from openopt import NLP
from numpy import cos, arange, ones, asarray, abs, zeros
N = 30
M = 5
ff = lambda x: ((x-M)**2).sum()
p = NLP(ff, cos(arange(N)))
def df(x):
r = 2*(x-M)
r[0] += 15 #incorrect derivative
r[8] += 80 #incorrect derivative
return r
p.df = df
p.c = lambda x: [2* x[0] **4-32, x[1]**2+x[2]**2 - 8]
def dc(x):
r = zeros((2, p.n))
r[0,0] = 2 * 4 * x[0]**3
r[1,1] = 2 * x[1]
r[1,2] = 2 * x[2] + 15 #incorrect derivative
return r
p.dc = dc
p.h = lambda x: (1e1*(x[-1]-1)**4, (x[-2]-1.5)**4)
def dh(x):
r = zeros((2, p.n))
r[0,-1] = 1e1*4*(x[-1]-1)**3
r[1,-2] = 4*(x[-2]-1.5)**3 + 15 #incorrect derivative
return r
from openopt import NLP
from numpy import cos, arange, ones, asarray, abs, zeros
N = 30
M = 5
ff = lambda x: ((x - M)**2).sum()
p = NLP(ff, cos(arange(N)))
p.df = lambda x: 2 * (x - M)
p.c = lambda x: [2 * x[0]**4 - 32, x[1]**2 + x[2]**2 - 8]
def dc(x):
r = zeros((2, p.n))
r[0, 0] = 2 * 4 * x[0]**3
r[1, 1] = 2 * x[1]
r[1, 2] = 2 * x[2]
return r
p.dc = dc
h1 = lambda x: 1e1 * (x[-1] - 1)**4
h2 = lambda x: (x[-2] - 1.5)**4
p.h = lambda x: (h1(x), h2(x))
def dh(x):
r = zeros((2, p.n))
r[0, -1] = 1e1 * 4 * (x[-1] - 1)**3
r[1, -2] = 4 * (x[-2] - 1.5)**3
return r
from openopt import NLP
from numpy import cos, arange, ones, asarray, abs, zeros
N = 30
M = 5
ff = lambda x: ((x-M)**2).sum()
p = NLP(ff, cos(arange(N)))
p.df = lambda x: 2*(x-M)
p.c = lambda x: [2* x[0] **4-32, x[1]**2+x[2]**2 - 8]
def dc(x):
r = zeros((2, p.n))
r[0,0] = 2 * 4 * x[0]**3
r[1,1] = 2 * x[1]
r[1,2] = 2 * x[2]
return r
p.dc = dc
h1 = lambda x: 1e1*(x[-1]-1)**4
h2 = lambda x: (x[-2]-1.5)**4
p.h = lambda x: (h1(x), h2(x))
def dh(x):
r = zeros((2, p.n))
r[0,-1] = 1e1*4*(x[-1]-1)**3
r[1,-2] = 4*(x[-2]-1.5)**3
return r
p.dh = dh
p.lb = -6*ones(N)
p.ub = 6*ones(N)
p.lb[3] = 5.5
x0fn = 'x0_' + infn[:-4] + '.txt'
x0 = None
if os.path.isfile(x0fn):
x0 = np.loadtxt(x0fn)
if x0 is None or x0.shape[0] != 2 * m + n:
x0 = np.ones(2 * m + n)
# x0[m + 1: 2 * m + 1] = I0 / 10
logger.debug(x0.shape)
lb = np.zeros(2 * m + n)
ub = np.ones(2 * m + n)
ub[m:] = np.inf
p = NLP(error_function2, x0, maxIter=1e5, maxFunEvals=1e7, lb=lb, ub=ub)
p.args.f = (I, m)
p.df = grad
p.checkdf()
r = p.solve('ralg', plot=1)
x = r.xf
logger.info(x)
xfn = 'x_' + infn[:-4] + '.txt'
np.savetxt(xfn, x)
# p = NLP(error_function2, x, maxIter=1e4, maxFunEvals=1e6, lb=lb, ub=ub)
# p.args.f = (I, m)
# r = p.solve('ralg', plot=1)
# x = r.xf
# logger.info(x)
p.maxIter=50
# p.maxfun=100
#p.df_iter = 50
p.maxTime = 4000
h_args=(h,k,l,fq,fqerr,x,z,cosmat_list,coslist,flist)
if 0:
#p.h=[pos_sum,neg_sum]
p.h=[pos_sum,neg_sum]
p.c=[chisq]
# p.h=[pos_sum,neg_sum]
p.args.h=h_args
p.args.c=h_args
p.dh=[pos_sum_grad,neg_sum_grad]
p.df=chisq_grad
if 1:
#p.h=[pos_sum,neg_sum,chisq]
p.c=[chisq]
p.h=[pos_sum,neg_sum]
p.args.h=h_args
p.args.c=h_args
p.dh=[pos_sum_grad,neg_sum_grad]
p.dc=chisq_grad
#p.dh=[pos_sum_grad,neg_sum_grad,neg_sum_grad]
p.df = S_grad
if 0:
print 'checking'
p.checkdf()
"""
this is an example of using d2f - Hesse matrix (2nd derivatives)
d2c, d2h, d2l are intended to be implemented soon
and to be connected to ALGENCAN and/or CVXOPT
and/or other NLP solvers
//Dmitrey
"""
from openopt import NLP
from numpy import cos, arange, ones, asarray, abs, zeros, diag
N = 300
M = 5
ff = lambda x: ((x-M)**4).sum()
p = NLP(ff, cos(arange(N)))
p.df = lambda x: 4*(x-M)**3
p.d2f = lambda x: diag(12*(x-M)**2)
# other valid assignment:
# p = NLP(lambda x: ((x-M)**4).sum(), cos(arange(N)), df = lambda x: 4*(x-M)**3, d2f = lambda x: diag(12*(x-M)**2))
# or
# p = NLP(x0 = cos(arange(N)), f = lambda x: ((x-M)**4).sum(), df = lambda x: 4*(x-M)**3, d2f = lambda x: diag(12*(x-M)**2))
r = p.solve('scipy_ncg')
print('objfunc val: %e' % r.ff) # it should be a small positive like 5.23656378549e-08
from openopt import NLP from numpy import cos, arange, ones, asarray, zeros, mat, array N = 50 # objfunc: # (x0-1)^4 + (x2-1)^4 + ... +(x49-1)^4 -> min (N=nVars=50) f = lambda x : ((x-1)**4).sum() x0 = cos(arange(N)) p = NLP(f, x0, maxIter = 1e3, maxFunEvals = 1e5) # f(x) gradient (optional): p.df = lambda x: 4*(x-1)**3 # lb<= x <= ub: # x4 <= -2.5 # 3.5 <= x5 <= 4.5 # all other: lb = -5, ub = +15 p.lb = -5*ones(N) p.ub = 15*ones(N) p.ub[4] = -2.5 p.lb[5], p.ub[5] = 3.5, 4.5 # Ax <= b # x0+...+xN>= 1.1*N # x9 + x19 <= 1.5 # x10+x11 >= 1.6 p.A = zeros((3, N)) p.A[0, 9] = 1
p.maxIter = 50
# p.maxfun=100
#p.df_iter = 50
p.maxTime = 4000
h_args = (h, k, l, fq, fqerr, x, z, cosmat_list, coslist, flist)
if 0:
#p.h=[pos_sum,neg_sum]
p.h = [pos_sum, neg_sum]
p.c = [chisq]
# p.h=[pos_sum,neg_sum]
p.args.h = h_args
p.args.c = h_args
p.dh = [pos_sum_grad, neg_sum_grad]
p.df = chisq_grad
if 1:
#p.h=[pos_sum,neg_sum,chisq]
p.c = [chisq]
p.h = [pos_sum, neg_sum]
p.args.h = h_args
p.args.c = h_args
p.dh = [pos_sum_grad, neg_sum_grad]
p.dc = chisq_grad
#p.dh=[pos_sum_grad,neg_sum_grad,neg_sum_grad]
p.df = S_grad
if 0:
print 'checking'
p.checkdf()
def single_shooting(model, initial_u=0.4, plot=True):
"""Run single shooting of model model with a constant u.
The function returns the optimal u.
Notes:
* Currently written specifically for VDP.
* Currently only supports one input/control signal.
Parameters:
model -- the model which is to be simulated. Only models with one control
signal is supported.
Keyword parameters:
initial_u -- the initial input U_0 used to initialize the optimization
with.
"""
assert len(model.u) == 1, "More than one control signal is " \
"not supported as of today."
start_time = model.opt_interval_get_start_time()
end_time = model.opt_interval_get_final_time()
u = model.u
u0 = N.array([initial_u])
print "Initial u:", u
gradient = None
gradient_u = None
def f(cur_u):
"""The cost evaluation function."""
model.reset()
u[:] = cur_u
print "u is", u
big_gradient, last_y, gradparams, sens = _shoot(
model, start_time, end_time)
model.set_x_p(last_y, 0)
model.set_dx_p(model.dx, 0)
model.set_u_p(model.u, 0)
cost = model.opt_eval_J()
gradient_u = cur_u.copy()
gradient = big_gradient[gradparams['u_start']:gradparams['u_end']]
print "Cost:", cost
print "Grad:", gradient
return cost
def df(cur_u):
"""The gradient of the cost function.
NOT USED right now.
"""
model.reset()
u[:] = cur_u
print "u is", u
big_gradient, last_y, gradparams, sens = _shoot(
model, start_time, end_time)
model.set_x_p(last_y, 0)
model.set_dx_p(model.dx, 0)
model.set_u_p(model.u, 0)
cost = model.opt_eval_J()
gradient_u = cur_u.copy()
gradient = big_gradient[gradparams['u_start']:gradparams['u_end']]
print "Cost:", cost
print "Grad:", gradient
return gradient
p = NLP(f, u0, maxIter=1e3, maxFunEvals=1e2)
p.df = df
if plot:
p.plot = 1
else:
p.plot = 0
p.iprint = 1
u_opt = p.solve('scipy_slsqp')
return u_opt
from openopt import NLP from numpy import cos, arange, ones, asarray, zeros, mat, array, sin, cos, sign, abs, inf N = 1500 K = 50 # 1st arg - objective function # 2nd arg - x0 p = NLP(lambda x: (abs(x-5)).sum(), 8*cos(arange(N)), iprint = 50, maxIter = 1e3) # f(x) gradient (optional): p.df = lambda x: sign(x-5) p.lb = 5*ones(N) + sin(arange(N)) - 0.1 p.ub = 5*ones(N) + sin(arange(N)) + 0.1 p.lb[:N/4] = -inf p.ub[3*N/4:] = inf #p.ub[4] = 4 #p.lb[5], p.ub[5] = 8, 15 #A = zeros((K, N)) #b = zeros(K) #for i in xrange(K): # A[i] = 1+cos(i+arange(N)) # b[i] = sin(i) #p.A = A #p.b = b #p.Aeq = zeros(p.n) #p.Aeq[100:102] = 1
"""
this is an example of using d2f - Hesse matrix (2nd derivatives)
d2c, d2h, d2l are intended to be implemented soon
and to be connected to ALGENCAN and/or CVXOPT
and/or other NLP solvers
//Dmitrey
"""
from openopt import NLP
from numpy import cos, arange, ones, asarray, abs, zeros, diag
N = 300
M = 5
ff = lambda x: ((x - M)**4).sum()
p = NLP(ff, cos(arange(N)))
p.df = lambda x: 4 * (x - M)**3
p.d2f = lambda x: diag(12 * (x - M)**2)
# other valid assignment:
# p = NLP(lambda x: ((x-M)**4).sum(), cos(arange(N)), df = lambda x: 4*(x-M)**3, d2f = lambda x: diag(12*(x-M)**2))
# or
# p = NLP(x0 = cos(arange(N)), f = lambda x: ((x-M)**4).sum(), df = lambda x: 4*(x-M)**3, d2f = lambda x: diag(12*(x-M)**2))
r = p.solve('scipy_ncg')
print('objfunc val: %e' %
r.ff) # it should be a small positive like 5.23656378549e-08
from openopt import NLP
from numpy import cos, arange, ones, asarray, zeros, mat, array, sin, cos, sign, abs, inf
N = 1500
K = 50
# 1st arg - objective function
# 2nd arg - x0
p = NLP(lambda x: (abs(x - 5)).sum(),
8 * cos(arange(N)),
iprint=50,
maxIter=1e3)
# f(x) gradient (optional):
p.df = lambda x: sign(x - 5)
p.lb = 5 * ones(N) + sin(arange(N)) - 0.1
p.ub = 5 * ones(N) + sin(arange(N)) + 0.1
p.lb[:N / 4] = -inf
p.ub[3 * N / 4:] = inf
#p.ub[4] = 4
#p.lb[5], p.ub[5] = 8, 15
#A = zeros((K, N))
#b = zeros(K)
#for i in xrange(K):
# A[i] = 1+cos(i+arange(N))
# b[i] = sin(i)
#p.A = A
