Q = KernelMatrix(XX) # Q_ij = K(x_i, x_j)
b = -ones(nx) # b_i = 1 (in dual)
# build the constraints (y.T * x = 0.0)
# 1.0*x0 + 1.0*x1 + ... - 1.0*xN = 0.0
Aeq = y
Beq = array([0.])
# set the bounds
lb = zeros(nx)
ub = 1 * ones(nx)
_b = .1 * ones(nx) # good starting value if most solved xi should be zero
# build the constraints operator
from mystic.symbolic import linear_symbolic, solve, simplify, \
generate_solvers as solvers, generate_constraint as constraint
constrain = linear_symbolic(Aeq, Beq)
#NOTE: HACK assumes a single equation of the form: '1.0*x0 + ... = 0.0\n'
x0, rhs = constrain.strip().split(' = ')
x0, xN = x0.split(' + ', 1)
N, x0 = x0.split("*")
constrain = "{x0} = ({rhs} - ({xN}))/{N}".format(x0=x0, xN=xN, N=N, rhs=rhs)
#NOTE: end HACK (as mystic.symbolic.solve takes __forever__)
constrain = constraint(solvers(constrain))
#constrain = constraint(solvers(solve(constrain)))
from mystic import suppressed
@suppressed(1e-2)
def conserve(x):
return constrain(x)
Subject to: x[0] + 1*x[1] <= 7
-x[0] + 2*x[1] <= 4
where: 0 <= x[0] <= inf
0 <= x[1] <= 4
"""
import numpy as np
import mystic.symbolic as ms
import mystic.solvers as my
import mystic.math as mm
# generate constraints and penalty for a linear system of equations
A = np.array([[1, 1], [-1, 2]])
b = np.array([7, 4])
eqns = ms.linear_symbolic(G=A, h=b)
cons = ms.generate_constraint(ms.generate_solvers(ms.simplify(eqns)))
pens = ms.generate_penalty(ms.generate_conditions(eqns), k=1e3)
bounds = [(0., None), (0., 4.)]
# get the objective
def objective(x):
x = np.asarray(x)
return x[0]**2 + 4 * x[1]**2 - 32 * x[1] + 64
x0 = np.random.rand(2)
# compare against the exact minimum
xs = np.array([2., 3.])
Subject to: x[0] + 1*x[1] <= 7
-x[0] + 2*x[1] <= 4
where: 0 <= x[0] <= inf
0 <= x[1] <= 4
"""
import numpy as np
import mystic.symbolic as ms
import mystic.solvers as my
import mystic.math as mm
# generate constraints and penalty for a linear system of equations
A = np.array([[1, 1],[-1, 2]])
b = np.array([7,4])
eqns = ms.linear_symbolic(G=A, h=b)
cons = ms.generate_constraint(ms.generate_solvers(ms.simplify(eqns)))
pens = ms.generate_penalty(ms.generate_conditions(eqns), k=1e3)
bounds = [(0., None), (0., 4.)]
# get the objective
def objective(x):
x = np.asarray(x)
return x[0]**2 + 4*x[1]**2 - 32*x[1] + 64
x0 = np.random.rand(2)
# compare against the exact minimum
xs = np.array([2., 3.])
ys = objective(xs)
Y = concatenate([y,-y])
svr_epsilon = 3
b = Y + svr_epsilon * ones(Y.size)
# build the constraints (y.T * x = 0.0)
# 1.0*x0 + 1.0*x1 + ... - 1.0*xN = 0.0
Aeq = concatenate([ones(nx), -ones(nx)]).reshape(1,N)
Beq = array([0.])
# set the bounds
lb = zeros(N)
ub = zeros(N) + 0.5
# build the constraints operator
from mystic.symbolic import linear_symbolic, solve, \
generate_solvers as solvers, generate_constraint as constraint
constrain = linear_symbolic(Aeq,Beq)
constrain = constraint(solvers(solve(constrain,target=['x0'])))
from mystic import suppressed
@suppressed(1e-5)
def conserve(x):
return constrain(x)
from mystic.monitors import VerboseMonitor
mon = VerboseMonitor(10)
# solve for alpha
from mystic.solvers import diffev
alpha = diffev(objective, list(zip(lb,.1*ub)), args=(Q,b), npop=N*3, gtol=200, \
itermon=mon, \
ftol=1e-5, bounds=list(zip(lb,ub)), constraints=conserve, disp=1)
# profit
def fixnet(net):
def profit(x):
return sum(xi * pi for xi, pi in zip(x, net))
return profit
profit = fixnet([i.net for i in items])
# item constraints
load = [i.mass for i in items]
invest = [i.buy for i in items]
constraints = ms.linear_symbolic(G=[load, invest], h=[max_load, max_spend])
# bounds (on x)
bounds = [(0, i.limit) for i in items]
# bounds constraints
lo = 'x%s >= %s'
lo = '\n'.join(lo % (i, str(float(j[0])).lstrip('0'))
for (i, j) in enumerate(bounds))
hi = 'x%s <= %s'
hi = '\n'.join(hi % (i, str(float(j[1])).lstrip('0'))
for (i, j) in enumerate(bounds))
constraints = '\n'.join([lo, hi]).strip() + '\n' + constraints
cf = ms.generate_constraint(ms.generate_solvers(ms.simplify(constraints)),
join=mc.and_)
pf = ms.generate_penalty(ms.generate_conditions(ms.simplify(constraints)))