Mit dem Verfahren lässt sich die Lösung eines linearen Gleichungssystem berechnen.
//written by Andre Betz 2007
//http://www.andrebetz.de
public class myMatrix {
private int m_XSize;
private int m_YSize;
private double[] m_Field;
private double m_Eps = 0.001;
public myMatrix(int XSize,int YSize){
m_XSize = XSize;
m_YSize = YSize;
m_Field = new double[m_XSize*m_YSize];
for(int i=0;i<m_XSize*m_YSize;i++){
m_Field[i] = 0.0;
}
}
public myMatrix(myMatrix m){
m_XSize = m.GetXSize();
m_YSize = m.GetYSize();
m_Field = new double[m_XSize*m_YSize];
CopyFields(m.m_Field);
}
public myMatrix(double[][] fld){
m_YSize = fld.length;
m_XSize = fld[0].length;
m_Field = new double[m_XSize*m_YSize];
for(int y=0;y<m_YSize;y++){
for(int x=0;x<m_XSize;x++){
SetVal(x,y,fld[y][x]);
}
}
}
public int GetXSize(){
return m_XSize;
}
public int GetYSize(){
return m_YSize;
}
public double GetVal(int x,int y){
double ret = 0.0;
if(x<m_XSize&&y<m_YSize)
{
ret = m_Field[y*m_XSize+x];
}
return ret;
}
public double SetVal(int x,int y,double val){
double ret = 0.0;
if(x<m_XSize&&y<m_YSize)
{
m_Field[y*m_XSize+x] = val;
}
else
throw new RuntimeException("Wrong Position");
return ret;
}
public myMatrix Add(myMatrix m){
if(m.GetXSize()!=m_XSize || m.GetYSize()!=m_YSize)
throw new RuntimeException("Different Matrix Size");
myMatrix n = new myMatrix(m_XSize,m_YSize);
for(int y=0;y<m_YSize;y++){
for(int x=0;x<m_XSize;x++){
n.SetVal(x,y,this.GetVal(x, y) + m.GetVal(x, y));
}
}
return n;
}
public myMatrix Minus(myMatrix m){
if(m.GetXSize()!=m_XSize || m.GetYSize()!=m_YSize)
throw new RuntimeException("Different Matrix Size");
myMatrix n = new myMatrix(m_XSize,m_YSize);
for(int y=0;y<m_YSize;y++){
for(int x=0;x<m_XSize;x++){
n.SetVal(x,y,this.GetVal(x, y) - m.GetVal(x, y));
}
}
return n;
}
public myMatrix Mul(myMatrix m){
if(m_XSize!=m.GetYSize())
throw new RuntimeException("Different Matrix Size");
myMatrix n = new myMatrix(m.GetXSize(),m_YSize);
for(int y=0;y<n.GetYSize();y++){
for(int x=0;x<n.GetXSize();x++){
double tmp = 0.0;
for(int i=0;i<m_XSize;i++){
tmp += this.GetVal(i, y) - m.GetVal(x, i);
}
n.SetVal(x,y,tmp);
}
}
return n;
}
public void SwapRow(int a,int b){
if(a<m_YSize&&b<m_YSize)
{
for(int i=0;i<m_XSize;i++){
double tmp = GetVal(i,a);
SetVal(i,a,GetVal(i,b));
SetVal(i,b,tmp);
}
}else
throw new RuntimeException("Wrong Positions");
}
public String getString() {
String str = "";
for(int y=0;y<m_YSize;y++){
for(int x=0;x<m_XSize;x++){
str += GetVal(x,y) + "\t";
}
str += "\n";
}
return str;
}
public myMatrix Solve_Gauss(myMatrix vec)
{
if(vec.GetXSize()!=1 || vec.GetYSize() != m_YSize || m_YSize != m_XSize)
throw new RuntimeException("Wrong Matrix Dimensions");
myMatrix A = new myMatrix(this);
myMatrix b = new myMatrix(vec);
myMatrix r = new myMatrix(m_XSize,1);
for(int r1=0;r1<m_YSize;r1++){
int maxPiv = r1;
double MaxVal = Math.abs(A.GetVal(r1,maxPiv));
for(int r2=r1+1;r2<m_XSize;r2++){
if(Math.abs(A.GetVal(r1,r2)) > Math.abs(A.GetVal(r1,maxPiv))){
maxPiv = r2;
MaxVal = Math.abs(A.GetVal(r1,r2));
}
}
if(MaxVal<m_Eps)
throw new RuntimeException("singular Matrix");
A.SwapRow(r1, maxPiv);
b.SwapRow(r1, maxPiv);
for(int r2=r1+1;r2<m_XSize;r2++){
double val = A.GetVal(r1,r2) / A.GetVal(r1,r1);
for(int i=r1+1;i<m_XSize;i++) {
double t = A.GetVal(i,r2) - A.GetVal(i,r1) * val;
A.SetVal(i,r2,t);
}
A.SetVal(r1,r2,0.0);
val = b.GetVal(0,r2) - b.GetVal(0,r1) * A.GetVal(r1,r2) / A.GetVal(r1,r1);
b.SetVal(0,r2,val);
}
}
for(int y=m_YSize-1;y>=0;y--){
double t = 0.0;
for(int x=y+1;x<m_XSize;x++){
t += A.GetVal(x,y) * r.GetVal(x,0);
}
double val = (b.GetVal(0,y) - t) / A.GetVal(y,y);
r.SetVal(y,0,val);
}
return r;
}
private void CopyFields(double[] fld){
for(int i=0;i<m_XSize*m_YSize;i++){
m_Field[i] = fld[i];
}
}
public static void main(String[] args) {
double[][] d = { { -1, 3, 0,-10 },
{ 0, 0, -3, 0 },
{ 1, -3, 0,11 },
{ 1, 0, 0, 1} };
double [][] e = {{5},{46.5},{-6},{-20}};
myMatrix A = new myMatrix(d);
myMatrix b = new myMatrix(e);
myMatrix c = A.Solve_Gauss(b);
System.out.println(A.getString());
System.out.println(b.getString());
System.out.println(c.getString());
System.out.println();
}
}
