Plotting two cross section intensity at the same time in one figure

Question

I have an array of shape(512,512). Looks like, (row=x, column=y, density=z=the number of the array)

[[0.012825 0.020408 0.022976 ... 0.015938 0.02165  0.024357]
 [0.036332 0.031904 0.025462 ... 0.031095 0.019812 0.024523]
 [0.015831 0.027392 0.031939 ... 0.016249 0.01697  0.028686]
 ...
 [0.024545 0.011895 0.022235 ... 0.033226 0.03223  0.030235]]

I had already drawn it into a 2D density plot. My goal is to find the center of the circle and draw a vertical and horizontal cross-section in one figure.

Now, I have the trouble to find the center of the circle and combine two cross-sections in one figure.

Please help.

This is my code:

    import matplotlib.pyplot as plt
    import numpy as np
    import pandas as pd
    import scipy.ndimage
    data = pd.read_csv('D:/BFP.csv', header=None)


    # create data
    data = np.array(data)
    print(data)

    #plot data
    side = np.linspace(-1.5,1.5,512)
    x,y = np.meshgrid(side,side)
    z = [[data[i][j] for i in range(len(data[0]))]for j in range(len(data))]


    #-- Extract the line...
    # Make a line with "num" points...
    x0, y0 = 270, 0  # These are in _pixel_ coordinates!!
    x1, y1 = 270, 500
    num = 512
    x_, y_ = np.linspace(x0, x1, num), np.linspace(y0, y1, num)

    # Extract the values along the line, using cubic interpolation
    zi = scipy.ndimage.map_coordinates(z, np.vstack((x_,y_)))


    #-- Plot...
    fig, axes = plt.subplots(nrows=2)
    axes[0].imshow(z,origin='lower')
    axes[0].plot([x0, x1], [y0, y1], 'ro-')
    #axes[0].axis('image')

    axes[1].plot(zi)
    plt.savefig('D:/vertical.png')
    plt.show()

image here:

Answer 1

I cannot help you with finding the center of the circle, but you can create a nice visualization of the cross section by creating 3 axes in a grid. Usually, I would use GridSpec for this, but imhsow has a tendency to mess up the relative size of the axes to maintain square pixels. Thankfully, the AxesGrid toolkit can help.

The base of the code is inspired by this matplotlib example.

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
from scipy.stats import multivariate_normal
import scipy

fig, main_ax = plt.subplots(figsize=(5, 5))
divider = make_axes_locatable(main_ax)
top_ax = divider.append_axes("top", 1.05, pad=0.1, sharex=main_ax)
right_ax = divider.append_axes("right", 1.05, pad=0.1, sharey=main_ax)

# make some labels invisible
top_ax.xaxis.set_tick_params(labelbottom=False)
right_ax.yaxis.set_tick_params(labelleft=False)

main_ax.set_xlabel('dim 1')
main_ax.set_ylabel('dim 2')
top_ax.set_ylabel('Z profile')
right_ax.set_xlabel('Z profile')

x, y = np.mgrid[-1:1:.01, -1:1:.01]
pos = np.empty(x.shape + (2,))
pos[:, :, 0] = x; pos[:, :, 1] = y
rv = multivariate_normal([-0.2, 0.2], [[1, 1.5], [0.25, 0.25]])
z = rv.pdf(pos)
z_max = z.max()

cur_x = 110
cur_y = 40

main_ax.imshow(z, origin='lower')
main_ax.autoscale(enable=False)
right_ax.autoscale(enable=False)
top_ax.autoscale(enable=False)
right_ax.set_xlim(right=z_max)
top_ax.set_ylim(top=z_max)
v_line = main_ax.axvline(cur_x, color='r')
h_line = main_ax.axhline(cur_y, color='g')
v_prof, = right_ax.plot(z[:,int(cur_x)],np.arange(x.shape[1]), 'r-')
h_prof, = top_ax.plot(np.arange(x.shape[0]),z[int(cur_y),:], 'g-')

plt.show()

Just for fun, you can even make it interactive

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.axes_grid1 import make_axes_locatable
from scipy.stats import multivariate_normal
import scipy

fig, main_ax = plt.subplots(figsize=(5, 5))
divider = make_axes_locatable(main_ax)
top_ax = divider.append_axes("top", 1.05, pad=0.1, sharex=main_ax)
right_ax = divider.append_axes("right", 1.05, pad=0.1, sharey=main_ax)

# make some labels invisible
top_ax.xaxis.set_tick_params(labelbottom=False)
right_ax.yaxis.set_tick_params(labelleft=False)

main_ax.set_xlabel('dim 1')
main_ax.set_ylabel('dim 2')
top_ax.set_ylabel('Z profile')
right_ax.set_xlabel('Z profile')

x, y = np.mgrid[-1:1:.01, -1:1:.01]
pos = np.empty(x.shape + (2,))
pos[:, :, 0] = x; pos[:, :, 1] = y
rv = multivariate_normal([-0.2, 0.2], [[1, 1.5], [0.25, 0.25]])
z = rv.pdf(pos)
z_max = z.max()

main_ax.imshow(z, origin='lower')
main_ax.autoscale(enable=False)
right_ax.autoscale(enable=False)
top_ax.autoscale(enable=False)
right_ax.set_xlim(right=z_max)
top_ax.set_ylim(top=z_max)
v_line = main_ax.axvline(np.nan, color='r')
h_line = main_ax.axhline(np.nan, color='g')
v_prof, = right_ax.plot(np.zeros(x.shape[1]),np.arange(x.shape[1]), 'r-')
h_prof, = top_ax.plot(np.arange(x.shape[0]),np.zeros(x.shape[0]), 'g-')

def on_move(event):
    if event.inaxes is main_ax:
        cur_x = event.xdata
        cur_y = event.ydata

        v_line.set_xdata([cur_x,cur_x])
        h_line.set_ydata([cur_y,cur_y])
        v_prof.set_xdata(z[:,int(cur_x)])
        h_prof.set_ydata(z[int(cur_y),:])

        fig.canvas.draw_idle()

fig.canvas.mpl_connect('motion_notify_event', on_move)

plt.show()

NB: the lag is just due to the convertion in gif, the update is much smoother on my machine