如何通过RealMatrix乘以RealVector？ [英] How to multiply a RealVector by a RealMatrix?

问题描述

如何通过 RealMatrix 乘以给定的 RealVector ？我在两个类上都找不到任何乘法方法，只有 preMultiply 但似乎不起作用：

How can I multiply a given RealVector by a RealMatrix? I can't find any "multiply" method on both classes, only preMultiply but it seems not work:

// point to translate
final RealVector p = MatrixUtils.createRealVector(new double[] {
        3, 4, 5, 1
});

// translation matrix (6, 7, 8)
final RealMatrix m = MatrixUtils.createRealMatrix(new double[][] {
        {1, 0, 0, 6},
        {0, 1, 0, 7},
        {0, 0, 1, 8},
        {0, 0, 0, 1}
});

// p2 = m x p
final RealVector p2 = m.preMultiply(p);
// prints {3; 4; 5; 87}
// expected {9; 11; 13; 1}
System.out.println(p2);

请将实际结果与预期结果进行比较。

Please compare the actual result with the expected result.

还有一种方法可以将 Vector3D 乘以4x4 RealMatrix ，其中w组件被丢弃？ （我不是在寻找自定义实现，而是在库中已有的方法）。

Is there also a way for multiplying a Vector3D by a 4x4 RealMatrix where the w component is throw away? (I'm looking not for custom implementation but an already existing method in the library).

推荐答案

preMultiply 不会给你 mxp 但是 pxm 。这适用于您的问题但不适用于您的评论 // p2 = mxp 。

preMultiply does not give you m x p but p x m. This would be suitable for your question but not for your comment // p2 = m x p.

要获得结果你想要你有两个选择：

To get the result you want you have two options:

1. 使用 RealMatrix #open（RealVector）产生 mxp ：

RealVector mxp = m.operate(p);    
System.out.println(mxp);    

在预乘之前转置矩阵：

Transpose the matrix before pre-multiplying:

RealVector pxm_t = m.transpose().preMultiply(p);
System.out.println(pxm_t);

结果：

{9; 11; 13; 1}

{9; 11; 13; 1}

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