在 C# 中计算 NxN 矩阵行列式 [英] Calculating an NxN matrix determinant in C#

问题描述

你如何计算 NxN 矩阵 C# 的行列式?

How do you calculate the determinant of an NxN matrix C# ?

推荐答案

OP 发布 另一个问题 专门询问 4x4 矩阵，该问题已作为此问题的完全重复而关闭.好吧，如果您不是在寻找通用解决方案，而是仅局限于 4x4 矩阵，那么您可以使用这个看起来很丑但经过验证的代码:

The OP posted another question asking specifically about 4x4 matrices, which has been closed as an exact duplicate of this question. Well, if you're not looking for a general solution but instead are constrained to 4x4 matrices alone, then you can use this ugly looking but tried-and-true code:

public double GetDeterminant() {
    var m = _values;
    return
         m[12] * m[9]  * m[6]  * m[3]   -  m[8] * m[13] * m[6]  * m[3]   -
         m[12] * m[5]  * m[10] * m[3]   +  m[4] * m[13] * m[10] * m[3]   +
         m[8]  * m[5]  * m[14] * m[3]   -  m[4] * m[9]  * m[14] * m[3]   -
         m[12] * m[9]  * m[2]  * m[7]   +  m[8] * m[13] * m[2]  * m[7]   +
         m[12] * m[1]  * m[10] * m[7]   -  m[0] * m[13] * m[10] * m[7]   -
         m[8]  * m[1]  * m[14] * m[7]   +  m[0] * m[9]  * m[14] * m[7]   +
         m[12] * m[5]  * m[2]  * m[11]  -  m[4] * m[13] * m[2]  * m[11]  -
         m[12] * m[1]  * m[6]  * m[11]  +  m[0] * m[13] * m[6]  * m[11]  +
         m[4]  * m[1]  * m[14] * m[11]  -  m[0] * m[5]  * m[14] * m[11]  -
         m[8]  * m[5]  * m[2]  * m[15]  +  m[4] * m[9]  * m[2]  * m[15]  +
         m[8]  * m[1]  * m[6]  * m[15]  -  m[0] * m[9]  * m[6]  * m[15]  -
         m[4]  * m[1]  * m[10] * m[15]  +  m[0] * m[5]  * m[10] * m[15];
}

它假设您将矢量数据存储在一个名为 _values(在这种情况下为 double，但 float 可以工作)的 16 元素数组中也是)，按以下顺序:

It assumes you store your vector data in a 16-element array called _values (of double in this case, but float would work too), in the following order:

0, 1, 2, 3,
4, 5, 6, 7,
8, 9, 10, 11,
12, 13, 14, 15

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