I would like to know how to smoothly draw a line on top of two lines I have. Take for example
the following code:
import matplotlib.pyplot as plt
x1, y1 = [-1, 12], [1, 4]
x2, y2 = [1, 10], [3, 2]
plt.plot(x1, y1, x2, y2, marker = 'o')
plt.show()
I would like a draw a line from the top orange dot down to the blue line
where they intersect and up to the top right blue dot. I want this line to be smooth
preferably. How do I do this?
I was thinking I could make an array of the orange line to the blue then
have an array of the blue line till the blue dot. I would then draw a line here but this
is quite a crude solution. I am not sure if there is something smarter I can do.
Also it would be good to know how to generalise this to smooth lines (which is why I don't want this array solution). Thanks in advance.
first you have to calculate intersection between lines. I gave you example how to do it. Function draw_smooth_line will draw smooth line between 3 points. You can add logic to getting top points from you list if you need it.
import matplotlib.pyplot as plt
from scipy.ndimage.filters import gaussian_filter1d
import numpy as np
from scipy.interpolate import interp1d
def draw_smooth_line(left_x, left_y, mid_x, mid_y, right_x, right_y):
x = [left_x, mid_x, right_x]
y = [left_y, mid_y, right_y]
x_new = np.linspace(left_x, right_x,500)
f = interp1d(x, y, kind='quadratic')
y_smooth=f(x_new)
plt.plot (x_new,y_smooth)
def findIntersection(x1,y1,x2,y2,x3,y3,x4,y4):
px= ( (x1*y2-y1*x2)*(x3-x4)-(x1-x2)*(x3*y4-y3*x4) ) / ( (x1-x2)*(y3-y4)-(y1-y2)*(x3-x4) )
py= ( (x1*y2-y1*x2)*(y3-y4)-(y1-y2)*(x3*y4-y3*x4) ) / ( (x1-x2)*(y3-y4)-(y1-y2)*(x3-x4) )
return [px, py]
x1, y1 = [-1, 12], [1, 4]
x2, y2 = [1, 10], [3, 2]
x3, y3 = findIntersection(x1[0],y1[0],x1[1],y1[1],x2[0],y2[0],x2[1],y2[1])
draw_smooth_line(x1[1], y1[1], x3, y3, x2[0], y2[0])
plt.plot(x1, y1, x2, y2, x3, y3, marker = 'o')
plt.show()
Here is result
Related
How can I plot line segments in python? Here's an example of the lines I want to plot alongside scatterplot data. However, in this example, the line with slope of 1 should run from 0 to 3 only, and the line with slope of -1 should run from 4 to 8 only. I have the slope and intercept of each line, as well as the starting and ending x values.
plt.scatter(x_1, y_1)
plt.axline((0,9), slope = -1, color = 'black')
plt.axline((0,0), slope = 1, color = 'black')
plt.show()
I'm not sure from your output but it looks like you have maybe two different data sets which you want to plot straight lines through. Below I am breaking 3 of your data points into two lists of x, y coordinates, and the other 4 into two lists of x, y coordinates.
Here is the link for the line of best fit one liner
import matplotlib.pyplot as plt
import numpy
# data which you want to fit lines through
x1 = [0, 1, 3]
y1 = [0, 1, 3]
x2 = [4, 5, 6, 8]
y2 = [5, 4, 3, 2]
# plots the two data set points
plt.scatter(x1, y1, color='black')
plt.scatter(x2, y2, color='blue')
# plot will connect a line between the range of the data
plt.plot(x1, y1, color='black')
plt.plot(x2, y2, color='blue')
# line of best fit one liner
plt.plot(np.unique(x1), np.poly1d(np.polyfit(x1, y1, 1))(np.unique(x1)),color='red')
plt.plot(np.unique(x2), np.poly1d(np.polyfit(x2, y2, 1))(np.unique(x2)), color='red')
plt.ylim([-1, 7])
plt.show()
By knowing both the intercept and the slope of your lines, you can essentially use the equation for a straight line to get the corresponding y-values of your endpoints on the x-axis. Then you can plot these points and style the plot to get a black line between the points. This solution looks like the following
import matplotlib.pyplot as plt
import numpy as np
slope1, intercept1 = 1, 0
slope2, intercept2 = -1, 9
l1x = np.array([0,3])
l1y = l1x*slope1+intercept1
l2x = np.array([4,8])
l2y = np.array(l2x*slope2+intercept2)
plt.plot(l1x, l1y, 'k-', l2x, l2y, 'k-')
# The following two lines are to make the plot look like the image in the question
plt.xlim([0,8])
plt.ylim([0,9])
plt.show()
The line can be defined either by two points xy1 and xy2, or by one point xy1 and a slope.
plt.scatter(x_1, y_1)
plt.axline((4,4), (8,0), color = 'blue')
plt.axline((0,0), (3,3), color = 'black')
plt.show()
I have a data set with two y values associated with each x value. How can I divide the data into "upper" and "lower" values?
Below, I show an example with such a data set. I show an image of the desired "top" and "bottom" groupings (the red is the top and the purple is the bottom). My best idea so far is to find a line dividing the top and bottom data using an iterative approach.This solution is complicated and does not work very well, so I did not include it.
import matplotlib.pyplot as plt
import numpy as np
# construct data using piecewise functions
x1 = np.linspace(0, 0.7, 70)
x2 = np.linspace(0.7, 1, 30)
x3 = np.linspace(0.01, 0.999, 100)
y1 = 4.164 * x1 ** 3
y2 = 1 / x2
y3 = x3 ** 4 - 0.1
# concatenate data
x = np.concatenate([x1, x2, x3])
y = np.concatenate([y1, y2, y3])
# I want to be able divide the data by top and bottom,
# like shown in the chart. The black is the unlabeled data
# and the red and purple show the top and bottom
plt.scatter(x, y, marker='^', s=10, c='k')
plt.scatter(x1, y1, marker='x', s=0.8, c='r')
plt.scatter(x2, y2, marker='x', s=0.8, c='r')
plt.scatter(x3, y3, marker='x', s=0.8, c='purple')
plt.show()
You can create a dividing line by re-ordering your data. Sort everything by x then apply a Gaussian filter. The two data sets are strictly above or below the results of the Gaussian filter:
import matplotlib.pyplot as plt
from scipy.ndimage.filters import gaussian_filter1d
import numpy as np
# construct data using piecewise functions
x1 = np.linspace(0, 0.7, 70)
x2 = np.linspace(0.7, 1, 30)
x3 = np.linspace(0.01, 0.999, 100)
y1 = 4.164 * x1 ** 3
y2 = 1 / x2
y3 = x3 ** 4 - 0.1
# concatenate data
x = np.concatenate([x1, x2, x3])
y = np.concatenate([y1, y2, y3])
# I want to be able divide the data by top and bottom,
# like shown in the chart. The black is the unlabeled data
# and the red and purple show the top and bottom
idx = np.argsort(x)
newy = y[idx]
newx = x[idx]
gf = gaussian_filter1d(newy, 5)
plt.scatter(x, y, marker='^', s=10, c='k')
plt.scatter(x1, y1, marker='x', s=0.8, c='r')
plt.scatter(x2, y2, marker='x', s=0.8, c='r')
plt.scatter(x3, y3, marker='x', s=0.8, c='purple')
plt.scatter(newx, gf, c='orange')
plt.show()
I would try as follows:
sort the points by increasing X if necessary;
maintain two indexes to the upper and lower subsets;
moving from left to right, for every new point assign it to the closest subset and update the corresponding index.
Initialization of the process seems a little tricky. Start with the first two points (they have high chance of belonging to the same subset). Progress until the two points have a significant separation so that you are sure they belong to different subsets. Then backtrack to the left.
I am trying to create a colored line with certain conditions. Basically I would like to have the line colored red when pointing down on the y axis, green when pointing up and blue when neither.
I played around with some similar examples I found but I have never been able to convert them to work with plot() on an axis. Just wondering how this could be done.
Here is some code that I have come up with so far:
#create x,y coordinates
x = numpy.random.choice(10,10)
y = numpy.random.choice(10,10)
#create an array of colors based on direction of line (0=r, 1=g, 2=b)
colors = []
#create an array that is one position away from original
#to determine direction of line
yCopy = list(y[1:])
for y1,y2 in zip(y,yCopy):
if y1 > y2:
colors.append(0)
elif y1 < y2:
colors.append(1)
else:
colors.append(2)
#add tenth spot to array as loop only does nine
colors.append(2)
#create a numpy array of colors
categories = numpy.array(colors)
#create a color map with the three colors
colormap = numpy.array([matplotlib.colors.colorConverter.to_rgb('r'),matplotlib.colors.colorConverter.to_rgb('g'),matplotlib.colors.colorConverter.to_rgb('b')])
#plot line
matplotlib.axes.plot(x,y,color=colormap[categories])
Not sure how to get plot() to accept an array of colors. I always get an error about the format type used as the color. Tried heximal, decimal, string and float. Works perfect with scatter().
I don't think that you can use an array of colors in plot (the documentation says that color can be any matlab color, while the scatter docs say you can use an array).
However, you could fake it by plotting each line separately:
import numpy
from matplotlib import pyplot as plt
x = range(10)
y = numpy.random.choice(10,10)
for x1, x2, y1,y2 in zip(x, x[1:], y, y[1:]):
if y1 > y2:
plt.plot([x1, x2], [y1, y2], 'r')
elif y1 < y2:
plt.plot([x1, x2], [y1, y2], 'g')
else:
plt.plot([x1, x2], [y1, y2], 'b')
plt.show()
OK. So I figured out how to do it using LineCollecion to draw the line on a axis.
import numpy as np
import pylab as pl
from matplotlib import collections as mc
segments = []
colors = np.zeros(shape=(10,4))
x = range(10)
y = np.random.choice(10,10)
i = 0
for x1, x2, y1,y2 in zip(x, x[1:], y, y[1:]):
if y1 > y2:
colors[i] = tuple([1,0,0,1])
elif y1 < y2:
colors[i] = tuple([0,1,0,1])
else:
colors[i] = tuple([0,0,1,1])
segments.append([(x1, y1), (x2, y2)])
i += 1
lc = mc.LineCollection(segments, colors=colors, linewidths=2)
fig, ax = pl.subplots()
ax.add_collection(lc)
ax.autoscale()
ax.margins(0.1)
pl.show()
There is an example on the matplotlib page showing how to use a LineCollection to plot a multicolored line.
The remaining problem is to get the colors for the line collection. So if y are the values to compare,
cm = dict(zip(range(-1,2,1),list("gbr")))
colors = list( map( cm.get , np.sign(np.diff(y)) ))
Complete code:
import numpy as np; np.random.seed(5)
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
x = np.arange(10)
y = np.random.choice(10,10)
points = np.array([x, y]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
cm = dict(zip(range(-1,2,1),list("rbg")))
colors = list( map( cm.get , np.sign(np.diff(y)) ))
lc = LineCollection(segments, colors=colors, linewidths=2)
fig, ax = plt.subplots()
ax.add_collection(lc)
ax.autoscale()
ax.margins(0.1)
plt.show()
I'm trying to emulate Excel's
Insert>Scatter>Scatter with smooth lines and markers
command in Matplotlib
The scipy function interpolate creates a similar effect, with some nice examples of how to simply implement this here:
How to draw cubic spline in matplotlib
However Excel's spline algorithm is also able to generate a smooth curve through just three points (e.g. x = [0,1,2] y = [4,2,1]); and it isn't possible to do this with cubic splines.
I have seen discussions that suggest that the Excel algorithm uses Catmull-Rom splines; but don't really understand these, or how they could be adapted to Matplotlib:
http://answers.microsoft.com/en-us/office/forum/office_2007-excel/how-does-excel-plot-smooth-curves/c751e8ff-9f99-4ac7-a74a-fba41ac80300
Is there a simple way of modifying the above examples to achieve smooth curves through three or more points using the interpolate library?
Many thanks
By now you may have found the Wikipedia page for the Centripetal Catmull-Rom spline, but in case you haven't, it includes this sample code:
import numpy
import matplotlib.pyplot as plt
def CatmullRomSpline(P0, P1, P2, P3, nPoints=100):
"""
P0, P1, P2, and P3 should be (x,y) point pairs that define the
Catmull-Rom spline.
nPoints is the number of points to include in this curve segment.
"""
# Convert the points to numpy so that we can do array multiplication
P0, P1, P2, P3 = map(numpy.array, [P0, P1, P2, P3])
# Calculate t0 to t4
alpha = 0.5
def tj(ti, Pi, Pj):
xi, yi = Pi
xj, yj = Pj
return ( ( (xj-xi)**2 + (yj-yi)**2 )**0.5 )**alpha + ti
t0 = 0
t1 = tj(t0, P0, P1)
t2 = tj(t1, P1, P2)
t3 = tj(t2, P2, P3)
# Only calculate points between P1 and P2
t = numpy.linspace(t1,t2,nPoints)
# Reshape so that we can multiply by the points P0 to P3
# and get a point for each value of t.
t = t.reshape(len(t),1)
A1 = (t1-t)/(t1-t0)*P0 + (t-t0)/(t1-t0)*P1
A2 = (t2-t)/(t2-t1)*P1 + (t-t1)/(t2-t1)*P2
A3 = (t3-t)/(t3-t2)*P2 + (t-t2)/(t3-t2)*P3
B1 = (t2-t)/(t2-t0)*A1 + (t-t0)/(t2-t0)*A2
B2 = (t3-t)/(t3-t1)*A2 + (t-t1)/(t3-t1)*A3
C = (t2-t)/(t2-t1)*B1 + (t-t1)/(t2-t1)*B2
return C
def CatmullRomChain(P):
"""
Calculate Catmull Rom for a chain of points and return the combined curve.
"""
sz = len(P)
# The curve C will contain an array of (x,y) points.
C = []
for i in range(sz-3):
c = CatmullRomSpline(P[i], P[i+1], P[i+2], P[i+3])
C.extend(c)
return C
which nicely computes the interpolation for n >= 4 points like so:
points = [[0,1.5],[2,2],[3,1],[4,0.5],[5,1],[6,2],[7,3]]
c = CatmullRomChain(points)
px, py = zip(*points)
x, y = zip(*c)
plt.plot(x, y)
plt.plot(px, py, 'or')
resulting in this matplotlib image:
Update:
Alternatively, there is a scipy.interpolate function for BarycentricInterpolator that appears to do what you're looking for. It is rather straightforward to use and works for cases in which you have only 3 data points.
from scipy.interpolate import BarycentricInterpolator
# create some data points
points1 = [[0, 2], [1, 4], [2, -2], [3, 6], [4, 2]]
points2 = [[1, 1], [2, 5], [3, -1]]
# put data into x, y tuples
x1, y1 =zip(*points1)
x2, y2 = zip(*points2)
# create the interpolator
bci1 = BarycentricInterpolator(x1, y1)
bci2 = BarycentricInterpolator(x2, y2)
# define dense x-axis for interpolating over
x1_new = np.linspace(min(x1), max(x1), 1000)
x2_new = np.linspace(min(x2), max(x2), 1000)
# plot it all
plt.plot(x1, y1, 'o')
plt.plot(x2, y2, 'o')
plt.plot(x1_new, bci1(x1_new))
plt.plot(x2_new, bci2(x2_new))
plt.xlim(-1, 5)
Update 2
Another option within scipy is akima interpolation via Akima1DInterpolator. It is as easy to implement as Barycentric, but has the advantage that it avoids large oscillations at the edge of a data set. Here's a few test cases that exhibit all the criteria you've asked for so far.
from scipy.interpolate import Akima1DInterpolator
x1, y1 = np.arange(13), np.random.randint(-10, 10, 13)
x2, y2 = [0,2,3,6,12], [100,50,30,18,14]
x3, y3 = [4, 6, 8], [60, 80, 40]
akima1 = Akima1DInterpolator(x1, y1)
akima2 = Akima1DInterpolator(x2, y2)
akima3 = Akima1DInterpolator(x3, y3)
x1_new = np.linspace(min(x1), max(x1), 1000)
x2_new = np.linspace(min(x2), max(x2), 1000)
x3_new = np.linspace(min(x3), max(x3), 1000)
plt.plot(x1, y1, 'bo')
plt.plot(x2, y2, 'go')
plt.plot(x3, y3, 'ro')
plt.plot(x1_new, akima1(x1_new), 'b', label='random points')
plt.plot(x2_new, akima2(x2_new), 'g', label='exponential')
plt.plot(x3_new, akima3(x3_new), 'r', label='3 points')
plt.xlim(-1, 15)
plt.ylim(-10, 110)
plt.legend(loc='best')
#Lanery: Re: Update 2: The best just got better!
Had to redefine the lists x2,y2,x3,y3 as numpy arrays to get your example to work on my system (Spyder / Python 2.7) :
x2 = np.array([0,2,3,6,12])
y2 = np.array([100,50,30,18,14])
x3 = np.array([4, 6, 8])
y3 = np.array([60, 80, 40])
But now works like a dream! Many thanks for your expertise and clear explanations.
I am trying to create a colored line with certain conditions. Basically I would like to have the line colored red when pointing down on the y axis, green when pointing up and blue when neither.
I played around with some similar examples I found but I have never been able to convert them to work with plot() on an axis. Just wondering how this could be done.
Here is some code that I have come up with so far:
#create x,y coordinates
x = numpy.random.choice(10,10)
y = numpy.random.choice(10,10)
#create an array of colors based on direction of line (0=r, 1=g, 2=b)
colors = []
#create an array that is one position away from original
#to determine direction of line
yCopy = list(y[1:])
for y1,y2 in zip(y,yCopy):
if y1 > y2:
colors.append(0)
elif y1 < y2:
colors.append(1)
else:
colors.append(2)
#add tenth spot to array as loop only does nine
colors.append(2)
#create a numpy array of colors
categories = numpy.array(colors)
#create a color map with the three colors
colormap = numpy.array([matplotlib.colors.colorConverter.to_rgb('r'),matplotlib.colors.colorConverter.to_rgb('g'),matplotlib.colors.colorConverter.to_rgb('b')])
#plot line
matplotlib.axes.plot(x,y,color=colormap[categories])
Not sure how to get plot() to accept an array of colors. I always get an error about the format type used as the color. Tried heximal, decimal, string and float. Works perfect with scatter().
I don't think that you can use an array of colors in plot (the documentation says that color can be any matlab color, while the scatter docs say you can use an array).
However, you could fake it by plotting each line separately:
import numpy
from matplotlib import pyplot as plt
x = range(10)
y = numpy.random.choice(10,10)
for x1, x2, y1,y2 in zip(x, x[1:], y, y[1:]):
if y1 > y2:
plt.plot([x1, x2], [y1, y2], 'r')
elif y1 < y2:
plt.plot([x1, x2], [y1, y2], 'g')
else:
plt.plot([x1, x2], [y1, y2], 'b')
plt.show()
OK. So I figured out how to do it using LineCollecion to draw the line on a axis.
import numpy as np
import pylab as pl
from matplotlib import collections as mc
segments = []
colors = np.zeros(shape=(10,4))
x = range(10)
y = np.random.choice(10,10)
i = 0
for x1, x2, y1,y2 in zip(x, x[1:], y, y[1:]):
if y1 > y2:
colors[i] = tuple([1,0,0,1])
elif y1 < y2:
colors[i] = tuple([0,1,0,1])
else:
colors[i] = tuple([0,0,1,1])
segments.append([(x1, y1), (x2, y2)])
i += 1
lc = mc.LineCollection(segments, colors=colors, linewidths=2)
fig, ax = pl.subplots()
ax.add_collection(lc)
ax.autoscale()
ax.margins(0.1)
pl.show()
There is an example on the matplotlib page showing how to use a LineCollection to plot a multicolored line.
The remaining problem is to get the colors for the line collection. So if y are the values to compare,
cm = dict(zip(range(-1,2,1),list("gbr")))
colors = list( map( cm.get , np.sign(np.diff(y)) ))
Complete code:
import numpy as np; np.random.seed(5)
import matplotlib.pyplot as plt
from matplotlib.collections import LineCollection
x = np.arange(10)
y = np.random.choice(10,10)
points = np.array([x, y]).T.reshape(-1, 1, 2)
segments = np.concatenate([points[:-1], points[1:]], axis=1)
cm = dict(zip(range(-1,2,1),list("rbg")))
colors = list( map( cm.get , np.sign(np.diff(y)) ))
lc = LineCollection(segments, colors=colors, linewidths=2)
fig, ax = plt.subplots()
ax.add_collection(lc)
ax.autoscale()
ax.margins(0.1)
plt.show()