imshow with non-orthogonal axes (i.e. parallelogram ) - python

I have 2D array of data sampled along two vectors non-orthogonal a, b
a = |a|.( cos(alfa), sin(alfa) )
b = |b|.( cos(beta), sin(beta) )
(i.e not along orthogonal cartesian direction x, y)
I would like to plot this data un-distorted (i.e. as parallelogram instead of rectangle)
is there any function to do that in matplotlib?
I need it for plotting data like this (c, f , i)

What about using an affine transform as in this example,
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.transforms as mtransforms
def get_image():
from scipy import misc
Z = misc.imread('31271907.jpg')
return Z
# Get image
fig, ax = plt.subplots(1,1)
Z = get_image()
# image skew
im = ax.imshow(Z, interpolation='none', origin='lower',
extent=[-2, 4, -3, 2], clip_on=True)
im._image_skew_coordinate = (3, -2)
plt.show()
Which uses the image
and turns it into,

Related

Drape outline of active values over another 2D array

Lets say I have a simple 2D numpy array that I display with imshow():
import numpy as np
import random
import matplotlib.pyplot as plt
a = np.random.randint(2, size=(10,10))
im = plt.imshow(a, cmap='spring', interpolation='none', vmin=0, vmax=1, aspect='equal')
plt.show()
And I have another 2D numpy array, like so:
bnd = np.zeros((10,10))
bnd[2,3] = bnd[3,2:5] = bnd[4,3] = 1
bnd[6,6] = bnd[7,5:8] = bnd[8,6] = 1
plt.imshow(bnd)
plt.show()
How can I generate an outline of all the continuous values of "1" in bnd and then overplot it on a, so I get something like the following (I manually added the black lines in the example below)?
You can compute the borders of the mask by finding the starting and ending indices of consecutive ones and converting those to border segments with coordinates of the image.
Setting up the image and the mask
import numpy as np
import matplotlib.pyplot as plt
a = np.random.randint(2, size=(10,10))
plt.imshow(a, cmap='spring', interpolation='none', vmin=0, vmax=1, aspect='equal')
bnd = np.zeros((10,10))
kernel = [[0,1,0],
[1,1,1],
[0,1,0]]
bnd[2:5, 2:5] = bnd[6:9, 5:8] = kernel
Finding the indices and convert them to coordinates of the image
# indices to vertical segments
v = np.array(np.nonzero(np.diff(bnd, axis=1))).T
vs = np.repeat(v, 3, axis=0) - np.tile([[1, 0],[0, 0],[np.nan, np.nan]], (len(v),1))
# indices to horizontal segments
h = np.array(np.nonzero(np.diff(bnd, axis=0))).T
hs = np.repeat(h, 3, axis=0) - np.tile([[0, 1],[0, 0],[np.nan, np.nan]], (len(h),1))
# convert to image coordinates
bounds = np.vstack([vs,hs])
x = np.interp(bounds[:,1], plt.xlim(), (0, bnd.shape[1]))
y = np.interp(bounds[:,0], sorted(plt.ylim()), (0, bnd.shape[0]))
plt.plot(x, y, color=(.1, .1, .1, .6), linewidth=5)
plt.show()
Output

How would you plot this 3D visualization in Python?

I want to take an image and represent the dimensions of the image as spatial coordinates and the pixel values as the 3rd dimension represented by height. Here is an example of what I would like to do.
How would you do this with matplotlib or plotly?
Assuming the image is in HWC format, is gray-scale (i.e. C=1) and is a numpy array, something along the lines of:
import matplotlib.pyplot as plt
import numpy as np
img = np.random.uniform(size=(10,10,1))
X = np.arange(0, img.shape[1])
Y = np.arange(0, img.shape[0])
X, Y = np.meshgrid(X, Y)
Z = img.squeeze()
# Plot the surface.
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z)
Inspired by: this.
Hope this helps!

Plotting 3D image form a data in NumPy-array

I have a data file in NumPy array, I would like to view the 3D-image. I am sharing an example, where I can view 2D image of size (100, 100), this is a slice in xy-plane at z = 0.
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
X, Y, Z = np.mgrid[-10:10:100j, -10:10:100j, -10:10:100j]
T = np.sin(X*Y*Z)/(X*Y*Z)
T=T[:,:,0]
im = plt.imshow(T, cmap='hot')
plt.colorbar(im, orientation='vertical')
plt.show()
How can I view a 3D image of the data T of shape (100, 100, 100)?
I think the main problem is, that you do have 4 informations for each point, so you are actually interessted in a 4-dimensional object. Plotting this is always difficult (maybe even impossible). I suggest one of the following solutions:
You change the question to: I'm not interessted in all combinations of x,y,z, but only the ones, where z = f(x,y)
You change the accuracy of you plot a bit, saying that you don't need 100 levels of z, but only maybe 5, then you simply make 5 of the plots you already have.
In case you want to use the first method, then there are several submethods:
A. Plot the 2-dim surface f(x,y)=z and color it with T
B. Use any technic that is used to plot complex functions, for more info see here.
The plot given by method 1.A (which I think is the best solution) with z=x^2+y^2 yields:
I used this programm:
import numpy as np
from matplotlib import pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib as mpl
X, Y = np.mgrid[-10:10:100j, -10:10:100j]
Z = (X**2+Y**2)/10 #definition of f
T = np.sin(X*Y*Z)
norm = mpl.colors.Normalize(vmin=np.amin(T), vmax=np.amax(T))
T = mpl.cm.hot(T) #change T to colors
fig = plt.figure()
ax = fig.gca(projection='3d')
surf = ax.plot_surface(X, Y, Z, facecolors=T, linewidth=0,
cstride = 1, rstride = 1)
plt.show()
The second method gives something like:
With the code:
norm = mpl.colors.Normalize(vmin=-1, vmax=1)
X, Y= np.mgrid[-10:10:101j, -10:10:101j]
fig = plt.figure()
ax = fig.gca(projection='3d')
for i in np.linspace(-1,1,5):
Z = np.zeros(X.shape)+i
T = np.sin(X*Y*Z)
T = mpl.cm.hot(T)
ax.plot_surface(X, Y, Z, facecolors=T, linewidth=0, alpha = 0.5, cstride
= 10, rstride = 10)
plt.show()
Note: I changed the function to T = sin(X*Y*Z) because dividing by X*Y*Zmakes the functions behavior bad, as you divide two number very close to 0.
I have got a solution to my question. If we have the NumPy data, then we can convert them into TVTK ImageData and then visualization is possible with the help of mlab form Mayavi. The code and its 3D visualization are the following
from tvtk.api import tvtk
import numpy as np
from mayavi import mlab
X, Y, Z = np.mgrid[-10:10:100j, -10:10:100j, -10:10:100j]
data = np.sin(X*Y*Z)/(X*Y*Z)
i = tvtk.ImageData(spacing=(1, 1, 1), origin=(0, 0, 0))
i.point_data.scalars = data.ravel()
i.point_data.scalars.name = 'scalars'
i.dimensions = data.shape
mlab.pipeline.surface(i)
mlab.colorbar(orientation='vertical')
mlab.show()
For another randomly generated data
from numpy import random
data = random.random((20, 20, 20))
The visualization will be

Plot aligned x,y 1d histograms from projected 2d histogram

I need to generate an image similar to the one shown in this example:
The difference is that, instead of having the scattered points in two dimensions, I have a two-dimensional histogram generated with numpy's histogram2d and plotted using with imshow and gridspec:
How can I project this 2D histogram into a horizontal and a vertical histogram (or curves) so that it looks aligned, like the first image?
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.gridspec as gridspec
data = # Uploaded to http://pastebin.com/tjLqM9gQ
# Create a meshgrid of coordinates (0,1,...,N) times (0,1,...,N)
y, x = np.mgrid[:len(data[0, :, 0]), :len(data[0, 0, :])]
# duplicating the grids
xcoord, ycoord = np.array([x] * len(data)), np.array([y] * len(data))
# compute histogram with coordinates as x,y
h, xe, ye = np.histogram2d(
xcoord.ravel(), ycoord.ravel(),
bins=[len(data[0, 0, :]), len(data[0, :, 0])],
weights=stars.ravel())
# Projected histograms inx and y
hx, hy = h.sum(axis=0), h.sum(axis=1)
# Define size of figure
fig = plt.figure(figsize=(20, 15))
gs = gridspec.GridSpec(10, 12)
# Define the positions of the subplots.
ax0 = plt.subplot(gs[6:10, 5:9])
axx = plt.subplot(gs[5:6, 5:9])
axy = plt.subplot(gs[6:10, 9:10])
ax0.imshow(h, cmap=plt.cm.viridis, interpolation='nearest',
origin='lower', vmin=0.)
# Remove tick labels
nullfmt = NullFormatter()
axx.xaxis.set_major_formatter(nullfmt)
axx.yaxis.set_major_formatter(nullfmt)
axy.xaxis.set_major_formatter(nullfmt)
axy.yaxis.set_major_formatter(nullfmt)
# Top plot
axx.plot(hx)
axx.set_xlim(ax0.get_xlim())
# Right plot
axy.plot(hy, range(len(hy)))
axy.set_ylim(ax0.get_ylim())
fig.tight_layout()
plt.savefig('del.png')
If you are ok with the marginal distributions all being upright, you could use corner
E.g.:
import corner
import numpy as np
import pandas as pd
N = 1000
CORNER_KWARGS = dict(
smooth=0.9,
label_kwargs=dict(fontsize=30),
title_kwargs=dict(fontsize=16),
truth_color="tab:orange",
quantiles=[0.16, 0.84],
levels=(1 - np.exp(-0.5), 1 - np.exp(-2), 1 - np.exp(-9 / 2.0)),
plot_density=False,
plot_datapoints=False,
fill_contours=True,
max_n_ticks=3,
verbose=False,
use_math_text=True,
)
def generate_data():
return pd.DataFrame(dict(
x=np.random.normal(0, 1, N),
y=np.random.normal(0, 1, N)
))
def main():
data = generate_data()
fig = corner.corner(data, **CORNER_KWARGS)
fig.show()
if __name__ == "__main__":
main()

Plotting a 2D heatmap

Using Matplotlib, I want to plot a 2D heat map. My data is an n-by-n Numpy array, each with a value between 0 and 1. So for the (i, j) element of this array, I want to plot a square at the (i, j) coordinate in my heat map, whose color is proportional to the element's value in the array.
How can I do this?
The imshow() function with parameters interpolation='nearest' and cmap='hot' should do what you want.
Please review the interpolation parameter details, and see Interpolations for imshow and Image antialiasing.
import matplotlib.pyplot as plt
import numpy as np
a = np.random.random((16, 16))
plt.imshow(a, cmap='hot', interpolation='nearest')
plt.show()
Seaborn is a high-level API for matplotlib, which takes care of a lot of the manual work.
seaborn.heatmap automatically plots a gradient at the side of the chart etc.
import numpy as np
import seaborn as sns
import matplotlib.pylab as plt
uniform_data = np.random.rand(10, 12)
ax = sns.heatmap(uniform_data, linewidth=0.5)
plt.show()
You can even plot upper / lower left / right triangles of square matrices. For example, a correlation matrix, which is square and is symmetric, so plotting all values would be redundant.
corr = np.corrcoef(np.random.randn(10, 200))
mask = np.zeros_like(corr)
mask[np.triu_indices_from(mask)] = True
with sns.axes_style("white"):
ax = sns.heatmap(corr, mask=mask, vmax=.3, square=True, cmap="YlGnBu")
plt.show()
I would use matplotlib's pcolor/pcolormesh function since it allows nonuniform spacing of the data.
Example taken from matplotlib:
import matplotlib.pyplot as plt
import numpy as np
# generate 2 2d grids for the x & y bounds
y, x = np.meshgrid(np.linspace(-3, 3, 100), np.linspace(-3, 3, 100))
z = (1 - x / 2. + x ** 5 + y ** 3) * np.exp(-x ** 2 - y ** 2)
# x and y are bounds, so z should be the value *inside* those bounds.
# Therefore, remove the last value from the z array.
z = z[:-1, :-1]
z_min, z_max = -np.abs(z).max(), np.abs(z).max()
fig, ax = plt.subplots()
c = ax.pcolormesh(x, y, z, cmap='RdBu', vmin=z_min, vmax=z_max)
ax.set_title('pcolormesh')
# set the limits of the plot to the limits of the data
ax.axis([x.min(), x.max(), y.min(), y.max()])
fig.colorbar(c, ax=ax)
plt.show()
For a 2d numpy array, simply use imshow() may help you:
import matplotlib.pyplot as plt
import numpy as np
def heatmap2d(arr: np.ndarray):
plt.imshow(arr, cmap='viridis')
plt.colorbar()
plt.show()
test_array = np.arange(100 * 100).reshape(100, 100)
heatmap2d(test_array)
This code produces a continuous heatmap.
You can choose another built-in colormap from here.
Here's how to do it from a csv:
import numpy as np
import matplotlib.pyplot as plt
from scipy.interpolate import griddata
# Load data from CSV
dat = np.genfromtxt('dat.xyz', delimiter=' ',skip_header=0)
X_dat = dat[:,0]
Y_dat = dat[:,1]
Z_dat = dat[:,2]
# Convert from pandas dataframes to numpy arrays
X, Y, Z, = np.array([]), np.array([]), np.array([])
for i in range(len(X_dat)):
X = np.append(X, X_dat[i])
Y = np.append(Y, Y_dat[i])
Z = np.append(Z, Z_dat[i])
# create x-y points to be used in heatmap
xi = np.linspace(X.min(), X.max(), 1000)
yi = np.linspace(Y.min(), Y.max(), 1000)
# Interpolate for plotting
zi = griddata((X, Y), Z, (xi[None,:], yi[:,None]), method='cubic')
# I control the range of my colorbar by removing data
# outside of my range of interest
zmin = 3
zmax = 12
zi[(zi<zmin) | (zi>zmax)] = None
# Create the contour plot
CS = plt.contourf(xi, yi, zi, 15, cmap=plt.cm.rainbow,
vmax=zmax, vmin=zmin)
plt.colorbar()
plt.show()
where dat.xyz is in the form
x1 y1 z1
x2 y2 z2
...
Use matshow() which is a wrapper around imshow to set useful defaults for displaying a matrix.
a = np.diag(range(15))
plt.matshow(a)
https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.matshow.html
This is just a convenience function wrapping imshow to set useful defaults for displaying a matrix. In particular:
Set origin='upper'.
Set interpolation='nearest'.
Set aspect='equal'.
Ticks are placed to the left and above.
Ticks are formatted to show integer indices.
Here is a new python package to plot complex heatmaps with different kinds of row/columns annotations in Python: https://github.com/DingWB/PyComplexHeatmap

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