Eigen 是一个基于C++模板的线性代数库，直接将库下载后放在项目目录下，然后包含头文件就能使用，非常方便。VS2012配置方法参见：http://blog.csdn.net/j_d_c/article/details/78899538
Eigen 矩阵定义
-
#include <Eigen/Dense>
-
-
Matrix<
double,
3,
3> A;
// Fixed rows and cols. Same as Matrix3d.
-
Matrix<
double,
3, Dynamic> B;
// Fixed rows, dynamic cols.
-
Matrix<
double, Dynamic, Dynamic> C;
// Full dynamic. Same as MatrixXd.
-
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
-
// 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) //
Eigen 基础使用
-
// 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 特殊矩阵生成
-
// 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)'
Eigen 矩阵分块
-
// 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<n>()
// x(1: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)
// 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>()
// 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)
Eigen 矩阵元素交换
-
// 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])
Eigen 矩阵转置
-
// 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)
Eigen 矩阵乘积
-
// 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;
Eigen 矩阵单个元素操作
-
// 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)
Eigen 矩阵化简
-
// 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)
Eigen 矩阵点乘
-
// 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 <Eigen/Geometry>
Eigen 矩阵类型转换
-
//// 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
Eigen 求解线性方程组 Ax = b
-
// Solve Ax = b. Result stored in x. Matlab:
x = A \ b.
-
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()
-
// .
qr() -> .matrixQ()
and .matrixR()
-
// .svd() -> .matrixU(), .singularValues(),
and .matrixV()
Eigen 矩阵特征值
-
// Eigenvalue problems
-
// Eigen // Matlab
-
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<>
参考文献
【1】http://eigen.tuxfamily.org/dox/AsciiQuickReference.txt
【2】http://blog.csdn.net/augusdi/article/details/12907341
转自：http://www.cnblogs.com/python27/p/EigenQuickRef.html
