線形代数方程式を解くために Jama と Apache Commons Math を使用しています。行列が小さい (4x4) 場合、どちらも正常に機能します。ただし、比較的大きい場合 (25x25) はそうではありません。以下は私の実装です:
ジャマ:
public double[][] solve(double[][] startState, double[][] input){
double[][] answer = new double[1][input.length-1];
Matrix A = new Matrix(input);
Matrix B = new Matrix(startState);
Matrix X = A.solve(B);
answer = X.getArray();
return answer;
}
これは、次の場合にうまく機能します。
double[][] startState = {{1},{2},{1},{2}};
double[][] input = {{1,1,0,0},{1,1,1,0},{0,1,1,1,},{0,0,1,1}};
double[][] answer = new JamaSolution().solve(startState, input);
ただし、次の場合は失敗します。
double[][] startState = { {0},{1},{2},{0},{2}, {0},{2},{1},{1},{0}, {0},{2},{1},{2},{2}, {1},{1},{1},{1},{2}, {1},{2},{1},{0},{0} };
double[][] input={
{1,1,0,0,0, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{1,1,1,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,1,1,1,0, 0,0,1,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,1,1,1, 0,0,0,1,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,1,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{1,0,0,0,0, 1,1,0,0,0, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,1,0,0,0, 1,1,1,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,1,0,0, 0,1,1,1,0, 0,0,1,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,1,0, 0,0,1,1,1, 0,0,0,1,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,1,1, 0,0,0,0,1, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 1,0,0,0,0, 1,1,0,0,0, 1,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,1,0,0,0, 1,1,1,0,0, 0,1,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,1,0,0, 0,1,1,1,0, 0,0,1,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,1,0, 0,0,1,1,1, 0,0,0,1,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,1, 0,0,0,1,1, 0,0,0,0,1, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 1,0,0,0,0, 1,1,0,0,0, 1,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,1,0,0,0, 1,1,1,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,1,0,0, 0,1,1,1,0, 0,0,1,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,1,0, 0,0,1,1,1, 0,0,0,1,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,1, 0,0,0,1,1, 0,0,0,0,1} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1,0,0,0,0, 1,1,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1,1,1,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,1,0,0, 0,1,1,1,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,1,0, 0,0,1,1,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,1, 0,0,0,0,1} ,
};
コモンズ数学:
public void solve(double[] startState, double[][] input){
RealMatrix coefficients = new Array2DRowRealMatrix(input, false);
DecompositionSolver solver = new LUDecomposition(coefficients).getSolver();
RealVector constants = new ArrayRealVector(startState, false);
RealVector solution = solver.solve(constants);
}
これは、次の場合にうまく機能します。
double[] startState = {1,2,1,2};
double[][] input = {{1,1,0,0},{1,1,1,0},{0,1,1,1,},{0,0,1,1}};
ただし、次の場合は失敗します。
double[] startState = { 0,1,2,0,2, 0,2,1,1,0, 0,2,1,2,2, 1,1,1,1,2, 1,2,1,0,0 };
double[][] input={
{1,1,0,0,0, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{1,1,1,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,1,1,1,0, 0,0,1,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,1,1,1, 0,0,0,1,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,1,1, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{1,0,0,0,0, 1,1,0,0,0, 1,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,1,0,0,0, 1,1,1,0,0, 0,1,0,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,1,0,0, 0,1,1,1,0, 0,0,1,0,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,1,0, 0,0,1,1,1, 0,0,0,1,0, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,1,1, 0,0,0,0,1, 0,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 1,0,0,0,0, 1,1,0,0,0, 1,0,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,1,0,0,0, 1,1,1,0,0, 0,1,0,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,1,0,0, 0,1,1,1,0, 0,0,1,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,1,0, 0,0,1,1,1, 0,0,0,1,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,1, 0,0,0,1,1, 0,0,0,0,1, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 1,0,0,0,0, 1,1,0,0,0, 1,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,1,0,0,0, 1,1,1,0,0, 0,0,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,1,0,0, 0,1,1,1,0, 0,0,1,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,1,0, 0,0,1,1,1, 0,0,0,1,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,1, 0,0,0,1,1, 0,0,0,0,1} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1,0,0,0,0, 1,1,0,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 1,1,1,0,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,1,0,0, 0,1,1,1,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,1,0, 0,0,1,1,0} ,
{0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,0, 0,0,0,0,1, 0,0,0,0,1} ,
};
「失敗」とは、すべての整数値を持つ解決策が少なくとも 1 つあることを知っていますが、私の実装では分数の値が得られるということです。