使用 Eigen C++ 库将每个矩阵列与每个向量元素相乘 [英] Multiplication of each matrix column by each vector element using Eigen C++ Library

问题描述

我需要使用 Eigen C++ 库 将每个矩阵列乘以每个向量元素.我试过 colwise 没有成功.

I need to multiply each matrix column by each vector element using Eigen C++ library. I tried colwise without success.

示例数据:

Eigen::Matrix3Xf A(3,2); //3x2
A << 1 2,
     2 2,
     3 5;

Eigen::Vector3f V = Eigen::Vector3f(2, 3);

//Expected result
C = A.colwise()*V;

//C
//2 6,
//4 6,
//6 15
//this means C 1st col by V first element and C 2nd col by V 2nd element.

矩阵 A 可以有 3xN 和 V Nx1.含义 (cols x rowls).

Matrix A can have 3xN and V Nx1. Meaning (cols x rowls).

推荐答案

我会这样做:

Eigen::Matrix3Xf A(3, 2);  // 3x2
A << 1, 2, 2, 2, 3, 5;

Eigen::Vector3f V = Eigen::Vector3f(1, 2, 3);

const Eigen::Matrix3Xf C = A.array().colwise() * V.array();
std::cout << C << std::endl;

示例输出:

 1  2
 4  4
 9 15

说明

你很接近，诀窍是使用 .array() 来做广播乘法.

colwiseReturnType 没有 .array() 方法，所以我们必须在 A 的数组视图上做我们的 colwise 恶作剧.

colwiseReturnType doesn't have a .array() method, so we have to do our colwise shenanigans on the array view of A.

如果你想计算两个向量的元素乘积(最酷的酷猫称之为 Hadamard 产品)，你可以做

If you want to compute the element-wise product of two vectors (The coolest of cool cats call this the Hadamard Product), you can do

Eigen::Vector3f a = ...;
Eigen::Vector3f b = ...;
Eigen::Vector3f elementwise_product = a.array() * b.array();

以上代码以列方式执行的操作.

Which is what the above code is doing, in a columnwise fashion.

要解决行情况，您可以使用 .rowwise()，并且您需要一个额外的 transpose() 以使事情适合

To address the row case, you can use .rowwise(), and you'll need an extra transpose() to make things fit

Eigen::Matrix<float, 3, 2> A;  // 3x2
A << 1, 2, 2, 2, 3, 5;

Eigen::Vector2f V = Eigen::Vector2f(2, 3);

// Expected result
Eigen::Matrix<float, 3, 2> C = A.array().rowwise() * V.transpose().array();
std::cout << C << std::endl;

示例输出:

 2  6
 4  6
 6 15

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