Guide
install
sudo apt-get install libeigen3-dev
install to
/usr/include/eigen3/and/usr/lib/cmake/eigen3
ll /usr/lib/cmake/eigen3
Eigen3Config.cmake
# -*- 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
# -*- cmake -*-
#
# UseEigen3.cmake
add_definitions ( ${EIGEN3_DEFINITIONS} )
include_directories ( ${EIGEN3_INCLUDE_DIRS} )
typedef
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
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
#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.
