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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。

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