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206 lines
9.5 KiB
206 lines
9.5 KiB
// A simple quickref for Eigen. Add anything that's missing.
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// Main author: Keir Mierle
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#include <StormEigen/Dense>
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Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d.
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Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols.
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Matrix<double, Dynamic, Dynamic> C; // Full dynamic. Same as MatrixXd.
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Matrix<double, 3, 3, RowMajor> E; // Row major; default is column-major.
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Matrix3f P, Q, R; // 3x3 float matrix.
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Vector3f x, y, z; // 3x1 float matrix.
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RowVector3f a, b, c; // 1x3 float matrix.
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VectorXd v; // Dynamic column vector of doubles
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double s;
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// Basic usage
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// Eigen // Matlab // comments
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x.size() // length(x) // vector size
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C.rows() // size(C,1) // number of rows
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C.cols() // size(C,2) // number of columns
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x(i) // x(i+1) // Matlab is 1-based
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C(i,j) // C(i+1,j+1) //
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A.resize(4, 4); // Runtime error if assertions are on.
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B.resize(4, 9); // Runtime error if assertions are on.
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A.resize(3, 3); // Ok; size didn't change.
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B.resize(3, 9); // Ok; only dynamic cols changed.
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A << 1, 2, 3, // Initialize A. The elements can also be
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4, 5, 6, // matrices, which are stacked along cols
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7, 8, 9; // and then the rows are stacked.
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B << A, A, A; // B is three horizontally stacked A's.
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A.fill(10); // Fill A with all 10's.
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// Eigen // Matlab
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MatrixXd::Identity(rows,cols) // eye(rows,cols)
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C.setIdentity(rows,cols) // C = eye(rows,cols)
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MatrixXd::Zero(rows,cols) // zeros(rows,cols)
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C.setZero(rows,cols) // C = ones(rows,cols)
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MatrixXd::Ones(rows,cols) // ones(rows,cols)
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C.setOnes(rows,cols) // C = ones(rows,cols)
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MatrixXd::Random(rows,cols) // rand(rows,cols)*2-1 // MatrixXd::Random returns uniform random numbers in (-1, 1).
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C.setRandom(rows,cols) // C = rand(rows,cols)*2-1
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VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)'
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v.setLinSpaced(size,low,high) // v = linspace(low,high,size)'
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// Matrix slicing and blocks. All expressions listed here are read/write.
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// Templated size versions are faster. Note that Matlab is 1-based (a size N
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// vector is x(1)...x(N)).
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// Eigen // Matlab
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x.head(n) // x(1:n)
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x.head<n>() // x(1:n)
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x.tail(n) // x(end - n + 1: end)
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x.tail<n>() // x(end - n + 1: end)
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x.segment(i, n) // x(i+1 : i+n)
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x.segment<n>(i) // x(i+1 : i+n)
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P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols)
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P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols)
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P.row(i) // P(i+1, :)
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P.col(j) // P(:, j+1)
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P.leftCols<cols>() // P(:, 1:cols)
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P.leftCols(cols) // P(:, 1:cols)
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P.middleCols<cols>(j) // P(:, j+1:j+cols)
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P.middleCols(j, cols) // P(:, j+1:j+cols)
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P.rightCols<cols>() // P(:, end-cols+1:end)
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P.rightCols(cols) // P(:, end-cols+1:end)
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P.topRows<rows>() // P(1:rows, :)
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P.topRows(rows) // P(1:rows, :)
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P.middleRows<rows>(i) // P(i+1:i+rows, :)
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P.middleRows(i, rows) // P(i+1:i+rows, :)
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P.bottomRows<rows>() // P(end-rows+1:end, :)
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P.bottomRows(rows) // P(end-rows+1:end, :)
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P.topLeftCorner(rows, cols) // P(1:rows, 1:cols)
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P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end)
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P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols)
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P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end)
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P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols)
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P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end)
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P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols)
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P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end)
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// Of particular note is Eigen's swap function which is highly optimized.
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// Eigen // Matlab
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R.row(i) = P.col(j); // R(i, :) = P(:, i)
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R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1])
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// Views, transpose, etc; all read-write except for .adjoint().
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// Eigen // Matlab
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R.adjoint() // R'
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R.transpose() // R.' or conj(R')
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R.diagonal() // diag(R)
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x.asDiagonal() // diag(x)
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R.transpose().colwise().reverse(); // rot90(R)
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// All the same as Matlab, but matlab doesn't have *= style operators.
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// Matrix-vector. Matrix-matrix. Matrix-scalar.
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y = M*x; R = P*Q; R = P*s;
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a = b*M; R = P - Q; R = s*P;
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a *= M; R = P + Q; R = P/s;
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R *= Q; R = s*P;
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R += Q; R *= s;
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R -= Q; R /= s;
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// Vectorized operations on each element independently
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// Eigen // Matlab
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R = P.cwiseProduct(Q); // R = P .* Q
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R = P.array() * s.array();// R = P .* s
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R = P.cwiseQuotient(Q); // R = P ./ Q
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R = P.array() / Q.array();// R = P ./ Q
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R = P.array() + s.array();// R = P + s
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R = P.array() - s.array();// R = P - s
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R.array() += s; // R = R + s
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R.array() -= s; // R = R - s
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R.array() < Q.array(); // R < Q
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R.array() <= Q.array(); // R <= Q
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R.cwiseInverse(); // 1 ./ P
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R.array().inverse(); // 1 ./ P
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R.array().sin() // sin(P)
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R.array().cos() // cos(P)
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R.array().pow(s) // P .^ s
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R.array().square() // P .^ 2
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R.array().cube() // P .^ 3
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R.cwiseSqrt() // sqrt(P)
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R.array().sqrt() // sqrt(P)
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R.array().exp() // exp(P)
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R.array().log() // log(P)
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R.cwiseMax(P) // max(R, P)
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R.array().max(P.array()) // max(R, P)
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R.cwiseMin(P) // min(R, P)
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R.array().min(P.array()) // min(R, P)
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R.cwiseAbs() // abs(P)
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R.array().abs() // abs(P)
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R.cwiseAbs2() // abs(P.^2)
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R.array().abs2() // abs(P.^2)
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(R.array() < s).select(P,Q); // (R < s ? P : Q)
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// Reductions.
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int r, c;
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// Eigen // Matlab
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R.minCoeff() // min(R(:))
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R.maxCoeff() // max(R(:))
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s = R.minCoeff(&r, &c) // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);
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s = R.maxCoeff(&r, &c) // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);
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R.sum() // sum(R(:))
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R.colwise().sum() // sum(R)
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R.rowwise().sum() // sum(R, 2) or sum(R')'
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R.prod() // prod(R(:))
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R.colwise().prod() // prod(R)
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R.rowwise().prod() // prod(R, 2) or prod(R')'
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R.trace() // trace(R)
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R.all() // all(R(:))
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R.colwise().all() // all(R)
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R.rowwise().all() // all(R, 2)
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R.any() // any(R(:))
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R.colwise().any() // any(R)
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R.rowwise().any() // any(R, 2)
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// Dot products, norms, etc.
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// Eigen // Matlab
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x.norm() // norm(x). Note that norm(R) doesn't work in Eigen.
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x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex
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x.dot(y) // dot(x, y)
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x.cross(y) // cross(x, y) Requires #include <StormEigen/Geometry>
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//// Type conversion
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// Eigen // Matlab
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A.cast<double>(); // double(A)
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A.cast<float>(); // single(A)
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A.cast<int>(); // int32(A)
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A.real(); // real(A)
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A.imag(); // imag(A)
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// if the original type equals destination type, no work is done
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// Note that for most operations Eigen requires all operands to have the same type:
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MatrixXf F = MatrixXf::Zero(3,3);
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A += F; // illegal in Eigen. In Matlab A = A+F is allowed
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A += F.cast<double>(); // F converted to double and then added (generally, conversion happens on-the-fly)
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// Eigen can map existing memory into Eigen matrices.
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float array[3];
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Vector3f::Map(array).fill(10); // create a temporary Map over array and sets entries to 10
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int data[4] = {1, 2, 3, 4};
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Matrix2i mat2x2(data); // copies data into mat2x2
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Matrix2i::Map(data) = 2*mat2x2; // overwrite elements of data with 2*mat2x2
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MatrixXi::Map(data, 2, 2) += mat2x2; // adds mat2x2 to elements of data (alternative syntax if size is not know at compile time)
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// Solve Ax = b. Result stored in x. Matlab: x = A \ b.
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x = A.ldlt().solve(b)); // A sym. p.s.d. #include <StormEigen/Cholesky>
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x = A.llt() .solve(b)); // A sym. p.d. #include <StormEigen/Cholesky>
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x = A.lu() .solve(b)); // Stable and fast. #include <StormEigen/LU>
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x = A.qr() .solve(b)); // No pivoting. #include <StormEigen/QR>
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x = A.svd() .solve(b)); // Stable, slowest. #include <StormEigen/SVD>
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// .ldlt() -> .matrixL() and .matrixD()
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// .llt() -> .matrixL()
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// .lu() -> .matrixL() and .matrixU()
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// .qr() -> .matrixQ() and .matrixR()
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// .svd() -> .matrixU(), .singularValues(), and .matrixV()
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// Eigenvalue problems
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// Eigen // Matlab
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A.eigenvalues(); // eig(A);
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EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A)
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eig.eigenvalues(); // diag(val)
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eig.eigenvectors(); // vec
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// For self-adjoint matrices use SelfAdjointEigenSolver<>
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