text: # Copyright (c) 2020, Manfred Moitzi
  # License: MIT License
  from typing import Iterable
  import pytest
  import math
  from ezdxf.math import (
      Matrix, detect_banded_matrix, compact_banded_matrix, BandedMatrixLU,
      gauss_vector_solver, banded_matrix,
  )
  
  BANDED_MATRIX = Matrix(matrix=[
      [3, 1, 0, 0, 0, 0, 0],
      [4, 1, 5, 0, 0, 0, 0],
      [9, 2, 6, 5, 0, 0, 0],
      [0, 3, 5, 8, 9, 0, 0],
      [0, 0, 7, 9, 3, 2, 0],
      [0, 0, 0, 3, 8, 4, 6],
      [0, 0, 0, 0, 2, 4, 4],
  ])
  TRICKY = Matrix(matrix=[
      [3, 1, 0, 0, 0, 0, 1],
      [4, 1, 5, 0, 0, 0, 0],
      [9, 2, 6, 5, 0, 0, 0],
      [0, 3, 5, 8, 9, 0, 0],
      [0, 0, 7, 9, 3, 2, 0],
      [0, 0, 0, 3, 8, 4, 6],
      [0, 1, 0, 0, 2, 4, 4],
  ])
  
  
  def are_close_vectors(v1: Iterable[float], v2: Iterable[float],
                        abs_tol: float = 1e-12):
      for i, j in zip(v1, v2):
          assert math.isclose(i, j, abs_tol=abs_tol)
  
  
  def test_detect_banded_matrix():
      m1, m2 = detect_banded_matrix(BANDED_MATRIX)
      assert (m1, m2) == (2, 1)
  
      m1, m2 = detect_banded_matrix(TRICKY, check_all=False)
      assert (m1, m2) == (2, 1)
  
      m1, m2 = detect_banded_matrix(TRICKY, check_all=True)
      assert (m1, m2) == (5, 6)
  
      assert detect_banded_matrix(Matrix(shape=(10, 10))) == (0, 0)
  
      identity = Matrix.identity(shape=(10, 10))
      assert detect_banded_matrix(identity) == (0, 0)
  
  
  def test_compact_banded_matrix():
      m1, m2 = detect_banded_matrix(BANDED_MATRIX)
      m = compact_banded_matrix(BANDED_MATRIX, m1, m2)
      assert m.ncols == 4
      assert m.nrows == 7
      assert m.col(0) == [0, 0, 9, 3, 7, 3, 2]
      assert m.col(1) == [0, 4, 2, 5, 9, 8, 4]
      assert m.col(2) == [3, 1, 6, 8, 3, 4, 4]
      assert m.col(3) == [1, 5, 5, 9, 2, 6, 0]
  
  
  B1 = [5, 3, 2, 6, 8, 2, 1]
  B2 = [9, 1, 7, 6, 4, 5, 0]
  B3 = [0, 9, 3, 7, 1, 9, 9]
  
  CHK1 = gauss_vector_solver(BANDED_MATRIX, B1)
  CHK2 = gauss_vector_solver(BANDED_MATRIX, B2)
  CHK3 = gauss_vector_solver(BANDED_MATRIX, B3)
  
  
  def test_solve_banded_matrix_vector():
      m, m1, m2 = banded_matrix(BANDED_MATRIX)
      lu = BandedMatrixLU(m, m1, m2)
      are_close_vectors(lu.solve_vector(B1), CHK1)
      are_close_vectors(lu.solve_vector(B2), CHK2)
      are_close_vectors(lu.solve_vector(B3), CHK3)
  
  
  def test_solve_banded_matrix_matrix():
      m, m1, m2 = banded_matrix(BANDED_MATRIX)
      lu = BandedMatrixLU(m, m1, m2)
      r = lu.solve_matrix(list(zip(B1, B2, B3)))
      are_close_vectors(r.col(0), CHK1)
      are_close_vectors(r.col(1), CHK2)
      are_close_vectors(r.col(2), CHK3)
  
      assert math.isclose(lu.determinant(), BANDED_MATRIX.determinant())
  
  
  if __name__ == '__main__':
      pytest.main([__file__])
  