def nlers2(qL, qR, xvect):
aL = eigenvalue(qL)
aR = eigenvalue(qR)
xvect = toarray(xvect)
if(aL > aR):
# is a Shock wave
s = ( flux(qR) - flux(qL) ) / ( qR - qL )
solution = shock(xvect, s, qL, qR)
else:
# is a Rarefaction
solution, rarefactionlist = rarefaction(xvect, aL, aR, qL, qR)
for rarefact in rarefactionlist:
solution[rarefact] = newton( 0.5 * ( qL + qR ), xvect[rarefact] )
return solution
def nlers(qL, qR, xi):
"""
function q = NLERS(qL,qR,xi)
aL = eigenvalue(qL);
aR = eigenvalue(qR);
eta=0.001;
if(aL > aR)
% Shock wave
s = (flux(qR)-flux(qL))/(qR-qL);
if(xi<=s)
q = qL;
else
q = qR;
end
else
% Rarefaction
if(xi<aL)
q = qL;
elseif(xi>aR)
q = qR;
else
q=0.5*(qL+qR);
q = Newton(q,xi);
end
end
"""
aL = eigenvalue(qL);
aR = eigenvalue(qR);
if aL > aR:
# is a Shock wave
s = ( flux(qR) - flux(qL) ) / ( qR - qL );
if (xi <= s):
q = qL;
else:
q = qR;
else:
# is a Rarefaction
if xi < aL:
q = qL
elif xi > aR:
q = qR
else:
#print( 'is a Rarefaction')
#import pdb; pdb.set_trace()
q = 0.5 * (qL + qR)
q = newton(q, xi)
return q
# Plotting rough interval estimate
plt.plot(-r(COEFF), 0, color='r', marker='>', markersize=7)
plt.plot(r(COEFF), 0, color='r', marker='<', markersize=7)
# Plotting accurate interval estimate
plt.plot(acc_lower(COEFF), 0, color='g', marker='>', markersize=5)
plt.plot(acc_upper(COEFF), 0, color='g', marker='<', markersize=5)
x1 = np.arange(x_from, x_to, 0.01)
y1 = f(x1)
plt.plot(x1, y1)
intervals = solve.get_all_intervals(f, acc_lower(COEFF), acc_upper(COEFF), 0.1)
for i, interval in enumerate(intervals):
cor, it_cor = solve.chord(f, interval[0], interval[1])
ntn, it_ntn = solve.newton(f, f_prime, interval[0])
scn, it_scn = solve.scan(f, interval[0], interval[1])
print('----- f(x) root #{} -----'.format(i + 1))
print('Chord = ', cor, ' iterations = ', it_cor)
print('Newton = ', ntn, ' iterations = ', it_ntn)
print('Scan = ', scn, ' iterations = ', it_scn)
print()
plt.plot(ntn, 0, 'ro')
print('f(x) np.roots = {}'.format(np.roots(COEFF)), end='\n\n\n')
# ---- Plotting g(x) ---- #
plt.figure(1)
plt.title('Function g(x)')