1 // A simple quickref for Eigen. Add anything that's missing. 2 // Main author: Keir Mierle 3 4 #include <Eigen/Core> 5 #include <Eigen/Array> 6 7 Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d. 8 Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols. 9 Matrix<double, Dynamic, Dynamic> C; // Full dynamic. Same as MatrixXd. 10 Matrix<double, 3, 3, RowMajor> E; // Row major; default is column-major. 11 Matrix3f P, Q, R; // 3x3 float matrix. 12 Vector3f x, y, z; // 3x1 float matrix. 13 RowVector3f a, b, c; // 1x3 float matrix. 14 double s; 15 16 // Basic usage 17 // Eigen // Matlab // comments 18 x.size() // length(x) // vector size 19 C.rows() // size(C)(1) // number of rows 20 C.cols() // size(C)(2) // number of columns 21 x(i) // x(i+1) // Matlab is 1-based 22 C(i,j) // C(i+1,j+1) // 23 24 A.resize(4, 4); // Runtime error if assertions are on. 25 B.resize(4, 9); // Runtime error if assertions are on. 26 A.resize(3, 3); // Ok; size didn't change. 27 B.resize(3, 9); // Ok; only dynamic cols changed. 28 29 A << 1, 2, 3, // Initialize A. The elements can also be 30 4, 5, 6, // matrices, which are stacked along cols 31 7, 8, 9; // and then the rows are stacked. 32 B << A, A, A; // B is three horizontally stacked A's. 33 A.fill(10); // Fill A with all 10's. 34 A.setRandom(); // Fill A with uniform random numbers in (-1, 1). 35 // Requires #include <Eigen/Array>. 36 A.setIdentity(); // Fill A with the identity. 37 38 // Matrix slicing and blocks. All expressions listed here are read/write. 39 // Templated size versions are faster. Note that Matlab is 1-based (a size N 40 // vector is x(1)...x(N)). 41 // Eigen // Matlab 42 x.head(n) // x(1:n) 43 x.head<n>() // x(1:n) 44 x.tail(n) // N = rows(x); x(N - n: N) 45 x.tail<n>() // N = rows(x); x(N - n: N) 46 x.segment(i, n) // x(i+1 : i+n) 47 x.segment<n>(i) // x(i+1 : i+n) 48 P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols) 49 P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols) 50 P.topLeftCorner(rows, cols) // P(1:rows, 1:cols) 51 P.topRightCorner(rows, cols) // [m n]=size(P); P(1:rows, n-cols+1:n) 52 P.bottomLeftCorner(rows, cols) // [m n]=size(P); P(m-rows+1:m, 1:cols) 53 P.bottomRightCorner(rows, cols) // [m n]=size(P); P(m-rows+1:m, n-cols+1:n) 54 P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols) 55 P.topRightCorner<rows,cols>() // [m n]=size(P); P(1:rows, n-cols+1:n) 56 P.bottomLeftCorner<rows,cols>() // [m n]=size(P); P(m-rows+1:m, 1:cols) 57 P.bottomRightCorner<rows,cols>() // [m n]=size(P); P(m-rows+1:m, n-cols+1:n) 58 59 // Of particular note is Eigen's swap function which is highly optimized. 60 // Eigen // Matlab 61 R.row(i) = P.col(j); // R(i, :) = P(:, i) 62 R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1]) 63 64 // Views, transpose, etc; all read-write except for .adjoint(). 65 // Eigen // Matlab 66 R.adjoint() // R' 67 R.transpose() // R.' or conj(R') 68 R.diagonal() // diag(R) 69 x.asDiagonal() // diag(x) 70 71 // All the same as Matlab, but matlab doesn't have *= style operators. 72 // Matrix-vector. Matrix-matrix. Matrix-scalar. 73 y = M*x; R = P*Q; R = P*s; 74 a = b*M; R = P - Q; R = s*P; 75 a *= M; R = P + Q; R = P/s; 76 R *= Q; R = s*P; 77 R += Q; R *= s; 78 R -= Q; R /= s; 79 80 // Vectorized operations on each element independently 81 // (most require #include <Eigen/Array>) 82 // Eigen // Matlab 83 R = P.cwiseProduct(Q); // R = P .* Q 84 R = P.array() * s.array();// R = P .* s 85 R = P.cwiseQuotient(Q); // R = P ./ Q 86 R = P.array() / Q.array();// R = P ./ Q 87 R = P.array() + s.array();// R = P + s 88 R = P.array() - s.array();// R = P - s 89 R.array() += s; // R = R + s 90 R.array() -= s; // R = R - s 91 R.array() < Q.array(); // R < Q 92 R.array() <= Q.array(); // R <= Q 93 R.cwiseInverse(); // 1 ./ P 94 R.array().inverse(); // 1 ./ P 95 R.array().sin() // sin(P) 96 R.array().cos() // cos(P) 97 R.array().pow(s) // P .^ s 98 R.array().square() // P .^ 2 99 R.array().cube() // P .^ 3 100 R.cwiseSqrt() // sqrt(P) 101 R.array().sqrt() // sqrt(P) 102 R.array().exp() // exp(P) 103 R.array().log() // log(P) 104 R.cwiseMax(P) // max(R, P) 105 R.array().max(P.array()) // max(R, P) 106 R.cwiseMin(P) // min(R, P) 107 R.array().min(P.array()) // min(R, P) 108 R.cwiseAbs() // abs(P) 109 R.array().abs() // abs(P) 110 R.cwiseAbs2() // abs(P.^2) 111 R.array().abs2() // abs(P.^2) 112 (R.array() < s).select(P,Q); // (R < s ? P : Q) 113 114 // Reductions. 115 int r, c; 116 // Eigen // Matlab 117 R.minCoeff() // min(R(:)) 118 R.maxCoeff() // max(R(:)) 119 s = R.minCoeff(&r, &c) // [aa, bb] = min(R); [cc, dd] = min(aa); 120 // r = bb(dd); c = dd; s = cc 121 s = R.maxCoeff(&r, &c) // [aa, bb] = max(R); [cc, dd] = max(aa); 122 // row = bb(dd); col = dd; s = cc 123 R.sum() // sum(R(:)) 124 R.colwise.sum() // sum(R) 125 R.rowwise.sum() // sum(R, 2) or sum(R')' 126 R.prod() // prod(R(:)) 127 R.colwise.prod() // prod(R) 128 R.rowwise.prod() // prod(R, 2) or prod(R')' 129 R.trace() // trace(R) 130 R.all() // all(R(:)) 131 R.colwise().all() // all(R) 132 R.rowwise().all() // all(R, 2) 133 R.any() // any(R(:)) 134 R.colwise().any() // any(R) 135 R.rowwise().any() // any(R, 2) 136 137 // Dot products, norms, etc. 138 // Eigen // Matlab 139 x.norm() // norm(x). Note that norm(R) doesn't work in Eigen. 140 x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex 141 x.dot(y) // dot(x, y) 142 x.cross(y) // cross(x, y) Requires #include <Eigen/Geometry> 143 144 // Eigen can map existing memory into Eigen matrices. 145 float array[3]; 146 Map<Vector3f>(array, 3).fill(10); 147 int data[4] = 1, 2, 3, 4; 148 Matrix2i mat2x2(data); 149 MatrixXi mat2x2 = Map<Matrix2i>(data); 150 MatrixXi mat2x2 = Map<MatrixXi>(data, 2, 2); 151 152 // Solve Ax = b. Result stored in x. Matlab: x = A \ b. 153 bool solved; 154 solved = A.ldlt().solve(b, &x)); // A sym. p.s.d. #include <Eigen/Cholesky> 155 solved = A.llt() .solve(b, &x)); // A sym. p.d. #include <Eigen/Cholesky> 156 solved = A.lu() .solve(b, &x)); // Stable and fast. #include <Eigen/LU> 157 solved = A.qr() .solve(b, &x)); // No pivoting. #include <Eigen/QR> 158 solved = A.svd() .solve(b, &x)); // Stable, slowest. #include <Eigen/SVD> 159 // .ldlt() -> .matrixL() and .matrixD() 160 // .llt() -> .matrixL() 161 // .lu() -> .matrixL() and .matrixU() 162 // .qr() -> .matrixQ() and .matrixR() 163 // .svd() -> .matrixU(), .singularValues(), and .matrixV() 164 165 // Eigenvalue problems 166 // Eigen // Matlab 167 A.eigenvalues(); // eig(A); 168 EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A) 169 eig.eigenvalues(); // diag(val) 170 eig.eigenvectors(); // vec 171
