final public class Matrix {
    private final int M;             // number of rows
    private final int N;             // number of columns
    private final float[][] data;    // M-by-N array

    public int getWidth() {
      return N;
    }
    
    public int getHeight(){
      return M;
    }

    public void setVal(int x, int y, float val) {
        data[x][y] = val;
    }
    
    public float getVal(int x, int y) {
        return data[x][y];  
    }

    // create M-by-N matrix of 0's
    public Matrix(int M, int N) {
        this.M = M;
        this.N = N;
        data = new float[M][N];
    }

    // create matrix based on 2d array
    public Matrix(float[][] data) {
        M = data.length;
        N = data[0].length;
        this.data = new float[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 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) throw new 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) throw new 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?
    public boolean eq(Matrix B) {
        Matrix A = this;
        if (B.M != A.M || B.N != A.N) throw new 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]) return false;
        return true;
    }

    // return C = A * B
    public Matrix times(Matrix B) {
        Matrix A = this;
        if (A.N != B.M) throw new 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;
    }

    // print matrix to standard output
    public void show() {
        for (int i = 0; i < M; i++) {
            for (int j = 0; j < N; j++) 
                System.out.print(data[i][j] + "\t" );
            System.out.println();
        }
    }
}