code: def test_rowspace_dense(self):
      A = np.array(
          [
              [1, 2, 3, 4, 0, 5, 0, 7],
              [0, 8, 7, 0, 1, 5, 9, 0],
              [1, 0, 0, 0, 0, 1, 2, 3],
          ]
      )
      test_points = ([1, 2, 3], [1, 10, 3], [1.12, 10, 0])
  
      for method in available_dense_methods:
          _, _, Y = projections(A, method)
          for z in test_points:
              # Test if x is solution of A x = z
              x = Y.matvec(z)
              assert_array_almost_equal(A.dot(x), z)
              # Test if x is in the return row space of A
              A_ext = np.vstack((A, x))
              assert_equal(
                  np.linalg.matrix_rank(A), np.linalg.matrix_rank(A_ext)
              )
  
imports: from __future__ import division, print_function, absolute_import
  import numpy
  import scipy.linalg
  from scipy.sparse import csc_matrix
  from scipy.optimize._trustregion_constr.projections import projections, orthogonality
  from numpy.testing import TestCase, assert_array_almost_equal, assert_array_equal, assert_array_less, assert_raises, assert_equal, assert_, run_module_suite, assert_allclose, assert_warns, dec
  import pytest
  import sys
  import platform
label_desc: Use image node_id 8 for calling the TestProjections obj's underlying member method code with example usage: obj.test_rowspace_dense() without return types