...

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]
+        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 __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)}]])'
+# 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()