def InitFeas(A, b, c, c_form=0):
if c_form == 0:
(A, c) = stdForm(A, c)
(AP, cP) = rep(A, b)
x, s, u = longpathPC(AP, b, cP)
r_A, c_A = np.shape(A)
D = np.concatenate((A.T, np.identity(c_A)), axis=1)
(T, w) = rep(D, c)
y, s, u = longpathPC(T, c, w)
return (x[0:c_A], y)
from MehrotraMethod2 import mehrotra2
from LPFMethod_PC import longpathPC
from matplotlib.ticker import NullFormatter # useful for `logit` scale
import pandas as pd # Export to excel
import matplotlib.pyplot as plt # Create graphics
from mpl_toolkits.mplot3d import Axes3D
''' _PLOT THE PATHs_ '''
# Recall lp istance with dimension 2
(A, b, c) = input_data(0)
xm, sm, um = mehrotra2(A, b, c)
#um = pd.DataFrame(um, columns = ['it', 'g', 'Current x', 'Current s', 'rb', 'rc'])
xl, sl, ul = longpathPC(A, b, c)
#ul = pd.DataFrame(ul, columns = ['it', 'g', 'Current x', 'Current s', 'rb', 'rc'])
# Create 3d point x*s for mehrotra
x1 = []
y1 = []
z1 = []
for i in range(len(um)):
g = um[i][2] * um[i][3]
x1.append(g[0].copy())
y1.append(g[1].copy())
z1.append(g[2].copy())
# Create 3d point x*s for Long-path predictor corrector
x2 = []
y2 = []
x, s , u = affine(A, b, c, c_form = 1, info = 1, ip = 1)
dfu = cent_meas(x, u, label = 'Affine', plot = 0) # 17 it
""" LPF1 """
# 161 iterations
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
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
dful = cent_meas(x_l, u_l, label = 'LPF', plot = 0)
""" LPF2 """
# 12 it
start = time.time()
x_c, s_c, u_c, sigma_l2 = longpath2(A, b, c, c_form = 1, info = 1)
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)
Compute: W = [ max|b - Ax_{k}| ] with x_{k} sequence generated by LPF2
Z = [ max|b - Ax_{k}| ] with x_{k} sequence generated by LPF_PC
Plot the speed of the convergence of the error of feasibility
"""
i = 0
A, b, c = input_data(i)
x2, s2, u2, sig2 = longpath2(A, b, c)
dlpf = cent_meas(x2, u2, 'LPF', plot = 0)
W = dlpf['pf']
x3, s3, u3, sig3 = longpathPC(A, b, c)
ul = cent_meas(x3, u3, 'LPF Predictor corrector', plot = 0)
Z = ul['pf']
plt.figure()
plt.subplot(211)
plt.plot(W)
plt.title('Speed error LPF2')
locs, labels = plt.xticks(np.arange(0, len(W), step = 1))
plt.yscale('log')
plt.grid(b = True)
plt.subplot(212)
plt.plot(Z)
plt.title('Speed error LPF_PC')
locs, labels = plt.xticks(np.arange(0, len(Z), step = 1))
(A, b, c) = onb() # input data in canonical form
IP = 0
""" Affine """
# IP = 1 doesn't work
x, s, u = affine(A, b, c, ip=IP)
dfu = cent_meas(x, u, label='Affine', plot=0) # 29 it
""" LPF1 """
# 307 iterations
x, s, u = longpath1(A, b, c, c_form=0, info=1, ip=IP)
dfu = cent_meas(x, u, label='LPF', plot=0)
""" LPF2 """
# 16 it
x, s, u, sigma_l2 = longpath2(A, b, c, c_form=0, info=1, ip=1)
""" LPF predictor corrector """
# 41 iterations / 17 iterations ip = 1
x_pc, s_pc, u_pc, sigma_pc = longpathPC(A, b, c, c_form=0, info=0)
x_pc, s_pc, u_pc, sigma_pc = longpathPC(A, b, c, c_form=0, info=0, ip=1)
dfpc = cent_meas(x_pc, u_pc, label='LPF PC', plot=0)
""" Mehrotra """
# 8 iterations
x_m, s_m, u_m, sigma_m = mehrotra2(A, b, c, c_form=0,
info=1) # Mehrotra1 doesn't work
x_m, s_m, u_m, sigma_m1 = mehrotra2(A, b, c, c_form=0, info=1,
ip=1) # Mehrotra1 doesn't work
dfm = cent_meas(x_m, u_m, label='Mehrotra', plot=0)
" Recall the simplex method "
Y = []
W = []
Z = []
O = []
P = []
q = np.log(2)
for i in range(29):
print(i)
if not i in {4, 20, 23, 25}:
(A, b, c) = input_data(i)
x, s, u, sigma_m = mehrotra2(A, b, c, info=1)
# x, v = SimplexMethod(A, b, c, rule = 0)
x, s, o = longpath1(A, b, c, c_form=0, info=1, ip=0)
x, s, p, sigma_2 = longpath2(A, b, c, c_form=0, info=1)
x, s, z, sigma_pc = longpathPC(A, b, c, info=1)
B.append(np.log(len(u) - 1))
# W.append(np.log(len(v)))
Z.append(np.log(len(z) - 1))
O.append(np.log(len(o) - 1))
P.append(np.log(len(p) - 1))
r = sum(A.shape)
a.append([q, np.log(r)])
Y.append(np.log(r))
it.append(i)
for i in range(29, 34): # we compute the models
it.append(i)
if i == 29: # FOREST
(A, b, c) = input_data(i)
B.append(np.log(8))
