I have data in form of a 3D array, with "intensities" at every point. Depending on the intensity, I want to plot the point with a higher alpha. There are a lot of low-value outliers, so color coding (with scalar floats) won't work since they eclipse the real data.
What I have tried:
#this generates a 3D array with higher values around the center
a = np.array([0,1,2,3,4,5,4,3,2,1])
aa = np.outer(a,a)
aaa = np.einsum("ij,jk,jl",aa,aa,aa)
x_,y_,z_,v_ = [],[],[],[]
from matplotlib.colors import to_rgb,to_rgba
for x in range(aaa.shape[0]):
for y in range(aaa.shape[1]):
for z in range(aaa.shape[2]):
x_.append(x)
y_.append(y)
z_.append(z)
v_.append(aaa[x,y,z])
r,g,b = to_rgb("blue")
color = np.array([[r,g,b,a] for a in v_])
fig = plt.figure()
ax = fig.add_subplot(projection = '3d')
ax.scatter(x_,y_,z_,c =color)
plt.show()
the scatterplot documentation says that color can be a 2D array of RGBA, which I do pass. Hoever when I try to run the code, I get the following error:
ValueError: 'c' argument has 4000 elements, which is inconsistent with 'x' and 'y' with size 1000.
I just found my own answer.
The "A 2D array in which the rows are RGB or RGBA." statement in the documentation was a bit confusing - one needs to convert the RGBA rows to RGBA objects first, so that list comprehension should read:
color = np.array([to_rgba([r,g,b,a]) for a in v_])
I am trying to plot an array, but run into a problem when the array gets too large. However, it seems to depend on whether or not the data is monotonic. In the example below, I increase the size of the array that I am plotting. The expected behaviour is the same image in the left and right hand sides, but this is not so. Furthermore, the size of the array I am able to plot correctly seems to depend on the size of the axis itself. When the figures are exported, there is no problem - just the display on the screen, which looks like the screenshot below:
len_xs = [4850,4860,4870] # sizes to try and plot
for j in np.arange(3):
x = np.arange(len_xs[j]); # dummy x variable
y = 2**np.linspace(-4.18676100,1.39659793,538) # log2 spaced y variable
z = np.random.random((len(y),len(x))) # random variable to plot
plt.subplot(3,2,j*2+1);
if j==0: plt.title('Right way up')
plt.pcolormesh(x,y,z,shading='Nearest');
plt.gca().set_yscale('log',base=2)```
plt.subplot(3,2,j*2+2);
if j==0: plt.title('Upside down')
plt.pcolormesh(x,y[::-1],z[::-1],shading='Nearest'); # flip y and z
plt.gca().set_yscale('log',base=2);
plt.text(1000,1,'nx = %g'%len_xs[j],bbox=dict(facecolor='white', alpha=0.8)) # annotate size of x
plt.savefig('demo.png',dpi=600)
The cause is unknown, but since the DPI of the saved image is high, it was displayed with the same content as the saved file, which matched the DPI of the display accordingly.
plt.rcParams['figure.dpi'] = 600
I am trying to segment the time-series data as shown in the figure. I have lots of data from the sensors, any of these data can have different number of isolated peaks region. In this figure, I have 3 of those. I would like to have a function that takes the time-series as the input and returns the segmented sections of equal length.
My initial thought was to have a sliding window that calculates the relative change in the amplitude. Since the window with the peaks will have relatively higher changes, I could just define certain threshold for the relative change that would help me take the window with isolated peaks. However, this will create problem when choosing the threshold as the relative change is very sensitive to the noises in the data.
Any suggestions?
To do this you need to find signal out of noise.
get mean value of you signal and add some multiplayer that place borders on top and on bottom of noise - green dashed line
find peak values below bottom of noise -> array 2 groups of data
find peak values on top of noise -> array 2 groups of data
get min index of bottom first peak and max index of top of first peak to find first peak range
get min index of top second peak and max index of bottom of second peak to find second peak range
Some description in code. With this method you can find other peaks.
One thing that you need to input by hand is to tell program thex value between peaks for splitting data into parts.
See graphic for summary.
import numpy as np
from matplotlib import pyplot as plt
# create noise data
def function(x, noise):
y = np.sin(7*x+2) + noise
return y
def function2(x, noise):
y = np.sin(6*x+2) + noise
return y
noise = np.random.uniform(low=-0.3, high=0.3, size=(100,))
x_line0 = np.linspace(1.95,2.85,100)
y_line0 = function(x_line0, noise)
x_line = np.linspace(0, 1.95, 100)
x_line2 = np.linspace(2.85, 3.95, 100)
x_pik = np.linspace(3.95, 5, 100)
y_pik = function2(x_pik, noise)
x_line3 = np.linspace(5, 6, 100)
# concatenate noise data
x = np.linspace(0, 6, 500)
y = np.concatenate((noise, y_line0, noise, y_pik, noise), axis=0)
# plot data
noise_band = 1.1
top_noise = y.mean()+noise_band*np.amax(noise)
bottom_noise = y.mean()-noise_band*np.amax(noise)
fig, ax = plt.subplots()
ax.axhline(y=y.mean(), color='red', linestyle='--')
ax.axhline(y=top_noise, linestyle='--', color='green')
ax.axhline(y=bottom_noise, linestyle='--', color='green')
ax.plot(x, y)
# split data into 2 signals
def split(arr, cond):
return [arr[cond], arr[~cond]]
# find bottom noise data indexes
botom_data_indexes = np.argwhere(y < bottom_noise)
# split by visual x value
splitted_bottom_data = split(botom_data_indexes, botom_data_indexes < np.argmax(x > 3))
# find top noise data indexes
top_data_indexes = np.argwhere(y > top_noise)
# split by visual x value
splitted_top_data = split(top_data_indexes, top_data_indexes < np.argmax(x > 3))
# get first signal range
first_signal_start = np.amin(splitted_bottom_data[0])
first_signal_end = np.amax(splitted_top_data[0])
# get x index of first signal
x_first_signal = np.take(x, [first_signal_start, first_signal_end])
ax.axvline(x=x_first_signal[0], color='orange')
ax.axvline(x=x_first_signal[1], color='orange')
# get second signal range
second_signal_start = np.amin(splitted_top_data[1])
second_signal_end = np.amax(splitted_bottom_data[1])
# get x index of first signal
x_second_signal = np.take(x, [second_signal_start, second_signal_end])
ax.axvline(x=x_second_signal[0], color='orange')
ax.axvline(x=x_second_signal[1], color='orange')
plt.show()
Output:
red line = mean value of all data
green line - top and bottom noise borders
orange line - selected peak data
1, It depends on how you want to define a "region", but looks like you just have feeling instead of strict definition. If you have a very clear definition of what kind of piece you want to cut out, you can try some method like "matched filter"
2, You might want to detect the peak of absolute magnitude. If not working, try peak of absolute magnitude of first-order difference, even 2nd-order.
3, it is hard to work on the noisy data like this. My suggestion is to do filtering before you pick up sections (on unfiltered data). Filtering will give you smooth peaks so that the position of peaks can be detected by the change of derivative sign. For filtering, try just "low-pass filter" first. If it doesn't work, I also suggest "Hilbert–Huang transform".
*, Looks like you are using matlab. The methods mentioned are all included in matlab.
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'm plotting a point cloud and coloring by residual error. I'd like the colormap to remain centered on 0, so that 0 error is white.
I see answers for matplotlib. What about Mayavi?
from mayavi import mlab
mlab.points3d(x, y, z, e, colormap='RdBu')
you can set the vmin and vmax of the colormap explicitly with mlab.points3d. So, you could just make sure that vmin = -vmax. Something like this:
mylimit = 10
mlab.points3d(x, y, z, e, colormap='RdBu',vmin=-mylimit,vmax=mylimit)
Or, you could set the limit automatically with something like:
mylimit = max(abs(e.min()),abs(e.max()))
In case anybody wishes to do this but so that the full extent of the colorbar is used, here is a solution I made (with help from here) for mayavi that stretches the colorbar so that the centre of it is on zero:
#Mayavi surface
s = mlab.surf(data)
#Get the lut table of the data
lut = s.module_manager.scalar_lut_manager.lut.table.asarray()
maxd = np.max(data)
mind = np.min(data)
#Data range
dran = maxd - mind
#Proportion of the data range at which the centred value lies
zdp = abs(mind / dran)
#The +0.5's here are because floats are rounded down when converted to ints
#index equal portion of distance along colormap
cmzi = int(zdp * 255 + 0.5)
#linspace from zero to 128, with number of points matching portion to side of zero
topi = np.linspace(0, 127, cmzi) + 0.5
#and for other side
boti = np.linspace(128, 255, 255 - cmzi) + 0.5
#convert these linspaces to ints and map the new lut from these
shift_index = np.hstack([topi.astype(int), boti.astype(int)])
s.module_manager.scalar_lut_manager.lut.table = self.lut[shift_index]
#Force update of the figure now that we have changed the LUT
mlab.draw()
Note that if you wish to do this multiple times for the same surface (ie. if you're modifying the mayavi scalars rather than redrawing the plot) you need to make a record of the initial lut table and modify that each time.