I'm trying to fit a curve with scipy.optimize.curve_fit and it works pretty good so far, except in the case that a value in my sigma array is zero. I understand that the algorithm can't handle this, as I divide by zero in this case. From the scipy documentation:
sigma : None or M-length sequence, optional
If not None, the uncertainties in the ydata array. These are used as weights in the least-squares problem i.e. minimising np.sum( ((f(xdata, *popt) - ydata) / sigma)**2 ) If None, the uncertainties are assumed to be 1.
Here's what my code looks like:
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
x = [0.125, 0.375, 0.625, 0.875, 1.125, 1.375, 1.625, 1.875, 2.125, 2.375, 2.625, 2.875, 3.125, 3.375, 3.625, 3.875, 4.125, 4.375]
y_para = [0, 0, 0.0414, 0.2164, 0.2616, 0.4254, 0.5698, 0.5921, 0.6286, 0.6452, 0.5879, 0.6032, 0.6667, 0.6325, 0.7629, 0.7164, 0.7091, 0.7887]
err = [0, 0, 0.0391, 0.0331, 0.0943, 0.0631, 0.1219, 0.1063, 0.0912, 0.0516, 0.0365, 0.0327, 0.0227, 0.103, 0.1344, 0.0697, 0.0114, 0.0465]
def logistic_growth(x, A1, A2, x_0, p):
return A2 + (A1-A2)/(1+(x/x_0)**p)
x_plot = np.linspace(0, 4.5, 100)
bounds_para = ([0.,0,-np.inf,-np.inf],[0.0000000001, 1,np.inf,np.inf])
paras, paras_cov = curve_fit(logistic_growth, x, y_para, bounds = bounds_para, sigma = err, absolute_sigma=True)
para_curve = logistic_growth(x_plot, *paras)
plt.figure()
plt.errorbar(x,y_para, err, color = 'b', fmt = 'o', label = "Data")
plt.plot(x_plot, para_curve, color = 'b', label = "Fit")
plt.show()
Executing this without the sigma-option in curve_fit works fine, but including it raises:
ValueError: Residuals are not finite in the initial point.
, which results from the zeros in the err-array.
Does anyone know a way to work around this?
Why not just drop the variable? If it has zero variance it cannot contribute in any meaningful way to your analysis.
This is what the scipy doc says about the curve_fit sigma parameter: 'These are used as weights in the least-squares problem ...' Then, in my opinion, they should be inverse to the errors. Here's what I suggest.
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
x = [0.125, 0.375, 0.625, 0.875, 1.125, 1.375, 1.625, 1.875, 2.125, 2.375, 2.625, 2.875, 3.125, 3.375, 3.625, 3.875, 4.125, 4.375]
y_para = [0, 0, 0.0414, 0.2164, 0.2616, 0.4254, 0.5698, 0.5921, 0.6286, 0.6452, 0.5879, 0.6032, 0.6667, 0.6325, 0.7629, 0.7164, 0.7091, 0.7887]
err = [0, 0, 0.0391, 0.0331, 0.0943, 0.0631, 0.1219, 0.1063, 0.0912, 0.0516, 0.0365, 0.0327, 0.0227, 0.103, 0.1344, 0.0697, 0.0114, 0.0465]
weights = [1/max(_,0.001) for _ in err]
print (weights)
def logistic_growth(x, A1, A2, x_0, p):
return A2 + (A1-A2)/(1+(x/x_0)**p)
x_plot = np.linspace(0, 4.5, 100)
bounds_para = ([0.,0,-np.inf,-np.inf],[0.0000000001, 1,np.inf,np.inf])
paras, paras_cov = curve_fit(logistic_growth, x, y_para, bounds = bounds_para,
absolute_sigma=True,
sigma = weights)
para_curve = logistic_growth(x_plot, *paras)
plt.figure()
plt.errorbar(x,y_para, err, color = 'b', fmt = 'o', label = "Data")
plt.plot(x_plot, para_curve, color = 'b', label = "Fit")
plt.show()
This results in the following plot, where those initial data points are made to lie very close to the fitted line.
Related
I try to make a fit of my curve. My raw data is in an xlsx file. I extract them using pandas. I want to do two different fit because there is a change in behavior from Ra = 1e6. We know that Ra is proportional to Nu**a. a = 0.25 for Ra <1e6 and if not a = 0.33.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from math import log10
from scipy.optimize import curve_fit
import lmfit
data=pd.read_excel('data.xlsx',sheet_name='Sheet2',index=False,dtype={'Ra': float})
print(data)
plt.xscale('log')
plt.yscale('log')
plt.scatter(data['Ra'].values, data['Nu_top'].values, label='Nu_top')
plt.scatter(data['Ra'].values, data['Nu_bottom'].values, label='Nu_bottom')
plt.errorbar(data['Ra'].values, data['Nu_top'].values , yerr=data['Ecart type top'].values, linestyle="None")
plt.errorbar(data['Ra'].values, data['Nu_bottom'].values , yerr=data['Ecart type bot'].values, linestyle="None")
def func(x,a):
return 10**(np.log10(x)/a)
"""maxX = max(data['Ra'].values)
minX = min(data['Ra'].values)
maxY = max(data['Nu_top'].values)
minY = min(data['Nu_top'].values)
maxXY = max(maxX, maxY)
parameterBounds = [-maxXY, maxXY]"""
from lmfit import Model
mod = Model(func)
params = mod.make_params(a=0.25)
ret = mod.fit(data['Nu_top'].head(10).values, params, x=data['Ra'].head(10).values)
print(ret.fit_report())
popt, pcov = curve_fit(func, data['Ra'].head(10).values,
data['Nu_top'].head(10).values, sigma=data['Ecart type top'].head(10).values,
absolute_sigma=True, p0=[0.25])
plt.plot(data['Ra'].head(10).values, func(data['Ra'].head(10).values, *popt),
'r-', label='fit: a=%5.3f' % tuple(popt))
popt, pcov = curve_fit(func, data['Ra'].tail(4).values, data['Nu_top'].tail(4).values,
sigma=data['Ecart type top'].tail(4).values,
absolute_sigma=True, p0=[0.33])
plt.plot(data['Ra'].tail(4).values, func(data['Ra'].tail(4).values, *popt),
'b-', label='fit: a=%5.3f' % tuple(popt))
print(pcov)
plt.grid
plt.title("Nusselt en fonction de Ra")
plt.xlabel('Ra')
plt.ylabel('Nu')
plt.legend()
plt.show()
So I use the log: logRa = a * logNu.
Ra = x axis
Nu = y axis
That's why I defined my function func in this way.
my two fit are not all correct as you can see. I have a covariance equal to [0.00010971]. So I had to do something wrong but I don't see it. I need help please.
Here the data file:
data.xlsx
I noticed that the data values for Ra are large, and after scaling them I performed an equation search - here is my result with code. I use the standard scipy genetic algorithm module differential_evolution to determine initial parameter values for curve_fit(), and that module uses the Latin Hypercube algorithm to ensure a thorough search of parameter space which requires bounds within which to search. It is much easier to give ranges for the initial parameter estimates than to find specific values. This equation works well for both nu_top and nu_bottom, note that the plots are not log scaled as it is unnecessary in this example.
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import pandas
import warnings
filename = 'data.xlsx'
data=pandas.read_excel(filename,sheet_name='Sheet2',index=False,dtype={'Ra': float})
# notice the Ra scaling by 10000.0
xData = data['Ra'].values / 10000.0
yData = data['Nu_bottom']
def func(x, a, b, c): # "Combined Power And Exponential" from zunzun.com
return a * numpy.power(x, b) * numpy.exp(c * x)
# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
val = func(xData, *parameterTuple)
return numpy.sum((yData - val) ** 2.0)
def generate_Initial_Parameters():
# min and max used for bounds
maxX = max(xData)
minX = min(xData)
maxY = max(yData)
minY = min(yData)
parameterBounds = []
parameterBounds.append([0.0, 10.0]) # search bounds for a
parameterBounds.append([0.0, 10.0]) # search bounds for b
parameterBounds.append([0.0, 10.0]) # search bounds for c
# "seed" the numpy random number generator for repeatable results
result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
return result.x
# by default, differential_evolution completes by calling curve_fit() using parameter bounds
geneticParameters = generate_Initial_Parameters()
# now call curve_fit without passing bounds from the genetic algorithm,
# just in case the best fit parameters are aoutside those bounds
fittedParameters, pcov = curve_fit(func, xData, yData, geneticParameters)
print('Fitted parameters:', fittedParameters)
print()
modelPredictions = func(xData, *fittedParameters)
absError = modelPredictions - yData
SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))
print()
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
print()
##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
# first the raw data as a scatter plot
axes.plot(xData, yData, 'D')
# create data for the fitted equation plot
xModel = numpy.linspace(min(xData), max(xData))
yModel = func(xModel, *fittedParameters)
# now the model as a line plot
axes.plot(xModel, yModel)
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
plt.show()
plt.close('all') # clean up after using pyplot
graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)
Here I put my data x and y in log10 (). The graph is in log scale. So normally I should have two affine functions with a coefficient of 0.25 and 0.33. I change the function func in your program James and bounds for b and c but I have no good result.
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from math import log10, log
from scipy.optimize import curve_fit
import lmfit
data=pd.read_excel('data.xlsx',sheet_name='Sheet2',index=False,dtype={'Ra': float})
print(data)
plt.xscale('log')
plt.yscale('log')
plt.scatter(np.log10(data['Ra'].values), np.log10(data['Nu_top'].values), label='Nu_top')
plt.scatter(np.log10(data['Ra'].values), np.log10(data['Nu_bottom'].values), label='Nu_bottom')
plt.errorbar(np.log10(data['Ra'].values), np.log10(data['Nu_top'].values) , yerr=data['Ecart type top'].values, linestyle="None")
plt.errorbar(np.log10(data['Ra'].values), np.log10(data['Nu_bottom'].values) , yerr=data['Ecart type bot'].values, linestyle="None")
def func(x,a):
return a*x
maxX = max(data['Ra'].values)
minX = min(data['Ra'].values)
maxY = max(data['Nu_top'].values)
minY = min(data['Nu_top'].values)
maxXY = max(maxX, maxY)
parameterBounds = [-maxXY, maxXY]
from lmfit import Model
mod = Model(func)
params = mod.make_params(a=0.25)
ret = mod.fit(np.log10(data['Nu_top'].head(10).values), params, x=np.log10(data['Ra'].head(10).values))
print(ret.fit_report())
popt, pcov = curve_fit(func, np.log10(data['Ra'].head(10).values), np.log10(data['Nu_top'].head(10).values), sigma=data['Ecart type top'].head(10).values, absolute_sigma=True, p0=[0.25])
plt.plot(np.log10(data['Ra'].head(10).values), func(np.log10(data['Ra'].head(10).values), *popt), 'r-', label='fit: a=%5.3f' % tuple(popt))
popt, pcov = curve_fit(func, np.log10(data['Ra'].tail(4).values), np.log10(data['Nu_top'].tail(4).values), sigma=data['Ecart type top'].tail(4).values, absolute_sigma=True, p0=[0.33])
plt.plot(np.log10(data['Ra'].tail(4).values), func(np.log10(data['Ra'].tail(4).values), *popt), 'b-', label='fit: a=%5.3f' % tuple(popt))
print(pcov)
plt.grid
plt.title("Nusselt en fonction de Ra")
plt.xlabel('log10(Ra)')
plt.ylabel('log10(Nu)')
plt.legend()
plt.show()
With polyfit I have better results.
With my code I open the file and I calculate log (Ra) and log (Nu) then plot (log (Ra), log (Nu)) in log scale.
I'm supposed to have a = 0.25 for Ra <1e6 and if not a = 0.33
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from math import log10
from numpy import polyfit
import numpy.polynomial.polynomial as poly
data=pd.read_excel('data.xlsx',sheet_name='Sheet2',index=False,dtype={'Ra': float})
print(data)
x=np.log10(data['Ra'].values)
y1=np.log10(data['Nu_top'].values)
y2=np.log10(data['Nu_bottom'].values)
x2=np.log10(data['Ra'].head(11).values)
y4=np.log10(data['Nu_top'].head(11).values)
x3=np.log10(data['Ra'].tail(4).values)
y5=np.log10(data['Nu_top'].tail(4).values)
plt.xscale('log')
plt.yscale('log')
plt.scatter(x, y1, label='Nu_top')
plt.scatter(x, y2, label='Nu_bottom')
plt.errorbar(x, y1 , yerr=data['Ecart type top'].values, linestyle="None")
plt.errorbar(x, y2 , yerr=data['Ecart type bot'].values, linestyle="None")
"""a=np.ones(10, dtype=np.float)
weights = np.insert(a,0,1E10)"""
coefs = poly.polyfit(x2, y4, 1)
print(coefs)
ffit = poly.polyval(x2, coefs)
plt.plot(x2, ffit, label='fit: b=%5.3f, a=%5.3f' % tuple(coefs))
absError = ffit - x2
SE = np.square(absError) # squared errors
MSE = np.mean(SE) # mean squared errors
RMSE = np.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (np.var(absError) / np.var(x2))
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
print()
print('Predicted value at x=0:', ffit[0])
print()
coefs = poly.polyfit(x3, y5, 1)
ffit = poly.polyval(x3, coefs)
plt.plot(x3, ffit, label='fit: b=%5.3f, a=%5.3f' % tuple(coefs))
plt.grid
plt.title("Nusselt en fonction de Ra")
plt.xlabel('log10(Ra)')
plt.ylabel('log10(Nu)')
plt.legend()
plt.show()
My problem is solved, I managed to fit my curves with more or less correct results
I have some x and y data, with which I would like to generate a 3D histogram, with a color gradient (bwr or whatever).
I have written a script which plot the interesting values, in between -2 and 2 for both x and y abscesses:
import numpy as np
import numpy.random
import matplotlib.pyplot as plt
# To generate some test data
x = np.random.randn(500)
y = np.random.randn(500)
XY = np.stack((x,y),axis=-1)
def selection(XY, limitXY=[[-2,+2],[-2,+2]]):
XY_select = []
for elt in XY:
if elt[0] > limitXY[0][0] and elt[0] < limitXY[0][1] and elt[1] > limitXY[1][0] and elt[1] < limitXY[1][1]:
XY_select.append(elt)
return np.array(XY_select)
XY_select = selection(XY, limitXY=[[-2,+2],[-2,+2]])
heatmap, xedges, yedges = np.histogram2d(XY_select[:,0], XY_select[:,1], bins = 7, range = [[-2,2],[-2,2]])
extent = [xedges[0], xedges[-1], yedges[0], yedges[-1]]
plt.figure("Histogram")
#plt.clf()
plt.imshow(heatmap.T, extent=extent, origin='lower')
plt.show()
And give this correct result:
Now, I would like to turn this into a 3D histogram. Unfortunatly I don't success to plot it correctly with bar3d because it takes by default the length of x and y for abscisse.
I am quite sure that there is a very easy way to plot this in 3D with imshow. Like an unknow option...
I finaly succeded in doing it. I am almost sure there is a better way to do it, but at leat it works:
import numpy as np
import numpy.random
import matplotlib.pyplot as plt
# To generate some test data
x = np.random.randn(500)
y = np.random.randn(500)
XY = np.stack((x,y),axis=-1)
def selection(XY, limitXY=[[-2,+2],[-2,+2]]):
XY_select = []
for elt in XY:
if elt[0] > limitXY[0][0] and elt[0] < limitXY[0][1] and elt[1] > limitXY[1][0] and elt[1] < limitXY[1][1]:
XY_select.append(elt)
return np.array(XY_select)
XY_select = selection(XY, limitXY=[[-2,+2],[-2,+2]])
xAmplitudes = np.array(XY_select)[:,0]#your data here
yAmplitudes = np.array(XY_select)[:,1]#your other data here
fig = plt.figure() #create a canvas, tell matplotlib it's 3d
ax = fig.add_subplot(111, projection='3d')
hist, xedges, yedges = np.histogram2d(x, y, bins=(7,7), range = [[-2,+2],[-2,+2]]) # you can change your bins, and the range on which to take data
# hist is a 7X7 matrix, with the populations for each of the subspace parts.
xpos, ypos = np.meshgrid(xedges[:-1]+xedges[1:], yedges[:-1]+yedges[1:]) -(xedges[1]-xedges[0])
xpos = xpos.flatten()*1./2
ypos = ypos.flatten()*1./2
zpos = np.zeros_like (xpos)
dx = xedges [1] - xedges [0]
dy = yedges [1] - yedges [0]
dz = hist.flatten()
cmap = cm.get_cmap('jet') # Get desired colormap - you can change this!
max_height = np.max(dz) # get range of colorbars so we can normalize
min_height = np.min(dz)
# scale each z to [0,1], and get their rgb values
rgba = [cmap((k-min_height)/max_height) for k in dz]
ax.bar3d(xpos, ypos, zpos, dx, dy, dz, color=rgba, zsort='average')
plt.title("X vs. Y Amplitudes for ____ Data")
plt.xlabel("My X data source")
plt.ylabel("My Y data source")
plt.savefig("Your_title_goes_here")
plt.show()
I use this example, but I modified it, because it introduced an offset. The result is this:
You can generate the same result using something as simple as the following:
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-2, 2, 7)
y = np.linspace(-2, 2, 7)
xx, yy = np.meshgrid(x, y)
z = xx*0+yy*0+ np.random.random(size=[7,7])
plt.imshow(z, interpolation='nearest', cmap=plt.cm.viridis, extent=[-2,2,2,2])
plt.show()
from mpl_toolkits.mplot3d import Axes3D
ax = Axes3D(plt.figure())
ax.plot_surface(xx, yy, z, cmap=plt.cm.viridis, cstride=1, rstride=1)
plt.show()
The results are given below:
I'd like to understand why, when I convert the PIL image imageRGB to a float array arrayRGB_f and use matplotlib's imshow() without a cmap it looks either black, or strange and unreadable, even though PIL's imageRGB.show() looks fine, and each of the individual r, g, b channels shown with cmap='gray' look okay as well.
I have workarounds, but I just don't understand why this happens.
matplotlib.__version__ returns '2.0.2' and I'm using MacOS with an Anaconda installation.
See this answer for more on the conversion of a ttf rendering to a 1bit.
fyi the output of the print statements are:
float64 (41, 101, 3)
int64 (41, 101, 3)
int64 (41, 101)
int64 (41, 101)
fontname = 'default'
imageRGB.show()
plt.imshow()
fontname = 'Arial Unicode.ttf'
imageRGB.show()
plt.imshow()
font = ImageFont.truetype(fontname, 20)
imageRGB.show()
plt.imshow()
from PIL import Image, ImageDraw, ImageFont
import numpy as np
import matplotlib.pyplot as plt
# fontname = 'Arial Unicode.ttf'
fontname = 'default'
if fontname == 'default':
font = ImageFont.load_default()
else:
font = ImageFont.truetype(fontname, 12)
string = "Hello " + fontname[:6]
ww, hh = 101, 41
threshold = 80 # https://stackoverflow.com/a/47546095/3904031
imageRGB = Image.new('RGB', (ww, hh))
draw = ImageDraw.Draw(imageRGB)
image8bit = draw.text((10, 12), string, font=font,
fill=(255, 255, 255, 255)) # R, G, B alpha
image8bit = imageRGB.convert("L")
image1bit = image8bit.point(lambda x: 0 if x < threshold else 1, mode='1') # https://stackoverflow.com/a/47546095/3904031
arrayRGB = np.array(list(imageRGB.getdata())).reshape(hh, ww, 3)
arrayRGB_f = arrayRGB.astype(float)
array8bit = np.array(list(image8bit.getdata())).reshape(hh, ww)
array1bit = np.array(list(image1bit.getdata())).reshape(hh, ww)
for a in (arrayRGB_f, arrayRGB, array8bit, array1bit):
print a.dtype, a.shape
imageRGB.show()
if True:
plt.figure()
a = arrayRGB_f
plt.subplot(2, 2, 1)
plt.imshow(a) # , interpolation='nearest', cmap='gray',
for i in range(3):
plt.subplot(2, 2, 2+i)
plt.imshow(a[:, :, i], cmap='gray')
plt.suptitle('arrayRGB_f, fontname = ' + fontname)
plt.show()
I can't find an ideal duplicate so I'll post an answer.
As #ImportanceOfBeingErnest mentions when .imshow() is given an n x m x 3 or n x m x 4 array, it is expecting a normalized array between 0.0 and 1.0.
Best way to do this is:
arrayRGB_f = arrayRGB.astype(float)/255.
though this seems to work as well:
arrayRGB_f = arrayRGB.astype(float)
arrayRGB_f = arrayRGB_f / arrayRGB_f.max()
For longer discussions, see this and this.
Hi I a have a data set which I project onto a sphere such that the magnitude of the data, as a function of theta and phi, is shown using a colour spectrum (which uses "ax.plot_surface", "plt.colorbar" and "facecolors"). My query is that at this stage I am limited to "cm.hot" and "cm.jet". Does anyone know of any other colour schemes which are available for this purpose. Please see my code and the figures below
Code:
from numpy import*
import math
import matplotlib.pyplot as plt
from matplotlib import cm
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import matplotlib.cm as cm
#theta inclination angle
#phi azimuthal angle
n_theta = 100 #number of values for theta
n_phi = 100 #number of values for phi
r = 1 #radius of sphere
theta, phi = np.mgrid[0: pi:n_theta*1j,-pi:pi:n_phi*1j ]
x = r*np.sin(theta)*np.cos(phi)
y = r*np.sin(theta)*np.sin(phi)
z = r*np.cos(theta)
inp = []
f = open("data.dat","r")
for line in f:
i = float(line.split()[0])
j = float(line.split()[1])
val = float(line.split()[2])
inp.append([i, j, val])
inp = np.array(inp)
#reshape the input array to the shape of the x,y,z arrays.
c = inp[:,2].reshape((n_phi,n_theta))
#Set colours and render
fig = plt.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection='3d')
#use facecolors argument, provide array of same shape as z
# cm.<cmapname>() allows to get rgba color from array.
# array must be normalized between 0 and 1
surf = ax.plot_surface(
x,y,z, rstride=1, cstride=1, facecolors=cm.jet(c), alpha=0.9, linewidth=1, shade=False)
ax.set_xlim([-2.0,2.0])
ax.set_ylim([-2.0,2.0])
ax.set_zlim([-2,2])
ax.set_aspect("equal")
plt.title('Plot with cm.jet')
#Label axis.
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_zlabel('Z')
#Creates array for colorbar from 0 to 1.
a = array( [1.0, 0.5, 0.0])
#Creates colorbar
m = cm.ScalarMappable(cmap=cm.jet)
m.set_array(a)
plt.colorbar(m)
plt.savefig('facecolor plots')
f.close()
plt.show()
The following is a list of colormaps provided directly by matplotlib. It's taken from the Colormap reference example.
cmaps = [('Perceptually Uniform Sequential', [
'viridis', 'plasma', 'inferno', 'magma', 'cividis']),
('Sequential', [
'Greys', 'Purples', 'Blues', 'Greens', 'Oranges', 'Reds',
'YlOrBr', 'YlOrRd', 'OrRd', 'PuRd', 'RdPu', 'BuPu',
'GnBu', 'PuBu', 'YlGnBu', 'PuBuGn', 'BuGn', 'YlGn']),
('Sequential (2)', [
'binary', 'gist_yarg', 'gist_gray', 'gray', 'bone', 'pink',
'spring', 'summer', 'autumn', 'winter', 'cool', 'Wistia',
'hot', 'afmhot', 'gist_heat', 'copper']),
('Diverging', [
'PiYG', 'PRGn', 'BrBG', 'PuOr', 'RdGy', 'RdBu',
'RdYlBu', 'RdYlGn', 'Spectral', 'coolwarm', 'bwr', 'seismic']),
('Qualitative', [
'Pastel1', 'Pastel2', 'Paired', 'Accent',
'Dark2', 'Set1', 'Set2', 'Set3',
'tab10', 'tab20', 'tab20b', 'tab20c']),
('Miscellaneous', [
'flag', 'prism', 'ocean', 'gist_earth', 'terrain', 'gist_stern',
'gnuplot', 'gnuplot2', 'CMRmap', 'cubehelix', 'brg', 'hsv',
'gist_rainbow', 'rainbow', 'jet', 'nipy_spectral', 'gist_ncar'])]
To easily view them all you may e.g. use the following 3D colormap viewer (written in PyQt5).
import numpy as np
from mpl_toolkits.mplot3d import Axes3D
from PyQt5 import QtGui, QtCore, QtWidgets
from matplotlib.backends.backend_qt5agg import FigureCanvasQTAgg as FigureCanvas
from matplotlib.figure import Figure
import sys
class MainWindow(QtWidgets.QMainWindow):
def __init__(self):
QtWidgets.QMainWindow.__init__(self)
self.main_widget = QtWidgets.QWidget(self)
self.fig = Figure()
self.canvas = FigureCanvas(self.fig)
self.ax = self.fig.add_subplot(111, projection=Axes3D.name)
u = np.linspace(0, 2 * np.pi, 100)
v = np.linspace(0, np.pi, 100)
x = 10 * np.outer(np.cos(u), np.sin(v))
y = 10 * np.outer(np.sin(u), np.sin(v))
z = 10 * np.outer(np.ones(np.size(u)), np.cos(v))
# Plot the surface
self.surf = self.ax.plot_surface(x, y, z, cmap="YlGnBu")
self.cb = self.fig.colorbar(self.surf)
self.canvas.setSizePolicy(QtWidgets.QSizePolicy.Expanding,
QtWidgets.QSizePolicy.Expanding)
self.canvas.updateGeometry()
self.dropdown1 = QtWidgets.QComboBox()
items = []
for cats in cmaps:
items.extend(cats[1])
self.dropdown1.addItems(items)
self.dropdown1.currentIndexChanged.connect(self.update)
self.label = QtWidgets.QLabel("A plot:")
self.layout = QtWidgets.QGridLayout(self.main_widget)
self.layout.addWidget(QtWidgets.QLabel("Select Colormap"))
self.layout.addWidget(self.dropdown1)
self.layout.addWidget(self.canvas)
self.setCentralWidget(self.main_widget)
self.show()
self.update()
def update(self):
self.surf.set_cmap(self.dropdown1.currentText())
self.fig.canvas.draw_idle()
if __name__ == '__main__':
app = QtWidgets.QApplication(sys.argv)
win = MainWindow()
sys.exit(app.exec_())
I have a point cloud in 4 dimensions, where each point in the cloud has a location and a value (x,y,z,Value). In addition, I have a 'special' point, S0, within the 3d point cloud; I've used this example to find the closest 10 points in the cloud, relative to S0. Now, I have a numpy array for each of the 10 closest points and their values. How can I interpolate these 10 points, to find the interpolated value at point S0? Example code is shown below:
import numpy as np
import matplotlib.pyplot as plt
numpoints = 20
linexs = 320
lineys = 40
linezs = 60
linexe = 20
lineye = 20
lineze = 0
# Create vectors of points
xpts = np.linspace(linexs, linexe, numpoints)
ypts = np.linspace(lineys, lineye, numpoints)
zpts = np.linspace(linezs, lineze, numpoints)
lin = np.dstack((xpts,ypts,zpts))
# Image line of points
fig = plt.figure()
ax = fig.add_subplot(211, projection='3d')
ax.set_xlim(0,365); ax.set_ylim(-85, 85); ax.set_zlim(0, 100)
ax.plot_wireframe(xpts, ypts, zpts)
ax.view_init(elev=12, azim=78)
def randrange(n, vmin, vmax):
return (vmax - vmin)*np.random.rand(n) + vmin
n = 10
for n in range(21):
xs = randrange(n, 0, 350)
ys = randrange(n, -75, 75)
zs = randrange(n, 0, 100)
ax.scatter(xs, ys, zs)
dat = np.dstack((xs,ys,zs))
ax.set_xlabel('X Label')
ax.set_xlim(0,350)
ax.set_ylabel('Y Label')
ax.set_ylim(-75,75)
ax.set_zlabel('Z Label')
ax.set_zlim(0,100)
ax = fig.add_subplot(212, projection='3d')
ax.set_xlim(0,365); ax.set_ylim(-85, 85); ax.set_zlim(0, 100)
ax.plot_wireframe(xpts,ypts,zpts)
ax.view_init(elev=12, azim=78)
plt.show()
dist = []
# Calculate distance from first point to all other points in cloud
for l in range(len(xpts)):
aaa = lin[0][0]-dat
dist.append(np.sqrt(aaa[0][l][0]**2+aaa[0][l][1]**2+aaa[0][l][2]**2))
full = np.dstack((dat,dist))
aaa = full[0][full[0][:,3].argsort()]
print(aaa[0:10])
A basic example. Note that the meshgrid is not needed for the interpolation, but only to make a fast ufunc to generate an example function A=f(x,y,z), here A=x+y+z.
from scipy.interpolate import interpn
import numpy as np
#make up a regular 3d grid
X=np.linspace(-5,5,11)
Y=np.linspace(-5,5,11)
Z=np.linspace(-5,5,11)
xv,yv,zv = np.meshgrid(X,Y,Z)
# make up a function
# see http://docs.scipy.org/doc/numpy/reference/ufuncs.html
A = np.add(xv,np.add(yv,zv))
#this one is easy enough for us to know what to expect at (.5,.5,.5)
# usage : interpn(points, values, xi, method='linear', bounds_error=True, fill_value=nan)
interpn((X,Y,Z),A,[0.5,0.5,0.5])
Output:
array([ 1.5])
If you pass in an array of points of interest, it will give you multiple answers.