diff --git a/tests/80_linalg.py b/tests/80_linalg.py index 5caeda7a..1c5cbe03 100644 --- a/tests/80_linalg.py +++ b/tests/80_linalg.py @@ -1,7 +1,91 @@ -from linalg import mat3x3, vec2, vec3 +from linalg import mat3x3, vec2, vec3, vec4 import random import sys +import math + + +# test vec2-------------------------------------------------------------------- + +def rotated_vec2(vec_2, radians: float): + cos_theta = math.cos(radians) + sin_theta = math.sin(radians) + new_x = vec_2.x * cos_theta - vec_2.y * sin_theta + new_y = vec_2.x * sin_theta + vec_2.y * cos_theta + return vec2(new_x, new_y) + +# 生成随机测试目标 +min_num = -10.0 +max_num = 10.0 +test_vec2 = vec2(*tuple([random.uniform(min_num, max_num) for _ in range(2)])) +static_test_vec2_float = vec2(3.1886954323, -1098399.59932453432) +static_test_vec2_int = vec2(278, -13919730938747) + +# test __repr__ +assert str(static_test_vec2_float) == 'vec2(3.1887, -1.0984e+06)' +assert str(static_test_vec2_int) == 'vec2(278, -1.39197e+13)' + +# test copy +element_name_list = [e for e in dir(test_vec2) if e in 'x,y,z,w'] +element_value_list = [getattr(test_vec2, attr) for attr in element_name_list] +copy_element_value_list = [getattr(test_vec2.copy(), attr) for attr in element_name_list] +assert element_value_list == copy_element_value_list + +# test rotate +test_vec2_copy = test_vec2.copy() +radians = random.uniform(-10*math.pi, 10*math.pi) +test_vec2_copy = rotated_vec2(test_vec2_copy, radians) +assert test_vec2.rotate(radians).__dict__ == test_vec2_copy.__dict__ + + +# test vec3-------------------------------------------------------------------- +# 生成随机测试目标 +min_num = -10.0 +max_num = 10.0 +test_vec3 = vec3(*tuple([random.uniform(min_num, max_num) for _ in range(3)])) +static_test_vec3_float = vec3(3.1886954323, -1098399.59932453432, 9.00000000000002765) +static_test_vec3_int = vec3(278, -13919730938747, 1364223456756456) + +# test __repr__ +assert str(static_test_vec3_float) == 'vec3(3.1887, -1.0984e+06, 9)' +assert str(static_test_vec3_int) == 'vec3(278, -1.39197e+13, 1.36422e+15)' + +# test __getnewargs__ +element_name_list = [e for e in dir(test_vec3) if e in 'x,y,z,w'] +element_value_list = [getattr(test_vec3, attr) for attr in element_name_list] +assert tuple(element_value_list) == test_vec3.__getnewargs__() + +# test copy +element_name_list = [e for e in dir(test_vec3) if e in 'x,y,z,w'] +element_value_list = [getattr(test_vec3, attr) for attr in element_name_list] +copy_element_value_list = [getattr(test_vec3.copy(), attr) for attr in element_name_list] +assert element_value_list == copy_element_value_list + +# test vec4-------------------------------------------------------------------- +# 生成随机测试目标 +min_num = -10.0 +max_num = 10.0 +test_vec4 = vec4(*tuple([random.uniform(min_num, max_num) for _ in range(4)])) +static_test_vec4_float = vec4(3.1886954323, -1098399.59932453432, 9.00000000000002765, 4565400000000.0000000045) +static_test_vec4_int = vec4(278, -13919730938747, 1364223456756456, -37) + +# test __repr__ +assert str(static_test_vec4_float) == 'vec4(3.1887, -1.0984e+06, 9, 4.5654e+12)' +assert str(static_test_vec4_int) == 'vec4(278, -1.39197e+13, 1.36422e+15, -37)' + +# test __getnewargs__ +element_name_list = [e for e in dir(test_vec4) if e in 'x,y,z,w'] +element_value_list = [getattr(test_vec4, attr) for attr in element_name_list] +assert tuple(element_value_list) == test_vec4.__getnewargs__() + +# test copy +element_name_list = [e for e in dir(test_vec4) if e in 'x,y,z,w'] +element_value_list = [getattr(test_vec4, attr) for attr in element_name_list] +copy_element_value_list = [getattr(test_vec4.copy(), attr) for attr in element_name_list] +assert element_value_list == copy_element_value_list + + +# test mat3x3-------------------------------------------------------------------- def mat_round(mat, pos): ''' 对mat的副本的每一个元素执行round(element, pos)，返回副本 @@ -34,16 +118,54 @@ def get_col(mat, col_index): ret.append(mat[i, col_index]) return ret +def calculate_inverse(matrix): + ''' + 返回逆矩阵 + ''' + # 获取矩阵的行数和列数 + rows = len(matrix) + cols = len(matrix[0]) + # 确保矩阵是方阵 + if rows != cols: + raise ValueError("输入矩阵必须是方阵") + # 构建单位矩阵 + identity = [[1 if i == j else 0 for j in range(cols)] for i in range(rows)] + # 将单位矩阵与输入矩阵进行初等行变换 + augmented_matrix = [row + identity[i] for i, row in enumerate(matrix)] + # 初等行变换，将输入矩阵转化为单位矩阵，同时在另一边进行相同的行变换 + for i in range(cols): + pivot = augmented_matrix[i][i] + if pivot == 0: + raise ValueError("输入矩阵不可逆") + scale_row(augmented_matrix, i, 1/pivot) + for j in range(cols): + if j != i: + scale = augmented_matrix[j][i] + row_operation(augmented_matrix, j, i, -scale) + # 提取逆矩阵 + inverse_matrix = [row[cols:] for row in augmented_matrix] + return inverse_matrix +def scale_row(matrix, row, scale): + matrix[row] = [element * scale for element in matrix[row]] + +def row_operation(matrix, target_row, source_row, scale): + matrix[target_row] = [target_element + scale * source_element for target_element, source_element in zip(matrix[target_row], matrix[source_row])] # 生成随机测试目标 min_num = -10.0 max_num = 10.0 test_mat = mat3x3([[random.uniform(min_num, max_num) for _ in range(3)] for _ in range(3)]) -# test_mat = mat3x3([ -# [1, 2, 3], -# [4, 5, 6], -# [7, 8, 9]] -# ) +static_test_mat_float= mat3x3([ + [7.264189733952545, -5.432187523625671, 1.8765304152872613], + [-2.4910524352374734, 8.989660807513068, -0.7168824333280513], + [9.558042327611506, -3.336280256662496, 4.951381528057387]] + ) + +static_test_mat_int = mat3x3([ + [1, 2, 3], + [4, 5, 6], + [7, 8, 9]] + ) # test incorrect number of parameters is passed for i in range(20): @@ -95,6 +217,18 @@ element_name_list = [e for e in dir(test_mat) if e[:2] != '__' and e[0] == '_'] for i, element in enumerate([getattr(test_mat, e) for e in element_name_list]): assert test_mat.__getitem__((int(i/3), i%3)) == element +try: + test_mat[1,2,3] + raise Exception('未能触发错误拦截, 此处应当报错 IndexError("index out of range")') +except: + pass + +try: + test_mat[-1][4] + raise Exception('未能触发错误拦截, 此处应当报错 IndexError("index out of range")') +except: + pass + # test __setitem__ test_mat_copy = test_mat.copy() element_name_list = [e for e in dir(test_mat_copy) if e[:2] != '__' and e[0] == '_'] @@ -102,6 +236,18 @@ for i, element in enumerate([getattr(test_mat_copy, e) for e in element_name_lis test_mat_copy.__setitem__((int(i/3), i%3), list(range(9))[i]) assert test_mat_copy == mat3x3([[0,1,2], [3,4,5], [6,7,8]]) +try: + test_mat[1,2,3] = 1 + raise Exception('未能触发错误拦截, 此处应当报错 TypeError("Mat3x3.__setitem__ takes a tuple of 2 integers")') +except: + pass + +try: + test_mat[-1][4] = 1 + raise Exception('未能触发错误拦截, 此处应当报错 IndexError("index out of range")') +except: + pass + # test __add__ test_mat_copy = test_mat.copy() ones = mat3x3() @@ -148,13 +294,105 @@ assert result_mat == correct_result_mat # test determinant test_mat_copy = test_mat.copy() +list_mat = [[0,0,0], [0,0,0], [0,0,0]] for i in range(3): for j in range(3): - test_mat_copy[i, j] = test_mat[j, i] - -# # test __repr__ -# test_mat_copy = test_mat.copy() -# print(test_mat_copy[0,0]) -# assert test_mat_copy.__repr__() == f'mat3x3([[{test_mat_copy[0,0].round(4)}, {test_mat_copy[1,0].round(4)}, {test_mat_copy[2,0].round(4)}],\n [{test_mat_copy[0,1].round(4)}, {test_mat_copy[1,1].round(4)}, {test_mat_copy[2,1].round(4)}],\n [{test_mat_copy[0,2].round(4)}, {test_mat_copy[1,2].round(4)}, {test_mat_copy[2,2].round(4)}]])' + list_mat[i][j] = test_mat[i, j] +determinant = list_mat[0][0]*(list_mat[1][1]*list_mat[2][2] - list_mat[1][2]*list_mat[2][1]) - list_mat[0][1]*(list_mat[1][0]*list_mat[2][2] - list_mat[1][2]*list_mat[2][0]) + list_mat[0][2]*(list_mat[1][0]*list_mat[2][1] - list_mat[1][1]*list_mat[2][0]) +assert str(determinant)[:6] == str(test_mat_copy.determinant())[:6] + +# test __repr__ +assert str(static_test_mat_float) == 'mat3x3([[7.2642, -5.4322, 1.8765],\n [-2.4911, 8.9897, -0.7169],\n [9.5580, -3.3363, 4.9514]])' +assert str(static_test_mat_int) == 'mat3x3([[1.0000, 2.0000, 3.0000],\n [4.0000, 5.0000, 6.0000],\n [7.0000, 8.0000, 9.0000]])' + + +# test __getnewargs__ +test_mat_copy = test_mat.copy() +element_name_list = [e for e in dir(test_mat_copy) if e[:2] != '__' and e[0] == '_'] +element_value_list = [getattr(test_mat, attr) for attr in element_name_list] +assert tuple(element_value_list) == test_mat.__getnewargs__() + +# test __truediv__ +test_mat_copy = test_mat.copy() +result_mat = test_mat_copy.__truediv__(12.345) +correct_result_mat = test_mat_copy.copy() +for i in range(3): + for j in range(3): + correct_result_mat[i, j] /= 12.345 +assert result_mat == correct_result_mat + + + +# test __rmul__ +test_mat_copy = test_mat.copy() +result_mat = 12.345 * test_mat_copy +correct_result_mat = test_mat_copy.copy() +for i in range(3): + for j in range(3): + correct_result_mat[i, j] *= 12.345 + +assert result_mat == correct_result_mat + + +# 此处测试不完全, 未验证正确性 +# test interface of "@" "matmul" "__matmul__" with vec3 and error handling +test_mat_copy = test_mat.copy() +test_mat_copy @ vec3(83,-9.12, 0.2983) +try: + test_mat_copy @ 12345 + raise Exception('未能拦截错误 BinaryOptError("@") 在处理表达式 test_mat_copy @ 12345') +except: + pass + + +# test transpose +test_mat_copy = test_mat.copy() +assert test_mat_copy.transpose() == test_mat_copy.transpose().transpose().transpose() + + +# test inverse +test_mat_copy = test_mat.copy() +if round(test_mat_copy.determinant(), 5) != 0: + list_mat = [[0,0,0], [0,0,0], [0,0,0]] + list_mat_2 = [[0,0,0], [0,0,0], [0,0,0]] + for i in range(3): + for j in range(3): + list_mat[i][j] = test_mat[i, j] + list_mat_2[i][j] = str(test_mat_copy.inverse()[i, j])[:6] +assert [[str(e)[:6] for e in layer] for layer in calculate_inverse(list_mat)] == list_mat_2 + + +try: + mat3x3([[1, 2, 3], [2, 4, 6], [3, 6, 9]]).inverse() + raise Exception('未能拦截错误 ValueError("matrix is not invertible") 在 test_mat_copy 的行列式为0') +except: + pass + +# test __invert__ +test_mat_copy = test_mat.copy() +if round(test_mat_copy.determinant(), 5) != 0: + list_mat = [[0,0,0], [0,0,0], [0,0,0]] + list_mat_2 = [[0,0,0], [0,0,0], [0,0,0]] + for i in range(3): + for j in range(3): + list_mat[i][j] = test_mat[i, j] + list_mat_2[i][j] = str((~test_mat_copy)[i, j])[:6] +assert [[str(e)[:6] for e in layer] for layer in calculate_inverse(list_mat)] == list_mat_2 + + +try: + ~mat3x3([[1, 2, 3], [2, 4, 6], [3, 6, 9]]) + raise Exception('未能拦截错误 ValueError("matrix is not invertible") 在 test_mat_copy 的行列式为0') +except: + pass + +# test zeros +assert mat3x3([[0 for _ in range(3)] for _ in range(3)]) == mat3x3.zeros() + +# test ones +assert mat3x3([[1 for _ in range(3)] for _ in range(3)]) == mat3x3.ones() + +# test identity +assert mat3x3([[1,0,0],[0,1,0],[0,0,1]]) == mat3x3.identity() \ No newline at end of file