?????? Eigen為Matlab轉換為C++提供了一個簡單的語法級別的代碼遷移工具.

???????對一些代碼進行了擴充，以便程序由Matlab到Eigen的移植...................

參考鏈接：http://eigen.tuxfamily.org/dox/AsciiQuickReference.txt

// A simple quickref for Eigen. Add anything that's missing.

// Main author: Keir Mierle

（對浮點數的計算使用MatrixXf ）

#include <Eigen/Dense>//基本數據類型說明 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 double s; //1.Basic usage //基本結構和成員運算符 // 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) ////2.動態形變Resize //Matlab不能resize 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 be4, 5, 6, // matrices, which are stacked along cols7, 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.//3.初始化方法 // Eigen // Matlab MatrixXd::Identity(rows,cols) <-----> // eye(rows,cols) //生成單位矩陣 C.setIdentity(rows,cols) <-----> // C = eye(rows,cols) MatrixXd::Zero(rows,cols) <-- --> // zeros(rows,cols) //生成全0矩陣 C.setZero(rows,cols) // C = ones(rows,cols) //生成全矩陣 MatrixXd::Ones(rows,cols) // ones(rows,cols) C.setOnes(rows,cols) // C = ones(rows,cols)//4.生成隨機矩陣 //Eigen生成歸一的絕對值小于1的數值//Matlab生成歸一的正值 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)*2-11.0/2* MatrixXf::Random(rows,cols) + 1.0/2 *MatrixXf::Ones(rows,cols) //rand(rows,cols):VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)' //用于產生x1,x2之間的N點行矢量 v.setLinSpaced(size,low,high) // v = linspace(low,high,size)'// 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)// Of particular note is Eigen's swap function which is highly optimized. // Eigen // Matlab R.row(i) = P.col(j); // R(i, :) = P(:, i) R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1])//6. 矩陣級內部運算/形變——轉置、求逆、求跡 // Views, transpose, etc; all read-write except for .adjoint(). // Eigen // Matlab R.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)//7. 矩陣間運算 // 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;//8. 矩陣的行列運算 // Vectorized operations on each element independently // Eigen // Matlab R = P.cwiseProduct(Q); // R = P .* Q R = P.array() * s.array();// R = P .* s R = P.cwiseQuotient(Q); // R = P ./ Q R = P.array() / Q.array();// R = P ./ Q R = P.array() + s.array();// R = P + s R = P.array() - s.array();// R = P - s R.array() += s; // R = R + s R.array() -= s; // R = R - s R.array() < Q.array(); // R < Q R.array() <= Q.array(); // R <= Q R.cwiseInverse(); // 1 ./ P R.array().inverse(); // 1 ./ P //求逆 inv(P) R.inverse(); // 1 ./ P //求逆 inv(P),必須包含 #include <Eigen/Dense>R.array().sin() // sin(P) R.array().cos() // cos(P) R.array().pow(s) // P .^ s R.array().square() // P .^ 2 R.array().cube() // P .^ 3 R.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)// Reductions.int r, <pre>// Reductions. int r, c; // Eigen // Matlab R.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 // Matlab x.norm() // norm(x). Note that norm(R) doesn't work in Eigen. x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex x.dot(y) // dot(x, y) x.cross(y) // cross(x, y) Requires #include <Eigen/Geometry>Type conversion // Eigen // Matlab A.cast<double>(); // double(A) A.cast<float>(); // single(A) A.cast<int>(); // 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 allowed A += F.cast<double>(); // 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 10 int data[4] = {1, 2, 3, 4}; Matrix2i mat2x2(data); // copies data into mat2x2 Matrix2i::Map(data) = 2*mat2x2; // overwrite elements of data with 2*mat2x2 MatrixXi::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 <Eigen/Cholesky> x = A.llt() .solve(b)); // A sym. p.d. #include <Eigen/Cholesky> x = A.lu() .solve(b)); // Stable and fast. #include <Eigen/LU> x = A.qr() .solve(b)); // No pivoting. #include <Eigen/QR> x = A.svd() .solve(b)); // Stable, slowest. #include <Eigen/SVD> // .ldlt() -> .matrixL() and .matrixD() // .llt() -> .matrixL() // .lu() -> .matrixL() and .matrixU() // .qr() -> .matrixQ() and .matrixR() // .svd() -> .matrixU(), .singularValues(), and .matrixV()// Eigenvalue problems // Eigen // Matlab A.eigenvalues(); // eig(A); EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A) eig.eigenvalues(); // diag(val) eig.eigenvectors(); // vec // For self-adjoint matrices use SelfAdjointEigenSolver<>

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