x, s, u = longpath1(A, b, c, c_form = 1, info = 1, ip = 0)
dful = cent_meas(x, u, label = 'LPF', plot = 0)
""" LPF2 """
# 13 it
x, s, u, sigma_l2 = longpath2(A, b, c, c_form = 1, info = 1, ip = 1)
dfc = cent_meas(x, u, label = 'LPF2', plot = 0)
""" LPF predictor corrector """
# 14 iterations
x, s, u, sigma_pc = longpathPC(A, b, c, c_form = 1, info = 1, ip = 0)
dfpc = cent_meas(x, u, label = 'LPF PC', plot = 0)
""" Mehrotra """
# 8 iterations
x, s, u, sigma_m = mehrotra(A, b, c, c_form = 1, info = 1, ip = 1)
dfm = cent_meas(x, u, label = 'Mehrotra', plot = 0)
""" Recall the simplex method """
(A2, b2, c2) = ssteel2()
P, u = SimplexMethod(A, b, c, rule = 1, c_form = 1) # 17!!!
# Start phase II
#Iteration: 12
#Current x: [ 75. 250. 568. 80.5 ... 24. 0. 0. 0. ]
#P2, u2 = SimplexMethodI(A, b, c, rule = 0, c_form = 1) # 0 it
# P, u = SimplexMethod(A2, b2, c2, rule = 0)
if __name__ == "__main__":
(A, b, c) = tubprod() # canonical form!
""" Affine """
# 29 it
x, s, u = affine(A, b, c, ip=1)
dfu = cent_meas(x, u, label='Affine', plot=0)
""" LPF1 """
# IT DOESN'T WORK!!!
# x_l, s_l, u_l = longpath1(A, b, c, info = 1, ip = 1)
""" LPF2 """
# 21 it
x, s, u, sigma_l2 = longpath2(A, b, c, info=1, ip=0)
dfc = cent_meas(x, u, label='LPF2', plot=0)
""" LPF predictor corrector """
# 20 iterations
x, s, u, sigma_pc = longpathPC(A, b, c, info=1, ip=1)
dfpc = cent_meas(x, u, label='LPF PC', plot=0)
""" Mehrotra """
# 10 iterations
start = time.time()
x_m, s_m, u_m, sigma_m = mehrotra(A, b, c, info=1, ip=1)
dfm = cent_meas(x_m, u_m, label='Mehrotra', plot=0)
plt.plot(sigma_m)
" Recall the simplex method "
#P, u = SimplexMethod(A, b, c, rule = 1) # 51 it
# it doesn't work with rule = 0
#dfu = pd.DataFrame(u)
x = linprog(c, method='simplex', A_ub=A, b_ub=b) # Exact solution
time_lpf2 = time.time()-start
print('Time of the algorithm is {} \n\n'.format("%2.2e"%time_lpf2))
dfc = cent_meas(x_c, u_c, label = 'LPF2', plot= 0)
""" LPF predictor corrector """
# 12 iterations/ 14 iteraions
start = time.time()
x_pc, s_pc, u_pc, sigma_pc = longpathPC(A, b, c, c_form = 1, info = 1, ip = 0)
time_lpfpc = time.time()-start
print('Time of the algorithm is {} \n\n'.format("%2.2e"%time_lpfpc))
dfpc = cent_meas(x_pc, u_pc, label = 'LPF PC', plot = 0)
""" Mehrotra """
# 7 iterations
start = time.time()
x_m, s_m, u_m, sigma_m = mehrotra(A, b, c, c_form = 1, info = 1, ip = 0)
time_mer = time.time()-start
print('Time of the algorithm is {} \n\n'.format("%2.2e"%time_mer))
dfm = cent_meas(x_m, u_m, label = 'Mehrotra', plot = 0)
" Recall the simplex method "
#P, u = SimplexMethod(A, b, c, rule = 1, c_form = 1) # BAD
x = linprog(c, A_eq = A, b_eq = b) # Exact solution
x = linprog(c, A, b) # BAD
#plt.show()
For every method we obtain the optimal vector (x,s), a dataframe with all sequences
time of the algorithm
'''
if __name__ == "__main__":
(A, b, c) = forest() # already in standard form
IP = 0
""" Affine """
# 29 it
x, s, u = affine(A, b, -c, c_form=1, ip=IP)
dfu = cent_meas(x, u, label='Affine', plot=0)
""" LPF1 """
# 183 it
x, s, u = longpath1(A, b, -c, c_form=1, info=1, ip=IP)
dful = cent_meas(x, u, label='LPF', plot=0)
""" LPF2 """
# 15 it
x_c, s_c, u_c, sigma_l2 = longpath2(A, b, -c, c_form=1, info=1, ip=IP)
dfc = cent_meas(x_c, u_c, label='LPF2', plot=0)
""" LPF predictor corrector """
# 19 iterations
x, s, u, sigma_pc = longpathPC(A, b, -c, c_form=1, info=1, ip=IP)
dfpc = cent_meas(x, u, label='LPF PC', plot=0)
""" Mehrotra """
# 9 iterations
x, s, u, sigma = mehrotra(A, b, -c, c_form=1, info=1, ip=IP)
dfm = cent_meas(x, u, label='Mehrotra', plot=0)
P1, u = SimplexMethod(A, b, -c, rule=0, c_form=1) # 45 iterations
# L2 regression of |Ax -b|_2 for LPF2 p = np.dot(np.linalg.pinv(A), P) y2 = p[0]*x + p[1] plt.plot(x, y2, c = 'blue', linewidth = 2) # L2 regression of |Ax -b|_2 for LPF pc t = np.dot(np.linalg.pinv(A), Z) yl = t[0]*x + t[1] plt.plot(x,yl, c = 'cyan', linewidth = 2) # L2 regression of |Ax -b|_2 for Simplex #p = np.dot(np.linalg.pinv(A), W) #ys = p[0]*x + p[1] #plt.plot(x,ys, c = 'red', linewidth = 2) #x = [-np.Inf, np.Inf] #%% # L1 regression of the function |Ax - b| r_A, c_A = np.shape(A) A1 = np.hstack((A, -np.identity(r_A))) A2 = np.hstack((-A, -np.identity(r_A))) A = np.vstack((A1, A2)) b = np.concatenate((-B, B)) c = np.concatenate((np.zeros(c_A),np.ones(r_A))) xm, sm, um, sigmam = mehrotra(A, b, c)