From 22b9de1849a94aad958ca097088cdef9646d1233 Mon Sep 17 00:00:00 2001 From: Keir Mierle Date: Thu, 19 Feb 2009 16:46:35 +0000 Subject: Fix some formatting in quick ref. Add references to headers. --- doc/AsciiQuickReference.txt | 273 ++++++++++++++++++++++---------------------- 1 file changed, 138 insertions(+), 135 deletions(-) (limited to 'doc/AsciiQuickReference.txt') diff --git a/doc/AsciiQuickReference.txt b/doc/AsciiQuickReference.txt index bcf402186..b868741f3 100644 --- a/doc/AsciiQuickReference.txt +++ b/doc/AsciiQuickReference.txt @@ -1,11 +1,17 @@ - Matrix A; // Fixed rows and cols. Same as Matrix3d. - Matrix B; // Fixed rows, dynamic cols. - Matrix C; // Full dynamic. Same as MatrixXd. - Matrix 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. - double s; +// A simple quickref for Eigen. Add anything that's missing. +// Main author: Keir Mierle + +#include +#include + +Matrix A; // Fixed rows and cols. Same as Matrix3d. +Matrix B; // Fixed rows, dynamic cols. +Matrix C; // Full dynamic. Same as MatrixXd. +Matrix 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. +double s; // Basic usage // Eigen // Matlab // comments @@ -15,145 +21,142 @@ 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) // - 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 be - 4, 5, 6, // matrices, which are stacked along cols - 7, 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. - A.setRandom(); // Fill A with uniform random numbers in (-1, 1). +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 be + 4, 5, 6, // matrices, which are stacked along cols + 7, 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. +A.setRandom(); // Fill A with uniform random numbers in (-1, 1). // Requires #include . - A.setIdentity(); // Fill A with the identity. +A.setIdentity(); // Fill A with the identity. - // 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.start(n) // x(1:n) - x.start() // x(1:n) - x.end(n) // N = rows(x); x(N - n: N) - x.end() // N = rows(x); x(N - n: N) - x.segment(i, n) // x(i+1 : i+n) - x.segment(i) // x(i+1 : i+n) - P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols) - P.block(i, j) // P(i+1 : i+rows, j+1 : j+cols) - P.corner(TopLeft, rows, cols) // P(1:rows, 1:cols) - P.corner(TopRight, rows, cols) // [m n]=size(P); P(1:rows, n-cols+1:n) - P.corner(BottomLeft, rows, cols) // [m n]=size(P); P(m-rows+1:m, 1:cols) - P.corner(BottomRight, rows, cols) // [m n]=size(P); P(m-rows+1:m, n-cols+1:n) - P.corner(TopLeft) // P(1:rows, 1:cols) - P.corner(TopRight) // [m n]=size(P); P(1:rows, n-cols+1:n) - P.corner(BottomLeft) // [m n]=size(P); P(m-rows+1:m, 1:cols) - P.corner(BottomRight) // [m n]=size(P); P(m-rows+1:m, n-cols+1:n) - P.minor(i, j) // Something nasty. +// 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.start(n) // x(1:n) +x.start() // x(1:n) +x.end(n) // N = rows(x); x(N - n: N) +x.end() // N = rows(x); x(N - n: N) +x.segment(i, n) // x(i+1 : i+n) +x.segment(i) // x(i+1 : i+n) +P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols) +P.block(i, j) // P(i+1 : i+rows, j+1 : j+cols) +P.corner(TopLeft, rows, cols) // P(1:rows, 1:cols) +P.corner(TopRight, rows, cols) // [m n]=size(P); P(1:rows, n-cols+1:n) +P.corner(BottomLeft, rows, cols) // [m n]=size(P); P(m-rows+1:m, 1:cols) +P.corner(BottomRight, rows, cols) // [m n]=size(P); P(m-rows+1:m, n-cols+1:n) +P.corner(TopLeft) // P(1:rows, 1:cols) +P.corner(TopRight) // [m n]=size(P); P(1:rows, n-cols+1:n) +P.corner(BottomLeft) // [m n]=size(P); P(m-rows+1:m, 1:cols) +P.corner(BottomRight) // [m n]=size(P); P(m-rows+1:m, n-cols+1:n) +P.minor(i, j) // Something nasty. - // 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]) +// 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]) - // 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) +// 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) - // 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; +// 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; // Vectorized operations on each element independently // (most require #include ) - // Eigen // Matlab - R = P.cwise() * Q; // R = P .* Q - R = P.cwise() / Q; // R = P ./ Q - R = P.cwise() + s; // R = P + s - R = P.cwise() - s; // R = P - s - R.cwise() += s; // R = R + s - R.cwise() -= s; // R = R - s - R.cwise() *= s; // R = R * s - R.cwise() /= s; // R = R / s - R.cwise() < Q; // R < Q - R.cwise() <= Q; // R <= Q - R.cwise().inverse(); // 1 ./ P - R.cwise().sin() // sin(P) - R.cwise().cos() // cos(P) - R.cwise().pow(s) // P .^ s - R.cwise().square() // P .^ 2 - R.cwise().cube() // P .^ 3 - R.cwise().sqrt() // sqrt(P) - R.cwise().exp() // exp(P) - R.cwise().log() // log(P) - R.cwise().max(P) // max(R, P) - R.cwise().min(P) // min(R, P) - R.cwise().abs() // abs(P) - R.cwise().abs2() // abs(P.^2) - (R.cwise() < s).select(P,Q); // (R < s ? P : Q) +// Eigen // Matlab +R = P.cwise() * Q; // R = P .* Q +R = P.cwise() / Q; // R = P ./ Q +R = P.cwise() + s; // R = P + s +R = P.cwise() - s; // R = P - s +R.cwise() += s; // R = R + s +R.cwise() -= s; // R = R - s +R.cwise() *= s; // R = R * s +R.cwise() /= s; // R = R / s +R.cwise() < Q; // R < Q +R.cwise() <= Q; // R <= Q +R.cwise().inverse(); // 1 ./ P +R.cwise().sin() // sin(P) +R.cwise().cos() // cos(P) +R.cwise().pow(s) // P .^ s +R.cwise().square() // P .^ 2 +R.cwise().cube() // P .^ 3 +R.cwise().sqrt() // sqrt(P) +R.cwise().exp() // exp(P) +R.cwise().log() // log(P) +R.cwise().max(P) // max(R, P) +R.cwise().min(P) // min(R, P) +R.cwise().abs() // abs(P) +R.cwise().abs2() // abs(P.^2) +(R.cwise() < s).select(P,Q); // (R < s ? P : Q) - // Reductions. - int r, c; - // Eigen // Matlab - R.minCoeff() // min(R(:)) - R.maxCoeff() // max(R(:)) - s = R.minCoeff(&r, &c) // [aa, bb] = min(R); [cc, dd] = min(aa); +// Reductions. +int r, c; +// Eigen // Matlab +R.minCoeff() // min(R(:)) +R.maxCoeff() // max(R(:)) +s = R.minCoeff(&r, &c) // [aa, bb] = min(R); [cc, dd] = min(aa); // r = bb(dd); c = dd; s = cc - s = R.maxCoeff(&r, &c) // [aa, bb] = max(R); [cc, dd] = max(aa); +s = R.maxCoeff(&r, &c) // [aa, bb] = max(R); [cc, dd] = max(aa); // row = bb(dd); col = dd; s = cc - R.sum() // sum(R(:)) - R.colwise.sum() // sum(R) - R.rowwise.sum() // sum(R, 2) or sum(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 +R.sum() // sum(R(:)) +R.colwise.sum() // sum(R) +R.rowwise.sum() // sum(R, 2) or sum(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) - // Eigen can map existing memory into Eigen matrices. - float array[3]; - Map(array, 3).fill(10); - int data[4] = 1, 2, 3, 4; - Matrix2i mat2x2(data); - MatrixXi mat2x2 = Map(data); - MatrixXi mat2x2 = Map(data, 2, 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 - // Solve Ax = b. Result stored in x. Matlab: x = A \ b. - bool solved; - solved = A.ldlt().solve(b, &x)); // A symmetric p.s.d. - solved = A.llt() .solve(b, &x)); // A symmetric p.d. - solved = A.lu() .solve(b, &x)); // Stable and fast. - solved = A.qr() .solve(b, &x)); // No pivoting. - solved = A.svd() .solve(b, &x)); // Most stable, slowest. - // .ldlt() -> .matrixL() and .matrixD() - // .llt() -> .matrixL() - // .lu() -> .matrixL() and .matrixU() - // .qr() -> .matrixQ() and .matrixR() - // .svd() -> .matrixU(), .singularValues(), and .matrixV() +// Eigen can map existing memory into Eigen matrices. +float array[3]; +Map(array, 3).fill(10); +int data[4] = 1, 2, 3, 4; +Matrix2i mat2x2(data); +MatrixXi mat2x2 = Map(data); +MatrixXi mat2x2 = Map(data, 2, 2); - // Eigenvalue problems - // Eigen // Matlab - A.eigenvalues(); // eig(A); - EigenSolver eig(A); // [vec val] = eig(A) - eig.eigenvalues(); // diag(val) - eig.eigenvectors(); // vec +// Solve Ax = b. Result stored in x. Matlab: x = A \ b. +bool solved; +solved = A.ldlt().solve(b, &x)); // A sym. p.s.d. #include +solved = A.llt() .solve(b, &x)); // A sym. p.d. #include +solved = A.lu() .solve(b, &x)); // Stable and fast. #include +solved = A.qr() .solve(b, &x)); // No pivoting. #include +solved = A.svd() .solve(b, &x)); // Stable, slowest. #include +// .ldlt() -> .matrixL() and .matrixD() +// .llt() -> .matrixL() +// .lu() -> .matrixL() and .matrixU() +// .qr() -> .matrixQ() and .matrixR() +// .svd() -> .matrixU(), .singularValues(), and .matrixV() -__________ -Main author: Keir Mierle \ No newline at end of file +// Eigenvalue problems +// Eigen // Matlab +A.eigenvalues(); // eig(A); +EigenSolver eig(A); // [vec val] = eig(A) +eig.eigenvalues(); // diag(val) +eig.eigenvectors(); // vec -- cgit v1.2.3