Java之矩阵求特征值

public class MatrixEigenValue {
public static int Hessenberg(double[][] Matrix,int n,double[][]ret)
{

	int i;
	int j;
	int k;
	double temp;
	int MaxNu;
	n-=1;
	for(k=1;k<=n-1;k++)
	{
		i=k-1;
		MaxNu=k;
		temp=Math.abs(Matrix[k][i]);
		for(j=k+1;j<=n;j++)
		{
			if(Math.abs(Matrix[j][i])>temp)
			{
				MaxNu=j;
			}
		}
		ret[0][0]=Matrix[MaxNu][i];
		i=MaxNu;
		if(ret[0][0]!=0)
		{
			if(i!=k)
			{
				for(j=k-1;j<=n;j++)
				{
					temp=Matrix[i][j];
					Matrix[i][j]=Matrix[k][j];
					Matrix[k][j]=temp;
				}
				for(j=0;j<=n;j++)
				{
					temp=Matrix[j][i];
					Matrix[j][i]=Matrix[j][k];
					Matrix[j][k]=temp;
				}
			}
			for(i=k+1;i<=n;i++)
			{
				temp=Matrix[i][k-1]/ret[0][0];
				Matrix[i][k-1]=0;
				for(j=k;j<=n;j++)
				{
					Matrix[i][j]-=temp*Matrix[k][j];
				}
				for(j=0;j<=n;j++)
				{
					Matrix[j][k]+=temp*Matrix[j][i];
				}
			}
		}
	}
	for(i=0;i<=n;i++)
	{
		for(j=0;j<=n;j++)
		{
			ret[i][j]=Matrix[i][j];
		}
	}
	return n+1;
}
////////////
public static boolean EigenValue(double[][]Matrix,int n,int LoopNu,int Erro,double[][]Ret)
{
	int i=Matrix.length;
	if(i!=n)
	{
		return false;
	}
	int j;
	int k;
	int t;
	int m;
	double[][]A=new double[n][n];
	double erro=Math.pow(0.1, Erro);
	double b;
	double c;
	double d;
	double g;
	double xy;
	double p;
	double q;
	double r;
	double x;
	double s;
	double e;
	double f;
	double z;
	double y;
	int loop1=LoopNu;
	Hessenberg(Matrix,n,A);//将方阵K1转化成上Hessenberg矩阵A
	m=n;
	while(m!=0)
	{
		t=m-1;
		while(t>0)
		{
			if(Math.abs(A[t][t-1])>erro*(Math.abs(A[t-1][t-1])+Math.abs(A[t][t])))
			{
				t-=1;
			}
			else
			{
				break;
			}
		}
		if(t==m-1)
		{
			Ret[m-1][0]=A[m-1][m-1];
			Ret[m-1][1]=0;
			m-=1;
			loop1=LoopNu;
			
		}
		else if(t==m-2)
		{
			b=-(A[m-1][m-1]+A[m-2][m-2]);
			c=A[m-1][m-1]*A[m-2][m-2]-A[m-1][m-2]*A[m-2][m-1];
			d=b*b-4*c;
			y=Math.pow(Math.abs(d), 0.5);
			if(d>0)
			{
				xy=1;
				if(b<0)
				{
					xy=-1;
				}
				Ret[m-1][0]=-(b+xy*y)/2;
				Ret[m-1][1]=0;
				Ret[m-2][0]=c/Ret[m-1][0];
				Ret[m-2][1]=0;
			}
			else
			{
				Ret[m-1][0]=-b/2;
				Ret[m-2][0]=Ret[m-1][0];
				Ret[m-1][1]=y/2;
				Ret[m-2][1]=-Ret[m-1][1];
			}
			m-=2;
			loop1=LoopNu;
		}
		else
		{
			if(loop1<1)
			{
				return false;
			}
			loop1-=1;
			j=t+2;
			while(j<m)
			{
				A[j][j-2]=0;
				j+=1;
			}
			j=t+3;
			while(j<m)
			{
				A[j][j-3]=0;
				j+=1;
			}
			k=t;
			while(k<m-1)
			{
				if(k!=t)
				{
					p=A[k][k-1];
					q=A[k+1][k-1];
					if(k!=m-2)
					{
						r=A[k+2][k-1];
					}
					else
					{
						r=0;
					}
				}
				else
				{
					b=A[m-1][m-1];
					c=A[m-2][m-2];
					x=b+c;
					y=c*b-A[m-2][m-1]*A[m-1][m-2];
					p=A[t][t]*(A[t][t]-x)+A[t][t+1]*A[t+1][t]+y;
					q=A[t+1][t]*(A[t][t]+A[t+1][t+1]-x);
					r=A[t+1][t]*A[t+2][t+1];
				}
				if(p!=0||q!=0||r!=0)
				{
					if(p<0)
					{
						xy=-1;
					}
					else
					{
						xy=1;
					}
					s=xy*Math.pow(p*p+q*q+r*r, 0.5);
					if(k!=t)
					{
						A[k][k-1]=-s;
					}
					e=-q/s;
					f=-r/s;
					x=-p/s;
					y=-x-f*r/(p+s);
					g=e*r/(p+s);
					z=-x-e*q/(p+s);
					for(j=k;j<=m-1;j++)
					{
						b=A[k][j];
						c=A[k+1][j];
						p=x*b+e*c;
						q=e*b+y*c;
						r=f*b+g*c;
						if(k!=m-2)
						{
							b=A[k+2][j];
							p+=f*b;
							q+=g*b;
							r+=z*b;
							A[k+2][j]=r;
						}
						A[k+1][j]=q;
						A[k][j]=p;
						
					}
					j=k+3;
					if(j>=m-1)
					{
						j=m-1;
					}
					for(i=t;i<=j;i++)
					{
						b=A[i][k];
						c=A[i][k+1];
						p=x*b+e*c;
						q=e*b+y*c;
						r=f*b+g*c;
						if(k!=m-2)
						{
							b=A[i][k+2];
							p+=f*b;
							q+=g*b;
							r+=z*b;
							A[i][k+2]=r;
						}
						A[i][k+1]=q;
						A[i][k]=p;
					}
				}
				k+=1;
			}
			
		}
		
	}
	return true;
}
public static void main(String[]args)//测试
{
	double[][] TestMatrix = {
			   {1, 22, 34,22}, 

			   {1, 11,5,21} ,
			   {0,1,5,11},
			   {7,2,13,19}};	
	double[][] TMatrix1={
			{1,2,3},{2,1,1},{2,2,2}	
	};
	double[][]TMatrix2={
			{1,2},{2,3}	
	};
	double[][] GetEV=new double[3][2];
    EigenValue(TMatrix2,2,400,4,GetEV);
	String Strr=new String("");
	for(int i=0;i<2;i++)
	{
		String str=String.valueOf(GetEV[i][0]);//
		Strr+=str;
		Strr+=" ";
		String str1=String.valueOf(GetEV[i][1]);
		Strr+=str1;
		Strr+="\n";
	
	}
	
	
   System.out.println(Strr);
	
}
}

运行结果如下：

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