/**
* 实现矩阵的乘法
*
* @param other - 与指定矩阵相乘的矩阵
* @return Matrix型，指定矩阵与other相乘之积
* @如果矩阵的行/列数不匹配，则会抛出异常
*/
public Matrix Multiply(Matrix other)
{
// 首先检查行列数是否符合要求
if (numColumns != other.GetNumRows())
{
throw new Exception("矩阵的行/列数不匹配。");
}
// ruct the object we are going to return
Matrix result = new Matrix(numRows, other.GetNumColumns());
// 矩阵乘法，即
//
// [A][B][C] [G][H] [A*G + B*I + C*K][A*H + B*J + C*L]
// [D][E][F] * [I][J] = [D*G + E*I + F*K][D*H + E*J + F*L]
// [K][L]
//
double value;
for (int i = 0; i < result.GetNumRows(); ++i)
{
for (int j = 0; j < other.GetNumColumns(); ++j)
{
value = 0.0;
for (int k = 0; k < numColumns; ++k)
{
value += GetElement(i, k) * other.GetElement(k, j);
}
result.SetElement(i, j, value);
}
}
return(result);
}
/**
* 矩阵的转置
*
* @return Matrix型，指定矩阵转置矩阵
*/
public Matrix Transpose()
{
// 构造目标矩阵
Matrix Trans = new Matrix(numColumns, numRows);
// 转置各元素
for (int i = 0; i < numRows; ++i)
{
for (int j = 0; j < numColumns; ++j)
{
Trans.SetElement(j, i, GetElement(i, j));
}
}
return(Trans);
}
/**
* 实现矩阵的数乘
*
* @param value - 与指定矩阵相乘的实数
* @return Matrix型，指定矩阵与value相乘之积
*/
public Matrix Multiply(double value)
{
// 构造目标矩阵
Matrix result = new Matrix(this); // copy ourselves
// 进行数乘
for (int i = 0; i < numRows; ++i)
{
for (int j = 0; j < numColumns; ++j)
{
result.SetElement(i, j, result.GetElement(i, j) * value);
}
}
return(result);
}
/**
* 实现矩阵的减法
*
* @param other - 与指定矩阵相减的矩阵
* @return Matrix型，指定矩阵与other相减之差
* @如果矩阵的行/列数不匹配，则会抛出异常
*/
public Matrix Subtract(Matrix other)
{
if (numColumns != other.GetNumColumns() ||
numRows != other.GetNumRows())
{
throw new Exception("矩阵的行/列数不匹配。");
}
// 构造结果矩阵
Matrix result = new Matrix(this); // 拷贝构造
// 进行减法操作
for (int i = 0; i < numRows; ++i)
{
for (int j = 0; j < numColumns; ++j)
{
result.SetElement(i, j, result.GetElement(i, j) - other.GetElement(i, j));
}
}
return(result);
}
/**
* 实现矩阵的加法
*
* @param other - 与指定矩阵相加的矩阵
* @return Matrix型，指定矩阵与other相加之和
* @如果矩阵的行/列数不匹配，则会抛出异常
*/
public Matrix Add(Matrix other)
{
// 首先检查行列数是否相等
if (numColumns != other.GetNumColumns() ||
numRows != other.GetNumRows())
{
throw new Exception("矩阵的行/列数不匹配。");
}
// 构造结果矩阵
Matrix result = new Matrix(this); // 拷贝构造
// 矩阵加法
for (int i = 0; i < numRows; ++i)
{
for (int j = 0; j < numColumns; ++j)
{
result.SetElement(i, j, result.GetElement(i, j) + other.GetElement(i, j));
}
}
return(result);
}
/**
* 实矩阵求逆的全选主元高斯－约当法
*
* @return bool型，求逆是否成功
*/
public Matrix InvertGaussJordan()
{
// 构造目标矩阵
Matrix invert = new Matrix(numColumns, numRows);
Matrix keep = new Matrix(numColumns, numRows);
// 保持各元素
for (int i1 = 0; i1 < numRows; ++i1)
{
for (int j1 = 0; j1 < numColumns; ++j1)
{
keep.SetElement(i1, j1, GetElement(i1, j1));
}
}
int i, j, k, l, u, v;
double d = 0, p = 0;
// 分配内存
int[] pnRow = new int[numColumns];
int[] pnCol = new int[numColumns];
// 消元
for (k = 0; k <= numColumns - 1; k++)
{
d = 0.0;
for (i = k; i <= numColumns - 1; i++)
{
for (j = k; j <= numColumns - 1; j++)
{
l = i * numColumns + j; p = Math.Abs(elements[l]);
if (p > d)
{
d = p;
pnRow[k] = i;
pnCol[k] = j;
}
}
}
// 失败
if (d == 0.0)
{
throw new Exception("求逆失败！矩阵行列式为零！");
}
if (pnRow[k] != k)
{
for (j = 0; j <= numColumns - 1; j++)
{
u = k * numColumns + j;
v = pnRow[k] * numColumns + j;
p = elements[u];
elements[u] = elements[v];
elements[v] = p;
}
}
if (pnCol[k] != k)
{
for (i = 0; i <= numColumns - 1; i++)
{
u = i * numColumns + k;
v = i * numColumns + pnCol[k];
p = elements[u];
elements[u] = elements[v];
elements[v] = p;
}
}
l = k * numColumns + k;
elements[l] = 1.0 / elements[l];
for (j = 0; j <= numColumns - 1; j++)
{
if (j != k)
{
u = k * numColumns + j;
elements[u] = elements[u] * elements[l];
}
}
for (i = 0; i <= numColumns - 1; i++)
{
if (i != k)
{
for (j = 0; j <= numColumns - 1; j++)
{
if (j != k)
{
u = i * numColumns + j;
elements[u] = elements[u] - elements[i * numColumns + k] * elements[k * numColumns + j];
}
}
}
}
for (i = 0; i <= numColumns - 1; i++)
{
if (i != k)
{
u = i * numColumns + k;
elements[u] = -elements[u] * elements[l];
}
}
}
// 调整恢复行列次序
for (k = numColumns - 1; k >= 0; k--)
{
if (pnCol[k] != k)
{
for (j = 0; j <= numColumns - 1; j++)
{
u = k * numColumns + j;
v = pnCol[k] * numColumns + j;
p = elements[u];
elements[u] = elements[v];
elements[v] = p;
}
}
if (pnRow[k] != k)
{
for (i = 0; i <= numColumns - 1; i++)
{
u = i * numColumns + k;
v = i * numColumns + pnRow[k];
p = elements[u];
elements[u] = elements[v];
elements[v] = p;
}
}
}
invert.SetData(elements); //存储求逆后的矩阵
this.SetData(keep); //保持原矩阵不变
//Console.WriteLine(invert);
//Console.WriteLine(keep);
//Console.WriteLine(this);
//Console.ReadLine();
// 成功返回
return(invert);
}