def test_matrix_frac(self):
x = Variable(5)
M = np.asmatrix(np.random.randn(5, 5))
P = M.T*M
s = matrix_frac(x, P)
self.assertFalse(s.is_constant())
self.assertFalse(s.is_affine())
self.assertTrue(s.is_quadratic())
self.assertTrue(s.is_dcp())
def test_matrix_frac(self):
x = Variable(5)
M = np.asmatrix(np.random.randn(5, 5))
P = M.T*M
s = matrix_frac(x, P)
self.assertFalse(s.is_constant())
self.assertFalse(s.is_affine())
self.assertTrue(s.is_quadratic())
self.assertTrue(s.is_dcp())
def equivalent_forms_3(self, solver):
m = 100
n = 80
r = 70
np.random.seed(1)
A = np.random.randn(m, n)
b = np.random.randn(m)
G = np.random.randn(r, n)
h = np.random.randn(r)
# ||Ax-b||^2 = x^T (A^T A) x - 2(A^T b)^T x + ||b||^2
P = np.dot(A.T, A)
q = -2 * np.dot(A.T, b)
r = np.dot(b.T, b)
Pinv = np.linalg.inv(P)
obj3 = .1 * (matrix_frac(self.xef, Pinv) + q.T * self.xef + r)
cons = [G * self.xef == h]
p3 = Problem(Minimize(obj3), cons)
self.solve_QP(p3, solver)
self.assertAlmostEqual(p3.value, 68.1119420108, places=4)
def equivalent_forms_3(self, solver):
m = 100
n = 80
r = 70
numpy.random.seed(1)
A = numpy.random.randn(m, n)
b = numpy.random.randn(m, 1)
G = numpy.random.randn(r, n)
h = numpy.random.randn(r, 1)
# ||Ax-b||^2 = x^T (A^T A) x - 2(A^T b)^T x + ||b||^2
P = numpy.dot(A.T, A)
q = -2 * numpy.dot(A.T, b)
r = numpy.dot(b.T, b)
Pinv = numpy.linalg.inv(P)
obj3 = matrix_frac(self.xef, Pinv) + q.T * self.xef + r
cons = [G * self.xef == h]
p3 = Problem(Minimize(obj3), cons)
s = self.solve_QP(p3, solver)
self.assertAlmostEqual(s.opt_val, 681.119420108)
