def test_basic(self):
import cvxopt
a = cvxopt.matrix([1.0, 2.0, 3.0])
assert list(a) == [1.0, 2.0, 3.0]
b = cvxopt.matrix([3.0, -2.0, -1.0])
c = cvxopt.spmatrix([1.0, -2.0, 3.0], [0, 2, 4], [1, 2, 4], (6, 5))
d = cvxopt.spmatrix([1.0, 2.0, 5.0], [0, 1, 2], [0, 0, 0], (3, 1))
e = cvxopt.mul(a, b)
self.assertEqualLists(e, [3.0, -4.0, -3.0])
self.assertAlmostEqualLists(list(cvxopt.div(a, b)),
[1.0 / 3.0, -1.0, -3.0])
self.assertAlmostEqual(cvxopt.div([1.0, 2.0, 0.25]), 2.0)
self.assertEqualLists(list(cvxopt.min(a, b)), [1.0, -2.0, -1.0])
self.assertEqualLists(list(cvxopt.max(a, b)), [3.0, 2.0, 3.0])
self.assertEqual(cvxopt.max([1.0, 2.0]), 2.0)
self.assertEqual(cvxopt.max(a), 3.0)
self.assertEqual(cvxopt.max(c), 3.0)
self.assertEqual(cvxopt.max(d), 5.0)
self.assertEqual(cvxopt.min([1.0, 2.0]), 1.0)
self.assertEqual(cvxopt.min(a), 1.0)
self.assertEqual(cvxopt.min(c), -2.0)
self.assertEqual(cvxopt.min(d), 1.0)
self.assertEqual(len(c.imag()), 0)
with self.assertRaises(OverflowError):
cvxopt.matrix(1.0, (32780 * 4, 32780))
with self.assertRaises(OverflowError):
cvxopt.spmatrix(1.0, (0, 32780 * 4), (0, 32780)) + 1
def test_basic(self):
import cvxopt
a = cvxopt.matrix([1.0,2.0,3.0])
b = cvxopt.matrix([3.0,-2.0,-1.0])
c = cvxopt.spmatrix([1.0,-2.0,3.0],[0,2,4],[1,2,4],(6,5))
d = cvxopt.spmatrix([1.0,2.0,5.0],[0,1,2],[0,0,0],(3,1))
self.assertEqualLists(list(cvxopt.mul(a,b)),[3.0,-4.0,-3.0])
self.assertAlmostEqualLists(list(cvxopt.div(a,b)),[1.0/3.0,-1.0,-3.0])
self.assertAlmostEqual(cvxopt.div([1.0,2.0,0.25]),2.0)
self.assertEqualLists(list(cvxopt.min(a,b)),[1.0,-2.0,-1.0])
self.assertEqualLists(list(cvxopt.max(a,b)),[3.0,2.0,3.0])
self.assertEqual(cvxopt.max([1.0,2.0]),2.0)
self.assertEqual(cvxopt.max(a),3.0)
self.assertEqual(cvxopt.max(c),3.0)
self.assertEqual(cvxopt.max(d),5.0)
self.assertEqual(cvxopt.min([1.0,2.0]),1.0)
self.assertEqual(cvxopt.min(a),1.0)
self.assertEqual(cvxopt.min(c),-2.0)
self.assertEqual(cvxopt.min(d),1.0)
def F(x=None, z=None): if x is None: x0 = cv.matrix([(1.-float(k)/n)/(n-1)]*n*n,(n*n,1)) for j in range(n): x0[j*n+j] = float(k)/n return (0,x0) if cv.min(x) < 0.: return None f = coef*x**h Df = cv.mul(h*coef,(x.T)**(h-1)) if z is None: return (f,Df) H = cv.spdiag(cv.mul(z[0]*h*(h-1)*coef.T,x**(h-2))) return (f,Df,H)
def test_basic(self):
import cvxopt
a = cvxopt.matrix([1.0,2.0,3.0])
b = cvxopt.matrix([3.0,-2.0,-1.0])
c = cvxopt.spmatrix([1.0,-2.0,3.0],[0,2,4],[1,2,4],(6,5))
d = cvxopt.spmatrix([1.0,2.0,5.0],[0,1,2],[0,0,0],(3,1))
self.assertEqualLists(list(cvxopt.mul(a,b)),[3.0,-4.0,-3.0])
self.assertAlmostEqualLists(list(cvxopt.div(a,b)),[1.0/3.0,-1.0,-3.0])
self.assertAlmostEqual(cvxopt.div([1.0,2.0,0.25]),2.0)
self.assertEqualLists(list(cvxopt.min(a,b)),[1.0,-2.0,-1.0])
self.assertEqualLists(list(cvxopt.max(a,b)),[3.0,2.0,3.0])
self.assertEqual(cvxopt.max([1.0,2.0]),2.0)
self.assertEqual(cvxopt.max(a),3.0)
self.assertEqual(cvxopt.max(c),3.0)
self.assertEqual(cvxopt.max(d),5.0)
self.assertEqual(cvxopt.min([1.0,2.0]),1.0)
self.assertEqual(cvxopt.min(a),1.0)
self.assertEqual(cvxopt.min(c),-2.0)
self.assertEqual(cvxopt.min(d),1.0)
with self.assertRaises(OverflowError):
cvxopt.matrix(1.0,(32780*4,32780))
with self.assertRaises(OverflowError):
cvxopt.spmatrix(1.0,(0,32780*4),(0,32780))+1
def KL(ww=None, zz=None):
if ww is None:
return 0, cvx.matrix(1., (self.k, 1))
if cvx.min(ww) <= 0.:
return None
xx = cvx.matrix(x.T)
HHww = HH * ww
kl = sum(
cvx.mul(xx,
cvx.log(cvx.div(xx, HHww)) + HHww - xx))
Dkl = (ep.T - cvx.div(xx.T, HHww.T)) * HH
if zz is None:
return kl, Dkl
else:
D2kl = HH.T * cvx.spdiag(
cvx.div(zz[0] * xx, HHww**2)) * HH
return kl, Dkl, D2kl
def estimate_range(A, xl, xu):
'''
Estimate the range of Ax, where xl <= x <= xu
Mathematically, the lower and upper bounds are:
'''
# Decide if A is sparse
# if 'sp' in str(type(A)) or 'sparse' in str(type(A)):
# pass
# Efficient, exploit the sparsity of A
Apos = copy(A)
Aneg = copy(A)
# For sparse matrices
Apos.V = cvxopt.max(Apos.V, 0)
Aneg.V = cvxopt.min(Aneg.V, 0)
# pdb.set_trace()
bl = Apos * xl + Aneg * xu
bu = Apos * xu + Aneg * xl
# Relatively efficient, but dense matrix means overhead
# bl = cvxopt.min(A,0)*xu + cvxopt.max(A,0)*xl
# bu = cvxopt.min(A,0)*xl + cvxopt.max(A,0)*xu
# This version is less efficient
# row, col = A.size
# bl = matrix(10.0,size=(row,1))
# bu = matrix(10.0,size=(row,1))
# for i in range(row):
# for j in range(col):
# if A[i,j] > 0.0:
# bl[i] += A[i,j]*xl[j]
# bu[i] += A[i,j]*xu[j]
# elif A[i] < 0.0:
# print A.size, xl.size, xu.size, i,j
# bl[i] += A[i,j]*xu[j]
# bu[i] += A[i,j]*xl[j]
return (bl, bu)