矩阵运算——矩阵加法+乘法+转置+求逆
矩阵运算——矩阵加法+乘法+转置+求逆__控制台程序
double[,] matrix;
public int row = 0, col = 0;
//定义三个不同情况下的构造函数
public Matrix() { }
public Matrix(int row)
{
matrix = new double[row, row];
}
public Matrix(int row, int col)
{
this.row = row;
this.col = col;
matrix = new double[row, col];
}
//复制构造函数
public Matrix(Matrix m)
{
int row = m.row;
int col = m.col;
matrix = new double[row, col];
for (int i = 0; i < row; i++)
{
for (int j = 0; j < col; j++)
{
matrix[i, j] = m.getNum(i, j);
}
}
}
//输入相应的值，对矩阵进行设置
public void SetNum(int i, int j, double num)
{
matrix[i, j] = num;
}
//得到相应的矩阵某个数
public double getNum(int i, int j)
{
return matrix[i, j];
}
//输出矩阵
public void OutputM()
{
Console.WriteLine("矩阵为：");
for (int p = 0; p < row; p++)
{
for (int q = 0; q < col; q++)
{
Console.Write("\t" + matrix[p, q]);
}
Console.Write("\n");
}
}
public void InputM(int Row, int Col)
{
for (int a = 0; a < Row; a++)//col——Michael
{
for (int b = 0; b < Col; b++)
{
Console.WriteLine("第{0}行，第{1}列", a + 1, b + 1);
double value = Convert.ToDouble(Console.ReadLine());
this.SetNum(a, b, value);
}
}
}
//得到matrix
public double[,] Detail
{
get
{
return matrix;
}
set { matrix = value; }
}
//矩阵转置实现
public Matrix Transpose()
{
Matrix another = new Matrix(row, col);
for (int i = 0; i < row; i++)
{
for (int j = 0; j < col; j++)
{
another.SetNum(j, i, matrix[i, j]);
}
}
return another;
}
/// <summary>
/// 矩阵相乘
/// </summary>
/// <param name="X">第一个矩阵</param>
/// <param name="Y">第二个矩阵</param>
/// <returns></returns>
public double[,] matrixMulti(double[,] X, double[,] Y)
{
double[,] A = X; double[,] B = Y;
double[,] C = new double[A.GetLength(0), B.GetLength(1)];
for (int i = 0; i < A.GetLength(0); i++)
for (int j = 0; j < B.GetLength(1); j++)
{
C[i, j] = 0;
for (int k = 0; k < A.GetLength(1); k++)
{
C[i, j] += A[i, k] * B[k, j];
}
}
return C;
}
//矩阵相乘
public static Matrix Multiply(Matrix lm, Matrix rm)
{
Matrix another = new Matrix(lm.row, rm.col);
if (lm.col == rm.row)
{
for (int i = 0; i < lm.row; i++)
{
for (int j = 0; j < rm.col; j++)
{
double temp=0;
for (int k = 0; k < lm.col; k++)
{
temp += lm.getNum(i, k) * rm.getNum(k, j);
}
another.SetNum(i, j, temp);
}
}
}
else
{
Console.WriteLine("左矩阵的列数不等于右矩阵的行数，不能参与计算");
}
return another;
}
//矩阵相加实现
public static Matrix Add(Matrix lm, Matrix rm)
{
//行出错
if (lm.row != rm.row)
{
System.Exception e = new Exception("相加的两个矩阵的行数不等");
throw e;
}
//列出错
if (lm.col != rm.col)
{
System.Exception e = new Exception("相加的两个矩阵的列数不等");
throw e;
}
Matrix another = new Matrix(lm.row, lm.col);
for (int i = 0; i < lm.row; i++)
{
for (int j = 0; j < lm.col; j++)
{
double temp = lm.getNum(i, j) + rm.getNum(i, j);
another.SetNum(i, j, temp);
}
}
return another;
}
//矩阵求逆实现
public static Matrix Inverse(Matrix M)
{
int m = M.row;
int n = M.col;
if (m != n)
{
Exception myException = new Exception("求逆的矩阵不是方阵");
throw myException;
}
Matrix ret = new Matrix(m, n);
double[,] a0 = M.Detail;
double[,] a = (double[,])a0.Clone();
double[,] b = ret.Detail;
int i, j, row, k; double max, temp;
//单位矩阵
for (i = 0; i < n; i++)
{
b[i, i] = 1;
}
for (k = 0; k < n; k++)
{
max = 0; row = k;
//找最大元，其所在行为row
for (i = k; i < n; i++)
{
temp = Math.Abs(a[i, k]);
if (max < temp)
{
max = temp; row = i;
}
}
if (max == 0)
{
Exception myException = new Exception("该矩阵无逆矩阵");
throw myException;
}
//交换k与row行
if (row != k)
{
for (j = 0; j < n; j++)
{
temp = a[row, j];
a[row, j] = a[k, j];
a[k, j] = temp;
temp = b[row, j];
b[row, j] = b[k, j];
b[k, j] = temp;
}
}
//首元化为1
for (j = k + 1; j < n; j++)
a[k, j] /= a[k, k];
for (j = 0; j < n; j++)
b[k, j] /= a[k, k];
a[k, k] = 1;
//k列化为0
//对a
for (j = k + 1; j < n; j++)
{
for (i = 0; i < k; i++)
a[i, j] -= a[i, k] * a[k, j];
for (i = k + 1; i < n; i++)
a[i, j] -= a[i, k] * a[k, j];
}
//对b
for (j = 0; j < n; j++)
{
for (i = 0; i < k; i++)
b[i, j] -= a[i, k] * b[k, j];
for (i = k + 1; i < n; i++)
b[i, j] -= a[i, k] * b[k, j];
}
for (i = 0; i < n; i++)
a[i, k] = 0;
a[k, k] = 1;
}
return ret;
}
//主函数
public static void Main()
{
int Row, Col, choice;
Console.WriteLine("请输入想要的矩阵行数与列数");
Row = Convert.ToInt32(Console.ReadLine());
Col = Convert.ToInt32(Console.ReadLine());
Matrix m = new Matrix(Row, Col);
Console.WriteLine("输入矩阵数据");
m.InputM(Row, Col); m.OutputM();
do
{
Console.WriteLine("请选择你想要进行的运算：\n（1）转置；\n（2）输入另一矩阵并相加；\n（3）求逆；\n（4）输入另一矩阵并相乘；\n(0)停止；");
choice = Convert.ToInt32(Console.ReadLine());
switch (choice)
{
case 1:
Matrix n = m.Transpose();
n.OutputM();
break;
case 2:
Console.WriteLine("请输入第二个矩阵行数与列数");
Row = Convert.ToInt32(Console.ReadLine());
Col = Convert.ToInt32(Console.ReadLine());
Matrix m2 = new Matrix(Row, Col);
Console.WriteLine("输入矩阵数据");
m2.InputM(Row, Col);
Console.WriteLine("第二个矩阵为：");
m2.OutputM();
Matrix result = Add(m, m2);
result.OutputM();
break;
case 3:
Matrix m3 = Inverse(m);
m3.OutputM();
break;
case 4:
Console.WriteLine("请输入第二个矩阵行数与列数");
Row = Convert.ToInt32(Console.ReadLine());
Col = Convert.ToInt32(Console.ReadLine());
Matrix m4 = new Matrix(Row, Col);
Console.WriteLine("输入矩阵数据");
m4.InputM(Row, Col);
Console.WriteLine("第二个矩阵为：");
m4.OutputM();
Matrix result2 = Multiply(m, m4);
result2.OutputM();
break;
case 0:
break;
}
}
while (choice != 0);
Console.Write("请按任意键继续");
Console.ReadLine();
}
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