转自 

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。  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，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 
     
      Matrix
      
        A;               // Fixed rows and cols. Same as Matrix3d.Matrix
       
         B;         // Fixed rows, dynamic cols.Matrix
        
          C;   // Full dynamic. Same as MatrixXd.Matrix
         
           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           // commentsx.size()          // length(x)        // vector sizeC.rows()          // size(C,1)        // number of rowsC.cols()          // size(C,2)        // number of columnsx(i)              // x(i+1)           // Matlab is 1-basedC(i,j)            // C(i+1,j+1)       //
         
        
       
      
     

Eigen 基础使用

// Basic usage// Eigen        // Matlab           // commentsx.size()        // length(x)        // vector sizeC.rows()        // size(C,1)        // number of rowsC.cols()        // size(C,2)        // number of columnsx(i)            // x(i+1)           // Matlab is 1-basedC(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                            // MatlabMatrixXd::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)*2-1VectorXd::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                           // Matlabx.head(n)                          // x(1:n)x.head
     
      ()                        // x(1:n)x.tail(n)                          // x(end - n + 1: end)x.tail
      
       ()                        // x(end - n + 1: end)x.segment(i, n)                    // x(i+1 : i+n)x.segment
       
        (i)                    // x(i+1 : i+n)P.block(i, j, rows, cols)          // P(i+1 : i+rows, j+1 : j+cols)P.block
        
         (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
         
          ()                 // P(:, 1:cols)P.leftCols(cols)                   // P(:, 1:cols)P.middleCols
          
           (j) // P(:, j+1:j+cols)P.middleCols(j, cols) // P(:, j+1:j+cols)P.rightCols
           
            () // P(:, end-cols+1:end)P.rightCols(cols) // P(:, end-cols+1:end)P.topRows
            
             () // P(1:rows, :)P.topRows(rows) // P(1:rows, :)P.middleRows
             
              (i) // P(i+1:i+rows, :)P.middleRows(i, rows) // P(i+1:i+rows, :)P.bottomRows
              
               () // 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
               
                () // P(1:rows, 1:cols)P.topRightCorner
                
                 () // P(1:rows, end-cols+1:end)P.bottomLeftCorner
                 
                  () // P(end-rows+1:end, 1:cols)P.bottomRightCorner
                  
                   () // P(end-rows+1:end, end-cols+1:end)
                  
                 
                
               
              
             
            
           
          
         
        
       
      
     

Eigen 矩阵元素交换

// Of particular note is Eigen's swap function which is highly optimized.// Eigen                           // MatlabR.row(i) = P.col(j);               // R(i, :) = P(:, i)R.col(j1).swap(mat1.col(j2));      // R(:, [j1 j2]) = R(:, [j2, j1])

Eigen 矩阵转置

// Views, transpose, etc; all read-write except for .adjoint().// Eigen                           // MatlabR.adjoint()                        // R'R.transpose()                      // R.' or conj(R')R.diagonal()                       // diag(R)x.asDiagonal()                     // diag(x)R.transpose().colwise().reverse(); // rot90(R)R.conjugate()                      // conj(R)

Eigen 矩阵乘积

// All the same as Matlab, but matlab doesn't have *= style operators.// Matrix-vector.  Matrix-matrix.   Matrix-scalar.y  = M*x;          R  = P*Q;        R  = P*s;a  = b*M;          R  = P - Q;      R  = s*P;a *= M;            R  = P + Q;      R  = P/s;                   R *= Q;          R  = s*P;                   R += Q;          R *= s;                   R -= Q;          R /= s;

Eigen 矩阵单个元素操作

// Vectorized operations on each element independently// Eigen                  // MatlabR = P.cwiseProduct(Q);    // R = P .* QR = P.array() * s.array();// R = P .* sR = P.cwiseQuotient(Q);   // R = P ./ QR = P.array() / Q.array();// R = P ./ QR = P.array() + s.array();// R = P + sR = P.array() - s.array();// R = P - sR.array() += s;           // R = R + sR.array() -= s;           // R = R - sR.array() < Q.array();    // R < QR.array() <= Q.array();   // R <= QR.cwiseInverse();         // 1 ./ PR.array().inverse();      // 1 ./ PR.array().sin()           // sin(P)R.array().cos()           // cos(P)R.array().pow(s)          // P .^ sR.array().square()        // P .^ 2R.array().cube()          // P .^ 3R.cwiseSqrt()             // sqrt(P)R.array().sqrt()          // sqrt(P)R.array().exp()           // exp(P)R.array().log()           // log(P)R.cwiseMax(P)             // max(R, P)R.array().max(P.array())  // max(R, P)R.cwiseMin(P)             // min(R, P)R.array().min(P.array())  // min(R, P)R.cwiseAbs()              // abs(P)R.array().abs()           // abs(P)R.cwiseAbs2()             // abs(P.^2)R.array().abs2()          // abs(P.^2)(R.array() < s).select(P,Q);  // (R < s ? P : Q)

Eigen 矩阵化简

// Reductions.int r, c;// Eigen                  // MatlabR.minCoeff()              // min(R(:))R.maxCoeff()              // max(R(:))s = R.minCoeff(&r, &c)    // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);s = R.maxCoeff(&r, &c)    // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);R.sum()                   // sum(R(:))R.colwise().sum()         // sum(R)R.rowwise().sum()         // sum(R, 2) or sum(R')'R.prod()                  // prod(R(:))R.colwise().prod()        // prod(R)R.rowwise().prod()        // prod(R, 2) or prod(R')'R.trace()                 // trace(R)R.all()                   // all(R(:))R.colwise().all()         // all(R)R.rowwise().all()         // all(R, 2)R.any()                   // any(R(:))R.colwise().any()         // any(R)R.rowwise().any()         // any(R, 2)

Eigen 矩阵点乘

// Dot products, norms, etc.// Eigen                  // Matlabx.norm()                  // norm(x).    Note that norm(R) doesn't work in Eigen.x.squaredNorm()           // dot(x, x)   Note the equivalence is not true for complexx.dot(y)                  // dot(x, y)x.cross(y)                // cross(x, y) Requires #include 
     

Eigen 矩阵类型转换

Type conversion// Eigen                           // MatlabA.cast
     
      ();                  // double(A)A.cast
      
       ();                   // single(A)A.cast
       
        ();                     // int32(A)A.real();                          // real(A)A.imag();                          // imag(A)// if the original type equals destination type, no work is done
       
      
     

Eigen 求解线性方程组 Ax = b

// Solve Ax = b. Result stored in x. Matlab: x = A \ b.x = A.ldlt().solve(b));  // A sym. p.s.d.    #include 
     
      x = A.llt() .solve(b));  // A sym. p.d.      #include 
      
       x = A.lu()  .solve(b));  // Stable and fast. #include 
       
        x = A.qr()  .solve(b));  // No pivoting.     #include 
        
         x = A.svd() .solve(b));  // Stable, slowest. #include 
         
          // .ldlt() -> .matrixL() and .matrixD()// .llt()  -> .matrixL()// .lu()   -> .matrixL() and .matrixU()// .qr()   -> .matrixQ() and .matrixR()// .svd()  -> .matrixU(), .singularValues(), and .matrixV()
         
        
       
      
     

Eigen 矩阵特征值

// Eigenvalue problems// Eigen                          // MatlabA.eigenvalues();                  // eig(A);EigenSolver
     
       eig(A);     // [vec val] = eig(A)eig.eigenvalues();                // diag(val)eig.eigenvectors();               // vec// For self-adjoint matrices use SelfAdjointEigenSolver<>
     

参考文献：

【1】http://eigen.tuxfamily.org/dox/AsciiQuickReference.txt

【2】http://blog.csdn.net/augusdi/article/details/12907341