matlab 使用eigen,Eigen与MATLAB使用对照表

梦里梦外; 2023-01-15 11:21 157阅读 0赞

// A simple quickref for Eigen. Add anything that‘s missing.

// Main author: Keir Mierle

\#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.

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

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.

// 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

// vector is x(1)...x(N)).

// Eigen // Matlab

x.head(n) // x(1:n)

x.head() // x(1:n)

x.tail(n) // x(end - n + 1: end)

x.tail() // x(end - n + 1: end)

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.row(i) // P(i+1, :)

P.col(j) // P(:, j+1)

P.leftCols() // P(:, 1:cols)

P.leftCols(cols) // P(:, 1:cols)

P.middleCols(j) // P(:, j+1:j+cols)

P.middleCols(j, cols) // P(:, j+1:j+cols)

P.rightCols() // P(:, end-cols+1:end)

P.rightCols(cols) // P(:, end-cols+1:end)

P.topRows() // P(1:rows, :)

P.topRows(rows) // P(1:rows, :)

P.middleRows(i) // P(i+1:i+rows, :)

P.middleRows(i, rows) // P(i+1:i+rows, :)

P.bottomRows() // 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) // 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() // P(1:rows, 1:cols)

P.topRightCorner() // P(1:rows, end-cols+1:end)

P.bottomLeftCorner() // P(end-rows+1:end, 1:cols)

P.bottomRightCorner() // P(end-rows+1:end, end-cols+1:end)

// 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)

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.

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

// Eigen // Matlab

R = P.cwiseProduct(Q); // R = P .\* Q

R = P.array() \* s.array();// R = P .\* s

R = P.cwiseQuotient(Q); // R = P ./ Q

R = P.array() / Q.array();// R = P ./ Q

R = P.array() + s.array();// R = P + s

R = P.array() - s.array();// R = P - s

R.array() += s; // R = R + s

R.array() -= s; // R = R - s

R.array() < Q.array(); // R < Q

R.array() <= Q.array(); // R <= Q

R.cwiseInverse(); // 1 ./ P

R.array().inverse(); // 1 ./ P

R.array().sin() // sin(P)

R.array().cos() // cos(P)

R.array().pow(s) // P .^ s

R.array().square() // P .^ 2

R.array().cube() // P .^ 3

R.cwiseSqrt() // sqrt(P)

R.array().sqrt() // sqrt(P)

R.array().exp() // exp(P)

R.array().log() // log(P)

R.cwiseMax(P) // max(R, P)

R.array().max(P.array()) // max(R, P)

R.cwiseMin(P) // min(R, P)

R.array().min(P.array()) // min(R, P)

R.cwiseAbs() // abs(P)

R.array().abs() // abs(P)

R.cwiseAbs2() // abs(P.^2)

R.array().abs2() // abs(P.^2)

(R.array() < 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) // \[s, i\] = 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.prod() // 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)

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

Type conversion

// Eigen // Matlab

A.cast(); // double(A)

A.cast(); // single(A)

A.cast(); // 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(); // F converted to double and then added (generally, conversion happens on-the-fly)

// Eigen can map existing memory into Eigen matrices.

float array\[3\];

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.

x = A.ldlt().solve(b)); // A sym. p.s.d. \#include

x = A.llt() .solve(b)); // A sym. p.d. \#include

x = A.lu() .solve(b)); // Stable and fast. \#include

x = A.qr() .solve(b)); // No pivoting. \#include

x = A.svd() .solve(b)); // Stable, slowest. \#include

// .ldlt() -> .matrixL() and .matrixD()

// .llt() -> .matrixL()

// .lu() -> .matrixL() and .matrixU()

// .qr() -> .matrixQ() and .matrixR()

// .svd() -> .matrixU(), .singularValues(), and .matrixV()

// Eigenvalue problems

// Eigen // Matlab

A.eigenvalues(); // eig(A);

EigenSolver eig(A); // \[vec val\] = eig(A)

eig.eigenvalues(); // diag(val)

eig.eigenvectors(); // vec

// For self-adjoint matrices use SelfAdjointEigenSolver<>

原文：http://www.cnblogs.com/jast/p/4244610.html

matlab 使用eigen,Eigen与MATLAB使用对照表

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