Question

我正在寻找用于解决linear complementarity problem的Projected Gauss-Seidel算法的C＃实现。到目前为止，我已经在Bullet库中找到了用C ++编写的文件，但遗憾的是它已经过高度优化（因此很难将其翻译成C＃）。

在similar问题中，建议您查看numerical libraries for .NET。所有这些都只包含解算systems of linear equations的算法。

编辑：即使我找到了，但它似乎并不完整，所以问题仍然存在。

Answer 1

经过一周的搜索，我终于找到了this出版物（俄语，基于Kenny Erleben的作品）。在那里描述了一个投射的Gauss-Seidel算法，然后用SOR和终止条件进行扩展。所有这些都与C ++中的示例有关，我将其用于此基本C＃实现：

public static double[] Solve (double[,] matrix, double[] right,
                              double relaxation, int iterations)
{
    // Validation omitted
    var x = right;
    double delta;

    // Gauss-Seidel with Successive OverRelaxation Solver
    for (int k = 0; k < iterations; ++k) {
        for (int i = 0; i < right.Length; ++i) {
            delta = 0.0f;

            for (int j = 0; j < i; ++j)
                delta += matrix [i, j] * x [j];
            for (int j = i + 1; j < right.Length; ++j)
                delta += matrix [i, j] * x [j];

            delta = (right [i] - delta) / matrix [i, i];
            x [i] += relaxation * (delta - x [i]);
        }
    }

    return x;
}

Answer 2

你没有投影就实现了高斯赛德尔。对于预测的Gauss Seidel，您需要在下限和上限内投影（或钳制）解决方案：

public static double[] Solve (double[,] matrix, double[] right,
                              double relaxation, int iterations, 
                              double[] lo, double[] hi)
{
    // Validation omitted
    var x = right;
    double delta;

    // Gauss-Seidel with Successive OverRelaxation Solver
    for (int k = 0; k < iterations; ++k) {
        for (int i = 0; i < right.Length; ++i) {
            delta = 0.0f;

            for (int j = 0; j < i; ++j)
                delta += matrix [i, j] * x [j];
            for (int j = i + 1; j < right.Length; ++j)
                delta += matrix [i, j] * x [j];

            delta = (right [i] - delta) / matrix [i, i];
            x [i] += relaxation * (delta - x [i]);
    // Project the solution within the lower and higher limits
            if (x[i]<lo[i])
                x[i]=lo[i];
            if (x[i]>hi[i])
                x[i]=hi[i];
        }
    }
    return x;
}

这是一个小修改。这是一个要点，展示如何从Bullet物理库中提取A矩阵和b矢量，并使用投影Gauss Seidel解决它：https://gist.github.com/erwincoumans/6666160

用于LCP的预计Gauss-Seidel

2 个答案: