# -*- coding: utf-8 -*- """ Created on Tue Jun 4 16:42:45 2019 @author: elena """ from input_data import input_data from LPFMethod import longpath from MehrotraMethod import mehrotra from cent_meas import cent_meas ''' * ANALYSIS LONG-STEP PATH-FOLLOWING METHOD * ''' # Input_data (A, b, c) = input_data(10) # Applicaton of longpath x, s, u = longpath(A, b, c) # Recall the dataframe dfu = cent_meas(x, u, 'LPF')
# Input data in canonical form
A2 = q[:,:7]
b2 = q[:,7]
c2 = np.array([16, 10, 8, 9, 48, 60, 53])
(A3, c3) = stdForm(A2, c2)
return(A2, b2, c2)
#%%
""" run the methods """
if __name__ == "__main__":
(A, b, c) = ssteel1()
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)
print(
'\nCurrent point:\n x = {} \n lambda = {} \n s = {}.\n'.format(
x.round(decimals=3), y.round(decimals=3),
s.round(decimals=3)))
print('Dual next gap: {}.\n'.format("%10.3f" % g))
#%%
print_boxed("Found optimal solution of the problem at\n x* = {}.\n\n".
format(x.round(decimals=3)) +
"Dual gap: {}\n".format("%2.2e" % g) +
"Optimal cost: {}\n".format("%10.8E" % z) +
"Number of iteration: {}".format(it))
return x, s, u, sig
#%%
''' ===============
LPF METHOD test
===============
'''
if __name__ == "__main__":
# Input data of canonical LP:
(A, b, c) = input_data(18)
x, s, u, sig = longpath2(A, b, c, info=1)
dlpf = cent_meas(x, u, 'LPF', plot=0)
V = np.concatenate((T, U), axis=0)
# RHS of the linear system with minus
rb = b - np.dot(A, x)
rc = c - np.dot(A.T, y) - s
rxs = -x * s + cp * (sum(x * s) / c_A) * np.ones(
c_A) # Newton step toward x*s = sigma*mi
r = np.hstack((rb, rc - np.dot(X_inv, rxs)))
o = np.linalg.solve(V, r)
# SEARCH DIRECTION:
y1 = o[:r_A]
x1 = o[r_A:c_A + r_A]
s1 = np.dot(X_inv, rxs) - np.dot(W1, x1)
return x1, y1, s1, rb, rc
#%%
''' ==================
LPF PC METHOD test
==================
'''
if __name__ == "__main__":
(A, b, c) = input_data(21)
x, s, u, sig = longpathPC(A, b, c)
ul = cent_meas(x, u, 'LPF Predictor corrector', plot=0)
q = r.as_matrix()
q = np.asarray(q)
c = q[0, :64]
A = q[1:21, :64]
b = q[1:21, 64]
return (A, b, c)
#%%
""" run the methods """
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)
#%%
""" run the methods """
#x_a, s_a , u_a = affine(A, b, c)
#dfu = cent_meas(x_a, u_a, label = 'Affine') # 29 it
""" LPF1 """
# 174 iterations / 174 iterations
start = time.time()
x_l, s_l, u_l = longpath1(A, b, c, c_form = 1, info = 1, ip = 0)
time_lpf1 = time.time()-start
print('Time of the algorithm is {} \n\n'.format("%2.2e"%time_lpf1))
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
g = z - np.dot(y, b)
# Termination elements
tm = term(it, b, c, rb, rc, z, g)
u.append([it, g, x.copy(), s.copy(), rb.copy(), rc.copy()])
print('Dual next gap: {}.\n'.format("%10.3f" % g))
print_boxed("Found optimal solution of the problem at\n x* = {}.\n\n".
format(x.round(decimals=3)) +
"Dual gap: {}\n".format("%10.6f" % g) +
"Optimal cost: {}\n".format("%10.3f" % z) +
"Number of iteration: {}".format(it))
print("Centering parameter sigma:{}.\n".format("%10.3f" % cp))
return x, s, u
#%%ù
"""Input data"""
if __name__ == "__main__":
# Input data of canonical LP:
(A, b, c) = input_data(1)
# Central parameter
cp1 = 0.9
x, s, u = longpathC(A, b, c, cp=cp1)
cent_meas(x, u, ' LPF_cp')
""" = PRINT PRIMAL FEASIBILITY SPEED CONVERGENCE =
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)
raise TimeoutError("Iterations maxed out")
if info == 0:
print('\nCurrent point:\n x = {} \n lambda = {} \n s = {}.\n'.format(x.round(decimals = 3), y.round(decimals = 3), s.round(decimals = 3)))
print('Dual next gap: {}.\n'.format("%2.2e"%g))
#%%
print_boxed("Found optimal solution of the problem at\n x* = {}.\n\n".format(x.round(decimals = 3)) +
"Dual gap: {}\n".format("%10.6e"%g) +
"Optimal cost: {}\n".format("%10.3f"%z) +
"Number of iteration: {}".format(it))
return x, s, u
#%%
''' ===============
LPF METHOD test
===============
'''
if __name__ == "__main__":
# Input data of canonical LP:
(A, b, c) = input_data(21)
x, s, u = longpath1(A, b, c)
dfm = cent_meas(x, u, 'LPF', plot = 0)
print("Iterations maxed out")
return x, s, u
print('\nCurrent point:\n x = {} \n lambda = {} \n s = {}.\n'.format(
x.round(decimals=3), y.round(decimals=3), s.round(decimals=3)))
z = np.dot(c, x)
g = z - np.dot(y, b)
u.append([it, g, x.copy(), s.copy(), rb.copy(), rc.copy()])
# Termination elements
tm = term(it, b, c, rb, rc, z, g)
print('Dual next gap: {}.\n'.format("%10.3f" % g))
print_boxed("Found optimal solution of the problem at\n x* = {}.\n\n".
format(x.round(decimals=3)) +
"Dual gap: {}\n".format("%10.6f" % g) +
"Optimal cost: {}\n".format("%10.3f" % z) +
"Number of iteration: {}".format(it))
return x, s, u
#%%
if __name__ == "__main__":
# Input data of canonical LP:
(A, b, c) = input_data(0)
x, s, u = longpath2(A, b, c)
ul = cent_meas(x, u, 'LPF2')
r_A, c_A = A.shape
A = np.vstack((A, np.zeros((10, c_A))))
for i in range(1, 11):
A[r_A - 1 + i, 12 + i] = 1
return (A, b, c)
#%%
""" run the methods """
(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
raise TimeoutError("Iterations maxed out")
if info == 0:
print('CORRECTOR STEP:\nCurrent primal-dual point: \n x = ', x,
'\nlambda = ', y, '\n s = ', s)
print('Current g: {}\n'.format("%.3f" % g))
#%%
print_boxed(
"Found optimal solution of the standard problem at\n x* = {}.\n\n".
format(x) + "Dual gap: {}\n".format("%2.2e" % g) +
"Optimal cost: {}\n".format("%10.3f" % z) +
"Number of iteration: {}".format(it))
return x, s, u, sig
#%%
''' ====================
MEHROTRA METHOD test
====================
'''
if __name__ == "__main__":
(A, b, c) = input_data(21) # Recall problem data
xm, sm, um, sigmam = mehrotra(A, b, c)
dm = cent_meas(xm, um, 'Mehrotra', plot=0)
tm = max(m, n, q)
if it == max_it:
raise TimeoutError("Iterations maxed out")
if info == 0:
print('Current point:\n x = {} \n lambda = {} \n s = {}.\n'.format(x, y, s))
print('Dual next gap: {}.\n'.format("%10.3f"%g))
#%%
print_boxed("Found optimal solution of the problem at\n x* = {}.\n".format(x) +
"Dual gap: {}\n".format("%10.6f"%g) +
"Optimal cost: {}\n".format("%.8E" %z) +
"Number of iterations: {}".format(it))
return x, s, u
#%%
''' ===
PRIMAL-DUAL AFFINE-SCALING METHOD test
===
'''
if __name__ == "__main__":
(A, b, c) = input_data(5)
x, s, u = affine(A, b, c, max_it = 1000, info = 1)
up = cent_meas(x, u, 'Affine', plot = 0)
print('Tollerance: {}.\n'.format("%10.3f" % tm))
print('CORRECTOR STEP:\nCurrent primal-dual point: \n x = ', x,
'\nlambda = ', y, '\n s = ', s)
print('Current g: {}\nCurrent g1: {}\n'.format(
"%.3f" % g, "%.3f" % g1))
print_boxed(
"Found optimal solution of the standard problem at\n x* = {}.\n\n".
format(x) + "Dual gap: {}\n".format("%2.2e" % g) +
"Optimal cost: {}\n".format("%2.8E" % z) +
"Number of iteration: {}".format(it))
return x, s, u, sig
#%%
"""Input data"""
# Input data of canonical LP:
if __name__ == "__main__":
# Input data of canonical LP:
(A, b, c) = input_data(20)
x, s, u, sigma = mehrotra2(A, b, c, info=1)
dm = cent_meas(x, u, 'Mehrotra with augmented system', plot=0)