Develop Reference

How to set widgets to link to array for jupyternotebooks

I am trying to set an interactive notebook up that plots some interpolated GPS data. I have the plotting working by itself, but I am trying to use the ipython widgets to make it more interactive for others.
Currently, my plotting looks like this
def create_grid(array,spacing=.01):
'''
creates evenly spaced grid from the min and max of an array
'''
grid = np.arange(np.amin(array), np.amax(array),spacing)
return grid
def interpolate(x, y, z, grid_spacing = .01, model='spherical',returngrid = False):
'''Interpolates z value and uses create_grid to create a grid of values based on min and max of x and y'''
grid_x = create_grid(x,spacing = grid_spacing)
grid_y = create_grid(y, spacing = grid_spacing)
OK = OrdinaryKriging(x, y, z, variogram_model=model, verbose = False,\
enable_plotting=False, nlags = 20)
z1, ss1 = OK.execute('grid', grid_x,grid_y,mask = False)
print('Interpolation Complete')
vals=np.ma.getdata(z1)
sigma = np.ma.getdata(ss1)
if returngrid == False:
return vals,sigma
else:
return vals, sigma, grid_x, grid_y
mesh_x, mesh_y = np.meshgrid(grid_x,grid_y)
plot = plt.scatter(mesh_x, mesh_y, c = z1, cmap = cm.hsv)
cb = plt.colorbar(plot)
cb.set_label('Northing Change')
plt.show()
'''
This works currently, but I am trying to set up a widget to change the variogram model in the kriging interpolation, as well as change the field to be interpolated.
Currently, to do that I have:
def update_plot(zfield,variogram):
plt.clf()
z1, ss1, grid_x,grid_y =interpolate(lon,lat,zfield,returngrid= True,model=variogram)
mesh_x, mesh_y = np.meshgrid(grid_x,grid_y)
plot = plt.scatter(mesh_x, mesh_y, c = z1, cmap = cm.hsv)
cb = plot.colorbar(plot)
cb.set_label('Interpolated Value')
variogram = widgets.Dropdown(options = ['linear', 'power', 'gaussian', 'spherical', 'exponential', 'hole-effect'],
value = 'spherical', description = "Variogram model for interpolation")
zfield = widgets.Dropdown(options = {'Delta N':delta_n, 'Delta E': delta_e,'Delta V':delta_v},value = 'Delta N',
description = 'Interpolated value')
widgets.interactive(update_plot, variogram = variogram,zfield =zfield)
Which brings up the error
TraitError: Invalid selection: value not found
the values delta_n, delta_e and delta_v are numpy arrays. I have tried looking at documentation but it is not as detailed as something like matplotlibs documentation or something so I feel like I am kind of flying blind here.
Thank you

In this line, you specify the possible values of the Dropdown as:
zfield = widgets.Dropdown(options = {'Delta N':delta_n, 'Delta E': delta_e,'Delta V':delta_v}
When a mapping is used, the values of the dict are interpreted as the possible options. So value = 'Delta N' causes an error as this is not one of the possible values of the Dropdown (although it is one of the keys in the mapping dict). I believe you want value = delta_n instead.

In matplotlib, how can I plot a multi-colored line, like a rainbow

I would like to plot parallel lines with different colors. E.g. rather than a single red line of thickness 6, I would like to have two parallel lines of thickness 3, with one red and one blue.
Any thoughts would be appreciated.
Merci
Even with the smart offsetting (s. below), there is still an issue in a view that has sharp angles between consecutive points.
Zoomed view of smart offsetting:
Overlaying lines of varying thickness:

Plotting parallel lines is not an easy task. Using a simple uniform offset will of course not show the desired result. This is shown in the left picture below.
Such a simple offset can be produced in matplotlib as shown in the transformation tutorial.
Method1
A better solution may be to use the idea sketched on the right side. To calculate the offset of the nth point we can use the normal vector to the line between the n-1st and the n+1st point and use the same distance along this normal vector to calculate the offset point.
The advantage of this method is that we have the same number of points in the original line as in the offset line. The disadvantage is that it is not completely accurate, as can be see in the picture.
This method is implemented in the function offset in the code below.
In order to make this useful for a matplotlib plot, we need to consider that the linewidth should be independent of the data units. Linewidth is usually given in units of points, and the offset would best be given in the same unit, such that e.g. the requirement from the question ("two parallel lines of width 3") can be met.
The idea is therefore to transform the coordinates from data to display coordinates, using ax.transData.transform. Also the offset in points o can be transformed to the same units: Using the dpi and the standard of ppi=72, the offset in display coordinates is o*dpi/ppi. After the offset in display coordinates has been applied, the inverse transform (ax.transData.inverted().transform) allows a backtransformation.
Now there is another dimension of the problem: How to assure that the offset remains the same independent of the zoom and size of the figure?
This last point can be addressed by recalculating the offset each time a zooming of resizing event has taken place.
Here is how a rainbow curve would look like produced by this method.
And here is the code to produce the image.
import numpy as np
import matplotlib.pyplot as plt
dpi = 100
def offset(x,y, o):
""" Offset coordinates given by array x,y by o """
X = np.c_[x,y].T
m = np.array([[0,-1],[1,0]])
R = np.zeros_like(X)
S = X[:,2:]-X[:,:-2]
R[:,1:-1] = np.dot(m, S)
R[:,0] = np.dot(m, X[:,1]-X[:,0])
R[:,-1] = np.dot(m, X[:,-1]-X[:,-2])
On = R/np.sqrt(R[0,:]**2+R[1,:]**2)*o
Out = On+X
return Out[0,:], Out[1,:]
def offset_curve(ax, x,y, o):
""" Offset array x,y in data coordinates
by o in points """
trans = ax.transData.transform
inv = ax.transData.inverted().transform
X = np.c_[x,y]
Xt = trans(X)
xto, yto = offset(Xt[:,0],Xt[:,1],o*dpi/72. )
Xto = np.c_[xto, yto]
Xo = inv(Xto)
return Xo[:,0], Xo[:,1]
# some single points
y = np.array([1,2,2,3,3,0])
x = np.arange(len(y))
#or try a sinus
x = np.linspace(0,9)
y=np.sin(x)*x/3.
fig, ax=plt.subplots(figsize=(4,2.5), dpi=dpi)
cols = ["#fff40b", "#00e103", "#ff9921", "#3a00ef", "#ff2121", "#af00e7"]
lw = 2.
lines = []
for i in range(len(cols)):
l, = plt.plot(x,y, lw=lw, color=cols[i])
lines.append(l)
def plot_rainbow(event=None):
xr = range(6); yr = range(6);
xr[0],yr[0] = offset_curve(ax, x,y, lw/2.)
xr[1],yr[1] = offset_curve(ax, x,y, -lw/2.)
xr[2],yr[2] = offset_curve(ax, xr[0],yr[0], lw)
xr[3],yr[3] = offset_curve(ax, xr[1],yr[1], -lw)
xr[4],yr[4] = offset_curve(ax, xr[2],yr[2], lw)
xr[5],yr[5] = offset_curve(ax, xr[3],yr[3], -lw)
for i in range(6):
lines[i].set_data(xr[i], yr[i])
plot_rainbow()
fig.canvas.mpl_connect("resize_event", plot_rainbow)
fig.canvas.mpl_connect("button_release_event", plot_rainbow)
plt.savefig(__file__+".png", dpi=dpi)
plt.show()
Method2
To avoid overlapping lines, one has to use a more complicated solution.
One could first offset every point normal to the two line segments it is part of (green points in the picture below). Then calculate the line through those offset points and find their intersection.
A particular case would be when the slopes of two subsequent line segments equal. This has to be taken care of (eps in the code below).
from __future__ import division
import numpy as np
import matplotlib.pyplot as plt
dpi = 100
def intersect(p1, p2, q1, q2, eps=1.e-10):
""" given two lines, first through points pn, second through qn,
find the intersection """
x1 = p1[0]; y1 = p1[1]; x2 = p2[0]; y2 = p2[1]
x3 = q1[0]; y3 = q1[1]; x4 = q2[0]; y4 = q2[1]
nomX = ((x1*y2-y1*x2)*(x3-x4)- (x1-x2)*(x3*y4-y3*x4))
denom = float( (x1-x2)*(y3-y4) - (y1-y2)*(x3-x4) )
nomY = (x1*y2-y1*x2)*(y3-y4) - (y1-y2)*(x3*y4-y3*x4)
if np.abs(denom) < eps:
#print "intersection undefined", p1
return np.array( p1 )
else:
return np.array( [ nomX/denom , nomY/denom ])
def offset(x,y, o, eps=1.e-10):
""" Offset coordinates given by array x,y by o """
X = np.c_[x,y].T
m = np.array([[0,-1],[1,0]])
S = X[:,1:]-X[:,:-1]
R = np.dot(m, S)
norm = np.sqrt(R[0,:]**2+R[1,:]**2) / o
On = R/norm
Outa = On+X[:,1:]
Outb = On+X[:,:-1]
G = np.zeros_like(X)
for i in xrange(0, len(X[0,:])-2):
p = intersect(Outa[:,i], Outb[:,i], Outa[:,i+1], Outb[:,i+1], eps=eps)
G[:,i+1] = p
G[:,0] = Outb[:,0]
G[:,-1] = Outa[:,-1]
return G[0,:], G[1,:]
def offset_curve(ax, x,y, o, eps=1.e-10):
""" Offset array x,y in data coordinates
by o in points """
trans = ax.transData.transform
inv = ax.transData.inverted().transform
X = np.c_[x,y]
Xt = trans(X)
xto, yto = offset(Xt[:,0],Xt[:,1],o*dpi/72., eps=eps )
Xto = np.c_[xto, yto]
Xo = inv(Xto)
return Xo[:,0], Xo[:,1]
# some single points
y = np.array([1,1,2,0,3,2,1.,4,3]) *1.e9
x = np.arange(len(y))
x[3]=x[4]
#or try a sinus
#x = np.linspace(0,9)
#y=np.sin(x)*x/3.
fig, ax=plt.subplots(figsize=(4,2.5), dpi=dpi)
cols = ["r", "b"]
lw = 11.
lines = []
for i in range(len(cols)):
l, = plt.plot(x,y, lw=lw, color=cols[i], solid_joinstyle="miter")
lines.append(l)
def plot_rainbow(event=None):
xr = range(2); yr = range(2);
xr[0],yr[0] = offset_curve(ax, x,y, lw/2.)
xr[1],yr[1] = offset_curve(ax, x,y, -lw/2.)
for i in range(2):
lines[i].set_data(xr[i], yr[i])
plot_rainbow()
fig.canvas.mpl_connect("resize_event", plot_rainbow)
fig.canvas.mpl_connect("button_release_event", plot_rainbow)
plt.show()
Note that this method should work well as long as the offset between the lines is smaller then the distance between subsequent points on the line. Otherwise method 1 may be better suited.

The best that I can think of is to take your data, generate a series of small offsets, and use fill_between to make bands of whatever color you like.
I wrote a function to do this. I don't know what shape you're trying to plot, so this may or may not work for you. I tested it on a parabola and got decent results. You can also play around with the list of colors.
def rainbow_plot(x, y, spacing=0.1):
fig, ax = plt.subplots()
colors = ['red', 'yellow', 'green', 'cyan','blue']
top = max(y)
lines = []
for i in range(len(colors)+1):
newline_data = y - top*spacing*i
lines.append(newline_data)
for i, c in enumerate(colors):
ax.fill_between(x, lines[i], lines[i+1], facecolor=c)
return fig, ax
x = np.linspace(0,1,51)
y = 1-(x-0.5)**2
rainbow_plot(x,y)

Python: Connecting list values with array values

I have created a tornado plot taking inspiration from here. It has input variables labelled on the y-axis (a1,b1,c1...) and their respective correlation coefficients plotted next to them. See pic below:
I then sorted the correlation coefficients in a way that the highest absolute value without loosing its sign gets plotted first, then the next highest and so on. using sorted(values,key=abs, reverse=True). See the result below
If you notice, in the second pic even though the bars were sorted in the absolute descending order, the y-axis label still stay the same.
Question: How do I make the y-axis label(variable) connect to the correlation coefficient such that it always corresponds to its correlation coefficient.
Below is my code:
import numpy as np
from matplotlib import pyplot as plt
#####Importing Data from csv file#####
dataset1 = np.genfromtxt('dataSet1.csv', dtype = float, delimiter = ',', skip_header = 1, names = ['a', 'b', 'c', 'x0'])
dataset2 = np.genfromtxt('dataSet2.csv', dtype = float, delimiter = ',', skip_header = 1, names = ['a', 'b', 'c', 'x0'])
dataset3 = np.genfromtxt('dataSet3.csv', dtype = float, delimiter = ',', skip_header = 1, names = ['a', 'b', 'c', 'x0'])
corr1 = np.corrcoef(dataset1['a'],dataset1['x0'])
corr2 = np.corrcoef(dataset1['b'],dataset1['x0'])
corr3 = np.corrcoef(dataset1['c'],dataset1['x0'])
corr4 = np.corrcoef(dataset2['a'],dataset2['x0'])
corr5 = np.corrcoef(dataset2['b'],dataset2['x0'])
corr6 = np.corrcoef(dataset2['c'],dataset2['x0'])
corr7 = np.corrcoef(dataset3['a'],dataset3['x0'])
corr8 = np.corrcoef(dataset3['b'],dataset3['x0'])
corr9 = np.corrcoef(dataset3['c'],dataset3['x0'])
np.set_printoptions(precision=4)
variables = ['a1','b1','c1','a2','b2','c2','a3','b3','c3']
base = 0
values = np.array([corr1[0,1],corr2[0,1],corr3[0,1],
corr4[0,1],corr5[0,1],corr6[0,1],
corr7[0,1],corr8[0,1],corr9[0,1]])
values = sorted(values,key=abs, reverse=True)
# The y position for each variable
ys = range(len(values))[::-1] # top to bottom
# Plot the bars, one by one
for y, value in zip(ys, values):
high_width = base + value
#print high_width
# Each bar is a "broken" horizontal bar chart
plt.broken_barh(
[(base, high_width)],
(y - 0.4, 0.8),
facecolors=['red', 'red'], # Try different colors if you like
edgecolors=['black', 'black'],
linewidth=1)
# Draw a vertical line down the middle
plt.axvline(base, color='black')
# Position the x-axis on the top/bottom, hide all the other spines (=axis lines)
axes = plt.gca() # (gca = get current axes)
axes.spines['left'].set_visible(False)
axes.spines['right'].set_visible(False)
axes.spines['top'].set_visible(False)
axes.xaxis.set_ticks_position('bottom')
# Make the y-axis display the variables
plt.yticks(ys, variables)
plt.ylim(-2, len(variables))
plt.show()
Many thanks in advance

use build-in zip function - returns a list of tuples, where the i-th tuple contains the i-th element from each of the argument sequences or iterables. But aware the returned list is truncated in length to the length of the shortest argument sequence.

change the positions and the labels for clabel

I am trying to overlay a contour plot on an astronomical image. The following code shows how I generate my contours:
print "contour map "
ny, nx = 50, 50
level=np.array([0.683,0.866,0.954,0.990, 0.997])
print "limits:"
print
print level
print
bins_x=np.linspace(min(xp),max(xp),nx)
bins_y=np.linspace(min(yp),max(yp),ny)
H, yedges, xedges = np.histogram2d(xp, yp, (bins_x,bins_y),weights=zp)
smooth=0.8
Hsmooth = scipy.ndimage.filters.gaussian_filter(H.T, smooth)
xcenters = (xedges[1:] + xedges[:-1])/2.
ycenters = (yedges[1:] + yedges[:-1])/2.
Xgrid, Ygrid = np.meshgrid(ycenters, xcenters)
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1] ]
print len(ra),len(Gcl_1_ra),len(Gcl_2_ra)
# Now we add contours
CS = plt.contour(Xgrid, Ygrid, Hsmooth, levels=level, extent=extent, linewidths=0.4, cmap=cm.Pastel1)
print CS.levels
plt.clabel(CS, CS.levels, colors='red',inline=True, inline_spacing=0.02,fontsize=7, fmt="%0.3f")
print "label coordinate :"
print CS.cl_xy
plt.show()
running the code gives me information about were contour labels are placed:
label coordinate :
[(479.11978392445798, 152.0), (183.33333333333337, 234.5705217606079), (394.86796408013157, 336.0), (462.33333333333337, 156.69957238363236), (183.33333333333337, 232.80998335706244), (399.34062255451977, 296.0), (462.33333333333337, 155.83083286816793), (183.33333333333337, 231.97448760480535), (402.06057288711821, 320.00000000000006), (452.00000000000006, 152.37778562776006), (183.33333333333337, 231.73316562697329), (399.50827125157235, 328.0), (452.00000000000006, 152.25467967915702), (183.33333333333337, 231.68624190906149), (399.44091390280244, 328.0)]
My questions are:
Since all the time the contour's labels are overlap with each other, how could I displace the labels in order that they don't get mixed up?
I would like to change the labels for clabel to label=[r'1$\sigma$',r'1.5$\sigma$',r'2$\sigma$',r'2.6$\sigma$',r'3$\sigma$']. How could I do that?
Thanks in advance.

For 1), you can pass a set of x,y values to clabel, where you would like the labels placed with
manual=[(x1,y1),(x2,y2)...
For 2), you can pass fmt as a function to be called with each numerical value, which returns a string for labelling; or a dictionary. For you, it could be
fmt={0.683:r'1$sigma$', 0.866:r'1.5$sigma$', 0.954:r'2$sigma$',
0.990:r'2.6$sigma$', 0.997:r'3$sigma$'}

Curved text rendering in matplotlib

In a project I'm doing, I have to take in a user input from a structured file (xml). The file contains road data of an area, which I have to plot on to the matplotlib canvas. The problem is that along with the road, I also have to render the road name, and most of the roads are curved. I know how to render text in an angle. But I was wondering whether it is possible to change the text angle midway through the string?
Something like this : Draw rotated text on curved path
But using matplotlib.

Here is my take on the problem:
In order to make the text robust to figure adjustments after drawing, I derive a child class, CurvedText, from matplotlib.text. The CurvedText object takes a string and a curve in the form of x- and y-value arrays. The text to be displayed itself is cut into separate characters, which each are added to the plot at the appropriate position. As matplotlib.text draws nothing if the string is empty, I replace all spaces by invisible 'a's. Upon figure adjustment, the overloaded draw() calls the update_positions() function, which takes care that the character positions and orientations stay correct. To assure the calling order (each character's draw() function will be called as well) the CurvedText object also takes care that the zorder of each character is higher than its own zorder. Following my example here, the text can have any alignment. If the text cannot be fit to the curve at the current resolution, the rest will be hidden, but will appear upon resizing. Below is the code with an example of application.
from matplotlib import pyplot as plt
from matplotlib import patches
from matplotlib import text as mtext
import numpy as np
import math
class CurvedText(mtext.Text):
"""
A text object that follows an arbitrary curve.
"""
def __init__(self, x, y, text, axes, **kwargs):
super(CurvedText, self).__init__(x[0],y[0],' ', **kwargs)
axes.add_artist(self)
##saving the curve:
self.__x = x
self.__y = y
self.__zorder = self.get_zorder()
##creating the text objects
self.__Characters = []
for c in text:
if c == ' ':
##make this an invisible 'a':
t = mtext.Text(0,0,'a')
t.set_alpha(0.0)
else:
t = mtext.Text(0,0,c, **kwargs)
#resetting unnecessary arguments
t.set_ha('center')
t.set_rotation(0)
t.set_zorder(self.__zorder +1)
self.__Characters.append((c,t))
axes.add_artist(t)
##overloading some member functions, to assure correct functionality
##on update
def set_zorder(self, zorder):
super(CurvedText, self).set_zorder(zorder)
self.__zorder = self.get_zorder()
for c,t in self.__Characters:
t.set_zorder(self.__zorder+1)
def draw(self, renderer, *args, **kwargs):
"""
Overload of the Text.draw() function. Do not do
do any drawing, but update the positions and rotation
angles of self.__Characters.
"""
self.update_positions(renderer)
def update_positions(self,renderer):
"""
Update positions and rotations of the individual text elements.
"""
#preparations
##determining the aspect ratio:
##from https://stackoverflow.com/a/42014041/2454357
##data limits
xlim = self.axes.get_xlim()
ylim = self.axes.get_ylim()
## Axis size on figure
figW, figH = self.axes.get_figure().get_size_inches()
## Ratio of display units
_, _, w, h = self.axes.get_position().bounds
##final aspect ratio
aspect = ((figW * w)/(figH * h))*(ylim[1]-ylim[0])/(xlim[1]-xlim[0])
#points of the curve in figure coordinates:
x_fig,y_fig = (
np.array(l) for l in zip(*self.axes.transData.transform([
(i,j) for i,j in zip(self.__x,self.__y)
]))
)
#point distances in figure coordinates
x_fig_dist = (x_fig[1:]-x_fig[:-1])
y_fig_dist = (y_fig[1:]-y_fig[:-1])
r_fig_dist = np.sqrt(x_fig_dist**2+y_fig_dist**2)
#arc length in figure coordinates
l_fig = np.insert(np.cumsum(r_fig_dist),0,0)
#angles in figure coordinates
rads = np.arctan2((y_fig[1:] - y_fig[:-1]),(x_fig[1:] - x_fig[:-1]))
degs = np.rad2deg(rads)
rel_pos = 10
for c,t in self.__Characters:
#finding the width of c:
t.set_rotation(0)
t.set_va('center')
bbox1 = t.get_window_extent(renderer=renderer)
w = bbox1.width
h = bbox1.height
#ignore all letters that don't fit:
if rel_pos+w/2 > l_fig[-1]:
t.set_alpha(0.0)
rel_pos += w
continue
elif c != ' ':
t.set_alpha(1.0)
#finding the two data points between which the horizontal
#center point of the character will be situated
#left and right indices:
il = np.where(rel_pos+w/2 >= l_fig)[0][-1]
ir = np.where(rel_pos+w/2 <= l_fig)[0][0]
#if we exactly hit a data point:
if ir == il:
ir += 1
#how much of the letter width was needed to find il:
used = l_fig[il]-rel_pos
rel_pos = l_fig[il]
#relative distance between il and ir where the center
#of the character will be
fraction = (w/2-used)/r_fig_dist[il]
##setting the character position in data coordinates:
##interpolate between the two points:
x = self.__x[il]+fraction*(self.__x[ir]-self.__x[il])
y = self.__y[il]+fraction*(self.__y[ir]-self.__y[il])
#getting the offset when setting correct vertical alignment
#in data coordinates
t.set_va(self.get_va())
bbox2 = t.get_window_extent(renderer=renderer)
bbox1d = self.axes.transData.inverted().transform(bbox1)
bbox2d = self.axes.transData.inverted().transform(bbox2)
dr = np.array(bbox2d[0]-bbox1d[0])
#the rotation/stretch matrix
rad = rads[il]
rot_mat = np.array([
[math.cos(rad), math.sin(rad)*aspect],
[-math.sin(rad)/aspect, math.cos(rad)]
])
##computing the offset vector of the rotated character
drp = np.dot(dr,rot_mat)
#setting final position and rotation:
t.set_position(np.array([x,y])+drp)
t.set_rotation(degs[il])
t.set_va('center')
t.set_ha('center')
#updating rel_pos to right edge of character
rel_pos += w-used
if __name__ == '__main__':
Figure, Axes = plt.subplots(2,2, figsize=(7,7), dpi=100)
N = 100
curves = [
[
np.linspace(0,1,N),
np.linspace(0,1,N),
],
[
np.linspace(0,2*np.pi,N),
np.sin(np.linspace(0,2*np.pi,N)),
],
[
-np.cos(np.linspace(0,2*np.pi,N)),
np.sin(np.linspace(0,2*np.pi,N)),
],
[
np.cos(np.linspace(0,2*np.pi,N)),
np.sin(np.linspace(0,2*np.pi,N)),
],
]
texts = [
'straight lines work the same as rotated text',
'wavy curves work well on the convex side',
'you even can annotate parametric curves',
'changing the plotting direction also changes text orientation',
]
for ax, curve, text in zip(Axes.reshape(-1), curves, texts):
#plotting the curve
ax.plot(*curve, color='b')
#adjusting plot limits
stretch = 0.2
xlim = ax.get_xlim()
w = xlim[1] - xlim[0]
ax.set_xlim([xlim[0]-stretch*w, xlim[1]+stretch*w])
ylim = ax.get_ylim()
h = ylim[1] - ylim[0]
ax.set_ylim([ylim[0]-stretch*h, ylim[1]+stretch*h])
#adding the text
text = CurvedText(
x = curve[0],
y = curve[1],
text=text,#'this this is a very, very long text',
va = 'bottom',
axes = ax, ##calls ax.add_artist in __init__
)
plt.show()
The result looks like this:
There are still some problems, when the text follows the concave side of a sharply bending curve. This is because the characters are 'stitched together' along the curve without accounting for overlap. If I have time, I'll try to improve on that. Any comments are very welcome.
Tested on python 3.5 and 2.7

I found your problem quite interesting, so I made something which comes pretty close using the matplotlib text tool:
from __future__ import division
import itertools
import matplotlib.pyplot as plt
import numpy as np
%matplotlib inline
# define figure and axes properties
fig, ax = plt.subplots(figsize=(8,6))
ax.set_xlim(left=0, right=10)
ax.set_ylim(bottom=-1.5, top=1.5)
(xmin, xmax), (ymin, ymax) = ax.get_xlim(), ax.get_ylim()
# calculate a shape factor, more explanation on usage further
# it is a representation of the distortion of the actual image compared to a
# cartesian space:
fshape = abs(fig.get_figwidth()*(xmax - xmin)/(ymax - ymin)/fig.get_figheight())
# the text you want to plot along your line
thetext = 'the text is flowing '
# generate a cycler, so that the string is cycled through
lettercycler = itertools.cycle(tuple(thetext))
# generate dummy river coordinates
xvals = np.linspace(1, 10, 300)
yvals = np.sin(xvals)**3
# every XX datapoints, a character is printed
markerevery = 10
# calculate the rotation angle for the labels (in degrees)
# the angle is calculated as the slope between two datapoints.
# it is then multiplied by a shape factor to get from the angles in a
# cartesian space to the angles in this figure
# first calculate the slope between two consecutive points, multiply with the
# shape factor, get the angle in radians with the arctangens functions, and
# convert to degrees
angles = np.rad2deg(np.arctan((yvals[1:]-yvals[:-1])/(xvals[1:]-xvals[:-1])*fshape))
# plot the 'river'
ax.plot(xvals, yvals, 'b', linewidth=3)
# loop over the data points, but only plot a character every XX steps
for counter in np.arange(0, len(xvals)-1, step=markerevery):
# plot the character in between two datapoints
xcoord = (xvals[counter] + xvals[counter+1])/2.
ycoord = (yvals[counter] + yvals[counter+1])/2.
# plot using the text method, set the rotation so it follows the line,
# aling in the center for a nicer look, optionally, a box can be drawn
# around the letter
ax.text(xcoord, ycoord, lettercycler.next(),
fontsize=25, rotation=angles[counter],
horizontalalignment='center', verticalalignment='center',
bbox=dict(facecolor='white', edgecolor='white', alpha=0.5))
The implementation is far from perfect, but it is a good starting point in my opinion.
Further, it seems that there is some development in matplotlib on having a scatterplot with rotation of the markers, which would be ideal for this case. However, my programming skills are nearly not as hardcore as they need to be to tackle this issue, so I cannot help here.
matplotlib on github: pull request
matplotlib on github: issue