通过代码实现矩阵类
欲了解矩阵的相关概念，请参考矩阵与空间坐标系变换。
不过由于概念性的东西相对来说较难理解，于是就想到了通过代码来实现一个矩阵类（该类包含矩阵创建，及基本运算功能），来加深对矩阵的理解。
设计思路
- 确定矩阵的初始化参数，并进行参数校验；
- 实现矩阵的转置、行列式、逆矩阵；
- 实现矩阵的等于、加、减、乘法功能；
1. 参数及校验
- 参数包含矩阵数据、行列数即可；
- 参数校验主要进行判断行列数的乘积是否与矩阵数据个数相同。
- 同时需对传入的数据进行拷贝，以免因为引用问题，而导致矩阵数据异常。
class Matrix(object):
def __init__(self, data = [], row = 0, col = 0):
self.__data, self.__row, self.__col = self.verify(data, row, col);
# verify data
def verify(self, data, row, col):
count = len(data);
if row <= 0:
row = (count > 0) and 1 or 0;
col = count;
elif col <= 0:
col = math.ceil(count / row);
# verify data length
if count != row * col:
raise Exception(f"failed to create matrix by invalid data count[{count}], row[{row}] and col[{col}]");
return [float(d) for d in data], row, col; # copy data
2. 矩阵的转置
- 只需要将矩阵的行数据换成对应列的数据，然后返回新的矩阵。
# transpose matrix
@property
def trans(self):
if not self.__trans:
data = [];
for i in range(self.__col):
for j in range(self.__row):
data.append(self.__data[j * self.__col + i]);
self.__trans = Matrix(data, self.__col, self.__row);
return self.__trans;
3. 矩阵的行列式
- 首先通过
__getDetParams__函数，获取数据元素的排列，以及对应排列的逆序数。 - 将以上得到的数据，传入
__getDetVal__函数，该函数根据行列式的定义，得到行列式的值。
# matrix determinant
@property
def det(self):
if self.__det == None:
groups, ionList = self.__getDetParams__();
if groups and ionList:
self.__det = self.__getDetVal__(groups, ionList);
return self.__det;
# get params of matrix determinant
def __getDetParams__(self):
groups, ionList = [], [];
if self.__row != self.__col:
return [], [];
def reverseOrdinal(group):
ion = 0;
for i in range(len(group)-1, -1, -1):
for j in range(i-1, -1, -1):
if group[j] > group[i]:
ion += 1;
ionList.append(ion);
def fullArrange(group = []):
for i in range(self.__row):
if i not in group:
group.append(i);
if len(group) == self.__row:
groups.append([g for g in group]);
reverseOrdinal(group);
else:
fullArrange(group);
group.pop();
pass;
fullArrange();
return groups, ionList;
# get value of matrix determinant by params
def __getDetVal__(self, groups, ionList, excludeRow = -1, excludeCol = -1):
det = 0;
for i, group in enumerate(groups):
ion = ionList[i];
adjustCnt, val = 0, 1;
for k,v in enumerate(group):
if k == excludeRow or v == excludeCol:
ion = self.__adjustIon__(ion, group, k);
adjustCnt += 1;
else:
val *= self.__data[k * self.__col + v];
if adjustCnt <= 1 and adjustCnt != len(group):
det += math.pow(-1, ion) * val;
return det;
# adjust inverse ordinal mumber
def __adjustIon__(self, ion, group, idx):
for v in group[:idx]:
if v > group[idx]:
ion -= 1;
for v in group[idx+1:]:
if v < group[idx]:
ion -= 1;
return ion;
4. 矩阵的逆矩阵
- 首先根据数据元素的排列和逆序数，得到矩阵的行列式、对应各个元素的余子式；
- 接着根据对应各个元素的余子式，得到新的矩阵，然后将矩阵进行转置，再除以源矩阵的行列式的值，即可得到源矩阵的逆矩阵。
# inverse matrix
@property
def inv(self):
if not self.__inv:
groups, ionList = self.__getDetParams__();
if groups and ionList:
det = self.__getDetVal__(groups, ionList);
if det == 0:
return None;
data = [];
for i in range(self.__col):
for j in range(self.__row):
mdet = math.pow(-1, i+j) * self.__getDetVal__(groups, ionList, excludeRow = i, excludeCol = j);
data.append(mdet);
self.__inv = Matrix(data, self.__col, self.__row).trans * (1/det);
return self.__inv;
5. 矩阵的等于、加、减、乘法功能
- 通过魔法方法，实现对象的等于（
__eq__）、加（__add__）、减（__sub__）、乘（__mul__）法功能; - 其中乘法考虑了矩阵与数相乘，和矩阵与矩阵相乘的情况。
def __eq__(self, other):
if not isinstance(other, Matrix):
raise TypeError("Matrix cannot campare to other instance");
if self.__row == other.row and self.__col == other.col:
for i,v in enumerate(self.__data):
if v != other.get(index = i):
return False;
return True;
def __ne__(self, other):
return not self.__eq__(other);
def __add__(self, other):
if not isinstance(other, Matrix):
raise TypeError("Matrix cannot add to other instance");
if self.__row != other.row or self.__col != other.col:
raise TypeError("Matrix cannot add Matrix with different size");
data = [];
for i,v in enumerate(self.__data):
data.append(v + other.get(index = i));
return Matrix(data, self.__row, self.__col);
def __sub__(self, other):
if not isinstance(other, Matrix):
raise TypeError("Matrix cannot sub to other instance");
if self.__row != other.row or self.__col != other.col:
raise TypeError("Matrix cannot sub Matrix with different size");
data = [];
for i,v in enumerate(self.__data):
data.append(v - other.get(index = i));
return Matrix(data, self.__row, self.__col);
def __mul__(self, other):
if isinstance(other, int) or isinstance(other, float):
data = [];
for i,v in enumerate(self.__data):
data.append(v * other);
return Matrix(data, self.__row, self.__col);
if not isinstance(other, Matrix):
raise TypeError("Matrix cannot mul to other instance[not int, float, Matrix]");
if self.__col != other.row:
raise TypeError("Matrix cannot mul Matrix with unqualified size");
data = [];
for i in range(self.__row):
for j in range(other.col):
val = 0;
for k in range(self.__col):
val += self.get(i, k) * other.get(k, j);
data.append(val);
return Matrix(data, self.__row, other.col);
完整代码
GitHub地址： https://github.com/JDreamHeart/DailyCodes/python/article/matrix.py