1 // A simple quickref for Eigen. Add anything that's missing. 2 // Main author: Keir Mierle 3 4 #include <Eigen/Dense> 5 6 Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d. 7 Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols. 8 Matrix<double, Dynamic, Dynamic> C; // Full dynamic. Same as MatrixXd. 9 Matrix<double, 3, 3, RowMajor> E; // Row major; default is column-major. 10 Matrix3f P, Q, R; // 3x3 float matrix. 11 Vector3f x, y, z; // 3x1 float matrix. 12 RowVector3f a, b, c; // 1x3 float matrix. 13 VectorXd v; // Dynamic column vector of doubles 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 35 // Eigen // Matlab 36 MatrixXd::Identity(rows,cols) // eye(rows,cols) 37 C.setIdentity(rows,cols) // C = eye(rows,cols) 38 MatrixXd::Zero(rows,cols) // zeros(rows,cols) 39 C.setZero(rows,cols) // C = zeros(rows,cols) 40 MatrixXd::Ones(rows,cols) // ones(rows,cols) 41 C.setOnes(rows,cols) // C = ones(rows,cols) 42 MatrixXd::Random(rows,cols) // rand(rows,cols)*2-1 // MatrixXd::Random returns uniform random numbers in (-1, 1). 43 C.setRandom(rows,cols) // C = rand(rows,cols)*2-1 44 VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)' 45 v.setLinSpaced(size,low,high) // v = linspace(low,high,size)' 46 VectorXi::LinSpaced(((hi-low)/step)+1, // low:step:hi 47 low,low+step*(size-1)) // 48 49 50 // Matrix slicing and blocks. All expressions listed here are read/write. 51 // Templated size versions are faster. Note that Matlab is 1-based (a size N 52 // vector is x(1)...x(N)). 53 // Eigen // Matlab 54 x.head(n) // x(1:n) 55 x.head<n>() // x(1:n) 56 x.tail(n) // x(end - n + 1: end) 57 x.tail<n>() // x(end - n + 1: end) 58 x.segment(i, n) // x(i+1 : i+n) 59 x.segment<n>(i) // x(i+1 : i+n) 60 P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols) 61 P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols) 62 P.row(i) // P(i+1, :) 63 P.col(j) // P(:, j+1) 64 P.leftCols<cols>() // P(:, 1:cols) 65 P.leftCols(cols) // P(:, 1:cols) 66 P.middleCols<cols>(j) // P(:, j+1:j+cols) 67 P.middleCols(j, cols) // P(:, j+1:j+cols) 68 P.rightCols<cols>() // P(:, end-cols+1:end) 69 P.rightCols(cols) // P(:, end-cols+1:end) 70 P.topRows<rows>() // P(1:rows, :) 71 P.topRows(rows) // P(1:rows, :) 72 P.middleRows<rows>(i) // P(i+1:i+rows, :) 73 P.middleRows(i, rows) // P(i+1:i+rows, :) 74 P.bottomRows<rows>() // P(end-rows+1:end, :) 75 P.bottomRows(rows) // P(end-rows+1:end, :) 76 P.topLeftCorner(rows, cols) // P(1:rows, 1:cols) 77 P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end) 78 P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols) 79 P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end) 80 P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols) 81 P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end) 82 P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols) 83 P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end) 84 85 // Of particular note is Eigen's swap function which is highly optimized. 86 // Eigen // Matlab 87 R.row(i) = P.col(j); // R(i, :) = P(:, j) 88 R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1]) 89 90 // Views, transpose, etc; 91 // Eigen // Matlab 92 R.adjoint() // R' 93 R.transpose() // R.' or conj(R') // Read-write 94 R.diagonal() // diag(R) // Read-write 95 x.asDiagonal() // diag(x) 96 R.transpose().colwise().reverse() // rot90(R) // Read-write 97 R.rowwise().reverse() // fliplr(R) 98 R.colwise().reverse() // flipud(R) 99 R.replicate(i,j) // repmat(P,i,j) 100 101 102 // All the same as Matlab, but matlab doesn't have *= style operators. 103 // Matrix-vector. Matrix-matrix. Matrix-scalar. 104 y = M*x; R = P*Q; R = P*s; 105 a = b*M; R = P - Q; R = s*P; 106 a *= M; R = P + Q; R = P/s; 107 R *= Q; R = s*P; 108 R += Q; R *= s; 109 R -= Q; R /= s; 110 111 // Vectorized operations on each element independently 112 // Eigen // Matlab 113 R = P.cwiseProduct(Q); // R = P .* Q 114 R = P.array() * s.array(); // R = P .* s 115 R = P.cwiseQuotient(Q); // R = P ./ Q 116 R = P.array() / Q.array(); // R = P ./ Q 117 R = P.array() + s.array(); // R = P + s 118 R = P.array() - s.array(); // R = P - s 119 R.array() += s; // R = R + s 120 R.array() -= s; // R = R - s 121 R.array() < Q.array(); // R < Q 122 R.array() <= Q.array(); // R <= Q 123 R.cwiseInverse(); // 1 ./ P 124 R.array().inverse(); // 1 ./ P 125 R.array().sin() // sin(P) 126 R.array().cos() // cos(P) 127 R.array().pow(s) // P .^ s 128 R.array().square() // P .^ 2 129 R.array().cube() // P .^ 3 130 R.cwiseSqrt() // sqrt(P) 131 R.array().sqrt() // sqrt(P) 132 R.array().exp() // exp(P) 133 R.array().log() // log(P) 134 R.cwiseMax(P) // max(R, P) 135 R.array().max(P.array()) // max(R, P) 136 R.cwiseMin(P) // min(R, P) 137 R.array().min(P.array()) // min(R, P) 138 R.cwiseAbs() // abs(P) 139 R.array().abs() // abs(P) 140 R.cwiseAbs2() // abs(P.^2) 141 R.array().abs2() // abs(P.^2) 142 (R.array() < s).select(P,Q ); // (R < s ? P : Q) 143 R = (Q.array()==0).select(P,R) // R(Q==0) = P(Q==0) 144 R = P.unaryExpr(ptr_fun(func)) // R = arrayfun(func, P) // with: scalar func(const scalar &x); 145 146 147 // Reductions. 148 int r, c; 149 // Eigen // Matlab 150 R.minCoeff() // min(R(:)) 151 R.maxCoeff() // max(R(:)) 152 s = R.minCoeff(&r, &c) // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i); 153 s = R.maxCoeff(&r, &c) // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i); 154 R.sum() // sum(R(:)) 155 R.colwise().sum() // sum(R) 156 R.rowwise().sum() // sum(R, 2) or sum(R')' 157 R.prod() // prod(R(:)) 158 R.colwise().prod() // prod(R) 159 R.rowwise().prod() // prod(R, 2) or prod(R')' 160 R.trace() // trace(R) 161 R.all() // all(R(:)) 162 R.colwise().all() // all(R) 163 R.rowwise().all() // all(R, 2) 164 R.any() // any(R(:)) 165 R.colwise().any() // any(R) 166 R.rowwise().any() // any(R, 2) 167 168 // Dot products, norms, etc. 169 // Eigen // Matlab 170 x.norm() // norm(x). Note that norm(R) doesn't work in Eigen. 171 x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex 172 x.dot(y) // dot(x, y) 173 x.cross(y) // cross(x, y) Requires #include <Eigen/Geometry> 174 175 //// Type conversion 176 // Eigen // Matlab 177 A.cast<double>(); // double(A) 178 A.cast<float>(); // single(A) 179 A.cast<int>(); // int32(A) 180 A.real(); // real(A) 181 A.imag(); // imag(A) 182 // if the original type equals destination type, no work is done 183 184 // Note that for most operations Eigen requires all operands to have the same type: 185 MatrixXf F = MatrixXf::Zero(3,3); 186 A += F; // illegal in Eigen. In Matlab A = A+F is allowed 187 A += F.cast<double>(); // F converted to double and then added (generally, conversion happens on-the-fly) 188 189 // Eigen can map existing memory into Eigen matrices. 190 float array[3]; 191 Vector3f::Map(array).fill(10); // create a temporary Map over array and sets entries to 10 192 int data[4] = {1, 2, 3, 4}; 193 Matrix2i mat2x2(data); // copies data into mat2x2 194 Matrix2i::Map(data) = 2*mat2x2; // overwrite elements of data with 2*mat2x2 195 MatrixXi::Map(data, 2, 2) += mat2x2; // adds mat2x2 to elements of data (alternative syntax if size is not know at compile time) 196 197 // Solve Ax = b. Result stored in x. Matlab: x = A \ b. 198 x = A.ldlt().solve(b)); // A sym. p.s.d. #include <Eigen/Cholesky> 199 x = A.llt() .solve(b)); // A sym. p.d. #include <Eigen/Cholesky> 200 x = A.lu() .solve(b)); // Stable and fast. #include <Eigen/LU> 201 x = A.qr() .solve(b)); // No pivoting. #include <Eigen/QR> 202 x = A.svd() .solve(b)); // Stable, slowest. #include <Eigen/SVD> 203 // .ldlt() -> .matrixL() and .matrixD() 204 // .llt() -> .matrixL() 205 // .lu() -> .matrixL() and .matrixU() 206 // .qr() -> .matrixQ() and .matrixR() 207 // .svd() -> .matrixU(), .singularValues(), and .matrixV() 208 209 // Eigenvalue problems 210 // Eigen // Matlab 211 A.eigenvalues(); // eig(A); 212 EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A) 213 eig.eigenvalues(); // diag(val) 214 eig.eigenvectors(); // vec 215 // For self-adjoint matrices use SelfAdjointEigenSolver<> 216
