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ALSSM Trajectory [ex102.0]#
Evaluation of a ALSSM over a time range with a given initial state.
See also:
trajectory(),
trajectories()
import matplotlib.pyplot as plt
import lmlib as lm
js = range(-20, 20) # ALSSM evaluation range
alssm = lm.AlssmPoly(poly_degree=1, label='1th degree')
x0_d1 = [-1, 2] # initial state vector
sx0_d1 = alssm.trajectory(x0_d1, js)
alssm = lm.AlssmPoly(poly_degree=2, label='2nd degree')
x0_d2 = [-1, 2, .1] # initial state vector
sx0_d2 = alssm.trajectory(x0_d2, js)
alssm = lm.AlssmPoly(poly_degree=3, label='3nd degree')
x0_d3 = [-1, 2, .1, -.01] # initial state vector
sx0_d3 = alssm.trajectory(x0_d3, js)
# plot
plt.plot(js, sx0_d1, '.-', lw=.5, label=r'$x_0 = ' + str(x0_d1) + '^\mathrm{T}$')
plt.plot(js, sx0_d2, '.-', lw=.5, label=r'$x_0 = ' + str(x0_d2) + '^\mathrm{T}$')
plt.plot(js, sx0_d3, '.-', lw=.5, label=r'$x_0 = ' + str(x0_d3) + '^\mathrm{T}$')
plt.xlabel('Evaluation index $j$')
plt.ylabel('$s_j(x_0)$')
plt.title('Polynomial ALSSM Evaluation $s_j(x_0)$')
plt.legend()
plt.show()
Total running time of the script: ( 0 minutes 0.068 seconds)