使用 Python 中的乘法运算符进行矩阵乘法：如何？
Matrix-matrix-multiplication using the multiplication operator in Python: How?
我想重载 Python 中的乘法运算符。我真正想做的是使用 Python 中的 * 运算符执行矩阵-矩阵-乘法。不允许使用 Numpy。
import math
class Vec4():
def __init__(self, x = 0, y = 0, z = 0, w = 0):
"""Constructor for Vec4
DO NOT MODIFY THIS METHOD"""
self.values = [x,y,z,w]
def __str__(self):
"""Returns the vector as a string representation
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00'
for c in range(0,4):
toReturn += "%.2f" % self.values[c]
if c != 3:
toReturn += ' '
return toReturn
class Matrix4():
def __init__(self, row1=None, row2=None, row3=None, row4=None):
"""Constructor for Matrix4
DO NOT MODIFY THIS METHOD"""
if row1 is None: row1 = Vec4()
if row2 is None: row2 = Vec4()
if row3 is None: row3 = Vec4()
if row4 is None: row4 = Vec4()
self.m_values = [row1,row2,row3,row4]
def __str__(self):
"""Returns a string representation of the matrix
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00'
for r in range(0,4):
for c in range(0,4):
toReturn += "%.2f" % self.m_values[r].values[c]
if c != 3:
toReturn += ' '
toReturn += '\n'
return toReturn
def __matmul__(self, m):
x = self.m_values[0].values[0]*m.m_values[0].values[0]+self.m_values[0].values[1]*m.m_values[1]*values[0]+self.m_values[0].values[2]*m.m_values[2].values[0]+self.m_values[0].values[3]*m.m_values[3].values[0]
y = self.m_values[1].values[0]*m.m_values[0].values[1]+self.m_values[1].values[1]*m.m_values[1]*values[1]+self.m_values[1].values[2]*m.m_values[2].values[1]+self.m_values[1].values[3]*m.m_values[3].values[1]
z = self.m_values[2].values[0]*m.m_values[0].values[2]+self.m_values[2].values[1]*m.m_values[1]*values[2]+self.m_values[2].values[2]*m.m_values[2].values[2]+self.m_values[2].values[3]*m.m_values[3].values[2]
w = self.m_values[3].values[0]*m.m_values[0].values[3]+self.m_values[3].values[1]*m.m_values[1]*values[3]+self.m_values[3].values[2]*m.m_values[2].values[3]+self.m_values[3].values[3]*m.m_values[3].values[3]
return Matrix4()
而不是得到如下结果：
A = Matrix4(Vec4(1, 0, 0, 0),
Vec4(0, 1, 0, 0),
Vec4(0, 0, 1, 0),
Vec4(0, 0, 0, 1))
B = Matrix4(Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4))
print(A * B)
输出应该是：
1.00 2.00 3.00 4.00
1.00 2.00 3.00 4.00
1.00 2.00 3.00 4.00
1.00 2.00 3.00 4.00
但在我的例子中它会导致错误：
Traceback (most recent call last):
File "<pyshell#14>", line 1, in <module>
print(A*B)
File "C:\Users\xxx\Downloads\Download-Stuff\Gmail\TransformMatrix.py", line 45, in __mul__
x = self.m_values[0].values[0]*v.values[0]+self.m_values[1].values[0]*v.values[1]+self.m_values[2].values[0]*v.values[2]+self.m_values[3].values[0]*v.values[3]
AttributeError: 'Matrix4' object has no attribute 'values'
我做错了什么？
感谢您的提前帮助。
您必须通过定义 def __mul__(self, m):
来重载
经过咨询https://en.wikipedia.org/wiki/Matrix_multiplication，
我首先实现了 dot_product() 并尝试获得更通用的解决方案：
import math
class Vec4():
def __init__(self, x = 0, y = 0, z = 0, w = 0):
"""Constructor for Vec4
DO NOT MODIFY THIS METHOD"""
self.values = [x,y,z,w]
def __str__(self):
"""Returns the vector as a string representation
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00'
for c in range(0,4):
toReturn += "%.2f" % self.values[c]
if c != 3:
toReturn += ' '
return toReturn
class Matrix4():
def __init__(self, row1=None, row2=None, row3=None, row4=None):
"""Constructor for Matrix4
DO NOT MODIFY THIS METHOD"""
if row1 is None: row1 = Vec4()
if row2 is None: row2 = Vec4()
if row3 is None: row3 = Vec4()
if row4 is None: row4 = Vec4()
self.m_values = [row1,row2,row3,row4]
def __str__(self):
"""Returns a string representation of the matrix
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00'
for r in range(0,4):
for c in range(0,4):
toReturn += "%.2f" % self.m_values[r].values[c]
if c != 3:
toReturn += ' '
toReturn += '\n'
return toReturn
def get_column(self, j):
return [vec.values[j] for vec in self.m_values]
def get_row(self, i):
return self.m_values[i].values
def dot_product(self, m, i, j):
return sum([x * y for x, y in zip(self.get_row(i), \
m.get_column(j))])
def shape(self):
return len(self.m_values), len(self.m_values[0].values)
def __mul__(self, mat):
# m = len(self.m_values[0].values)
n = self.shape()[0]
p = mat.shape()[1]
return Matrix4(*[Vec4(*[self.dot_product(mat, i, j) for j in range(p)]) for i in range(n)])
A = Matrix4(Vec4(1, 0, 0, 0),
Vec4(0, 1, 0, 0),
Vec4(0, 0, 1, 0),
Vec4(0, 0, 0, 1))
B = Matrix4(Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4))
print(A * B)
# 1.00 2.00 3.00 4.00
# 1.00 2.00 3.00 4.00
# 1.00 2.00 3.00 4.00
# 1.00 2.00 3.00 4.00
一般解决方案
对于任意大小的矩阵。
并使用 __repr__()，这样就不必总是打印 print() 来查看
字符串表示形式。
class Vec4():
def __init__(self, *args):
"""Generalized constructor for Vec4"""
self.values = args
def __str__(self):
"""Returns the vector as a string representation"""
if self.values == []:
return "Empy Vector of class Vec4"
else:
return ' '.join(["{0:.2f}".format(c) for c in self.values])
def __repr__(self):
return self.__str__()
class Matrix4():
def __init__(self, *args):
"""Constructor for Matrix4"""
self.values = args
def __str__(self):
"""Returns a string representation of the matrix"""
if self.values == []:
return "Empty Matrix of class Matrix4"
else:
return '\n'.join([str(v) for v in self.values])
def __repr__(self):
return self.__str__()
def get_column(self, j):
return [vec.values[j] for vec in self.values]
def get_row(self, i):
return self.values[i].values
def dot_product(self, m, i, j):
return sum([x * y for x, y in zip(self.get_row(i), \
m.get_column(j))])
def shape(self):
return len(self.values), len(self.values[0].values)
def __mul__(self, mat):
# m = len(self.values[0].values)
n = self.shape()[0]
p = mat.shape()[1]
return Matrix4(*[Vec4(*[self.dot_product(mat, i, j) for j in range(p)]) for i in range(n)])
我想重载 Python 中的乘法运算符。我真正想做的是使用 Python 中的 * 运算符执行矩阵-矩阵-乘法。不允许使用 Numpy。
import math
class Vec4():
def __init__(self, x = 0, y = 0, z = 0, w = 0):
"""Constructor for Vec4
DO NOT MODIFY THIS METHOD"""
self.values = [x,y,z,w]
def __str__(self):
"""Returns the vector as a string representation
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00'
for c in range(0,4):
toReturn += "%.2f" % self.values[c]
if c != 3:
toReturn += ' '
return toReturn
class Matrix4():
def __init__(self, row1=None, row2=None, row3=None, row4=None):
"""Constructor for Matrix4
DO NOT MODIFY THIS METHOD"""
if row1 is None: row1 = Vec4()
if row2 is None: row2 = Vec4()
if row3 is None: row3 = Vec4()
if row4 is None: row4 = Vec4()
self.m_values = [row1,row2,row3,row4]
def __str__(self):
"""Returns a string representation of the matrix
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00'
for r in range(0,4):
for c in range(0,4):
toReturn += "%.2f" % self.m_values[r].values[c]
if c != 3:
toReturn += ' '
toReturn += '\n'
return toReturn
def __matmul__(self, m):
x = self.m_values[0].values[0]*m.m_values[0].values[0]+self.m_values[0].values[1]*m.m_values[1]*values[0]+self.m_values[0].values[2]*m.m_values[2].values[0]+self.m_values[0].values[3]*m.m_values[3].values[0]
y = self.m_values[1].values[0]*m.m_values[0].values[1]+self.m_values[1].values[1]*m.m_values[1]*values[1]+self.m_values[1].values[2]*m.m_values[2].values[1]+self.m_values[1].values[3]*m.m_values[3].values[1]
z = self.m_values[2].values[0]*m.m_values[0].values[2]+self.m_values[2].values[1]*m.m_values[1]*values[2]+self.m_values[2].values[2]*m.m_values[2].values[2]+self.m_values[2].values[3]*m.m_values[3].values[2]
w = self.m_values[3].values[0]*m.m_values[0].values[3]+self.m_values[3].values[1]*m.m_values[1]*values[3]+self.m_values[3].values[2]*m.m_values[2].values[3]+self.m_values[3].values[3]*m.m_values[3].values[3]
return Matrix4()
而不是得到如下结果：
A = Matrix4(Vec4(1, 0, 0, 0),
Vec4(0, 1, 0, 0),
Vec4(0, 0, 1, 0),
Vec4(0, 0, 0, 1))
B = Matrix4(Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4))
print(A * B)
输出应该是：
1.00 2.00 3.00 4.00
1.00 2.00 3.00 4.00
1.00 2.00 3.00 4.00
1.00 2.00 3.00 4.00
但在我的例子中它会导致错误：
Traceback (most recent call last):
File "<pyshell#14>", line 1, in <module>
print(A*B)
File "C:\Users\xxx\Downloads\Download-Stuff\Gmail\TransformMatrix.py", line 45, in __mul__
x = self.m_values[0].values[0]*v.values[0]+self.m_values[1].values[0]*v.values[1]+self.m_values[2].values[0]*v.values[2]+self.m_values[3].values[0]*v.values[3]
AttributeError: 'Matrix4' object has no attribute 'values'
我做错了什么？
感谢您的提前帮助。
您必须通过定义 def __mul__(self, m):
经过咨询https://en.wikipedia.org/wiki/Matrix_multiplication，
我首先实现了 dot_product() 并尝试获得更通用的解决方案：
import math
class Vec4():
def __init__(self, x = 0, y = 0, z = 0, w = 0):
"""Constructor for Vec4
DO NOT MODIFY THIS METHOD"""
self.values = [x,y,z,w]
def __str__(self):
"""Returns the vector as a string representation
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00'
for c in range(0,4):
toReturn += "%.2f" % self.values[c]
if c != 3:
toReturn += ' '
return toReturn
class Matrix4():
def __init__(self, row1=None, row2=None, row3=None, row4=None):
"""Constructor for Matrix4
DO NOT MODIFY THIS METHOD"""
if row1 is None: row1 = Vec4()
if row2 is None: row2 = Vec4()
if row3 is None: row3 = Vec4()
if row4 is None: row4 = Vec4()
self.m_values = [row1,row2,row3,row4]
def __str__(self):
"""Returns a string representation of the matrix
DO NOT MODIFY THIS METHOD"""
toReturn = ''
if self is None: return '0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00\n0.00 0.00 0.00 0.00'
for r in range(0,4):
for c in range(0,4):
toReturn += "%.2f" % self.m_values[r].values[c]
if c != 3:
toReturn += ' '
toReturn += '\n'
return toReturn
def get_column(self, j):
return [vec.values[j] for vec in self.m_values]
def get_row(self, i):
return self.m_values[i].values
def dot_product(self, m, i, j):
return sum([x * y for x, y in zip(self.get_row(i), \
m.get_column(j))])
def shape(self):
return len(self.m_values), len(self.m_values[0].values)
def __mul__(self, mat):
# m = len(self.m_values[0].values)
n = self.shape()[0]
p = mat.shape()[1]
return Matrix4(*[Vec4(*[self.dot_product(mat, i, j) for j in range(p)]) for i in range(n)])
A = Matrix4(Vec4(1, 0, 0, 0),
Vec4(0, 1, 0, 0),
Vec4(0, 0, 1, 0),
Vec4(0, 0, 0, 1))
B = Matrix4(Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4),
Vec4(1,2,3,4))
print(A * B)
# 1.00 2.00 3.00 4.00
# 1.00 2.00 3.00 4.00
# 1.00 2.00 3.00 4.00
# 1.00 2.00 3.00 4.00
一般解决方案
对于任意大小的矩阵。
并使用 __repr__()，这样就不必总是打印 print() 来查看
字符串表示形式。
class Vec4():
def __init__(self, *args):
"""Generalized constructor for Vec4"""
self.values = args
def __str__(self):
"""Returns the vector as a string representation"""
if self.values == []:
return "Empy Vector of class Vec4"
else:
return ' '.join(["{0:.2f}".format(c) for c in self.values])
def __repr__(self):
return self.__str__()
class Matrix4():
def __init__(self, *args):
"""Constructor for Matrix4"""
self.values = args
def __str__(self):
"""Returns a string representation of the matrix"""
if self.values == []:
return "Empty Matrix of class Matrix4"
else:
return '\n'.join([str(v) for v in self.values])
def __repr__(self):
return self.__str__()
def get_column(self, j):
return [vec.values[j] for vec in self.values]
def get_row(self, i):
return self.values[i].values
def dot_product(self, m, i, j):
return sum([x * y for x, y in zip(self.get_row(i), \
m.get_column(j))])
def shape(self):
return len(self.values), len(self.values[0].values)
def __mul__(self, mat):
# m = len(self.values[0].values)
n = self.shape()[0]
p = mat.shape()[1]
return Matrix4(*[Vec4(*[self.dot_product(mat, i, j) for j in range(p)]) for i in range(n)])