计算在C＃中的N×N矩阵的行列式 [英] Calculating an NxN matrix determinant in C#

问题描述

您是如何计算的N×N矩阵C＃的行列式

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

推荐答案

发布的OP的another问题专门询问4X4矩阵，它已关闭作为这个问题完全重复。好吧，如果你不是在寻找一个通用的解决方案，而是被限制独自4X4矩阵，那么你可以使用此难看，但尝试和真正的代码：

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];
}

它假定您存储称为16个元素的数组<你的矢量数据code> _values​​ （双击在这种情况下，但浮动将工作太），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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