//幂法求矩阵绝对值最大的特征值
public static double Characteristic(CzSquareMatrix m,double eps, int N)
{
int k=1;
double[] a=new double[m.dim];
for (int i = 0; i < m.dim; i++)
{
a[i]=1;
}
CzVector v = new CzVector(a);
CzVector v1 = (CzVector)transposition(m*transposition((CzMatrix)v));
double b = CzVector.max(v1);
double z = 0;
while (Math.Abs(z - b) > eps && k < N)
{
k = k + 1;
z = b;
if (CzVector.max(v1)==0)
throw new DivideByZeroException("幂法求解过程中出现全0向量，请检查输入数据后重新运算！");
double mv = CzVector.max(v1);
v1 = v1 * (1 / mv);
v1 = (CzVector)transposition(m * transposition((CzMatrix)v1));
b = CzVector.max(v1);
}
return b;
}
//矩阵构造
public CzMatrix(params CzVector[] a)
{
nrow = a.Length;
int temp = a[0].length;
foreach (CzVector b in a)
{
if (temp != b.length)
throw new ArgumentException("矩阵向量长度不一致");
}
ncol = temp;
col = new CzVector[ncol];
row = new CzVector[nrow];
double[] temp1 = new double[ncol];
double[] temp2 = new double[nrow];
matrix = new double[nrow, ncol];
for (int i = 0; i < nrow; i++)
{
for (int j = 0; j < ncol; j++)
{
temp1[j] = a[i].values[j];
matrix[i, j] = a[i].values[j];
}
row[i]=(new CzVector(temp1));
}
for (int i = 0; i < ncol; i++)
{
for (int j = 0; j < nrow; j++)
temp2[j] = matrix[j, i];
col[i] = new CzVector(temp2);
}
}
//CzSquareMatrix带参构造函数
public CzSquareMatrix(CzVector[] a)
: base(a)
{
if (a.Length != a[0].Length) throw new ArgumentException("该矩阵不是方阵");
CzSquareMatrix UnitMatrix = new CzSquareMatrix(a.Length,a.Length);
CzSquareMatrix ZeroMatrix = new CzSquareMatrix(a.Length,a.Length);
dim = this.nrow;
for (int i = 0; i < dim; i++)
{
for (int j = 0; j < dim; j++)
{
ZeroMatrix.matrix[i, j] = 0;
if (i != j)
UnitMatrix.matrix[i, j] = 0;
else
UnitMatrix.matrix[i, i] = 1;
}
}
}
//LinearEquations构造函数
public LinearEquations(CzSquareMatrix A, CzVector b)
{
this.m = A;
this.c = CzMatrix.transposition((CzMatrix)b);
}
//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;
}
//重载Parse方法
public static CzMatrix Parse(string s)
{
CzVector[] Vresult;
string[] ss = s.Split(';');
Vresult = new CzVector[ss.Length];
for (int i = 0; i < ss.Length; i++)
{
Vresult[i] = CzVector.Parse(ss[i]);
}
return (new CzMatrix(Vresult));
}
//矩阵乘法重载
public static CzMatrix operator *(CzMatrix m1, CzMatrix m2)
{
CzVector[] Vresult;
double[] varray=new double[m2.ncol];
if (m1.ncol != m2.nrow)
throw new ArgumentException("矩阵乘法时维数不同");
Vresult = new CzVector[m1.nrow];
for (int i = 0; i < m1.nrow; i++)
{
for (int j=0;j<m2.ncol;j++)
varray[j] =m1.row[i]*m2.col[j];
Vresult[i] = new CzVector(varray);
}
return new CzMatrix(Vresult);
}
public static bool TryParse(string s, out CzVector v)
{
double c;
string[] ss = s.Split(' ');
v = new CzVector(ss.Length);
for (int i = 0; i < v.Length; i++)
{
if (!double.TryParse(ss[i], out c))
return false;
else
v.values[i] = double.Parse(ss[i]);
}
return true;
}
public static CzVector Parse(string s)
{
double c;
string[] ss = s.Split(' ');
CzVector v = new CzVector(ss.Length);
for (int i = 0; i < v.Length; i++)
{
if (!double.TryParse(ss[i], out c))
throw new FormatException();
else
v.values[i] = double.Parse(ss[i]);
}
return v;
}
public static double max(CzVector v)
{
double rmax = Math.Abs(v.values[0]);
for (int i = 1; i < v.Length; i++)
{
if (Math.Abs(v.values[i]) > rmax)
rmax = Math.Abs(v.values[i]);
}
return rmax;
}
public static CzVector operator -(CzVector v1, CzVector v2)
{
if (v1.Length != v2.Length)
throw new ArgumentException();
CzVector result = new CzVector(v1.Length);
for (int i = 0; i < v1.Length; i++)
result[i] = v1[i] - v2[i];
return result;
}
public static CzVector operator *(CzVector v2, double l)
{
CzVector result = new CzVector(v2.Length);
for (int i = 0; i < v2.Length; i++)
result[i] = l * v2[i];
return result;
}
