Python visualizing optimization parameters - python

I have the following code where I iterate through a grid of 2 parameters in order to see which set of parameters will yield the best result.
from sklearn.grid_search import ParameterGrid
ar1= np.arange(1,10,0.1)
ar2= np.arange(0.1,3,0.01)
param_grid = {'p1': ar1, 'p2' : ar2}
grid = ParameterGrid(param_grid)
result=[]
p1=[]
p2=[]
for params in grid:
r = getresult(params['p1'], params['p2'])
result.append(r)
p1.append(params['p1'])
p2.append(params['p2'])
As a result I get 3 arrays, one with the result of every iteration and two arrays (p1,p2) with the corresponding parameters. I would now like to plot this data with matplotlib to visualize how the result varies across the parameter plane.
I tried the following but i got a blank plot:
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(p1, p2, result)
Ideally I would like to be able to create something like the plot below. How can I accomplish this with matplotlib?

I ended up going with the following solution:
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_trisurf(X, Y, Z, cmap=cm.jet, linewidth=0)
fig.tight_layout()
plt.show()
The above yielded the desired visualization, as seen below:

plot_surface requires the input arrays to be two-dimensional. As I interprete it, your arrays are 1D. So reshaping them into 2D could be a solution.
import numpy as np
shape = (len(ar2), len(ar1))
p1 = np.array(p1).reshape(shape)
p2 = np.array(p2).reshape(shape)
result = result.reshape(shape)
Then plotting it via
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(p1, p2, result)
might work. (I cannot test it at the moment.)

Related

Choosing a specific contour in oscillatory data to plot with matplotlib

I have oscillatory data to which I would like to add a specific contour line. For example, the data pass through a value several times, and I would like to pick a specific instance of that value to highlight with a contour. As an example, consider a Bessel function. Below, I plot the contours with a single level, 0.2. I would like to choose to show only the outer contour, however, and not the other interior ones.
from scipy.special import jv
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-20,20,num=500)
y = np.linspace(-20,20,num=500)
[X,Y] = np.meshgrid(x,y)
Z = jv(1,np.sqrt(X**2.+Y**2.))
fig = plt.figure()
ax = fig.add_subplot(111)
cb = ax.pcolormesh(X,Y,Z)
ax.contour(X,Y,Z,[.2],linestyles='dashed')
cbar = fig.colorbar(cb)
plt.show()
If helpful, this is a plot of my actual data (the code used to create is far too long to include here). I would only like to plot the outermost purple contour:
Thank you
Let's see how you like this ;) ... I plot all contour lines invisibly, but extract the contour object and replot the first one (that I just figured out by trial and error, and might be different in your case).
from scipy.special import jv
import numpy as np
import matplotlib.pyplot as plt
x = np.linspace(-20, 20, num=500)
y = np.linspace(-20, 20, num=500)
[X, Y] = np.meshgrid(x, y)
Z = jv(1, np.sqrt(X**2. + Y**2.))
fig = plt.figure()
ax = fig.add_subplot(111)
cb = ax.pcolormesh(X, Y, Z)
cont = ax.contour(X, Y, Z, [.2], alpha=0) # alpha = 0 -> invisible
the_interesting_one = cont.allsegs[0][0]
plt.plot(the_interesting_one[:, 0], the_interesting_one[:, 1], "k--")
cbar = fig.colorbar(cb)
plt.show()

plotting an mXnXk matrix as a 3d model in python

I have a matrix generated by parsing a file the numpy array is the size 101X101X41 and each entry has a value which represents the magnitude at each point.
Now what I want to do is to plot it in a 3d plot where the 4th dimension will be represented by color. so that I will be able to see the shape of the data points (represent molecular orbitals) and deduce its magnitude at that point.
If I plot each slice of data I get the desired outcome, but in a 2d with the 3rd dimension as the color.
Is there a way to plot this model in python using Matplotlib or equivalent library
Thanks
EDIT:
Im trying to get the question clearer to what I desire.
Ive tried the solution suggested but ive received the following plot:
as one can see, due to the fact the the mesh has lots of zeros in it it "hide" the 3d orbitals. in the following plot one can see a slice of the data, where I get the following plot:
So as you can see I have a certain structure I desire to show in the plot.
my question is, is there a way to plot only the structure and ignore the zeroes such that they won't "hide" the structure.
the code I used to generate the plots:
x = np.linspase(1,101,101)
y = np.linspase(1,101,101)
z = np.linspase(1,101,101)
xx,yy,zz = np.meshgrid(x,y,z)
fig=plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(xx, yy, zz, c=cube.calc_data.flatten())
plt.show()
plt.imshow(cube.calc_data[:,:,11],cmap='jet')
plt.show()
Hope that now the question is much clearer, and that you'd appreciate the question enough now to upvote
Thanks.
you can perform the following:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
epsilon = 2.5e-2 # threshold
height, width, depth = data.shape
global_min = np.inf
global_max = -np.inf
for d in range(depth):
slice = data[:, :, d]
minima = slice.min()
if (minima < global_min): global_min = minima
maxima = slice.max()
if (maxima>global_max): global_max=maxima
norm = colors.Normalize(vmin=minima, vmax=maxima, clip=True)
mapper = cm.ScalarMappable(norm=norm, cmap=cm.jet)
points_gt_epsilon = np.where(slice >= epsilon)
ax.scatter(points_gt_epsilon[0], points_gt_epsilon[1], d,
c=mapper.to_rgba(data[points_gt_epsilon[0],points_gt_epsilon[1],d]), alpha=0.015, cmap=cm.jet)
points_lt_epsilon = np.where(slice <= -epsilon)
ax.scatter(points_lt_epsilon[0], points_lt_epsilon[1], d,
c=mapper.to_rgba(data[points_lt_epsilon[0], points_lt_epsilon[1], d]), alpha=0.015, cmap=cm.jet)
ax.set_xlabel('X Label')
ax.set_ylabel('Y Label')
ax.set_zlabel('Z Label')
plt.title('Electron Density Prob.')
norm = colors.Normalize(vmin=global_min, vmax=global_max, clip=True)
cax, _ = colorbar.make_axes(ax)
colorbar.ColorbarBase(cax, cmap=cm.jet,norm=norm)
plt.savefig('test.png')
plt.clf()
What this piece of code does is going slice by slice from the data matrix and for each scatter plot only the points desired (depend on epsilon).
in this case you avoid plotting a lot of zeros that 'hide' your model, using your words.
Hope this helps
You can adjust the color and size of the markers for the scatter. So for example you can filter out all markers below a certain threshold by putting their size to 0. You can also make the size of the marker adaptive to the field strength.
As an example:
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
f = lambda x,y,z: np.exp(-(x-3)**2-(y-3)**2-(z-1)**2) - \
np.exp(-(x+3)**2-(y+3)**2-(z+1)**2)
t1 = np.linspace(-6,6,101)
t2 = np.linspace(-3,3,41)
# Data of shape 101,101,41
data = f(*np.meshgrid(t1,t1,t2))
print(data.shape)
# Coordinates
x = np.linspace(1,101,101)
y = np.linspace(1,101,101)
z = np.linspace(1,101,41)
xx,yy,zz = np.meshgrid(x,y,z)
fig=plt.figure()
ax = fig.add_subplot(111, projection='3d')
s = np.abs(data/data.max())**2*25
s[np.abs(data) < 0.05] = 0
ax.scatter(xx, yy, zz, s=s, c=data.flatten(), linewidth=0, cmap="jet", alpha=.5)
plt.show()

python piecewise linear interpolation

I'm trying to create a piecewise linear interpolation routine and I'm pretty new to all of this so I'm very uncertain of what needs to be done.
I've generate a set of data points in 3D which gives variation in all 3 directions. I want to interpolate between these data points and plot in 3D.
The current data set is much smaller than the final one will be. Linear interpolation is important.
here's the current code
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import scipy.interpolate as interp
x = np.linspace(-1.3,1.3,10)
y1 = np.linspace(.5,0.,5)
y2 = np.linspace(0.,.5,5)
y = np.hstack((y1,y2))
z1 = np.linspace(.1,0.,5)
z2 = np.linspace(0.,.1,5)
z = np.hstack((z1,z2))
data = np.dstack([x,y,z])
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
f = interp.interp2d(x, y, z, kind='linear')
xnew = np.linspace(-1.3,1.3,100)
y1new = np.linspace(.5,0.,50)
y2new = np.linspace(0.,.5,50)
ynew = np.hstack((y1new,y2new))
znew = f(xnew,ynew)
ax.plot(x,y,znew, 'b-')
ax.scatter(x,y,z,'ro')
plt.show()
As I said, dataset is just to add variation. The real set will be much bigger but have less variation. I don't really understand the interpolation tool and the scipy documentation isn't very clear
would appreciate suggestions
2D ok. Please help with 3D
What I'm trying to do is build something that takes data points for deflections of a beam an interpolates between the data points. I wanted to to this in 3D and get a 3D plot showing the deflection along the x-axis in both y and z directions at the same time. As a stop gap measure I've used the below code to individually show deflection in y dir and z dir. Note, the data set is randomly generated for the moment. Some choices might look strange at the mo, but that's to sorta stick to the kinda range the final data set will use. The code below works for a 2D system so may be helpful to someone. I'd still really appreciate if someone could help me do this in 3D.
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import CubicSpline
u=10
x = np.linspace(-1.3,1.3,u) #regular x-data
y = np.random.random_sample(u)/4 #random y data
z = np.random.random_sample(u)/10 # random zdata
ynone = np.ones(u)*0.1 #no deflection dataset
znone = np.ones(u)*0.05
xspace = np.linspace(-1.3, 1.3, u*100)
ydefl = CubicSpline(x, y) #creating cubinc spline function for original data
zdefl = CubicSpline(x, z)
plt.subplot(2, 1, 1)
plt.plot(x, ynone, '-',label='y - no deflection')
plt.plot(x, y, 'go',label='y-deflection data')
plt.plot(xspace, ydefl(xspace), label='spline') #plot xspace vs spline function of xspace
plt.title('X [m]s')
plt.ylabel('Y [m]')
plt.legend(loc='best', ncol=3)
plt.subplot(2, 1, 2)
plt.plot(x, znone, '-',label='z - no deflection')
plt.plot(x, z, 'go',label='z-deflection data')
plt.plot(xspace, zdefl(xspace),label='spline')
plt.xlabel('X [m]')
plt.ylabel('Z [m]')
plt.legend(loc='best', ncol=3)
plt.show()

Contour plotting complex numbers and conjugates

I am trying to make a contour plot in python with complex numbers (i am using matplotlib, pylab).
I am working with sharp bounds on harmonic polynomials, but specifically right now I am trying to plot:
Re(z(bar) - e^(z))= 0
Im(z(bar) - e^z) = 0
and plot them over each other in a contour in order to find their zeros to determine how many solutions there are to the equation z(bar) = e^(z).
Does anyone have experience in contour plotting, specifically with complex numbers?
import numpy as np
from matplotlib import pyplot as plt
x = np.r_[0:10:30j]
y = np.r_[0:10:20j]
X, Y = np.meshgrid(x, y)
Z = X*np.exp(1j*Y) # some arbitrary complex data
def plotit(z, title):
plt.figure()
cs = plt.contour(X,Y,z) # contour() accepts complex values
plt.clabel(cs, inline=1, fontsize=10) # add labels to contours
plt.title(title)
plt.savefig(title+'.png')
plotit(Z, 'real')
plotit(Z.real, 'explicit real')
plotit(Z.imag, 'imaginary')
plt.show()
EDIT: Above is my code, and note that for Z, I need to plot both real and imaginary parts of (x- iy) - e^(x+iy)=0. The current Z that is there is simply arbitrary. It is giving me an error for not having a 2D array when I try to plug mine in.
I don't know how you are plotting since you didn't post any code, but in general I advise moving away from using pylab or the pyplot interface to matplotlib, using the direct object methods is much more robust and just as simple. Here is an example of plotting contours of two sets of data on the same plot.
import numpy as np
import matplotlib.pyplot as plt
# making fake data
x = np.linspace(0, 2)
y = np.linspace(0, 2)
c = x[:,np.newaxis] * y
c2 = np.flipud(c)
# plot
fig, ax = plt.subplots(1, 1)
cont1 = ax.contour(x, y, c, colors='b')
cont2 = ax.contour(x, y, c2, colors='r')
cont1.clabel()
cont2.clabel()
plt.show()
For tom10, here is the plot this code produces. Note that setting colors to a single color makes distinguishing the two plots much easier.

Shifting the triangles order to match colormap

This question is a sequel of a previous one but regarding this time the colormap and the order of the triangle. I want to interpolate experimental data over a surface so as to enable a continuous colormap with however the surface known only at its corner node. To interpolate, I put a canonical example which works quite well but fails on real data.
Indeed as shown in the example below, the initial triangulation results in two triangles with a huge gap between them, cf first picture. When the interpolation is done, it doesn't get any better and the colormap is also lost, cf. second picture. The best so far is by interverting z and y to get adjacent triangles from the beginning which results in a successful interpolation. However as you might notice in the third picture, the surface is tilted by 90° which is normal since I switch y for z and vice-versa.
However when I switch back y and z in the tri_surf function with ax.plot_trisurf(new.x, new_z, new.y, **kwargs), the colormap doesn't follow, cf. picture 4.
I thought of rotating the colormap in somehow or generate new triangles from the interpolated ones with triang = tri.Triangulation(new.x, new_z) but without any success. So any idea or hint about properly doing the initial triangulation with two adjacent triangles, as for the third picture, but with the surface oriented correclty and ultimately the colormap proportional to the Y-value.
import numpy
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import matplotlib.tri as tri
x=numpy.array([0.00498316, 0.00498316, 0.00996632, 0.00996632])
y=numpy.array([-0.00037677, -0.00027191, -0.00078681, -0.00088475])
z=numpy.array([0., -0.0049926, 0., -0.00744763])
# Initial Triangle
fig = plt.figure()
ax = Axes3D(fig)
triang = tri.Triangulation(x, y)
norm = plt.Normalize(vmax=y.max(), vmin=y.min())
ax.plot_trisurf(x, y, z, triangles=triang.triangles)
# Interpolated Triangle
fig = plt.figure()
ax = Axes3D(fig)
triang = tri.Triangulation(x, y)
refiner = tri.UniformTriRefiner(triang)
interpolator = tri.LinearTriInterpolator(triang, z)
new, new_z = refiner.refine_field(z, interpolator, subdiv=4)
kwargs = dict(triangles=new.triangles, cmap=cm.jet, norm=norm, linewidth=0, antialiased=False)
ax.plot_trisurf(new.x, new.y, new_z, **kwargs)
# Best so far
fig = plt.figure()
ax = Axes3D(fig)
triang = tri.Triangulation(x, z)
refiner = tri.UniformTriRefiner(triang)
interpolator = tri.LinearTriInterpolator(triang, y)
new, new_z = refiner.refine_field(y, interpolator, subdiv=4)
kwargs = dict(triangles=new.triangles, cmap=cm.jet, norm=norm, linewidth=0, antialiased=False)
ax.plot_trisurf(new.x, new.y, new_z, **kwargs)
plt.show()
Apparently the automatic triangulation doesn't produce the right triangles for you, but you can specify how you want your triangles manually:
triang = tri.Triangulation(x, y, [[3,2,1],[1,2,0]])
# alternatively:
triang = tri.Triangulation(x, y, [[3,2,0],[1,3,0]])
These two ways give rather different results:
However, now the interpolation becomes awkward, because for some (x,y) there are multiple z-values.. One way of bypassing this issue is interpolating and plotting the 2 large triangles separately:
import numpy
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from matplotlib import cm
import matplotlib.tri as tri
def plot_refined_tri(x, y, z, ax, subdiv=4, **kwargs):
triang = tri.Triangulation(x, y)
refiner = tri.UniformTriRefiner(triang)
interpolator = tri.LinearTriInterpolator(triang, z)
new, new_z = refiner.refine_field(z, interpolator, subdiv=subdiv)
ax.plot_trisurf(new.x, new.y, new_z, triangles=new.triangles, **kwargs)
x=numpy.array([0.00498316, 0.00498316, 0.00996632, 0.00996632])
y=numpy.array([-0.00037677, -0.00027191, -0.00078681, -0.00088475])
z=numpy.array([0., -0.0049926, 0., -0.00744763])
fig = plt.figure()
ax = Axes3D(fig)
# note: I normalized on z-values to "fix" the colormap
norm = plt.Normalize(vmax=z.max(), vmin=z.min())
kwargs = kwargs = dict(linewidth=0.2, cmap=cm.jet, norm=norm)
idx = [3,2,1]
plot_refined_tri(x[idx], y[idx], z[idx], ax, **kwargs)
idx = [1,2,0]
plot_refined_tri(x[idx], y[idx], z[idx], ax, **kwargs)
plt.show()
Result:

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