最近需要用 C++ 做一些数值计算,之前一直采用Matlab 混合编程的方式处理矩阵运算,非常麻烦,直到发现了 Eigen 库,简直相见恨晚,好用哭了。 Eigen 是一个基于C++模板的线性代数库,直接将库下载后放在项目目录下,然后包含头文件就能使用,非常方便。此外,Eigen的接口清晰,稳定高效。唯一的问题是之前一直用 Matlab,对 Eigen 的 API 接口不太熟悉,如果能有 Eigen 和 Matlab 对应的说明想必是极好的,终于功夫不负有心人,让我找到了,原文在这里,不过排版有些混乱,我将其重新整理了一下,方便日后查询。
Eigen 矩阵定义
#include <Eigen/Dense> Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d. Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols. Matrix<double, Dynamic, Dynamic> C; // Full dynamic. Same as MatrixXd. Matrix<double, 3, 3, RowMajor> E; // Row major; default is column-major. Matrix3f P, Q, R; // 3x3 float matrix. Vector3f x, y, z; // 3x1 float matrix. RowVector3f a, b, c; // 1x3 float matrix. VectorXd v; // Dynamic column vector of doubles // Eigen // Matlab // comments x.size() // length(x) // vector size C.rows() // size(C,1) // number of rows C.cols() // size(C,2) // number of columns x(i) // x(i+1) // Matlab is 1-based C(i,j) // C(i+1,j+1) // |
Eigen 基础使用
// Basic usage // Eigen // Matlab // comments x.size() // length(x) // vector size C.rows() // size(C,1) // number of rows C.cols() // size(C,2) // number of columns x(i) // x(i+1) // Matlab is 1-based C(i, j) // C(i+1,j+1) // A.resize(4, 4); // Runtime error if assertions are on. B.resize(4, 9); // Runtime error if assertions are on. A.resize(3, 3); // Ok; size didn't change. B.resize(3, 9); // Ok; only dynamic cols changed. A << 1, 2, 3, // Initialize A. The elements can also be 4, 5, 6, // matrices, which are stacked along cols 7, 8, 9; // and then the rows are stacked. B << A, A, A; // B is three horizontally stacked A's. A.fill(10); // Fill A with all 10's. Eigen 特殊矩阵生成 // Eigen // Matlab MatrixXd::Identity(rows,cols) // eye(rows,cols) C.setIdentity(rows,cols) // C = eye(rows,cols) MatrixXd::Zero(rows,cols) // zeros(rows,cols) C.setZero(rows,cols) // C = ones(rows,cols) MatrixXd::Ones(rows,cols) // ones(rows,cols) C.setOnes(rows,cols) // C = ones(rows,cols) MatrixXd::Random(rows,cols) // rand(rows,cols)*2-1 // MatrixXd::Random returns uniform random numbers in (-1, 1). C.setRandom(rows,cols) // C = rand(rows,cols)*2-1 VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)' v.setLinSpaced(size,low,high) // v = linspace(low,high,size)' |
Eigen 矩阵分块
// Matrix slicing and blocks. All expressions listed here are read/write. // Templated size versions are faster. Note that Matlab is 1-based (a size N // vector is x(1)...x(N)). // Eigen // Matlab x.head(n) // x(1:n) x.head<n>() // x(1:n) x.tail(n) // x(end - n + 1: end) x.tail<n>() // x(end - n + 1: end) x.segment(i, n) // x(i+1 : i+n) x.segment<n>(i) // x(i+1 : i+n) P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols) P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols) P.row(i) // P(i+1, :) P.col(j) // P(:, j+1) P.leftCols<cols>() // P(:, 1:cols) P.leftCols(cols) // P(:, 1:cols) P.middleCols<cols>(j) // P(:, j+1:j+cols) P.middleCols(j, cols) // P(:, j+1:j+cols) P.rightCols<cols>() // P(:, end-cols+1:end) P.rightCols(cols) // P(:, end-cols+1:end) P.topRows<rows>() // P(1:rows, :) P.topRows(rows) // P(1:rows, :) P.middleRows<rows>(i) // P(i+1:i+rows, :) P.middleRows(i, rows) // P(i+1:i+rows, :) P.bottomRows<rows>() // P(end-rows+1:end, :) P.bottomRows(rows) // P(end-rows+1:end, :) P.topLeftCorner(rows, cols) // P(1:rows, 1:cols) P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end) P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols) P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end) P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols) P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end) P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols) P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end) |