pocketpy/tests/80_linalg.py

from linalg import mat3x3, vec2, vec3, vec4
import random
import sys
import math

# 出于对精度转换的考虑,在本测试中具体将采用str(floating_num)[:6]来比较两个浮点数是否相等

# 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)]))
test_vec2_2 = 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_to_str_list(mat):
    ret = [[0,0,0], [0,0,0], [0,0,0]]
    for i in range(3):
        for j in range(3):
            ret[i][j] = str(mat[i, j])[:6]
    return ret

def mat_list_to_str_list(mat_list):
    ret = [[0,0,0], [0,0,0], [0,0,0]]
    for i in range(3):
        for j in range(3):
            ret[i][j] = str(mat_list[i][j])[:6]
    return ret

def mat_to_list(mat):
    ret = [[0,0,0], [0,0,0], [0,0,0]]
    for i in range(3):
        for j in range(3):
            ret[i][j] = mat[i, j]
    return ret
    
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
    用于校对元素是浮点数的矩阵
    '''
    ret = mat.copy()
    
    for i, row in enumerate(ret):
        for j, element in enumerate(row):
            row[j] = round(element, pos)
        ret[i] = row
    
    return ret

def get_row(mat, row_index):
    '''
    返回mat的row_index行元素构成的列表
    '''
    ret = []
    for i in range(3):
        ret.append(mat[row_index, i])
    return ret

def get_col(mat, col_index):
    '''
    返回mat的col_index列元素构成的列表
    '''
    ret = []
    for i in range(3):
        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)])
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):
    
    if i in [0, 9]:
        continue
    
    try:
        test_mat_copy = mat3x3(*tuple([e+0.1 for e in range(i)]))
        
        # 既然参数数量不是合法的0个或9个,并且这里也没有触发TypeError,那么引发测试失败
        print(f'When there are {i} arguments, no TypeError is triggered')
        exit(1)
        
    except TypeError:
        pass

# test 9 floating parameters is passed
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 mat3x3(*tuple(element_value_list)) == test_mat

        
# test copy
test_mat_copy = test_mat.copy()
assert test_mat is not test_mat_copy
element_name_list = [e for e in dir(test_mat_copy) if e[:2] != '__' and e[0] == '_']
for i, element in enumerate([getattr(test_mat_copy, e) for e in element_name_list]):
    assert [getattr(test_mat, e) for e in element_name_list][i] == element

# test setzeros
test_mat_copy = test_mat.copy()
test_mat_copy.set_zeros()
assert test_mat_copy == mat3x3([[0,0,0],[0,0,0],[0,0,0]])

# test set_ones
test_mat_copy = test_mat.copy()
test_mat_copy.set_ones()
assert test_mat_copy == mat3x3([[1,1,1],[1,1,1],[1,1,1]])

# test set_identity
test_mat_copy = test_mat.copy()
test_mat_copy.set_identity()
assert test_mat_copy == mat3x3([[1, 0, 0],[0, 1, 0],[0, 0, 1]])

# test __getitem__
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] == '_']
for i, element in enumerate([getattr(test_mat_copy, e) for e in element_name_list]):
    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()
ones.set_ones()
result_mat = test_mat_copy.__add__(ones)
correct_result_mat = test_mat_copy.copy()
for i in range(3):
    for j in range(3):
        correct_result_mat[i, j] += 1
assert result_mat == correct_result_mat

# test __sub__
test_mat_copy = test_mat.copy()
ones = mat3x3()
ones.set_ones()
result_mat = test_mat_copy.__sub__(ones)
correct_result_mat = test_mat_copy.copy()
for i in range(3):
    for j in range(3):
        correct_result_mat[i, j] -= 1
assert result_mat == correct_result_mat

# test __mul__
test_mat_copy = test_mat.copy()
result_mat = test_mat_copy.__mul__(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
# print(result_mat)
# print(correct_result_mat)
assert result_mat == correct_result_mat


# test matmul
test_mat_copy = test_mat.copy()
test_mat_copy_2 = test_mat.copy()
result_mat = test_mat_copy.matmul(test_mat_copy_2)
correct_result_mat = mat3x3()
for i in range(3):
    for j in range(3):
        correct_result_mat[i, j] = sum([e1*e2 for e1, e2 in zip(get_row(test_mat_copy, i), get_col(test_mat_copy_2, j))])
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):
        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()


# test affine transformations-----------------------------------------------
# test trs
def trs(t, radian, s):
    cr = math.cos(radian)
    sr = math.sin(radian)
    elements = [[s[0] * cr, -s[1] * sr, t[0]],
                [s[0] * sr, s[1] * cr, t[1]],
                [0.0, 0.0, 1.0]]
    return elements

test_vec2_copy = test_vec2.copy()
test_vec2_2_copy = test_vec2_2.copy()

test_vec2_list = [test_vec2_copy.x, test_vec2_copy.y]
test_vec2_2_list = [test_vec2_2_copy.x, test_vec2_2_copy.y]

radian = random.uniform(-10*math.pi, 10*math.pi)

assert mat_to_str_list(mat3x3.trs(test_vec2_copy, radian, test_vec2_2_copy)) == mat_list_to_str_list(trs(test_vec2_list, radian, test_vec2_2_list))


# test is_affine
def mat_is_affine(mat_list):
    return mat_list[2][0] == 0 and mat_list[2][1] == 0 and mat_list[2][2] == 1

# 通过random.unifrom的返回值不可能是整数0或1, 因此认为test_mat不可能is_affine
test_mat_copy = test_mat.copy()
assert test_mat_copy.is_affine() == mat_is_affine(mat_to_list(test_mat_copy))

test_mat_copy[2,0] = 0
test_mat_copy[2,1] = 0
test_mat_copy[2,2] = 1
assert test_mat_copy.is_affine() == mat_is_affine(mat_to_list(test_mat_copy))


# test translation
test_mat_copy = test_mat.copy()
assert test_mat_copy.translation() == vec2(test_mat_copy[0, 2], test_mat_copy[1, 2])

# 该方法的测试未验证计算的准确性
# test rotation
test_mat_copy = test_mat.copy()
assert type(test_mat_copy.rotation()) is float


# test scale
def mat_scale(mat_list):
    return [(mat_list[0][0] ** 2 + mat_list[1][0] ** 2) ** 0.5, (mat_list[0][1] ** 2 + mat_list[1][1] ** 2) ** 0.5]
    
test_mat_copy = test_mat.copy()
temp_vec2 = test_mat_copy.scale()
temp_vec2_list = [str(temp_vec2.x)[:6], str(temp_vec2.y)[:6]]
assert [str(e)[:6] for e in mat_scale(mat_to_list(test_mat_copy))] == temp_vec2_list


# test transform_point
def mat_transform_point(mat_list, vec2_list):
    return [mat_list[0][0] * vec2_list[0] + mat_list[0][1] * vec2_list[1] + mat_list[0][2], mat_list[1][0] * vec2_list[0] + mat_list[1][1] * vec2_list[1] + mat_list[1][2]]
    
test_mat_copy = test_mat.copy()
test_mat_copy = test_mat.copy()
test_vec2_copy = test_vec2.copy()
temp_vec2 = test_mat_copy.transform_point(test_vec2_copy)
temp_vec2_list = [str(temp_vec2.x)[:6], str(temp_vec2.y)[:6]]
assert [str(e)[:6] for e in mat_transform_point(mat_to_list(test_mat_copy), [test_vec2_copy.x, test_vec2_copy.y])] == temp_vec2_list


# test transform_vector
def mat_transform_vector(mat_list, vec2_list):
    return [mat_list[0][0] * vec2_list[0] + mat_list[0][1] * vec2_list[1], mat_list[1][0] * vec2_list[0] + mat_list[1][1] * vec2_list[1]]
    
test_mat_copy = test_mat.copy()
test_mat_copy = test_mat.copy()
test_vec2_copy = test_vec2.copy()
temp_vec2 = test_mat_copy.transform_vector(test_vec2_copy)
temp_vec2_list = [str(temp_vec2.x)[:6], str(temp_vec2.y)[:6]]
assert [str(e)[:6] for e in mat_transform_vector(mat_to_list(test_mat_copy), [test_vec2_copy.x, test_vec2_copy.y])] == temp_vec2_list