth edged on these data? I am attaching the code, data and curve.
from datetime import datetime
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.dates
from matplotlib import style
# changing matplotlib the default style
matplotlib.style.use('ggplot')
#one of {'b', 'g', 'r', 'c', 'm', 'y', 'k', 'w'}
plt.rcParams['lines.linewidth']=1
plt.rcParams['axes.facecolor']='.3'
plt.rcParams['xtick.color']='b'
plt.rcParams['ytick.color']='r'
x,y= np.loadtxt('MaxMin.txt', dtype=str, unpack=True)
x = np.array([datetime.strptime(i, "%H:%M:%S.%f") for i in x])
y = y.astype(float)
# naming the x axis
plt.xlabel('<------Clock-Time(HH:MM:SS)------>')
# naming the y axis
plt.ylabel('Acceleration (m/sq.sec)')
# giving a title to my graph
plt.title('Sample graph!')
# plotting the points
plt.plot(x, y)
# beautify the x-labels
plt.gcf().autofmt_xdate()
#Custom Format
loc = matplotlib.dates.MicrosecondLocator(1000000)
plt.gca().xaxis.set_major_locator(loc)
plt.gca().xaxis.set_major_formatter(matplotlib.dates.DateFormatter('%H:%M:%S'))
# function to show the plot
plt.show()
I have searched similar threads but the mathematical concepts used by them went over my head. So I cannot identify what exactly has to be done for my data.
Generated Graph from RAW data
I am also giving the sample data file so that you can re-construct it at your end.
Get Data File
PS. I am also not being able to change the line color in the graph from default red even after using
plt.rcParams['lines.color']='g'
Although that is a minor issue in this case.

The input data has wrong timestamps, the original author should have used zero-padding when formatting the milliseconds (%03d).
[...]
10:27:19.3 9.50560385141
10:27:19.32 9.48882194058
10:27:19.61 9.75936468731
10:27:19.91 9.96021690527
10:27:19.122 9.48972151383
10:27:19.151 9.49265161533
[...]
We need to fix that first:
x, y = np.loadtxt('MaxMin.txt', dtype=str, unpack=True)
# fix the zero-padding issue
x_fixed = []
for xx in x:
xs = xx.split(".")
xs[1] = "0"*(3-len(xs[1])) + xs[1]
x_fixed.append(xs[0] + '.' + xs[1])
x = np.array([datetime.strptime(i, "%H:%M:%S.%f") for i in x_fixed])
y = y.astype(float)
You can then use a smoothing kernel (e.g. moving average) to smooth the data:
window_len = 3
kernel = np.ones(window_len, dtype=float)/window_len
y_smooth = np.convolve(y, kernel, 'same')

The scipy module has some ways of getting smooth curves through your points. Try adding this to the top:
from scipy import interpolate
Then add these lines just before your plt.show():
xnew = np.linspace(x.min(), x.max(), 100)
bspline = interpolate.make_interp_spline(x, y)
y_smoothed = bspline(xnew)
plt.plot(xnew, y_smoothed)
If you do a little search for scipy.interpolate.make_interp_spline, you can find more info on what that does. But essentially, the combination of that and np.linspace generates a bunch of fake data points to make up a smooth curve.

Flow visualisation in python using curved (path-following) vectors

I would like to plot a vector field with curved arrows in python, as can be done in vfplot (see below) or IDL.
You can get close in matplotlib, but using quiver() limits you to straight vectors (see below left) whereas streamplot() doesn't seem to permit meaningful control over arrow length or arrowhead position (see below right), even when changing integration_direction, density, and maxlength.
So, is there a python library that can do this? Or is there a way of getting matplotlib to do it?

If you look at the streamplot.py that is included in matplotlib, on lines 196 - 202 (ish, idk if this has changed between versions - I'm on matplotlib 2.1.2) we see the following:
... (to line 195)
# Add arrows half way along each trajectory.
s = np.cumsum(np.sqrt(np.diff(tx) ** 2 + np.diff(ty) ** 2))
n = np.searchsorted(s, s[-1] / 2.)
arrow_tail = (tx[n], ty[n])
arrow_head = (np.mean(tx[n:n + 2]), np.mean(ty[n:n + 2]))
... (after line 196)
changing that part to this will do the trick (changing assignment of n):
... (to line 195)
# Add arrows half way along each trajectory.
s = np.cumsum(np.sqrt(np.diff(tx) ** 2 + np.diff(ty) ** 2))
n = np.searchsorted(s, s[-1]) ### THIS IS THE EDITED LINE! ###
arrow_tail = (tx[n], ty[n])
arrow_head = (np.mean(tx[n:n + 2]), np.mean(ty[n:n + 2]))
... (after line 196)
If you modify this to put the arrow at the end, then you could generate the arrows more to your liking.
Additionally, from the docs at the top of the function, we see the following:
*linewidth* : numeric or 2d array
vary linewidth when given a 2d array with the same shape as velocities.
The linewidth can be a numpy.ndarray, and if you can pre-calculate the desired width of your arrows, you'll be able to modify the pencil width while drawing the arrows. It looks like this part has already been done for you.
So, in combination with shortening the arrows maxlength, increasing the density, and adding start_points, as well as tweaking the function to put the arrow at the end instead of the middle, you could get your desired graph.
With these modifications, and the following code, I was able to get a result much closer to what you wanted:
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import matplotlib.patches as pat
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U*U + V*V)
fig = plt.figure(figsize=(14, 18))
gs = gridspec.GridSpec(nrows=3, ncols=2, height_ratios=[1, 1, 2])
grains = 10
tmp = tuple([x]*grains for x in np.linspace(-2, 2, grains))
xs = []
for x in tmp:
xs += x
ys = tuple(np.linspace(-2, 2, grains))*grains
seed_points = np.array([list(xs), list(ys)])
# Varying color along a streamline
ax1 = fig.add_subplot(gs[0, 1])
strm = ax1.streamplot(X, Y, U, V, color=U, linewidth=np.array(5*np.random.random_sample((100, 100))**2 + 1), cmap='winter', density=10,
minlength=0.001, maxlength = 0.07, arrowstyle='fancy',
integration_direction='forward', start_points = seed_points.T)
fig.colorbar(strm.lines)
ax1.set_title('Varying Color')
plt.tight_layout()
plt.show()
tl;dr: go copy the source code, and change it to put the arrows at the end of each path, instead of in the middle. Then use your streamplot instead of the matplotlib streamplot.
Edit: I got the linewidths to vary

Starting with David Culbreth's modification, I rewrote chunks of the streamplot function to achieve the desired behaviour. Slightly too numerous to specify them all here, but it includes a length-normalising method and disables the trajectory-overlap checking. I've appended two comparisons of the new curved quiver function with the original streamplot and quiver.

Here's a way to obtain the desired output in vanilla pyplot (i.e., without modifying the streamplot function or anything that fancy). For reminder, the goal is to visualize a vector field with curved arrows whose length is proportional to the norm of the vector.
The trick is to:
make streamplot with no arrows that is traced backward from a given point (see)
plot a quiver from that point. Make the quiver small enough so that only the arrow is visible
repeat 1. and 2. in a loop for every seed and scale the length of the streamplot to be proportional to the norm of the vector.
import matplotlib.pyplot as plt
import numpy as np
w = 3
Y, X = np.mgrid[-w:w:8j, -w:w:8j]
U = -Y
V = X
norm = np.sqrt(U**2 + V**2)
norm_flat = norm.flatten()
start_points = np.array([X.flatten(),Y.flatten()]).T
plt.clf()
scale = .2/np.max(norm)
plt.subplot(121)
plt.title('scaling only the length')
for i in range(start_points.shape[0]):
plt.streamplot(X,Y,U,V, color='k', start_points=np.array([start_points[i,:]]),minlength=.95*norm_flat[i]*scale, maxlength=1.0*norm_flat[i]*scale,
integration_direction='backward', density=10, arrowsize=0.0)
plt.quiver(X,Y,U/norm, V/norm,scale=30)
plt.axis('square')
plt.subplot(122)
plt.title('scaling length, arrowhead and linewidth')
for i in range(start_points.shape[0]):
plt.streamplot(X,Y,U,V, color='k', start_points=np.array([start_points[i,:]]),minlength=.95*norm_flat[i]*scale, maxlength=1.0*norm_flat[i]*scale,
integration_direction='backward', density=10, arrowsize=0.0, linewidth=.5*norm_flat[i])
plt.quiver(X,Y,U/np.max(norm), V/np.max(norm),scale=30)
plt.axis('square')
Here's the result:

Just looking at the documentation on streamplot(), found here -- what if you used something like streamplot( ... ,minlength = n/2, maxlength = n) where n is the desired length -- you will need to play with those numbers a bit to get your desired graph
you can control for the points using start_points, as shown in the example provided by #JohnKoch
Here's an example of how I controlled the length with streamplot() -- it's pretty much a straight copy/paste/crop from the example from above.
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
import matplotlib.patches as pat
w = 3
Y, X = np.mgrid[-w:w:100j, -w:w:100j]
U = -1 - X**2 + Y
V = 1 + X - Y**2
speed = np.sqrt(U*U + V*V)
fig = plt.figure(figsize=(14, 18))
gs = gridspec.GridSpec(nrows=3, ncols=2, height_ratios=[1, 1, 2])
grains = 10
tmp = tuple([x]*grains for x in np.linspace(-2, 2, grains))
xs = []
for x in tmp:
xs += x
ys = tuple(np.linspace(-2, 2, grains))*grains
seed_points = np.array([list(xs), list(ys)])
arrowStyle = pat.ArrowStyle.Fancy()
# Varying color along a streamline
ax1 = fig.add_subplot(gs[0, 1])
strm = ax1.streamplot(X, Y, U, V, color=U, linewidth=1.5, cmap='winter', density=10,
minlength=0.001, maxlength = 0.1, arrowstyle='->',
integration_direction='forward', start_points = seed_points.T)
fig.colorbar(strm.lines)
ax1.set_title('Varying Color')
plt.tight_layout()
plt.show()
Edit: made it prettier, though still not quite what we were looking for.

Histogram bars overlapping matplotlib

I am able to build the histogram I need. However, the bars overlap over one another.
As you can see I changed the width of the bars to 0.2 but it still overlaps. What is the mistake I am doing?
from matplotlib import pyplot as plt
import numpy as np
from matplotlib.font_manager import FontProperties
from random import randrange
color = ['r', 'b', 'g','c','m','y','k','darkgreen', 'darkkhaki', 'darkmagenta', 'darkolivegreen', 'darkorange', 'darkorchid', 'darkred']
label = ['2','6','10','14','18','22','26','30','34','38','42','46']
file_names = ['a','b','c']
diff = [[randrange(10) for a in range(0, len(label))] for a in range(0, len(file_names))]
print diff
x = diff
name = file_names
y = zip(*x)
pos = np.arange(len(x))
width = 1. / (1 + len(x))
fig, ax = plt.subplots()
for idx, (serie, color,label) in enumerate(zip(y, color,label)):
ax.bar(pos + idx * width, serie, width, color=color, label=label)
ax.set_xticks(pos + width)
plt.xlabel('foo')
plt.ylabel('bar')
ax.set_xticklabels(name)
ax.legend()
plt.savefig("final" + '.eps', bbox_inches='tight', pad_inches=0.5,dpi=100,format="eps")
plt.clf()
Here is the graph:

As you can see in the below example, you can easily get non-overlapping bars using a heavily simplified version of your plotting code. I'd suggest you to have a closer look at whether x and y really are what you expect them to be. (And that you try to simplify your code as much as possible when you are looking for an error in the code.)
Also have a look at the computation of the width of the bars. You appear to use the number of subjects for this, while it should be the number of bars per subject instead.
Have a look at this example:
import numpy as np
import matplotlib.pyplot as plt
subjects = ('Tom', 'Dick', 'Harry', 'Sally', 'Sue')
# number of bars per subject
n = 5
# y-data per subject
y = np.random.rand(n, len(subjects))
# x-positions for the bars
x = np.arange(len(subjects))
# plot bars
width = 1./(1+n) # <-- n.b., use number of bars, not number of subjects
for i, yi in enumerate(y):
plt.bar(x+i*width, yi, width)
# add labels
plt.xticks(x+n/2.*width, subjects)
plt.show()
This is the result image:
For reference:
http://matplotlib.org/examples/api/barchart_demo.html
http://matplotlib.org/api/pyplot_api.html#matplotlib.pyplot.bar

The problem is that the width of your bars is calculated from the three subjects, not the twelve bars per subject. That means you're placing multiple bars at each x-position. Try swapping in these lines where appropriate to fix that:
n = len(x[0]) # New variable with the right length to calculate bar width
width = 1. / (1 + n)
ax.set_xticks(pos + n/2. * width)