Eigen3 Library

Constructors

 

 

#include <iostream> #include <Eigen/Dense> using namespace Eigen; Matrix3f A; MatrixXf B; MatrixXf C( 10, 15 ); VectorXf d( 30 ); Matrix3F E; E << 1, 2, 3, 4, 5, 6, 7, 8 ,9; MatrixXd F(2, 2); F(0, 0) = 3; F(1, 0) = 2.5; F(0, 1) = -1; F(1, 1) = 1.5

 

• A is a 3-by-3 matrix, with a plain float[9] array of uninitialized coefficients.
• B is a dynamic-size matrix whose size is currently 0-by-0, and whose array of coefficients hasn't yet been allocated at all.
• C is a 10x15 dynamic-size matrix, with allocated but currently uninitialized coefficients.
• d is a dynamic-size vector of size 30, with allocated but currently uninitialized coefficients.

 

cout << "The matrix A is size of : " << A.rows() << " x " << A.cols() << endl; cout << "The vector d is size of : " << d.size() << endl; F.resize(3, 3);

 

rows()

cols()

size()

resize() : destructive; the values of the coefficients may change

conservativeResize() : does not change the coefficients

 

 

 

Arithmetic

 

 

VectorXf a(50), b(50), c(50), d(50); a = 3*b + 2*c - 5*d; MatrixXf m(2,3); m << 1, 2, 3, 4, 5, 6; cout << "m^T : " << m.transpose() << endl; cout << "m^- : " << m.conjugate() << endl; cout << "m^* : " << m. adjoint() << endl;

 

transpose()

conjugate()

adjoint() : conjugate transpose

 

 

Vector3d v(1,2,3); Vector3d w(0,1,2); cout << "Dot product: " << v.dot(w) << endl; double dp = v.adjoint()*w; // automatic conversion of the inner product to a scalar cout << "Dot product via a matrix product: " << dp << endl; cout << "Cross product:\n" << v.cross(w) << endl;

 

operator * : matrix * matrix multiplication

dot() : inner product

cross() : cross product

 

 

sum() : summation of elements

prod() : multiplication

mean() : avg

maxCoeff()

minCoeff()

trace() : sum of diagonal elements; same with = a.diagonal().sum()

 

 

 

 

Catalogue of dense decompositions

 

http://eigen.tuxfamily.org/dox/group__TopicLinearAlgebraDecompositions.html

 

 

 

 

Sparse Linear Algebra

 

 

#include <Eigen/Sparse> SparseMatrix<std::complex<float> > mat(1000,2000); // declares a 1000x2000 column-major compressed sparse matrix of complex<float> SparseMatrix<double,RowMajor> mat(1000,2000); // declares a 1000x2000 row-major compressed sparse matrix of double SparseVector<std::complex<float> > vec(1000); // declares a column sparse vector of complex<float> of size 1000 SparseVector<double,RowMajor> vec(1000); // declares a row sparse vector of double of size 1000

 

mat.rows()

mat.cols()

vec.size()

mat.innerSize()

mat.outerSize()

mat.nonZeros()

vec.nonZeros()

 

 

 

Solving Sparse Linear Systems

 

http://eigen.tuxfamily.org/dox/group__TopicSparseSystems.html

 

 

 

Quick Reference Guide For Sparse Matrices

 

http://eigen.tuxfamily.org/dox/group__SparseQuickRefPage.html