code: def generate_matrix(
      N,
      complex_=False,
      hermitian=False,
      pos_definite=False,
      sparse=False,
  ):
      M = np.random.random((N, N))
      if complex_:
          M = M + 1j * np.random.random((N, N))
  
      if hermitian:
          if pos_definite:
              if sparse:
                  i = np.arange(N)
                  j = np.random.randint(N, size=N - 2)
                  i, j = np.meshgrid(i, j)
                  M[i, j] = 0
              M = np.dot(M.conj(), M.T)
          else:
              M = np.dot(M.conj(), M.T)
              if sparse:
                  i = np.random.randint(N, size=N * N // 4)
                  j = np.random.randint(N, size=N * N // 4)
                  ind = np.nonzero(i == j)
                  j[ind] = (j[ind] + 1) % N
                  M[i, j] = 0
                  M[j, i] = 0
      else:
          if sparse:
              i = np.random.randint(N, size=N * N // 2)
              j = np.random.randint(N, size=N * N // 2)
              M[i, j] = 0
      return M
  
imports: import threading
  import itertools
  import numpy
  from numpy.testing import assert_allclose, assert_equal, suppress_warnings
  from pytest import raises
  import pytest
  from numpy import dot, conj, random
  from scipy.linalg import eig, eigh
  from scipy.sparse import csc_matrix, csr_matrix, diags, rand
  from scipy.sparse.linalg import LinearOperator, aslinearoperator
  from scipy.sparse.linalg._eigen.arpack import eigs, eigsh, arpack, ArpackNoConvergence
  from scipy._lib._gcutils import assert_deallocated, IS_PYPY
label_desc: Use image node_id 2 for calling a global function with example usage: generate_matrix(N, complex_, hermitian, pos_definite, sparse) and returns: M