Example #1
0
    def test_partial_optimize_numeric_fn(self):
        x, y = Variable(1), Variable(1)
        xval = 4

        # Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
        p1 = Problem(Minimize(y), [xval + y >= 3])
        p1.solve()

        # Solve the two-stage problem via partial_optimize
        constr = [y >= -100]
        p2 = Problem(Minimize(y), [x + y >= 3] + constr)
        g = cvxpy.partial_optimize(p2, [y], [x])
        x.value = xval
        y.value = 42
        constr[0].dual_variable.value = 42
        result = g.value
        self.assertAlmostEqual(result, p1.value)
        self.assertAlmostEqual(y.value, 42)
        self.assertAlmostEqual(constr[0].dual_value, 42)

        # No variables optimized over.
        p2 = Problem(Minimize(y), [x + y >= 3])
        g = cvxpy.partial_optimize(p2, [], [x, y])
        x.value = xval
        y.value = 42
        p2.constraints[0].dual_variable.value = 42
        result = g.value
        self.assertAlmostEqual(result, y.value)
        self.assertAlmostEqual(y.value, 42)
        self.assertAlmostEqual(p2.constraints[0].dual_value, 42)
Example #2
0
    def test_assign_var_value(self):
        """Test assigning a value to a variable.
        """
        # Scalar variable.
        a = Variable()
        a.value = 1
        self.assertEqual(a.value, 1)
        with self.assertRaises(Exception) as cm:
            a.value = [2, 1]
        self.assertEqual(str(cm.exception),
                         "Invalid dimensions (2, 1) for Variable value.")

        # Test assigning None.
        a.value = 1
        a.value = None
        assert a.value is None

        # Vector variable.
        x = Variable(2)
        x.value = [2, 1]
        self.assertItemsAlmostEqual(x.value, [2, 1])
        # Matrix variable.
        A = Variable(3, 2)
        A.value = np.ones((3, 2))
        self.assertItemsAlmostEqual(A.value, np.ones((3, 2)))
Example #3
0
    def test_partial_optimize_numeric_fn(self):
        x, y = Variable(1), Variable(1)
        xval = 4

        # Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
        p1 = Problem(Minimize(y), [xval+y >= 3])
        p1.solve()

        # Solve the two-stage problem via partial_optimize
        constr = [y >= -100]
        p2 = Problem(Minimize(y), [x+y >= 3] + constr)
        g = cvxpy.partial_optimize(p2, [y], [x])
        x.value = xval
        y.value = 42
        constr[0].dual_variable.value = 42
        result = g.value
        self.assertAlmostEqual(result, p1.value)
        self.assertAlmostEqual(y.value, 42)
        self.assertAlmostEqual(constr[0].dual_value, 42)

        # No variables optimized over.
        p2 = Problem(Minimize(y), [x+y >= 3])
        g = cvxpy.partial_optimize(p2, [], [x, y])
        x.value = xval
        y.value = 42
        p2.constraints[0].dual_variable.value = 42
        result = g.value
        self.assertAlmostEqual(result, y.value)
        self.assertAlmostEqual(y.value, 42)
        self.assertAlmostEqual(p2.constraints[0].dual_value, 42)
Example #4
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    def test_affine(self):
        """Test grad for affine atoms.
        """
        expr = -self.a
        self.a.value = 2
        self.assertAlmostEquals(expr.grad[self.a], -1)

        expr = -(self.x)
        self.x.value = [3, 4]
        val = np.zeros((2, 2)) - np.diag([1, 1])
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)

        expr = -(self.A)
        self.A.value = [[1, 2], [3, 4]]
        val = np.zeros((4, 4)) - np.diag([1, 1, 1, 1])
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)

        expr = self.A[0, 1]
        self.A.value = [[1, 2], [3, 4]]
        val = np.zeros((4, 1))
        val[2] = 1
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)

        z = Variable(3)
        expr = vstack(self.x, z)
        self.x.value = [1, 2]
        z.value = [1, 2, 3]
        val = np.zeros((2, 5))
        val[:, 0:2] = np.eye(2)
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)

        val = np.zeros((3, 5))
        val[:, 2:] = np.eye(3)
        self.assertItemsAlmostEqual(expr.grad[z].todense(), val)
Example #5
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    def test_affine(self):
        """Test grad for affine atoms.
        """
        expr = -self.a
        self.a.value = 2
        self.assertAlmostEquals(expr.grad[self.a], -1)

        expr = -(self.x)
        self.x.value = [3,4]
        val = np.zeros((2,2)) - np.diag([1,1])
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)

        expr = -(self.A)
        self.A.value = [[1,2], [3,4]]
        val = np.zeros((4,4)) - np.diag([1,1,1,1])
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)

        expr = self.A[0,1]
        self.A.value = [[1,2], [3,4]]
        val = np.zeros((4,1))
        val[2] = 1
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)

        z = Variable(3)
        expr = vstack(self.x, z)
        self.x.value = [1,2]
        z.value = [1,2,3]
        val = np.zeros((2,5))
        val[:,0:2] = np.eye(2)
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)

        val = np.zeros((3,5))
        val[:,2:] = np.eye(3)
        self.assertItemsAlmostEqual(expr.grad[z].todense(), val)
Example #6
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    def test_log_det(self):
        """Test gradient for log_det
        """
        expr = log_det(self.A)
        self.A.value = 2 * np.eye(2)
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(),
                                    1.0 / 2 * np.eye(2))

        mat = np.matrix([[1, 2], [3, 5]])
        self.A.value = mat.T * mat
        val = np.linalg.inv(self.A.value).T
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)

        self.A.value = np.zeros((2, 2))
        self.assertAlmostEqual(expr.grad[self.A], None)

        self.A.value = -np.matrix([[1, 2], [3, 4]])
        self.assertAlmostEqual(expr.grad[self.A], None)

        K = Variable(8, 8)
        expr = log_det(K[[1, 2]][:, [1, 2]])
        K.value = np.eye(8)
        val = np.zeros((8, 8))
        val[[1, 2], [1, 2]] = 1
        self.assertItemsAlmostEqual(expr.grad[K].todense(), val)
Example #7
0
    def test_min_elemwise(self):
        """Test domain for min_elemwise.
        """
        b = Variable()
        expr = min_elemwise(self.a, b)
        self.a.value = 2
        b.value = 4
        self.assertAlmostEqual(expr.grad[self.a], 1)
        self.assertAlmostEqual(expr.grad[b], 0)

        self.a.value = 3
        b.value = 0
        self.assertAlmostEqual(expr.grad[self.a], 0)
        self.assertAlmostEqual(expr.grad[b], 1)

        self.a.value = -1
        b.value = 2
        self.assertAlmostEqual(expr.grad[self.a], 1)
        self.assertAlmostEqual(expr.grad[b], 0)

        y = Variable(2)
        expr = min_elemwise(self.x, y)
        self.x.value = [3, 4]
        y.value = [5, -5]
        val = np.zeros((2, 2)) + np.diag([1, 0])
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
        val = np.zeros((2, 2)) + np.diag([0, 1])
        self.assertItemsAlmostEqual(expr.grad[y].todense(), val)

        expr = min_elemwise(self.x, y)
        self.x.value = [-1e-9, 4]
        y.value = [1, 4]
        val = np.zeros((2, 2)) + np.diag([1, 1])
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
        val = np.zeros((2, 2)) + np.diag([0, 0])
        self.assertItemsAlmostEqual(expr.grad[y].todense(), val)

        expr = min_elemwise(self.A, self.B)
        self.A.value = [[1, 2], [3, 4]]
        self.B.value = [[5, 1], [3, 2.3]]
        div = (self.A.value / self.B.value).A.ravel(order='F')
        val = np.zeros((4, 4)) + np.diag([1, 0, 1, 0])
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
        val = np.zeros((4, 4)) + np.diag([0, 1, 0, 1])
        self.assertItemsAlmostEqual(expr.grad[self.B].todense(), val)
Example #8
0
    def test_assign_var_value(self):
        """Test assigning a value to a variable.
        """
        # Scalar variable.
        a = Variable()
        a.value = 1
        self.assertEqual(a.value, 1)
        with self.assertRaises(Exception) as cm:
            a.value = [2, 1]
        self.assertEqual(str(cm.exception), "Invalid dimensions (2, 1) for Variable value.")

        # Test assigning None.
        a.value = 1
        a.value = None
        assert a.value is None

        # Vector variable.
        x = Variable(2)
        x.value = [2, 1]
        self.assertItemsAlmostEqual(x.value, [2, 1])
        # Matrix variable.
        A = Variable(3, 2)
        A.value = np.ones((3, 2))
        self.assertItemsAlmostEqual(A.value, np.ones((3, 2)))

        # Test assigning negative val to nonnegative variable.
        x = NonNegative()
        with self.assertRaises(Exception) as cm:
            x.value = -2
        self.assertEqual(str(cm.exception), "Invalid sign for NonNegative value.")

        # Small negative values are rounded to 0.
        x.value = -1e-8
        self.assertEqual(x.value, 0)
Example #9
0
    def test_min_elemwise(self):
        """Test domain for min_elemwise.
        """
        b = Variable()
        expr = min_elemwise(self.a, b)
        self.a.value = 2
        b.value = 4
        self.assertAlmostEqual(expr.grad[self.a], 1)
        self.assertAlmostEqual(expr.grad[b], 0)

        self.a.value = 3
        b.value = 0
        self.assertAlmostEqual(expr.grad[self.a], 0)
        self.assertAlmostEqual(expr.grad[b], 1)

        self.a.value = -1
        b.value = 2
        self.assertAlmostEqual(expr.grad[self.a], 1)
        self.assertAlmostEqual(expr.grad[b], 0)

        y = Variable(2)
        expr = min_elemwise(self.x, y)
        self.x.value = [3, 4]
        y.value = [5, -5]
        val = np.zeros((2, 2)) + np.diag([1, 0])
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
        val = np.zeros((2, 2)) + np.diag([0, 1])
        self.assertItemsAlmostEqual(expr.grad[y].todense(), val)

        expr = min_elemwise(self.x, y)
        self.x.value = [-1e-9, 4]
        y.value = [1, 4]
        val = np.zeros((2, 2)) + np.diag([1, 1])
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
        val = np.zeros((2, 2)) + np.diag([0, 0])
        self.assertItemsAlmostEqual(expr.grad[y].todense(), val)

        expr = min_elemwise(self.A, self.B)
        self.A.value = [[1, 2], [3, 4]]
        self.B.value = [[5, 1], [3, 2.3]]
        div = (self.A.value/self.B.value).A.ravel(order='F')
        val = np.zeros((4, 4)) + np.diag([1, 0, 1, 0])
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
        val = np.zeros((4, 4)) + np.diag([0, 1, 0, 1])
        self.assertItemsAlmostEqual(expr.grad[self.B].todense(), val)
Example #10
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 def test_assign_var_value(self):
     """Test assigning a value to a variable.
     """
     # Scalar variable.
     a = Variable()
     a.value = 1
     self.assertEqual(a.value, 1)
     with self.assertRaises(Exception) as cm:
         a.value = [2, 1]
     self.assertEqual(str(cm.exception), "Invalid dimensions (2, 1) for Variable value.")
     # Vector variable.
     x = Variable(2)
     x.value = [2, 1]
     self.assertItemsAlmostEqual(x.value, [2, 1])
     # Matrix variable.
     A = Variable(3, 2)
     A.value = np.ones((3, 2))
     self.assertItemsAlmostEqual(A.value, np.ones((3, 2)))
Example #11
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    def test_kl_div(self):
        """Test domain for kl_div.
        """
        b = Variable()
        expr = kl_div(self.a, b)
        self.a.value = 2
        b.value = 4
        self.assertAlmostEqual(expr.grad[self.a], np.log(2 / 4))
        self.assertAlmostEqual(expr.grad[b], 1 - (2 / 4))

        self.a.value = 3
        b.value = 0
        self.assertAlmostEqual(expr.grad[self.a], None)
        self.assertAlmostEqual(expr.grad[b], None)

        self.a.value = -1
        b.value = 2
        self.assertAlmostEqual(expr.grad[self.a], None)
        self.assertAlmostEqual(expr.grad[b], None)

        y = Variable(2)
        expr = kl_div(self.x, y)
        self.x.value = [3, 4]
        y.value = [5, 8]
        val = np.zeros((2, 2)) + np.diag(np.log([3, 4]) - np.log([5, 8]))
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
        val = np.zeros((2, 2)) + np.diag([1 - 3 / 5, 1 - 4 / 8])
        self.assertItemsAlmostEqual(expr.grad[y].todense(), val)

        expr = kl_div(self.x, y)
        self.x.value = [-1e-9, 4]
        y.value = [1, 2]
        self.assertAlmostEqual(expr.grad[self.x], None)
        self.assertAlmostEqual(expr.grad[y], None)

        expr = kl_div(self.A, self.B)
        self.A.value = [[1, 2], [3, 4]]
        self.B.value = [[5, 1], [3.5, 2.3]]
        div = (self.A.value / self.B.value).A.ravel(order='F')
        val = np.zeros((4, 4)) + np.diag(np.log(div))
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
        val = np.zeros((4, 4)) + np.diag(1 - div)
        self.assertItemsAlmostEqual(expr.grad[self.B].todense(), val)
Example #12
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    def test_kl_div(self):
        """Test domain for kl_div.
        """
        b = Variable()
        expr = kl_div(self.a, b)
        self.a.value = 2
        b.value = 4
        self.assertAlmostEqual(expr.grad[self.a], np.log(2/4))
        self.assertAlmostEqual(expr.grad[b], 1 - (2/4))

        self.a.value = 3
        b.value = 0
        self.assertAlmostEqual(expr.grad[self.a], None)
        self.assertAlmostEqual(expr.grad[b], None)

        self.a.value = -1
        b.value = 2
        self.assertAlmostEqual(expr.grad[self.a], None)
        self.assertAlmostEqual(expr.grad[b], None)

        y = Variable(2)
        expr = kl_div(self.x, y)
        self.x.value = [3, 4]
        y.value = [5, 8]
        val = np.zeros((2, 2)) + np.diag(np.log([3, 4]) - np.log([5, 8]))
        self.assertItemsAlmostEqual(expr.grad[self.x].todense(), val)
        val = np.zeros((2, 2)) + np.diag([1 - 3/5, 1 - 4/8])
        self.assertItemsAlmostEqual(expr.grad[y].todense(), val)

        expr = kl_div(self.x, y)
        self.x.value = [-1e-9, 4]
        y.value = [1, 2]
        self.assertAlmostEqual(expr.grad[self.x], None)
        self.assertAlmostEqual(expr.grad[y], None)

        expr = kl_div(self.A, self.B)
        self.A.value = [[1, 2], [3, 4]]
        self.B.value = [[5, 1], [3.5, 2.3]]
        div = (self.A.value/self.B.value).A.ravel(order='F')
        val = np.zeros((4, 4)) + np.diag(np.log(div))
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)
        val = np.zeros((4, 4)) + np.diag(1 - div)
        self.assertItemsAlmostEqual(expr.grad[self.B].todense(), val)
Example #13
0
    def test_partial_optimize_numeric_fn(self):
        x,y = Variable(1), Variable(1)
        xval = 4

        # Solve the (simple) two-stage problem by "combining" the two stages (i.e., by solving a single linear program)
        p1 = Problem(Minimize(y), [xval+y>=3])
        p1.solve()

        # Solve the two-stage problem via partial_optimize
        p2 = Problem(Minimize(y), [x+y>=3])
        g = partial_optimize(p2, [y], [x])
        x.value = xval
        result = g.value
        self.assertAlmostEqual(result, p1.value)
Example #14
0
    def test_log_det(self):
        """Test gradient for log_det
        """
        expr = log_det(self.A)
        self.A.value = 2*np.eye(2)
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), 1.0/2*np.eye(2))

        mat = np.matrix([[1, 2], [3, 5]])
        self.A.value = mat.T*mat
        val = np.linalg.inv(self.A.value).T
        self.assertItemsAlmostEqual(expr.grad[self.A].todense(), val)

        self.A.value = np.zeros((2, 2))
        self.assertAlmostEqual(expr.grad[self.A], None)

        self.A.value = -np.matrix([[1, 2], [3, 4]])
        self.assertAlmostEqual(expr.grad[self.A], None)

        K = Variable(8, 8)
        expr = log_det(K[[1,2]][:,[1,2]])
        K.value = np.eye(8)
        val = np.zeros((8,8))
        val[[1,2],[1,2]] = 1
        self.assertItemsAlmostEqual(expr.grad[K].todense(), val)