def test_l1(self):
setseed(100)
m, n = 500, 250
P = normal(m, n)
q = normal(m, 1)
u1, st1 = l1(P, q)
u2, st2 = l1blas(P, q)
self.assertTrue(st1 == 'optimal')
self.assertTrue(st2 == 'optimal')
self.assertAlmostEqualLists(list(u1), list(u2), places=3)
def test_l1regls(self):
setseed(100)
m, n = 250, 500
A = normal(m, n)
b = normal(m, 1)
x, st = l1regls(A, b)
self.assertTrue(st == 'optimal')
# Check optimality conditions (list should be empty, e.g., False)
self.assertFalse([
t for t in zip(A.T * (A * x - b), x)
if abs(t[1]) > 1e-6 and abs(t[0]) > 1.0
])
def test_case3(self):
m, n = 500, 100
setseed(100)
A = normal(m, n)
b = normal(m)
x1 = variable(n)
lp1 = op(max(abs(A * x1 - b)))
lp1.solve()
self.assertTrue(lp1.status == 'optimal')
x2 = variable(n)
lp2 = op(sum(abs(A * x2 - b)))
lp2.solve()
self.assertTrue(lp2.status == 'optimal')
x3 = variable(n)
lp3 = op(
sum(max(0,
abs(A * x3 - b) - 0.75, 2 * abs(A * x3 - b) - 2.25)))
lp3.solve()
self.assertTrue(lp3.status == 'optimal')
m, n = A.size
def F(x=None, z=None):
if x is None: return 0, matrix(0.0, (n, 1))
y = A * x - b
w = sqrt(rho + y**2)
f = sum(w)
Df = div(y, w).T * A
if z is None: return f, Df
H = A.T * spdiag(z[0] * rho * (w**-3)) * A
return f, Df, H
return solvers.cp(F)['x']
setseed()
m, n = 500, 100
A = normal(m, n)
b = normal(m, 1)
xh = robls(A, b, 0.1)
try:
import pylab
except ImportError:
pass
else:
# Least-squares solution.
pylab.subplot(211)
xls = +b
lapack.gels(+A, xls)
# The norm and penalty approximation problems of section 10.5 (Examples).
from kvxopt import normal, setseed
from kvxopt.modeling import variable, op, max, sum
setseed(0)
m, n = 500, 100
A = normal(m,n)
b = normal(m)
x1 = variable(n)
prob1=op(max(abs(A*x1+b)))
prob1.solve()
x2 = variable(n)
prob2=op(sum(abs(A*x2+b)))
prob2.solve()
x3 = variable(n)
prob3=op(sum(max(0, abs(A*x3+b)-0.75, 2*abs(A*x3+b)-2.25)))
prob3.solve()
try: import pylab
except ImportError: pass
else:
pylab.subplot(311)
pylab.hist(list(A*x1.value + b), m//5)
pylab.subplot(312)
pylab.hist(list(A*x2.value + b), m//5)
pylab.subplot(313)
pylab.hist(list(A*x3.value + b), m//5)