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install and use eigen3 on ubuntu 16.04

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Guide

install

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sudo apt-get install libeigen3-dev

install to /usr/include/eigen3/ and /usr/lib/cmake/eigen3

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ll /usr/lib/cmake/eigen3

Eigen3Config.cmake

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#                                               -*- cmake -*-
#
#  Eigen3Config.cmake(.in)

# Use the following variables to compile and link against Eigen:
#  EIGEN3_FOUND              - True if Eigen was found on your system
#  EIGEN3_USE_FILE           - The file making Eigen usable
#  EIGEN3_DEFINITIONS        - Definitions needed to build with Eigen
#  EIGEN3_INCLUDE_DIR        - Directory where signature_of_eigen3_matrix_library can be found
#  EIGEN3_INCLUDE_DIRS       - List of directories of Eigen and it's dependencies
#  EIGEN3_ROOT_DIR           - The base directory of Eigen
#  EIGEN3_VERSION_STRING     - A human-readable string containing the version
#  EIGEN3_VERSION_MAJOR      - The major version of Eigen
#  EIGEN3_VERSION_MINOR      - The minor version of Eigen
#  EIGEN3_VERSION_PATCH      - The patch version of Eigen

set ( EIGEN3_FOUND 1 )
set ( EIGEN3_USE_FILE     "${CMAKE_CURRENT_LIST_DIR}/UseEigen3.cmake" )

set ( EIGEN3_DEFINITIONS  "" )
set ( EIGEN3_INCLUDE_DIR  "/usr/include/eigen3" )
set ( EIGEN3_INCLUDE_DIRS "/usr/include/eigen3" )
set ( EIGEN3_ROOT_DIR     "/usr" )

set ( EIGEN3_VERSION_STRING "3.2.92" )
set ( EIGEN3_VERSION_MAJOR  "3" )
set ( EIGEN3_VERSION_MINOR  "2" )
set ( EIGEN3_VERSION_PATCH  "92" )

UseEigen3.cmake

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# -*- cmake -*-
#
#  UseEigen3.cmake

add_definitions     ( ${EIGEN3_DEFINITIONS} )
include_directories ( ${EIGEN3_INCLUDE_DIRS} )

typedef

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typedef Matrix< std::complex<double> , 2 , 2 > Eigen::Matrix2cd
typedef Matrix< std::complex<float> , 2 , 2 > Eigen::Matrix2cf
typedef Matrix< double , 2 , 2 > Eigen::Matrix2d
typedef Matrix< float , 2 , 2 > Eigen::Matrix2f
typedef Matrix< int , 2 , 2 > Eigen::Matrix2i
typedef Matrix< std::complex<double> , 2 , Dynamic> Eigen::Matrix2Xcd
typedef Matrix< std::complex<float> , 2 , Dynamic> Eigen::Matrix2Xcf
typedef Matrix< double , 2 , Dynamic> Eigen::Matrix2Xd
typedef Matrix< float , 2 , Dynamic> Eigen::Matrix2Xf
typedef Matrix< int , 2 , Dynamic> Eigen::Matrix2Xi
typedef Matrix< std::complex<double> , 3 , 3 > Eigen::Matrix3cd
########
transpose  转置
conjugate  共轭
adjoint    伴随

Example

CMakeLists.txt

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cmake_minimum_required(VERSION 2.8)
project(Test)

find_package(Eigen3 REQUIRED)
MESSAGE( [Main] " EIGEN3_INCLUDE_DIRS = ${EIGEN3_INCLUDE_DIRS}") 
# EIGEN3_INCLUDE_DIRS = /usr/include/eigen3

include_directories(${EIGEN3_INCLUDE_DIRS})

add_executable(main test.cpp)

No need to link libraries for eigen3.

c++ code

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#include <Eigen/Dense>
using namespace Eigen;

void test0()
{
	//------------------------
	MatrixXd m(2,2);
	m(0,0) = 3;
	m(1,0) = 2.5;
	m(0,1) = -1;
	m(1,1) = m(1,0) + m(0,1);
	cout << "Here is the matrix m:\n" << m << endl;

	VectorXd v(2);
	v(0) = 4;
	v(1) = v(0) - 1;
	cout << "Here is the vector v:\n" << v << endl;

	//------------------------
	Matrix3f m2;
	m2 << 1, 2, 3,
		4, 5, 6,
		7, 8, 9;
	cout << m2 << endl;
}

void test1()
{
	// stats
	Eigen::Matrix2d mat;
	mat << 1, 2,
			3, 4;
	cout << "Here is mat.sum():       " << mat.sum()       << endl;
	cout << "Here is mat.prod():      " << mat.prod()      << endl;
	cout << "Here is mat.mean():      " << mat.mean()      << endl;
	cout << "Here is mat.minCoeff():  " << mat.minCoeff()  << endl; // min value = 1
	cout << "Here is mat.maxCoeff():  " << mat.maxCoeff()  << endl; // max value = 4
	cout << "Here is mat.trace():     " << mat.trace()     << endl; // 
}

/*
Here is mat.sum():       10
Here is mat.prod():      24
Here is mat.mean():      2.5
Here is mat.minCoeff():  1
Here is mat.maxCoeff():  4
Here is mat.trace():     5
*/

void test2()
{ 
	// l1-norm = |v1|+|v2|+...|vn|
	// l2-norm = v1*v1 + v2*v2+...vn*vn     squareNorm(), Norm()
	//  lpNorm< p >():  lpNorm< 1 >()   lpNorm< 2 >()

	VectorXf v(2);
	MatrixXf m(2,2), n(2,2);
	
	v << -1,
		2;
	
	m << 1,-2,
		-3,4;
	cout << "v.squaredNorm() = " << v.squaredNorm() << endl;
	cout << "v.norm() = " << v.norm() << endl;
	cout << "v.lpNorm<1>() = " << v.lpNorm<1>() << endl;
	cout << "v.lpNorm<Infinity>() = " << v.lpNorm<Infinity>() << endl; // max value
	cout << endl;
	cout << "m.squaredNorm() = " << m.squaredNorm() << endl;
	cout << "m.norm() = " << m.norm() << endl;
	cout << "m.lpNorm<1>() = " << m.lpNorm<1>() << endl;
	cout << "m.lpNorm<Infinity>() = " << m.lpNorm<Infinity>() << endl;  // max value


	n << 1,-2,
		-3,4;
	cout << "1-norm(n)     = " << n.cwiseAbs().colwise().sum().maxCoeff()
		<< " == "             << n.colwise().lpNorm<1>().maxCoeff() << endl;
	cout << "infty-norm(n) = " << n.cwiseAbs().rowwise().sum().maxCoeff()
		<< " == "             << n.rowwise().lpNorm<1>().maxCoeff() << endl;
}
/*
v.squaredNorm() = 5
v.norm() = 2.23607
v.lpNorm<1>() = 3
v.lpNorm<Infinity>() = 2

m.squaredNorm() = 30
m.norm() = 5.47723
m.lpNorm<1>() = 10
m.lpNorm<Infinity>() = 4


1-norm(n)     = 6 == 6
infty-norm(n) = 7 == 7
*/


void test3()
{
	// bool
	ArrayXXf a(2,2);
	
	a << 1,2,
		3,4;
	cout << "(a > 0).all()   = " << (a > 0).all() << endl; // bool 
	cout << "(a > 0).any()   = " << (a > 0).any() << endl; // bool
	cout << "(a > 0).count() = " << (a > 0).count() << endl; // int
	cout << endl;
	cout << "(a > 2).all()   = " << (a > 2).all() << endl;
	cout << "(a > 2).any()   = " << (a > 2).any() << endl;
	cout << "(a > 2).count() = " << (a > 2).count() << endl;
}
/*
(a > 0).all()   = 1
(a > 0).any()   = 1
(a > 0).count() = 4

(a > 2).all()   = 0
(a > 2).any()   = 1
(a > 2).count() = 2
*/

void test4()
{
	// get min/max index
	Eigen::MatrixXf m(2,2);
	
	m << 1, 2,
		3, 4;

	//get location of maximum
	MatrixXf::Index maxRow, maxCol;
	float max = m.maxCoeff(&maxRow, &maxCol);

	//get location of minimum
	MatrixXf::Index minRow, minCol;
	float min = m.minCoeff(&minRow, &minCol);

	cout << "Max: " << max <<  ", at: " << maxRow << "," << maxCol << endl;
	cout << "Min: " << min <<  ", at: " << minRow << "," << minCol << endl;
}
/*
Max: 4, at: 1,1
Min: 1, at: 0,0
*/

void test5()
{
	// colwise rowwise
	Eigen::MatrixXf mat(2,4);
	mat << 1, 2, 6, 9,
			3, 1, 7, 2;
	
	std::cout << "Column's maximum: " << std::endl
	<< mat.colwise().maxCoeff() << std::endl;

	std::cout << "Row's maximum: " << std::endl
	<< mat.rowwise().maxCoeff() << std::endl;
}
/*
Column's maximum: 
3 2 7 9
Row's maximum: 
9
7
*/

void test6()
{
	// colwise + max/min
	MatrixXf mat(2,4);
	mat << 1, 2, 6, 9,
			3, 1, 7, 2;
	
	MatrixXf::Index   maxIndex;
	float maxSum = mat.colwise().sum().maxCoeff(&maxIndex);
	
	std::cout << "Maximum sum at position " << maxIndex << std::endl;
	std::cout << "The corresponding vector is: " << std::endl;
	std::cout << mat.col( maxIndex ) << std::endl;
	std::cout << "And its sum is is: " << maxSum << std::endl;
}
/*
Maximum sum at position 2
The corresponding vector is: 
6
7
And its sum is is: 13
*/

void test7()
{
	// broadcast with vector
	Eigen::MatrixXf mat(2,4);
	Eigen::VectorXf v(2);
	
	mat << 1, 2, 6, 9,
			3, 1, 7, 2;
			
	v << 0,
		1;
		
	//add v to each column of m
	mat.colwise() += v;
	//mat += v; // ERROR
	
	std::cout << "Broadcasting result: " << std::endl;
	std::cout << mat << std::endl;
}
/*
Broadcasting result: 
1 2 6 9
4 2 8 3
*/

void test8()
{
	Eigen::MatrixXf m(2,4);
	Eigen::VectorXf v(2);
	
	m << 1, 23, 6, 9,
		3, 11, 7, 2;
		
	v << 2,
		3;
	MatrixXf::Index index;
	// find nearest neighbour
	(m.colwise() - v).colwise().squaredNorm().minCoeff(&index);
	cout << "Nearest neighbour is column " << index << ":" << endl;
	cout << m.col(index) << endl;
}
/*
Nearest neighbour is column 0:
1
3
*/

void test_eigen3()
{
	//test0();
	//test1();
	//test2();
	//test3();
	//test4();
	//test5();
	//test6();
	//test7();
	test8();
}

Reference

History

  • 20190315: created.