I'm trying to implement some algorithms in Python from different papers and some require a peak/through detection where local minima and maxima are alternating. That should always be the case of course in an analog signal.
However when working with discrete Signals this is not always the case as you can see with this simple example:
from scipy.signal import argrelmax,argrelmin,argrelextrema
import numpy as np
import matplotlib.pyplot as plt
fig = plt.figure("local extrema")
ax = fig.subplots()
x = range(0,10)
y = np.array([0,1,0,0,1,2,1,0,0,0])
local_minima, = list(argrelmin(np.array(y)))
local_maxima, = list(argrelmax(np.array(y)))
ax.plot(local_maxima, y[local_maxima],"x",color="orange")
ax.plot(local_minima, y[local_minima],"x",color="orange")
ax.plot(x,y)
plt.show()
I know that I can adjust the argrelmax and argrelmin functions but no matter what I do, its always somehow flawed.
Here only two maxima are found. So there are no alternating extrema.
Is there a way to automatically detect extremas and assure they are alternating, or do I have to implement some kind of workaround? (Ideas for that are welcome too)
I found a solution I previously disregarded unfortunately. The Problem with argrelmax,argrelmin and argrelextrema was that they had difficulties detecting flat peaks/throughs because sometimes they found two maxima using np.greater_equal as comparator (beginning and end of flat peak), which lead to non alternating maxima/minima.
After Flows answer I revisited find_peaks from scipy.signal, which I previously disregarded, because in the first few sentences it said: "finds all local maxima by simple comparison of neighboring values" so I thought it had the same flaws as the others.
But in reality it detects flat peaks with only one index at the middle (rounded down) of the peak, no matter how wide apparently.
Thus this solved my Problem for this simple case:
from scipy.signal import argrelmax,argrelmin, argrelextrema, find_peaks
fig = plt.figure("local extrema")
ax = fig.subplots()
x = range(0,10)
y = np.array([0,1,0,0,1,2,1,0,0,0])
peaks,_ = find_peaks(y)
throughs,_ = find_peaks(np.negative(y))
local_maxima = list(peaks)
local_minima = list(throughs)
ax.plot(x,y)
ax.plot(local_maxima, y[local_maxima],"x",color="orange")
ax.plot(local_minima, y[local_minima],"x",color="orange")
plt.show()
As you can see now the minima is detected.
I will have to see if it works on my real world data though, but I think it should. Thx!
Alright, so I was working on a simple program to just pull coordinates out of a text pad and then graph what was in the text pad on a graph. I thought it would be pretty simple, but I am VERY new to matplotlib, so I still don't fully understand. I got most of the code done correctly, but the only thing that is not working is that when I put the values in the graph, they come all out of order. I want to order the xticks and yticks so that it actually looks like a real line graph you'd see in math, so you can see how the lower coordinates lower than the higher coordinates, and vice versa. Here is my code:
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
def split(word):
return list(word)
fileIWant = open('C:/Users/JustA/Desktop/Python Shenanigans/Converting Coordinates in a .txt to a Graph/Coordinates.txt', 'r');
stopwords = ['\n']
array = fileIWant.readlines()
array = [array.replace('\n', '') for array in array if array not in stopwords]
fileIWant.close()
editFile = open('C:/Users/JustA/Desktop/Python Shenanigans/Converting Coordinates in a .txt to a Graph/Coordinates.txt', 'w')
array_length = len(array)
x = []
y = []
for i in range(array_length):
dataSplit = array[i].split()
getCoordinateX = dataSplit[1]
getCoordinateY = dataSplit[3]
x.append(getCoordinateX)
y.append(getCoordinateY)
plt.scatter(x, y)
plt.plot(x, y) #Add this line in if you want to show lines.
plt.title('Your Coordinate Graph')
plt.xlabel('X Coordinates')
plt.ylabel('Y Coordinates')
#plt.xticks([-100,-80,-60,-40,-20,0,20,40,60,80,100])
#plt.yticks([-100,-80,-60,-40,-20,0,20,40,60,80,100])
plt.show()
editFile.close()
I commented out what I put for the ticks, because it was not working at all. With those commented out, it looks okay, but it is very confusing. I think it just puts them in the order they are at in the .txt, when I want them to order themselves in the code. Here is what it is outputting right now:
Sorry if this is so simple that it has never been asked before, like I said, very new to matplotlib, and numpy if I have to use that at all. I imported it because I thought I may have to, but I don't think I really used it as of yet. Also, I am going to rewrite the coordinates into the graph in order, but I think I can do that myself later.
The problem is that your coordinates are strings, which means matplotlib is just plotting strings against strings ("categorical" axis labels). To fix, you simply have to convert your strings to numbers, e.g. x.append(int(getCoordinateX)).
Note that you also don't have to put plt.scatter/plt.plot in the loop - you only have to call one of those once on the full array. That'll probably make things a little faster too.
When looking closely at contour plots made with matplotlib, I noticed that smaller contours have inaccurate endpoints which do not close perfectly in PDF figures. Consider the minimal example:
plt.gca().set_aspect('equal')
x,y = np.meshgrid(np.linspace(-1,1,100), np.linspace(-1,1,100))
r = x*x + y*y
plt.contour(np.log(r))
plt.savefig("test.pdf")
The central part of the resulting test.pdf file, shown below, clearly shows the problem. Is there a way to solve this or is it a bug/intrinsic inaccuracy of matploplib?
Disclaimer: this is more an explanation + hack than a real answer.
I believe that there is a fundamental problem the way matplotlib makes contour plots. Essentially, all contours are collections of lines (LineCollection), while they should be collection of possibly closed lines (PolyCollection). There might be good reasons why things are done this way, but in the simple example I made this choice clearly produces artifacts. A not-very-nice solution is to convert a posteriori all LineCollection's into PolyCollection's. This is what is done in the following code
from matplotlib.collections import PolyCollection
eps = 1e-5
plt.gca().set_aspect('equal')
x,y = np.meshgrid(np.linspace(-1,1,100), np.linspace(-1,1,100))
r = x*x + y*y
plt.contour(np.log(r/1.2))
ca = plt.gca()
N = len(ca.collections)
for n in range(N):
c = ca.collections.pop(0)
for s in c.get_segments():
closed = (abs(s[0,0] - s[-1,0]) < eps) and (abs(s[0,1] - s[-1,1]) < eps)
p = PolyCollection([s], edgecolors=c.get_edgecolors(),
linewidths=c.get_linewidths(), linestyles=c.get_linestyles(),
facecolors=c.get_facecolors(), closed=closed)
ca.add_collection(p)
plt.savefig("test.pdf")
A zoom of the result obtained shows that everything is OK now:
Some care is taken to check if a contour is closed: in the present code, this is done with an approximate equality check for the first and last point: I am wandering if there is a better way to do this (perhaps matplotlib returns some data to check closed contours?). In any case, again, this is hack: I would be happy to hear if anyone has a better solution (or has a way to fix this within matplotlib).
So I just did the same thing, but got closed contours (see images). Did you check for any updates on the package?
import matplotlib.pyplot as plt
import numpy as np
plt.gca().set_aspect('equal')
x,y = np.meshgrid(np.linspace(-1,1,100), np.linspace(-1,1,100))
r = x*x + y*y
plt.contour(np.log(r))
plt.show()
Zoomed Out
Zoomed In
I am trying to plot contour lines of pressure level. I am using a netCDF file which contain the higher resolution data (ranges from 3 km to 27 km). Due to higher resolution data set, I get lot of pressure values which are not required to be plotted (rather I don't mind omitting certain contour line of insignificant values). I have written some plotting script based on the examples given in this link http://matplotlib.org/basemap/users/examples.html.
After plotting the image looks like this
From the image I have encircled the contours which are small and not required to be plotted. Also, I would like to plot all the contour lines smoother as mentioned in the above image. Overall I would like to get the contour image like this:-
Possible solution I think of are
Find out the number of points required for plotting contour and mask/omit those lines if they are small in number.
or
Find the area of the contour (as I want to omit only circled contour) and omit/mask those are smaller.
or
Reduce the resolution (only contour) by increasing the distance to 50 km - 100 km.
I am able to successfully get the points using SO thread Python: find contour lines from matplotlib.pyplot.contour()
But I am not able to implement any of the suggested solution above using those points.
Any solution to implement the above suggested solution is really appreciated.
Edit:-
# Andras Deak
I used print 'diameter is ', diameter line just above del(level.get_paths()[kp]) line to check if the code filters out the required diameter. Here is the filterd messages when I set if diameter < 15000::
diameter is 9099.66295612
diameter is 13264.7838257
diameter is 445.574234531
diameter is 1618.74618114
diameter is 1512.58974168
However the resulting image does not have any effect. All look same as posed image above. I am pretty sure that I have saved the figure (after plotting the wind barbs).
Regarding the solution for reducing the resolution, plt.contour(x[::2,::2],y[::2,::2],mslp[::2,::2]) it works. I have to apply some filter to make the curve smooth.
Full working example code for removing lines:-
Here is the example code for your review
#!/usr/bin/env python
from netCDF4 import Dataset
import matplotlib
matplotlib.use('agg')
import matplotlib.pyplot as plt
import numpy as np
import scipy.ndimage
from mpl_toolkits.basemap import interp
from mpl_toolkits.basemap import Basemap
# Set default map
west_lon = 68
east_lon = 93
south_lat = 7
north_lat = 23
nc = Dataset('ncfile.nc')
# Get this variable for later calucation
temps = nc.variables['T2']
time = 0 # We will take only first interval for this example
# Draw basemap
m = Basemap(projection='merc', llcrnrlat=south_lat, urcrnrlat=north_lat,
llcrnrlon=west_lon, urcrnrlon=east_lon, resolution='l')
m.drawcoastlines()
m.drawcountries(linewidth=1.0)
# This sets the standard grid point structure at full resolution
x, y = m(nc.variables['XLONG'][0], nc.variables['XLAT'][0])
# Set figure margins
width = 10
height = 8
plt.figure(figsize=(width, height))
plt.rc("figure.subplot", left=.001)
plt.rc("figure.subplot", right=.999)
plt.rc("figure.subplot", bottom=.001)
plt.rc("figure.subplot", top=.999)
plt.figure(figsize=(width, height), frameon=False)
# Convert Surface Pressure to Mean Sea Level Pressure
stemps = temps[time] + 6.5 * nc.variables['HGT'][time] / 1000.
mslp = nc.variables['PSFC'][time] * np.exp(9.81 / (287.0 * stemps) * nc.variables['HGT'][time]) * 0.01 + (
6.7 * nc.variables['HGT'][time] / 1000)
# Contour only at 2 hpa interval
level = []
for i in range(mslp.min(), mslp.max(), 1):
if i % 2 == 0:
if i >= 1006 and i <= 1018:
level.append(i)
# Save mslp values to upload to SO thread
# np.savetxt('mslp.txt', mslp, fmt='%.14f', delimiter=',')
P = plt.contour(x, y, mslp, V=2, colors='b', linewidths=2, levels=level)
# Solution suggested by Andras Deak
for level in P.collections:
for kp,path in enumerate(level.get_paths()):
# include test for "smallness" of your choice here:
# I'm using a simple estimation for the diameter based on the
# x and y diameter...
verts = path.vertices # (N,2)-shape array of contour line coordinates
diameter = np.max(verts.max(axis=0) - verts.min(axis=0))
if diameter < 15000: # threshold to be refined for your actual dimensions!
#print 'diameter is ', diameter
del(level.get_paths()[kp]) # no remove() for Path objects:(
#level.remove() # This does not work. produces ValueError: list.remove(x): x not in list
plt.gcf().canvas.draw()
plt.savefig('dummy', bbox_inches='tight')
plt.close()
After the plot is saved I get the same image
You can see that the lines are not removed yet. Here is the link to mslp array which we are trying to play with http://www.mediafire.com/download/7vi0mxqoe0y6pm9/mslp.txt
If you want x and y data which are being used in the above code, I can upload for your review.
Smooth line
You code to remove the smaller circles working perfectly. However the other question I have asked in the original post (smooth line) does not seems to work. I have used your code to slice the array to get minimal values and contoured it. I have used the following code to reduce the array size:-
slice = 15
CS = plt.contour(x[::slice,::slice],y[::slice,::slice],mslp[::slice,::slice], colors='b', linewidths=1, levels=levels)
The result is below.
After searching for few hours I found this SO thread having simmilar issue:-
Regridding regular netcdf data
But none of the solution provided over there works.The questions similar to mine above does not have proper solutions. If this issue is solved then the code is perfect and complete.
General idea
Your question seems to have 2 very different halves: one about omitting small contours, and another one about smoothing the contour lines. The latter is simpler, since I can't really think of anything else other than decreasing the resolution of your contour() call, just like you said.
As for removing a few contour lines, here's a solution which is based on directly removing contour lines individually. You have to loop over the collections of the object returned by contour(), and for each element check each Path, and delete the ones you don't need. Redrawing the figure's canvas will get rid of the unnecessary lines:
# dummy example based on matplotlib.pyplot.clabel example:
import matplotlib
import numpy as np
import matplotlib.cm as cm
import matplotlib.mlab as mlab
import matplotlib.pyplot as plt
delta = 0.025
x = np.arange(-3.0, 3.0, delta)
y = np.arange(-2.0, 2.0, delta)
X, Y = np.meshgrid(x, y)
Z1 = mlab.bivariate_normal(X, Y, 1.0, 1.0, 0.0, 0.0)
Z2 = mlab.bivariate_normal(X, Y, 1.5, 0.5, 1, 1)
# difference of Gaussians
Z = 10.0 * (Z2 - Z1)
plt.figure()
CS = plt.contour(X, Y, Z)
for level in CS.collections:
for kp,path in reversed(list(enumerate(level.get_paths()))):
# go in reversed order due to deletions!
# include test for "smallness" of your choice here:
# I'm using a simple estimation for the diameter based on the
# x and y diameter...
verts = path.vertices # (N,2)-shape array of contour line coordinates
diameter = np.max(verts.max(axis=0) - verts.min(axis=0))
if diameter<1: # threshold to be refined for your actual dimensions!
del(level.get_paths()[kp]) # no remove() for Path objects:(
# this might be necessary on interactive sessions: redraw figure
plt.gcf().canvas.draw()
Here's the original(left) and the removed version(right) for a diameter threshold of 1 (note the little piece of the 0 level at the top):
Note that the top little line is removed while the huge cyan one in the middle doesn't, even though both correspond to the same collections element i.e. the same contour level. If we didn't want to allow this, we could've called CS.collections[k].remove(), which would probably be a much safer way of doing the same thing (but it wouldn't allow us to differentiate between multiple lines corresponding to the same contour level).
To show that fiddling around with the cut-off diameter works as expected, here's the result for a threshold of 2:
All in all it seems quite reasonable.
Your actual case
Since you've added your actual data, here's the application to your case. Note that you can directly generate the levels in a single line using np, which will almost give you the same result. The exact same can be achieved in 2 lines (generating an arange, then selecting those that fall between p1 and p2). Also, since you're setting levels in the call to contour, I believe the V=2 part of the function call has no effect.
import numpy as np
import matplotlib.pyplot as plt
# insert actual data here...
Z = np.loadtxt('mslp.txt',delimiter=',')
X,Y = np.meshgrid(np.linspace(0,300000,Z.shape[1]),np.linspace(0,200000,Z.shape[0]))
p1,p2 = 1006,1018
# this is almost the same as the original, although it will produce
# [p1, p1+2, ...] instead of `[Z.min()+n, Z.min()+n+2, ...]`
levels = np.arange(np.maximum(Z.min(),p1),np.minimum(Z.max(),p2),2)
#control
plt.figure()
CS = plt.contour(X, Y, Z, colors='b', linewidths=2, levels=levels)
#modified
plt.figure()
CS = plt.contour(X, Y, Z, colors='b', linewidths=2, levels=levels)
for level in CS.collections:
for kp,path in reversed(list(enumerate(level.get_paths()))):
# go in reversed order due to deletions!
# include test for "smallness" of your choice here:
# I'm using a simple estimation for the diameter based on the
# x and y diameter...
verts = path.vertices # (N,2)-shape array of contour line coordinates
diameter = np.max(verts.max(axis=0) - verts.min(axis=0))
if diameter<15000: # threshold to be refined for your actual dimensions!
del(level.get_paths()[kp]) # no remove() for Path objects:(
# this might be necessary on interactive sessions: redraw figure
plt.gcf().canvas.draw()
plt.show()
Results, original(left) vs new(right):
Smoothing by resampling
I've decided to tackle the smoothing problem as well. All I could come up with is downsampling your original data, then upsampling again using griddata (interpolation). The downsampling part could also be done with interpolation, although the small-scale variation in your input data might make this problem ill-posed. So here's the crude version:
import scipy.interpolate as interp #the new one
# assume you have X,Y,Z,levels defined as before
# start resampling stuff
dN = 10 # use every dN'th element of the gridded input data
my_slice = [slice(None,None,dN),slice(None,None,dN)]
# downsampled data
X2,Y2,Z2 = X[my_slice],Y[my_slice],Z[my_slice]
# same as X2 = X[::dN,::dN] etc.
# upsampling with griddata over original mesh
Zsmooth = interp.griddata(np.array([X2.ravel(),Y2.ravel()]).T,Z2.ravel(),(X,Y),method='cubic')
# plot
plt.figure()
CS = plt.contour(X, Y, Zsmooth, colors='b', linewidths=2, levels=levels)
You can freely play around with the grids used for interpolation, in this case I just used the original mesh, as it was at hand. You can also play around with different kinds of interpolation: the default 'linear' one will be faster, but less smooth.
Result after downsampling(left) and upsampling(right):
Of course you should still apply the small-line-removal algorithm after this resampling business, and keep in mind that this heavily distorts your input data (since if it wasn't distorted, then it wouldn't be smooth). Also, note that due to the crude method used in the downsampling step, we introduce some missing values near the top/right edges of the region under consideraton. If this is a problem, you should consider doing the downsampling based on griddata as I've noted earlier.
This is a pretty bad solution, but it's the only one that I've come up with. Use the get_contour_verts function in this solution you linked to, possibly with the matplotlib._cntr module so that nothing gets plotted initially. That gives you a list of contour lines, sections, vertices, etc. Then you have to go through that list and pop the contours you don't want. You could do this by calculating a minimum diameter, for example; if the max distance between points is less than some cutoff, throw it out.
That leaves you with a list of LineCollection objects. Now if you make a Figure and Axes instance, you can use Axes.add_collection to add all of the LineCollections in the list.
I checked this out really quick, but it seemed to work. I'll come back with a minimum working example if I get a chance. Hope it helps!
Edit: Here's an MWE of the basic idea. I wasn't familiar with plt._cntr.Cntr, so I ended up using plt.contour to get the initial contour object. As a result, you end up making two figures; you just have to close the first one. You can replace checkDiameter with whatever function works. I think you could turn the line segments into a Polygon and calculate areas, but you'd have to figure that out on your own. Let me know if you run into problems with this code, but it at least works for me.
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
def checkDiameter(seg, tol=.3):
# Function for screening line segments. NB: Not actually a proper diameter.
diam = (seg[:,0].max() - seg[:,0].min(),
seg[:,1].max() - seg[:,1].min())
return not (diam[0] < tol or diam[1] < tol)
# Create testing data
x = np.linspace(-1,1, 21)
xx, yy = np.meshgrid(x,x)
z = np.exp(-(xx**2 + .5*yy**2))
# Original plot with plt.contour
fig0, ax0 = plt.subplots()
# Make sure this contour object actually has a tiny contour to remove
cntrObj = ax0.contour(xx,yy,z, levels=[.2,.4,.6,.8,.9,.95,.99,.999])
# Primary loop: Copy contours into a new LineCollection
lineNew = list()
for lineOriginal in cntrObj.collections:
# Get properties of the original LineCollection
segments = lineOriginal.get_segments()
propDict = lineOriginal.properties()
propDict = {key: value for (key,value) in propDict.items()
if key in ['linewidth','color','linestyle']} # Whatever parameters you want to carry over
# Filter out the lines with small diameters
segments = [seg for seg in segments if checkDiameter(seg)]
# Create new LineCollection out of the OK segments
if len(segments) > 0:
lineNew.append(mpl.collections.LineCollection(segments, **propDict))
# Make new plot with only these line collections; display results
fig1, ax1 = plt.subplots()
ax1.set_xlim(ax0.get_xlim())
ax1.set_ylim(ax0.get_ylim())
for line in lineNew:
ax1.add_collection(line)
plt.show()
FYI: The bit with propDict is just to automate bringing over some of the line properties from the original plot. You can't use the whole dictionary at once, though. First, it contains the old plot's line segments, but you can just swap those for the new ones. But second, it appears to contain a number of parameters that are in conflict with each other: multiple linewidths, facecolors, etc. The {key for key in propDict if I want key} workaround is my way to bypass that, but I'm sure someone else can do it more cleanly.
I would like to plot 2 curves in the same figure with the following code:
import sympy as syp
x, y = syp.symbols('x, y')
my_function = syp.exp(-(x-2)**2)*syp.exp(-(y-3)**2) + 2*syp.exp(-(x+1)**2)*syp.exp(-(y-1)**2)
gradient_1 = syp.diff(my_function, x)
gradient_2 = syp.diff(my_function, y)
curve_1 = syp.plot_implicit(syp.Eq(gradient_1, 0))
curve_2 = syp.plot_implicit(syp.Eq(gradient_2, 0))
What I see is only the first plot, while I would like to have both the curves in the same picture, maybe also with a grid if possible.
Any ideas?
Note: with matplotlib it's very easy, but I cannot find any specific example for the function syp.plot_implicit
Another, perhaps more efficient way, would be to compute both at the same time using Or
plot_implicit(Or(Eq(gradient_1, 0), Eq(gradient_2, 0)))
It might work if you do:
>>> curve_1.extend(curve_2)
>>> curve_1.show()
However mixing implicit plots might not be implemented yet.
Be aware that your curve_1 and curve_2 are not what sympy considers "single curves" i.e. Series instance, but rather "collections of a number of curves", i.e. Plot instances.
You can also extract the matplotlib objects from curve_1._backend.fig and other _backend attributes.
In conclusion, there is a nice API to do what you want, but probably the methods behind it are not finished yet.
Another way:
curve_1.append(curve_2[0])
curve_1.show()