/// <summary>
/// 二维矩阵乘法运算，矩阵相乘
/// </summary>
/// <param name="martix1"></param>
/// <param name="martix2"></param>
/// <returns></returns>
public static Martix operator *(Martix martix1, Martix martix2)
{
double[,] array = new double[martix1.Rows, martix2.Columns];
Martix result = new Martix(array);
try
{
if (martix1.Columns == martix2.Rows)
{
for (int row1 = 0; row1 < martix1.Rows; row1++)
{
int row2 = 0;
for (int column2 = 0; column2 < martix2.Columns; column2++)
{
double Sum = 0;
for (int column1 = 0; column1 < martix1.Columns; column1++)
{
Sum += martix1[row1, column1] * martix2[column1, row2];
}
result[row1, column2] = Sum;
row2++;
}
}
}
else
{
MessageBox.Show("矩阵乘法运算两个矩阵行列不匹配!");
}
}
catch
{
MessageBox.Show("矩阵乘法运算错误!");
}
return(result);
}
/// <summary>
/// 二维矩阵减法运算
/// </summary>
/// <param name="martix1"></param>
/// <param name="martix2"></param>
/// <returns></returns>
public static Martix operator -(Martix martix1, Martix martix2)
{
double[,] array = new double[martix1.Rows, martix1.Columns];
Martix result = new Martix(array);
try
{
if (martix1.Rows == martix2.Rows && martix1.Columns == martix2.Columns)
{
for (int i = 0; i < martix1.Rows; i++)
{
for (int j = 0; j < martix1.Columns; j++)
{
result[i, j] = martix1[i, j] - martix2[i, j];
}
}
}
}
catch
{
if (martix1.Rows != martix2.Rows)
{
MessageBox.Show("减法运算行数不匹配!");
}
if (martix1.Columns != martix2.Columns)
{
MessageBox.Show("减法运算列数不匹配!");
}
}
return(result);
}
/// <summary>
/// 求解七参数
/// </summary>
/// <param name="knownPoints">已知点构成的点集</param>
/// <param name="B"></param>
/// <param name="N"></param>
/// <returns>七参数构成的数组</returns>
public static double[,] ComputeSevenParameter(List <Point> knownPoints, out double[,] B, out double[,] N)
{
Martix tempB = new Martix(GetB(knownPoints));
Martix l = new Martix(Getl(knownPoints));
Martix tempN = tempB.Transpose() * tempB;
Martix W = tempB.Transpose() * l;
Martix x = tempN.Inverse(tempN.Element) * W;
Martix V = tempB * x - l;
string str = FileHandle.ArrayToStr(tempN.Element);
B = tempB.Element;
N = tempN.Element;
return(x.Element);
}
/// <summary>
/// 计算方阵伴随矩阵
/// </summary>
/// <param name="martix"></param>
/// <returns></returns>
private Martix complement(Martix martix)
{
double[,] array = new double[martix.Rows, martix.Columns];
Martix result = new Martix(array);
try
{
if (martix.Rows == martix.Columns)//方阵
{
for (int i = 0; i < martix.Rows; i++)
{
for (int j = 0; j < martix.Columns; j++)
{
//生成aij的余子式矩阵
double[,] complement = new double[martix.Rows - 1, martix.Columns - 1]; //n-1阶
Martix martix1 = new Martix(complement); //aij的余子式矩阵
int row = 0;
for (int k = 0; k < martix.Rows; k++)
{
int column = 0;
if (k == i)//去除第i行
{
continue;
}
for (int l = 0; l < martix.Rows; l++)
{
if (l == j)//去除第j列
{
continue;
}
martix1[row, column++] = martix[k, l];
}
row++;
}
result[i, j] = Math.Pow(-1, i + j) * Determinant(martix1);
}
}
}
}
catch
{
MessageBox.Show("非方阵无法求伴随矩阵!");
}
return(result);
}
/// <summary>
/// 递归计算方阵的行列式,代数余子式法
/// </summary>
/// <param name="martix"></param>
/// <returns></returns>
public double Determinant(Martix martix)
{
//注：运用此方法求解行列式，有时结果错误。下例：det(test1)求解结果正确，但det(test2)结果错误。原因不明。
//double[,] test1 = { { 1, 2, 3, 5,1,2,5 }, { 3, 4, 5, 9,5,9,7 }, { 8, 6, 9, 10,10,25,36 }, { 12, 23, 15, 20 ,15,20,12} ,
// { 12,14,15,52,36,25,14},{ 48,56,19,47,23,14,15},{ 42,20,23,12,14,15,26} };
//double[,] test2 = {
// { 6, 0, 0, 0, -24457908.6589, 26916348.4769, -11760075.3881},
// { 0,6 ,0,24457908.6589,0,11760075.3881,26916348.4769},
// { 0,0,6 ,-26916348.4769,-11760075.3881,0,24457908.6589},
// { 0,24457908.6589,-26916348.476900,22044684068435,52756432634080.4,47937688228728.8,0},
// { -24457908.6589,0,-11760075.388100,52756432634080.4,122748456455284 ,-109719457014783 ,0},
// { 26916348.4769,11760075.3881,0,47937688228728.8,-109719457014783 ,143798427582131 ,0},
// { -11760075.3881,26916348.4769,24457908.6589,0,0,0,243496862360883 } };
double sum = 0;
try
{
int sign = 1;
if (martix.Rows == 1)//递归出口
{
return(martix[0, 0]);
}
for (int i = 0; i < martix.Rows; i++)
{
double[,] _tempmatrix = new double[martix.Rows - 1, martix.Columns - 1];
Martix tempmatrix = new Martix(_tempmatrix);
for (int j = 0; j < martix.Rows - 1; j++)
{
for (int k = 0; k < martix.Columns - 1; k++)
{
tempmatrix[j, k] = martix[j + 1, k >= i ? k + 1 : k];
}
}
sum += sign * martix[0, i] * Determinant(tempmatrix);//递归，调用函数自身
sign = sign * (-1);
}
}
catch
{
MessageBox.Show("矩阵求行列式错误!");
}
return(sum);
}
/// <summary>
/// 二维矩阵转置运算
/// </summary>
/// <returns></returns>
public Martix Transpose()
{
double[,] array = new double[Element.GetLength(1), Element.GetLength(0)];
Martix result = new Martix(array);
try
{
for (int i = 0; i < Element.GetLength(0); i++)
{
for (int j = 0; j < Element.GetLength(1); j++)
{
result[j, i] = Element[i, j];
}
}
}
catch
{
MessageBox.Show("矩阵转置错误!");
}
return(result);
}
/// <summary>
/// 二维矩阵乘法运算,矩阵右乘一个数
/// </summary>
/// <param name="num"></param>
/// <param name="martix1"></param>
/// <returns></returns>
public static Martix operator *(int num, Martix martix1)
{
double[,] array = new double[martix1.Rows, martix1.Columns];
Martix result = new Martix(array);
try
{
for (int i = 0; i < martix1.Rows; i++)
{
for (int j = 0; j < martix1.Columns; j++)
{
result[i, j] = martix1[i, j] * num;
}
}
}
catch
{
MessageBox.Show("矩阵右乘一个数错误!");
}
return(result);
}
/// <summary>
/// 二维矩阵求逆运算
/// </summary>
/// <returns></returns>
public Martix Inverse()
{
double[,] array = new double[Element.GetLength(1), Element.GetLength(0)];
Martix result = new Martix(array);
try
{
if (Element.GetLength(0) == Element.GetLength(1))//方阵
{
Martix martix = new Martix(Element);
if (Determinant(martix) != 0)
{
if (martix.Rows > 1)
{
result = complement(martix).Transpose() * (1 / Determinant(martix));
}
else
{
result.Element[0, 0] = 1 / martix[0, 0];
}
}
else
{
MessageBox.Show("矩阵行列式为0!");
}
}
else
{
MessageBox.Show("非方阵矩阵无法求逆!");
}
}
catch
{
MessageBox.Show("矩阵求逆错误!");
}
return(result);
}