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// A simple quickref for Eigen. Add anything that's missing.// Main author: Keir Mierle#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 doublesdouble s;                      // 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                                    // 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 = zeros(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)'VectorXi::LinSpaced(((hi-low)/step)+1,      // low:step:hi                    low,low+step*(size-1))  //// 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)// Of particular note is Eigen's swap function which is highly optimized.// Eigen // MatlabR.row(i) = P.col(j); // R(i, :) = P(:, j)R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1])// Views, transpose, etc;// Eigen // MatlabR.adjoint() // R'R.transpose() // R.' or conj(R') // Read-writeR.diagonal() // diag(R) // Read-writex.asDiagonal() // diag(x)R.transpose().colwise().reverse() // rot90(R) // Read-writeR.rowwise().reverse() // fliplr(R)R.colwise().reverse() // flipud(R)R.replicate(i,j) // repmat(P,i,j)// 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;// 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)R = (Q.array()==0).select(P,R) // R(Q==0) = P(Q==0)R = P.unaryExpr(ptr_fun(func)) // R = arrayfun(func, P) // with: scalar func(const scalar &x);// 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)// 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 
                      
                        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// Note that for most operations Eigen requires all operands to have the same type:MatrixXf F = MatrixXf::Zero(3,3);A += F; // illegal in Eigen. In Matlab A = A+F is allowedA += F.cast
                          
                           (); // F converted to double and then added (generally, conversion happens on-the-fly)// Eigen can map existing memory into Eigen matrices.float array[3];Vector3f::Map(array).fill(10); // create a temporary Map over array and sets entries to 10int data[4] = { 1, 2, 3, 4};Matrix2i mat2x2(data); // copies data into mat2x2Matrix2i::Map(data) = 2*mat2x2; // overwrite elements of data with 2*mat2x2MatrixXi::Map(data, 2, 2) += mat2x2; // adds mat2x2 to elements of data (alternative syntax if size is not know at compile time)// 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()// 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<>
                                
                               
                              
                             
                            
                           
                          
                         
                        
                       
                      
                     
                    
                   
                  
                 
                
               
              
             
            
           
          
         
        
       
      
     
    
   

Eigen求广义逆

// 转自https://www.cnblogs.com/dzw2017/p/8427677.html//Eigen中并没有求广义逆的函数，这里用SVD实现，数据类型大家可以看需修改为doubelusing Eigen::Dynamic;using Eigen::Matrix;using Eigen::RowMajor;typedef Matrix
   
     MatXf;MatXf pinv(MatXf x){
       JacobiSVD
    
      svd(x,ComputeFullU | ComputeFullV);    float  pinvtoler=1.e-8; //tolerance    MatXf singularValues_inv = svd.singularValues();    for ( long i=0; i
     
       pinvtoler )            singularValues_inv(i)=1.0/singularValues_inv(i);        else singularValues_inv(i)=0;    }    return svd.matrixV()*singularValues_inv.asDiagonal()*svd.matrixU().transpose();}
     
    
   

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