Question about matrix determinant
I completed the Matrix and It runs right, but I'm concerned about determinant
section and I believe it may be wrong, any suggestion on how i can improve the determinant method? any help would be great! I've tried everything and is not sure on how to do it.
finalpublicclass Matrix{
privatefinalint M;// number of rows
privatefinalint N;// number of columns
privatefinaldouble[][] data;// M-by-N array
// create M-by-N matrix of 0's
public Matrix(int M,int N){
this.M = M;
this.N = N;
data =newdouble[M][N];
}
// create matrix based on 2d array
public Matrix(double[][] data){
M = data.length;
N = data[0].length;
this.data =newdouble[M][N];
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
this.data[i][j] = data[i][j];
}
// copy constructor
private Matrix(Matrix A){this(A.data);}
// create and return a random M-by-N matrix with values between 0 and 1
publicstatic Matrix random(int M,int N){
Matrix A =new Matrix(M, N);
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
A.data[i][j] = Math.random();
return A;
}
// create and return the N-by-N identity matrix
publicstatic Matrix identity(int N){
Matrix I =new Matrix(N, N);
for (int i = 0; i < N; i++)
I.data[i][i] = 1;
return I;
}
// swap rows i and j
privatevoid swap(int i,int j){
double[] temp = data[i];
data[i] = data[j];
data[j] = temp;
}
// create and return the transpose of the invoking matrix
public Matrix transpose(){
Matrix A =new Matrix(N, M);
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
A.data[j][i] = this.data[i][j];
return A;
}
// return C = A + B
public Matrix plus(Matrix B){
Matrix A =this;
if (B.M != A.M || B.N != A.N)thrownew RuntimeException("Illegal matrix dimensions.");
Matrix C =new Matrix(M, N);
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
C.data[i][j] = A.data[i][j] + B.data[i][j];
return C;
}
// return C = A - B
public Matrix minus(Matrix B){
Matrix A =this;
if (B.M != A.M || B.N != A.N)thrownew RuntimeException("Illegal matrix dimensions.");
Matrix C =new Matrix(M, N);
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
C.data[i][j] = A.data[i][j] - B.data[i][j];
return C;
}
// does A = B exactly?
publicboolean eq(Matrix B){
Matrix A =this;
if (B.M != A.M || B.N != A.N)thrownew RuntimeException("Illegal matrix dimensions.");
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
if (A.data[i][j] != B.data[i][j])returnfalse;
returntrue;
}
// return C = A * B
public Matrix times(Matrix B){
Matrix A =this;
if (A.N != B.M)thrownew RuntimeException("Illegal matrix dimensions.");
Matrix C =new Matrix(A.M, B.N);
for (int i = 0; i < C.M; i++)
for (int j = 0; j < C.N; j++)
for (int k = 0; k < A.N; k++)
C.data[i][j] += (A.data[i][k] * B.data[k][j]);
return C;
}
// return deteriment value
public Matrix det(Matrix B)
{
Matrix A =this;
if (B.M != A.M || B.N != A.N)thrownew RuntimeException("Illegal matrix dimensions.");
Matrix C=new Matrix(M, N);
for (int i = 0; i < M; i++)
for (int j = 0; j < N; j++)
C.data[i][j] = A.data[i][j] *B.data[i][j];
return C;
}
// return x = A^-1 b, assuming A is square and has full rank
public Matrix solve(Matrix rhs){
if (M != N || rhs.M != N || rhs.N != 1)
thrownew RuntimeException("Illegal matrix dimensions.");
// create copies of the data
Matrix A =new Matrix(this);
Matrix b =new Matrix(rhs);
// Gaussian elimination with partial pivoting
for (int i = 0; i < N; i++){
// find pivot row and swap
int max = i;
for (int j = i + 1; j < N; j++)
if (Math.abs(A.data[j][i]) > Math.abs(A.data[max][i]))
max = j;
A.swap(i, max);
b.swap(i, max);
// singular
if (A.data[i][i] == 0.0)thrownew RuntimeException("Matrix is singular.");
// pivot within b
for (int j = i + 1; j < N; j++)
b.data[j][0] -= b.data[i][0] * A.data[j][i] / A.data[i][i];
// pivot within A
for (int j = i + 1; j < N; j++){
double m = A.data[j][i] / A.data[i][i];
for (int k = i+1; k < N; k++){
A.data[j][k] -= A.data[i][k] * m;
}
A.data[j][i] = 0.0;
}
}
// back substitution
Matrix x =new Matrix(N, 1);
for (int j = N - 1; j >= 0; j--){
double t = 0.0;
for (int k = j + 1; k < N; k++)
t += A.data[j][k] * x.data[k][0];
x.data[j][0] = (b.data[j][0] - t) / A.data[j][j];
}
return x;
}
// print matrix to standard output
publicvoid show(){
for (int i = 0; i < M; i++){
for (int j = 0; j < N; j++)
System.out.printf("%9.4f ", data[i][j]);
System.out.println();
}
}
// test client
publicstaticvoid main(String[] args){
double[][] d ={{ 1, 2, 3},{ 4, 5, 6},{ 9, 1, 3}};
Matrix D =new Matrix(d);
D.show();
System.out.println();
Matrix A = Matrix.random(5, 5);
A.show();
System.out.println();
A.swap(1, 2);
A.show();
System.out.println();
Matrix B = A.transpose();
B.show();
System.out.println();
Matrix C = Matrix.identity(5);
C.show();
System.out.println();
A.plus(B).show();
System.out.println();
B.times(A).show();
System.out.println();
// shouldn't be equal since AB != BA in general
System.out.println(A.times(B).eq(B.times(A)));
System.out.println();
Matrix b = Matrix.random(5, 1);
b.show();
System.out.println();
Matrix x = A.solve(b);
x.show();
System.out.println();
A.times(x).show();
}
}
