Add get freqmap

[oscarxblanco]

Dear all,
this is a Work-In-Progress branch open to address the limitations on the frequency map analysis found by @TeresiaOlsson and mentioned here #755.

No need to review yet.

[oscarxblanco]

Dear @TeresiaOlsson ,

here is a script you could use to start the test on the function get_freqmap. Please, try it with a ring you have.
This function runs well on the axes ['x','y']. It also works on ['x','dp'] but I have not checked if the results make sense.

Best regards,
o

''' 
This file is used to test the new function get_freqmap
oblanco 2024apr16
'''
import at
import numpy
from matplotlib import pyplot as plt

print(f'{at.__version__}=')

ring = at.load_mat('testring.mat')
# ring.disable_6d()
print(f'{ring.get_tune()=}')

fmaout = at.get_freqmap(ring,
                     ['x','y'],
                     numpy.array([200,200]),
                     numpy.array([10e-3,10e-3]),
                     bounds=[[-1,1],[0,1]],
                     verbose=True,
                     )

fmadata = fmaout[0][0]

print('Plot')
# plot diffusion map
fig = plt.figure()
sc = plt.scatter(1e3*fmadata[:,0],1e3*fmadata[:,1],c=fmadata[:,6],s=1)
plt.grid()
plt.xlabel(r'x (mm)')
plt.ylabel(r'y (mm)')
plt.xlim(-10,10)
plt.ylim(-5,5)
clb = plt.colorbar(sc)
clb.ax.set_title(r'$\log_{10} \sqrt{(\Delta\nu_x^2 + \Delta\nu_y^2)/turn}$')
plt.savefig('diffussionmap.pdf')


# plot frequency map
fig = plt.figure()
sc = plt.scatter(fmadata[:,2],fmadata[:,3],c=fmadata[:,6],s=1)
plt.grid()
plt.xlim(0,0.5)
plt.ylim(0,0.5)
plt.xlabel(r'$\nu_x$')
plt.ylabel(r'$\nu_y$')
clb = plt.colorbar(sc)
clb.ax.set_title(r'$\log_{10} \sqrt{(\Delta\nu_x^2 + \Delta\nu_y^2)/turn}$')
plt.savefig('fmap.pdf')