不仅有函数的基本形式，还有对应的matlab函数，用起来很方便。
Eigen 矩阵定义
1 #include <Eigen/Dense>
2
3 Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d.
4 Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols.
5 Matrix<double, Dynamic, Dynamic> C; // Full dynamic. Same as MatrixXd.
6 Matrix<double, 3, 3, RowMajor> E; // Row major; default is column-major.
7 Matrix3f P, Q, R; // 3x3 float matrix.
8 Vector3f x, y, z; // 3x1 float matrix.
9 RowVector3f a, b, c; // 1x3 float matrix.
10 VectorXd v; // Dynamic column vector of doubles
11 // Eigen // Matlab // comments
12 x.size() // length(x) // vector size
13 C.rows() // size(C,1) // number of rows
14 C.cols() // size(C,2) // number of columns
15 x(i) // x(i+1) // Matlab is 1-based
16 C(i,j) // C(i+1,j+1) //
Eigen 基础使用
1 // Basic usage
2 // Eigen // Matlab // comments
3 x.size() // length(x) // vector size
4 C.rows() // size(C,1) // number of rows
5 C.cols() // size(C,2) // number of columns
6 x(i) // x(i+1) // Matlab is 1-based
7 C(i, j) // C(i+1,j+1) //
8
9 A.resize(4, 4); // Runtime error if assertions are on.
10 B.resize(4, 9); // Runtime error if assertions are on.
11 A.resize(3, 3); // Ok; size didn't change.
12 B.resize(3, 9); // Ok; only dynamic cols changed.
13
14 A << 1, 2, 3, // Initialize A. The elements can also be
15 4, 5, 6, // matrices, which are stacked along cols
16 7, 8, 9; // and then the rows are stacked.
17 B << A, A, A; // B is three horizontally stacked A's.
18 A.fill(10); // Fill A with all 10's.
Eigen 特殊矩阵生成
1 // Eigen // Matlab
2 MatrixXd::Identity(rows,cols) // eye(rows,cols)
3 C.setIdentity(rows,cols) // C = eye(rows,cols)
4 MatrixXd::Zero(rows,cols) // zeros(rows,cols)
5 C.setZero(rows,cols) // C = ones(rows,cols)
6 MatrixXd::Ones(rows,cols) // ones(rows,cols)
7 C.setOnes(rows,cols) // C = ones(rows,cols)
8 MatrixXd::Random(rows,cols) // rand(rows,cols)*2-1 // MatrixXd::Random returns uniform random numbers in (-1, 1).
9 C.setRandom(rows,cols) // C = rand(rows,cols)*2-1
10 VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)'
11 v.setLinSpaced(size,low,high) // v = linspace(low,high,size)'
Eigen 矩阵分块
1 // Matrix slicing and blocks. All expressions listed here are read/write.
2 // Templated size versions are faster. Note that Matlab is 1-based (a size N
3 // vector is x(1)...x(N)).
4 // Eigen // Matlab
5 x.head(n) // x(1:n)
6 x.head<n>() // x(1:n)
7 x.tail(n) // x(end - n + 1: end)
8 x.tail<n>() // x(end - n + 1: end)
9 x.segment(i, n) // x(i+1 : i+n)
10 x.segment<n>(i) // x(i+1 : i+n)
11 P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols)
12 P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols)
13 P.row(i) // P(i+1, :)
14 P.col(j) // P(:, j+1)
15 P.leftCols<cols>() // P(:, 1:cols)
16 P.leftCols(cols) // P(:, 1:cols)
17 P.middleCols<cols>(j) // P(:, j+1:j+cols)
18 P.middleCols(j, cols) // P(:, j+1:j+cols)
19 P.rightCols<cols>() // P(:, end-cols+1:end)
20 P.rightCols(cols) // P(:, end-cols+1:end)
21 P.topRows<rows>() // P(1:rows, :)
22 P.topRows(rows) // P(1:rows, :)
23 P.middleRows<rows>(i) // P(i+1:i+rows, :)
24 P.middleRows(i, rows) // P(i+1:i+rows, :)
25 P.bottomRows<rows>() // P(end-rows+1:end, :)
26 P.bottomRows(rows) // P(end-rows+1:end, :)
27 P.topLeftCorner(rows, cols) // P(1:rows, 1:cols)
28 P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end)
29 P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols)
30 P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end)
31 P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols)
32 P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end)
33 P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols)
34 P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end)
Eigen 矩阵元素交换
1 // Of particular note is Eigen's swap function which is highly optimized.
2 // Eigen // Matlab
3 R.row(i) = P.col(j); // R(i, :) = P(:, i)
4 R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1])
Eigen 矩阵转置
1 // Views, transpose, etc; all read-write except for .adjoint().
2 // Eigen // Matlab
3 R.adjoint() // R'
4 R.transpose() // R.' or conj(R')
5 R.diagonal() // diag(R)
6 x.asDiagonal() // diag(x)
7 R.transpose().colwise().reverse(); // rot90(R)
8 R.conjugate() // conj(R)
Eigen 矩阵乘积
1 // All the same as Matlab, but matlab doesn't have *= style operators.
2 // Matrix-vector. Matrix-matrix. Matrix-scalar.
3 y = M*x; R = P*Q; R = P*s;
4 a = b*M; R = P - Q; R = s*P;
5 a *= M; R = P + Q; R = P/s;
6 R *= Q; R = s*P;
7 R += Q; R *= s;
8 R -= Q; R /= s;
Eigen 矩阵单个元素操作
1 // Vectorized operations on each element independently
2 // Eigen // Matlab
3 R = P.cwiseProduct(Q); // R = P .* Q
4 R = P.array() * s.array();// R = P .* s
5 R = P.cwiseQuotient(Q); // R = P ./ Q
6 R = P.array() / Q.array();// R = P ./ Q
7 R = P.array() + s.array();// R = P + s
8 R = P.array() - s.array();// R = P - s
9 R.array() += s; // R = R + s
10 R.array() -= s; // R = R - s
11 R.array() < Q.array(); // R < Q
12 R.array() <= Q.array(); // R <= Q
13 R.cwiseInverse(); // 1 ./ P
14 R.array().inverse(); // 1 ./ P
15 R.array().sin() // sin(P)
16 R.array().cos() // cos(P)
17 R.array().pow(s) // P .^ s
18 R.array().square() // P .^ 2
19 R.array().cube() // P .^ 3
20 R.cwiseSqrt() // sqrt(P)
21 R.array().sqrt() // sqrt(P)
22 R.array().exp() // exp(P)
23 R.array().log() // log(P)
24 R.cwiseMax(P) // max(R, P)
25 R.array().max(P.array()) // max(R, P)
26 R.cwiseMin(P) // min(R, P)
27 R.array().min(P.array()) // min(R, P)
28 R.cwiseAbs() // abs(P)
29 R.array().abs() // abs(P)
30 R.cwiseAbs2() // abs(P.^2)
31 R.array().abs2() // abs(P.^2)
32 (R.array() < s).select(P,Q); // (R < s ? P : Q)
Eigen 矩阵化简
1 // Reductions.
2 int r, c;
3 // Eigen // Matlab
4 R.minCoeff() // min(R(:))
5 R.maxCoeff() // max(R(:))
6 s = R.minCoeff(&r, &c) // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);
7 s = R.maxCoeff(&r, &c) // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);
8 R.sum() // sum(R(:))
9 R.colwise().sum() // sum(R)
10 R.rowwise().sum() // sum(R, 2) or sum(R')'
11 R.prod() // prod(R(:))
12 R.colwise().prod() // prod(R)
13 R.rowwise().prod() // prod(R, 2) or prod(R')'
14 R.trace() // trace(R)
15 R.all() // all(R(:))
16 R.colwise().all() // all(R)
17 R.rowwise().all() // all(R, 2)
18 R.any() // any(R(:))
19 R.colwise().any() // any(R)
20 R.rowwise().any() // any(R, 2)
Eigen 矩阵点乘
1 // Dot products, norms, etc.
2 // Eigen // Matlab
3 x.norm() // norm(x). Note that norm(R) doesn't work in Eigen.
4 x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex
5 x.dot(y) // dot(x, y)
6 x.cross(y) // cross(x, y) Requires #include <Eigen/Geometry>
Eigen 矩阵类型转换
1 //// Type conversion
2 // Eigen // Matlab
3 A.cast<double>(); // double(A)
4 A.cast<float>(); // single(A)
5 A.cast<int>(); // int32(A)
6 A.real(); // real(A)
7 A.imag(); // imag(A)
8 // if the original type equals destination type, no work is done
Eigen 求解线性方程组 Ax = b
1 // Solve Ax = b. Result stored in x. Matlab: x = A b.
2 x = A.ldlt().solve(b)); // A sym. p.s.d. #include <Eigen/Cholesky>
3 x = A.llt() .solve(b)); // A sym. p.d. #include <Eigen/Cholesky>
4 x = A.lu() .solve(b)); // Stable and fast. #include <Eigen/LU>
5 x = A.qr() .solve(b)); // No pivoting. #include <Eigen/QR>
6 x = A.svd() .solve(b)); // Stable, slowest. #include <Eigen/SVD>
7 // .ldlt() -> .matrixL() and .matrixD()
8 // .llt() -> .matrixL()
9 // .lu() -> .matrixL() and .matrixU()
10 // .qr() -> .matrixQ() and .matrixR()
11 // .svd() -> .matrixU(), .singularValues(), and .matrixV()
Eigen 矩阵特征值
1 // Eigenvalue problems
2 // Eigen // Matlab
3 A.eigenvalues(); // eig(A);
4 EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A)
5 eig.eigenvalues(); // diag(val)
6 eig.eigenvectors(); // vec
7 // For self-adjoint matrices use SelfAdjointEigenSolver<>
