})
# Solve the profile
p, s = profile_flux(p, sol)
x = np.linspace(s['L'], s['R'], 200)
y = soln(x, s)
# Plot the profile
plt.figure("Profile")
plt.plot(x, y)
plt.show()
s, e, m, c = emcset(s, 'front', [2, 2], 'reg_adj_compound', A, Ak)
circpnts, imagpnts, innerpnts = 30, 30, 32
r = 1
spread = 4
zerodist = 10**(-4)
# ksteps, lambda_steps = 32, 0
preimage = semicirc(circpnts, imagpnts, c['ksteps'], r, spread, zerodist)
out, domain = Evans_compute(preimage, c, s, p, m, e)
out = out / out[0]
w = reflect_image(out)
windnum = winding_number(w)
print('Winding Number: {:f}\n'.format(windnum))
Evans_plot(w)
# This choice solves the right hand side via exterior products
s, e, m, c = emcset(s, 'front', [2, 2], 'adj_reg_compound', A, Ak)
# display a waitbar
c.stats = 'print' # 'on', 'print', or 'off'
c.ksteps = 2**8
# Preimage Contour
# This is a semi circle. You can also do a semi annulus or a rectangle
circpnts = 30
imagpnts = 30
R = 10
spread = 2
zerodist = 10**(-2)
preimage = semicirc(circpnts, imagpnts, c.ksteps, R, spread, zerodist)
# compute Evans function
halfw, domain = Evans_compute(preimage, c, s, p, m, e)
w = halfw / halfw[0]
# We compute Evans function on half of contour then reflect across reals
w = reflect_image(w)
# Process and display data
wnd = winding_number(w) # determine the number of roots inside the contour
print("Winding Number: ", wnd)
# plot the Evans function (normalized)
Evans_plot(w)
# set STABLAB structures to local default values
# default for Burgers is reg_reg_polar
s['A'] = A
s, e, m, c = emcset(s,'front',[1,1],'default')
# Create the Preimage Contour
circpnts, imagpnts, innerpnts = 20, 20, 5
r = 10
spread = 4
zerodist = 10**(-2)
# Can set custom ksteps and lambda_steps here, if desired
# ksteps, lambda_steps = 32, 0
preimage = semicirc2(circpnts, imagpnts, innerpnts, c['ksteps'],
r,spread,zerodist,c['lambda_steps'])
# plot the preimage
plt.title("Preimage")
plt.plot(np.real(preimage), np.imag(preimage))
plt.show()
# Compute the Evans function
halfw, domain = Evans_compute(preimage,c,s,p,m,e)
# Normalize the solution
halfw = halfw/halfw[0]
w = reflect_image(halfw)
windnum = winding_number(w)
Evans_plot(w)
plt.show()
})
p, s = profile_flux(p, sol)
x = np.linspace(s['L'], s['R'], 200)
y = soln(x, s)
plt.figure("Profile")
plt.plot(x, y)
plt.show()
# set STABLAB structures to local default values
#s, e, m, c = emcset(s, 'front', [2,3], 'reg_adj_compound', A, A_k)
s, e, m, c = emcset(s, 'front', [2, 3], 'reg_reg_polar', A)
circpnts, imagpnts, innerpnts = 20, 30, 5
r = 10
spread = 4
zerodist = 10**(-2)
# ksteps, lambda_steps = 32, 0
preimage = semicirc2(circpnts, imagpnts, innerpnts, c['ksteps'], r, spread,
zerodist, c['lambda_steps'])
pre_w, preimage = Evans_compute(preimage, c, s, p, m, e)
pre_w = pre_w / pre_w[0]
w = reflect_image(pre_w)
windnum = winding_number(w)
Evans_plot(w)
plt.show()
m.options['RelTol'] = 1e-9
# display a waitbar
c.stats = 'print' # 'on', 'print', or 'off'
c.ksteps = 2**6
# Preimage Contour
# This is a semi circle. You can also do a semi annulus or a rectangle
circpnts = 30
imagpnts = 10
innerpts = 10
R = 1
spread = 2
zerodist = .0001
preimage = stablab.semicirc2(circpnts, imagpnts, innerpts, c.ksteps, R,
spread, zerodist)
# compute Evans function
halfw, domain = stablab.Evans_compute(preimage, c, s, p, m, e)
w = halfw / halfw[0]
# We compute the Evans function on half of contour then reflect
w = stablab.reflect_image(w)
# process and display data
wnd = stablab.winding_number(
w) # determine the number of roots inside the contour
print('Winding Number: {:f}\n'.format(wnd))
# plot the Evans function (normalized)
stablab.Evans_plot(w)
})
# Solve the profile
p,s = profile_flux(p,sol)
x = np.linspace(s['L'],s['R'],200)
y = soln(x,s)
# Plot the profile
plt.figure("Profile")
plt.plot(x,y)
plt.show()
s, e, m, c = emcset(s,'front',[2,2],'reg_adj_compound',A,Ak)
circpnts, imagpnts, innerpnts = 30, 30, 32
r = 1
spread = 4
zerodist = 10**(-4)
# ksteps, lambda_steps = 32, 0
preimage = semicirc(circpnts, imagpnts, c['ksteps'], r, spread, zerodist)
out, domain = Evans_compute(preimage,c,s,p,m,e)
out = out/out[0]
w = reflect_image(out)
windnum = winding_number(w)
print('Winding Number: {:f}\n'.format(windnum))
Evans_plot(w)
})
p,s = profile_flux(p,sol)
x = np.linspace(s['L'],s['R'],200)
y = soln(x,s)
plt.figure("Profile")
plt.plot(x,y)
plt.show()
# set STABLAB structures to local default values
#s, e, m, c = emcset(s, 'front', [2,3], 'reg_adj_compound', A, A_k)
s, e, m, c = emcset(s,'front',[2,3],'reg_reg_polar',A)
circpnts, imagpnts, innerpnts = 20, 30, 5
r = 10
spread = 4
zerodist = 10**(-2)
# ksteps, lambda_steps = 32, 0
preimage = semicirc2(circpnts, imagpnts, innerpnts, c['ksteps'],
r,spread,zerodist,c['lambda_steps'])
pre_w,preimage = Evans_compute(preimage,c,s,p,m,e)
pre_w = pre_w/pre_w[0]
w = reflect_image(pre_w)
windnum = winding_number(w)
Evans_plot(w)
plt.show()
# set STABLAB Structs to local default values
#s,e,m,c = emcset(s,'front',[2,2],'reg_reg_polar')
#s,e,m,c = emcset(s,'front',[2,2],'reg_adj_polar')
#s,e,m,c = emcset(s,'front',[2,2],'adj_reg_polar')
s,e,m,c = emcset(s,'front',[2,2],'reg_adj_compound')
# display a waitbar
c.stats = 'print'
# Preimage
points = 50
preimage = 0.16+0.05*np.exp(2*np.pi*1j*np.linspace(0,0.5,points+(points-1)*c.ksteps)) #FIXME: this line could probably be easier to understand
# Compute the Evans function
halfw,preimage = Evans_compute(preimage,c,s,p,m,e)
w = reflect_image(halfw)
# Normalize the Evans Output
w = w/w[0]
# Process and display data:
wnd = winding_number(w)
print("Winding Number: {:f}\n".format(wnd))
Evans_plot(w)
plt.show()
#Set variables in preparation for root solving
c.lambda_steps = 0
c.stats = 'off'
c.pic_stats = 'on'
c.ksteps = 2**8
c.moments = 'off'