//LinearEquations构造函数
public LinearEquations(CzSquareMatrix A, CzVector b)
{
this.m = A;
this.c = CzMatrix.transposition((CzMatrix)b);
}
//矩阵元素更新方法
protected static void matrixrefresh(CzMatrix m)
{
double[] temp1 = new double[m.ncol];
double[] temp2 = new double[m.nrow];
for (int i = 0; i < m.nrow; i++)
{
for (int j = 0; j < m.ncol; j++)
{
temp1[j] = m.matrix[i,j];
}
m.row[i] = new CzVector(temp1);
}
for (int i = 0; i < m.ncol; i++)
{
for (int j = 0; j < m.nrow; j++)
temp2[j] = m.matrix[j, i];
m.col[i] = new CzVector(temp2);
}
}
//行向量更新方法
protected static void rowrefresh(CzMatrix m)
{
double[] temp=new double[m.nrow];
for (int i = 0; i < m.nrow; i++)
{
for (int j = 0; j < m.ncol; j++)
m.matrix[i, j] = m.row[i].values[j];
}
for (int i = 0; i < m.ncol; i++)
{
for (int j = 0; j < m.nrow; j++)
temp[j] = m.matrix[j, i];
m.col[i] = new CzVector(temp);
}
}
//初等行数乘变换
public CzMatrix Mutiplyrow(CzMatrix m, int a, double c)
{
for (int i = 0; i < m.row[a].length; i++)
{
m.row[a][i] *= c;
}
rowrefresh(m);
return m;
}
//删除行
public CzMatrix Removerow( int a)
{
CzMatrix Mresult;
List<CzVector> list = this.row.ToList();
list.RemoveAt(a);
CzVector[] row = list.ToArray();
//for (int i = a ; i < this.nrow-1;i++ )
//this.row[i] = new CzVector(this.row[i + 1].values);
this.nrow -= 1;
rowrefresh(this);
Mresult = new CzMatrix(row);
return Mresult;
}
//重载TryParse方法
public static bool TryParse(string s, out CzMatrix Mresult)
{
CzVector[] Vresult;
string[] ss = s.Split(';');
Vresult = new CzVector[ss.Length];
for (int i = 0; i < ss.Length; i++)
{
if (!CzVector.TryParse(ss[i], out Vresult[i]))
{
Mresult = null;
return false;
}
else
Vresult[i] = CzVector.Parse(ss[i]);
}
Mresult = new CzMatrix(Vresult);
return true;
}
//初等列数乘变换
public CzMatrix Mutiplycol(CzMatrix m, int a, double c)
{
for (int i = 0; i < m.col[a].length; i++)
{
m.col[a][i] *= c;
}
colrefresh(m);
return m;
}
//静态删除行
public static void Removerow(CzMatrix m, int a)
{
List<CzVector> list = m.row.ToList();
list.RemoveAt(a);
m.row = list.ToArray();
m.nrow -= 1;
rowrefresh(m);
}
//矩阵转置
public static CzMatrix transposition(CzMatrix m)
{
CzMatrix Mresult=new CzMatrix(m.ncol,m.nrow);
for (int i = 0; i < m.ncol; i++)
{
for (int j = 0; j < m.nrow; j++)
Mresult.matrix[i, j] = m.matrix[j, i];
}
matrixrefresh(Mresult);
return Mresult;
}
//静态初等行消法变换,第a行乘c加到第b行上
public static void Multiplyaddrow(CzMatrix m, int a, int b, double c)
{
for (int i = 0; i < m.row[b].length; i++)
{
m.row[b][i] += c * m.row[a][i];
}
rowrefresh(m);
}
//静态删除列
public static void Removecol(CzMatrix m, int a)
{
List<CzVector> list = m.col.ToList();
list.RemoveAt(a);
m.col = list.ToArray();
m.ncol -= 1;
colrefresh(m);
}
//静态初等列消法变换,第a列乘c加到第b列上
public static void Multiplyaddcol(CzMatrix m, int a, int b, double c)
{
for (int i = 0; i < m.col[b].length; i++)
{
m.col[b][i] += c * m.col[a][i];
}
colrefresh(m);
}
//初等行变换
public static CzMatrix Exchangerow(CzMatrix m, int a, int b)
{
CzVector temp = m.row[a];
m.row[a] = m.row[b];
m.row[b] = temp;
rowrefresh(m);
return m;
}
//初等列变换
public static CzMatrix Exchangecol(CzMatrix m, int a, int b)
{
CzVector temp = m.col[a];
m.col[a] = m.col[b];
m.col[b] = temp;
colrefresh(m);
return m;
}
//减法重载
public static CzMatrix operator -(CzMatrix m1, CzMatrix m2)
{
if (m1.ncol != m2.ncol || m1.nrow != m2.nrow)
throw new ArgumentException("矩阵减法时维数不同");
CzMatrix Mresult = new CzMatrix(m1.nrow, m1.ncol);
for (int i = 0; i < m1.nrow; i++)
{
Mresult.row[i] = m1.row[i]-m2.row[i];
}
rowrefresh(Mresult);
return Mresult;
}
//列变换计算行列式的值
public static double Determinant(CzSquareMatrix mfactor)
{
CzMatrix m = new CzMatrix(mfactor.row);
int dim = m.nrow;
int count=0;//count用来记录矩阵行列变换引起的行列式值的变化
for (int i = dim-1; i >= 0; i--)
{
if (m.matrix[i, i] == 0)
{
int k = i;
while (m.matrix[k, i] == 0)
{
k--;
if (k < 0)
break;
}
if (k >= 0)
{
CzMatrix.Exchangerow(m, k, i);
count++;
}
}
for(int j=dim-1;j>i;j--)
{
if (m.matrix[j, j] != 0)
{
Multiplyaddcol(m, j, i, -m.matrix[j, i] / m.matrix[j, j]);
colrefresh(m);
}
}
}
colrefresh(m);
double product=1;
for (int i=0;i<dim;i++)
product*=m.matrix[i,i];
return product*Math.Pow(-1,count);
}
