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-rw-r--r--doc/AsciiQuickReference.txt109
1 files changed, 73 insertions, 36 deletions
diff --git a/doc/AsciiQuickReference.txt b/doc/AsciiQuickReference.txt
index d2e973f5d..1e74e0528 100644
--- a/doc/AsciiQuickReference.txt
+++ b/doc/AsciiQuickReference.txt
@@ -1,8 +1,7 @@
// A simple quickref for Eigen. Add anything that's missing.
// Main author: Keir Mierle
-#include <Eigen/Core>
-#include <Eigen/Array>
+#include <Eigen/Dense>
Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d.
Matrix<double, 3, Dynamic> B; // Fixed rows, dynamic cols.
@@ -11,13 +10,14 @@ Matrix<double, 3, 3, RowMajor> 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.
+VectorXd v; // Dynamic column vector of doubles
double s;
// Basic usage
// Eigen // Matlab // comments
x.size() // length(x) // vector size
-C.rows() // size(C)(1) // number of rows
-C.cols() // size(C)(2) // number of columns
+C.rows() // size(C,1) // number of rows
+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) //
@@ -31,9 +31,19 @@ A << 1, 2, 3, // Initialize A. The elements can also be
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 <Eigen/Array>.
-A.setIdentity(); // Fill A with the identity.
+
+// Eigen // Matlab
+MatrixXd::Identity(rows,cols) // eye(rows,cols)
+C.setIdentity(rows,cols) // C = eye(rows,cols)
+MatrixXd::Zero(rows,cols) // zeros(rows,cols)
+C.setZero(rows,cols) // C = ones(rows,cols)
+MatrixXd::Ones(rows,cols) // ones(rows,cols)
+C.setOnes(rows,cols) // C = ones(rows,cols)
+MatrixXd::Random(rows,cols) // rand(rows,cols)*2-1 // MatrixXd::Random returns uniform random numbers in (-1, 1).
+C.setRandom(rows,cols) // C = rand(rows,cols)*2-1
+VectorXd::LinSpaced(size,low,high) // linspace(low,high,size)'
+v.setLinSpaced(size,low,high) // v = linspace(low,high,size)'
+
// 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
@@ -41,20 +51,34 @@ A.setIdentity(); // Fill A with the identity.
// Eigen // Matlab
x.head(n) // x(1:n)
x.head<n>() // x(1:n)
-x.tail(n) // N = rows(x); x(N - n: N)
-x.tail<n>() // N = rows(x); x(N - n: N)
+x.tail(n) // x(end - n + 1: end)
+x.tail<n>() // x(end - n + 1: end)
x.segment(i, n) // x(i+1 : i+n)
x.segment<n>(i) // x(i+1 : i+n)
P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols)
P.block<rows, cols>(i, j) // P(i+1 : i+rows, j+1 : j+cols)
+P.row(i) // P(i+1, :)
+P.col(j) // P(:, j+1)
+P.leftCols<cols>() // P(:, 1:cols)
+P.leftCols(cols) // P(:, 1:cols)
+P.middleCols<cols>(j) // P(:, j+1:j+cols)
+P.middleCols(j, cols) // P(:, j+1:j+cols)
+P.rightCols<cols>() // P(:, end-cols+1:end)
+P.rightCols(cols) // P(:, end-cols+1:end)
+P.topRows<rows>() // P(1:rows, :)
+P.topRows(rows) // P(1:rows, :)
+P.middleRows<rows>(i) // P(:, i+1:i+rows)
+P.middleRows(i, rows) // P(:, i+1:i+rows)
+P.bottomRows<rows>() // P(:, end-rows+1:end)
+P.bottomRows(rows) // P(:, end-rows+1:end)
P.topLeftCorner(rows, cols) // P(1:rows, 1:cols)
-P.topRightCorner(rows, cols) // [m n]=size(P); P(1:rows, n-cols+1:n)
-P.bottomLeftCorner(rows, cols) // [m n]=size(P); P(m-rows+1:m, 1:cols)
-P.bottomRightCorner(rows, cols) // [m n]=size(P); P(m-rows+1:m, n-cols+1:n)
+P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end)
+P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols)
+P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end)
P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols)
-P.topRightCorner<rows,cols>() // [m n]=size(P); P(1:rows, n-cols+1:n)
-P.bottomLeftCorner<rows,cols>() // [m n]=size(P); P(m-rows+1:m, 1:cols)
-P.bottomRightCorner<rows,cols>() // [m n]=size(P); P(m-rows+1:m, n-cols+1:n)
+P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end)
+P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols)
+P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end)
// Of particular note is Eigen's swap function which is highly optimized.
// Eigen // Matlab
@@ -67,6 +91,8 @@ R.adjoint() // R'
R.transpose() // R.' or conj(R')
R.diagonal() // diag(R)
x.asDiagonal() // diag(x)
+R.transpose().colwise().reverse(); // rot90(R)
+R.conjugate() // conj(R)
// All the same as Matlab, but matlab doesn't have *= style operators.
// Matrix-vector. Matrix-matrix. Matrix-scalar.
@@ -77,8 +103,7 @@ a *= M; R = P + Q; R = P/s;
R += Q; R *= s;
R -= Q; R /= s;
- // Vectorized operations on each element independently
- // (most require #include <Eigen/Array>)
+// Vectorized operations on each element independently
// Eigen // Matlab
R = P.cwiseProduct(Q); // R = P .* Q
R = P.array() * s.array();// R = P .* s
@@ -116,16 +141,14 @@ 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);
- // row = bb(dd); col = dd; s = cc
+s = R.minCoeff(&r, &c) // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);
+s = R.maxCoeff(&r, &c) // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);
R.sum() // sum(R(:))
-R.colwise.sum() // sum(R)
-R.rowwise.sum() // sum(R, 2) or sum(R')'
+R.colwise().sum() // sum(R)
+R.rowwise().sum() // sum(R, 2) or sum(R')'
R.prod() // prod(R(:))
-R.colwise.prod() // prod(R)
-R.rowwise.prod() // prod(R, 2) or prod(R')'
+R.colwise().prod() // prod(R)
+R.rowwise().prod() // prod(R, 2) or prod(R')'
R.trace() // trace(R)
R.all() // all(R(:))
R.colwise().all() // all(R)
@@ -141,21 +164,34 @@ x.squaredNorm() // dot(x, x) Note the equivalence is not true for co
x.dot(y) // dot(x, y)
x.cross(y) // cross(x, y) Requires #include <Eigen/Geometry>
+//// Type conversion
+// Eigen // Matlab
+A.cast<double>(); // double(A)
+A.cast<float>(); // single(A)
+A.cast<int>(); // int32(A)
+A.real(); // real(A)
+A.imag(); // imag(A)
+// if the original type equals destination type, no work is done
+
+// Note that for most operations Eigen requires all operands to have the same type:
+MatrixXf F = MatrixXf::Zero(3,3);
+A += F; // illegal in Eigen. In Matlab A = A+F is allowed
+A += F.cast<double>(); // F converted to double and then added (generally, conversion happens on-the-fly)
+
// Eigen can map existing memory into Eigen matrices.
float array[3];
-Map<Vector3f>(array, 3).fill(10);
-int data[4] = 1, 2, 3, 4;
-Matrix2i mat2x2(data);
-MatrixXi mat2x2 = Map<Matrix2i>(data);
-MatrixXi mat2x2 = Map<MatrixXi>(data, 2, 2);
+Vector3f::Map(array).fill(10); // create a temporary Map over array and sets entries to 10
+int data[4] = {1, 2, 3, 4};
+Matrix2i mat2x2(data); // copies data into mat2x2
+Matrix2i::Map(data) = 2*mat2x2; // overwrite elements of data with 2*mat2x2
+MatrixXi::Map(data, 2, 2) += mat2x2; // adds mat2x2 to elements of data (alternative syntax if size is not know at compile time)
// 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 <Eigen/Cholesky>
-solved = A.llt() .solve(b, &x)); // A sym. p.d. #include <Eigen/Cholesky>
-solved = A.lu() .solve(b, &x)); // Stable and fast. #include <Eigen/LU>
-solved = A.qr() .solve(b, &x)); // No pivoting. #include <Eigen/QR>
-solved = A.svd() .solve(b, &x)); // Stable, slowest. #include <Eigen/SVD>
+x = A.ldlt().solve(b)); // A sym. p.s.d. #include <Eigen/Cholesky>
+x = A.llt() .solve(b)); // A sym. p.d. #include <Eigen/Cholesky>
+x = A.lu() .solve(b)); // Stable and fast. #include <Eigen/LU>
+x = A.qr() .solve(b)); // No pivoting. #include <Eigen/QR>
+x = A.svd() .solve(b)); // Stable, slowest. #include <Eigen/SVD>
// .ldlt() -> .matrixL() and .matrixD()
// .llt() -> .matrixL()
// .lu() -> .matrixL() and .matrixU()
@@ -168,3 +204,4 @@ A.eigenvalues(); // eig(A);
EigenSolver<Matrix3d> eig(A); // [vec val] = eig(A)
eig.eigenvalues(); // diag(val)
eig.eigenvectors(); // vec
+// For self-adjoint matrices use SelfAdjointEigenSolver<>
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-20 09:19:55 +0000