def test_basic_no_gsl(self):
import sys
sys.modules['gsl'] = None
import kvxopt
kvxopt.normal(4, 8)
kvxopt.uniform(4, 8)
step = 1.0
while 1-step*max(y) < 0: step *= BETA
while True:
if -sum(log(1-step*y)) < ALPHA*step*lam: break
step *= BETA
x += step*v
# Generate an analytic centering problem
#
# -b1 <= Ar*x <= b2
#
# with random mxn Ar and random b1, b2.
m, n = 500, 500
Ar = normal(m,n);
A = matrix([Ar, -Ar])
b = uniform(2*m,1)
x, ntdecrs = acent(A, b)
try:
import pylab
except ImportError:
pass
else:
pylab.semilogy(range(len(ntdecrs)), ntdecrs, 'o',
range(len(ntdecrs)), ntdecrs, '-')
pylab.xlabel('Iteration number')
pylab.ylabel('Newton decrement')
pylab.show()
# The robust LP example of section 10.5 (Examples).
from kvxopt import normal, uniform
from kvxopt.modeling import variable, dot, op, sum
from kvxopt.blas import nrm2
m, n = 500, 100
A = normal(m, n)
b = uniform(m)
c = normal(n)
x = variable(n)
op(dot(c, x), A * x + sum(abs(x)) <= b).solve()
x2 = variable(n)
y = variable(n)
op(dot(c, x2), [A * x2 + sum(y) <= b, -y <= x2, x2 <= y]).solve()
print("\nDifference between two solutions %e" % nrm2(x.value - x2.value))
S = matrix(0.0, (m, m))
v = matrix(0.0, (m, 1))
def Fkkt(x, z, W):
ds = (2.0 * div(1 + x**2, (1 - x**2)**2))**-0.5
Asc = A * spdiag(ds)
blas.syrk(Asc, S)
S[::m + 1] += 1.0
lapack.potrf(S)
a = z[0]
def g(x, y, z):
x[:] = mul(x, ds) / a
blas.gemv(Asc, x, v)
lapack.potrs(S, v)
blas.gemv(Asc, v, x, alpha=-1.0, beta=1.0, trans='T')
x[:] = mul(x, ds)
return g
return solvers.cp(F, kktsolver=Fkkt)['x']
m, n = 200, 2000
setseed()
A = normal(m, n)
x = uniform(n, 1)
b = A * x
x = l2ac(A, b)