makeFriedelPlots.py

import numpy as np

from matplotlib import pyplot as plt
plt.ion()

from hexrd.xrd import rotations as rot
from hexrd.xrd import crystallography as xtl

r2d = 180. / np.pi
d2r = np.pi / 180.

eta0 = np.arange(-90, 270.05, 0.05)
tth0 = 10*np.ones_like(eta0)

chi  = [0, 1, 5, 10, 20, 30]

lc = ['k', 'r', 'g', 'b', 'c', 'm', 'y']
lt = [lc[i] + '-' for i in range(len(lc))]

set1 = eta0 <= 90.
set2 = eta0 >  90.

lw = 2
fig1 = plt.figure(1); fig1.clf(); axes1 = fig1.gca()
fig2 = plt.figure(2); fig2.clf(); axes2 = fig2.gca()
for i in range(len(chi)):
    ome1, eta1 = xtl.getFriedelPair(tth0, eta0,
                                    chiTilt=chi[i],
                                    units='degrees',
                                    convention='hexrd')
    axes1.plot(d2r*eta0[set1], ome1[set1], lt[i],
               label='$\chi$=%d$^\circ$' %chi[i], linewidth=lw)
    axes1.plot(d2r*eta0[set2], ome1[set2], lt[i],
               label='$\chi$=%d$^\circ$' %chi[i], linewidth=lw)

    #eta = np.pi - rot.angularDifference(d2r*eta0, eta1)
    eta =  rot.mapAngle(np.pi - (d2r*eta0 - eta1))

    #axes2.plot(d2r*eta0, eta, lt[i], linewidth=lw)    
    axes2.plot(d2r*eta0[set1], eta[set1], lt[i], linewidth=lw)
    axes2.plot(d2r*eta0[set2], eta[set2], lt[i], linewidth=lw)
    #axes2.plot(d2r*eta0[set3], eta[set3], lt[i], linewidth=lw)

axes1.grid(True)
axes1.axis('tight')

axes1.set_xlabel('starting azimuth, $\eta_0$')
axes1.set_ylabel('minimum $\Delta\omega_{FP}$')

axes1.set_xticks(np.arange(-90, 315, 45)*d2r)
axes1.set_xticklabels(['$-\pi/2$', '$-\pi/4$', '$0$', '$\pi/4$',
                      '$\pi/2$', '$3\pi/4$', '$\pi$', '$5\pi/4$', '$3\pi/2$'])
axes1.set_yticks(np.r_[-180, -120, -60, -tth0[0], 0, tth0[0], 60, 120, 180]*d2r)
axes1.set_yticklabels(['$-\pi$', '$-2\pi/3$', '$-\pi/3$',
                      '$-2\\theta$', '$0$', '$2\\theta$',
                      '$\pi/3$', '$2\pi/3$', '$\pi$'])
# fig1.show()
fig1.savefig("friedel_omegas.pdf", dpi=None, orientation='landscape')

axes2.set_xlabel('starting azimuth, $\eta_0$')
axes2.set_ylabel('azimuthal difference, $\pi - \eta_{FP}$')

axes2.set_xlim(-0.5*np.pi, 1.5*np.pi)
axes2.set_ylim(-np.pi/6., np.pi/6.)

axes2.set_xticks(np.arange(-90, 315, 45)*d2r)
axes2.set_xticklabels(['$-\pi/2$', '$-\pi/4$', '$0$', '$\pi/4$',
                      '$\pi/2$', '$3\pi/4$', '$\pi$', '$5\pi/4$', '$3\pi/2$'])
axes2.set_yticks(np.arange(-6, 7)*tth0[0]*d2r)
axes2.set_yticklabels(['$-12\\theta$', '$-10\\theta$', '$-8\\theta$', '$-6\\theta$', '$-4\\theta$', '$-2\\theta$',
                       '$0$',
                       '$2\\theta$', '$4\\theta$', '$6\\theta$', '$8\\theta$', '$10\\theta$', '$12\\theta$'])
axes2.grid(True)

# fig2.show()
fig2.savefig("friedel_etas.pdf", dpi=None, orientation='landscape')

#%%
plt.show()