text: """
  Copyright 2013 Steven Diamond, Eric Chu
  
  Licensed under the Apache License, Version 2.0 (the "License");
  you may not use this file except in compliance with the License.
  You may obtain a copy of the License at
  
      http://www.apache.org/licenses/LICENSE-2.0
  
  Unless required by applicable law or agreed to in writing, software
  distributed under the License is distributed on an "AS IS" BASIS,
  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  See the License for the specific language governing permissions and
  limitations under the License.
  """
  
  import cvxpy as cvx
  from cvxpy.expressions.variable import Variable
  import numpy as np
  from cvxpy.tests.base_test import BaseTest
  
  
  class TestSemidefiniteVariable(BaseTest):
      """ Unit tests for the expressions/shape module. """
  
      def setUp(self) -> None:
          self.X = Variable((2, 2), PSD=True)
          self.Y = Variable((2, 2))
          self.F = np.array([[1, 0], [0, -1]])
  
      def test_symm(self) -> None:
          """Test that results are symmetric.
          """
          M = Variable((3, 3), PSD=True)
          C1 = np.array([[0, 0, 1/2], [0, 0, 0], [1/2, 0, 1]])
          C2 = np.array([[0, 0, 0], [0, 0, 1/2], [0, 1/2, 1]])
          x1 = Variable((3, 3), PSD=True)
          x2 = Variable((3, 3), PSD=True)
          constraints = [M + C1 == x1]
          constraints += [M + C2 == x2]
          objective = cvx.Minimize(cvx.trace(M))
          prob = cvx.Problem(objective, constraints)
          prob.solve(solver="SCS")
          assert (M.value == M.T.value).all()
  
      def test_sdp_problem(self) -> None:
          # PSD in objective.
          obj = cvx.Minimize(cvx.sum(cvx.square(self.X - self.F)))
          p = cvx.Problem(obj, [])
          result = p.solve(solver="SCS")
          self.assertAlmostEqual(result, 1, places=4)
  
          self.assertAlmostEqual(self.X.value[0, 0], 1, places=3)
          self.assertAlmostEqual(self.X.value[0, 1], 0)
          self.assertAlmostEqual(self.X.value[1, 0], 0)
          self.assertAlmostEqual(self.X.value[1, 1], 0)
  
          # PSD in constraint.
          # ECHU: note to self, apparently this is a source of redundancy
          obj = cvx.Minimize(cvx.sum(cvx.square(self.Y - self.F)))
          p = cvx.Problem(obj, [self.Y == Variable((2, 2), PSD=True)])
          result = p.solve(solver="SCS")
          self.assertAlmostEqual(result, 1, places=2)
  
          self.assertAlmostEqual(self.Y.value[0, 0], 1, places=3)
          self.assertAlmostEqual(self.Y.value[0, 1], 0)
          self.assertAlmostEqual(self.Y.value[1, 0], 0)
          self.assertAlmostEqual(self.Y.value[1, 1], 0, places=3)
  
          # Index into semidef.
          obj = cvx.Minimize(cvx.square(self.X[0, 0] - 1) +
                             cvx.square(self.X[1, 0] - 2) +
                             # square(self.X[0,1] - 3) +
                             cvx.square(self.X[1, 1] - 4))
          p = cvx.Problem(obj, [])
          result = p.solve(solver="SCS")
          print(self.X.value)
          self.assertAlmostEqual(result, 0)
  
          self.assertAlmostEqual(self.X.value[0, 0], 1, places=2)
          self.assertAlmostEqual(self.X.value[0, 1], 2, places=2)
          self.assertAlmostEqual(self.X.value[1, 0], 2, places=2)
          self.assertAlmostEqual(self.X.value[1, 1], 4, places=3)
  