eigen笔记

• 重复用<<赋值，是可以的

int main()
{
	Eigen::Vector2f v;
	v << 1, 2;
	v << 3, 4;
	std::cout << v << std::endl;
	return 0;
}
3
4

• <<的输入顺序是先排满行，再排满列。

int main()
{
	Eigen::MatrixXf m(3,2);
	m << 1, 2,
		3, 4,
		5, 6;
	std::cout << m << std::endl;
	return 0;
}
1 2
3 4
5 6

• vector组成矩阵

int main()
{
	Eigen::Vector2f v{ 1,2 };
	Eigen::MatrixXf m(2,2);
	m << v, v;
	std::cout << m << std::endl;
	return 0;
}
1 1
2 2

矩阵组成矩阵，按先排满行，再排满列

int main()
{
	Eigen::MatrixXf m1(2,2);
	m1.fill(1);
	auto m2 = m1 * 2;
	auto m3 = m1 * 3;
	auto m4 = m1 * 4;
	Eigen::MatrixXf res(4, 4);
	res << m1, m2, m3, m4;
	std::cout << res << std::endl;
	return 0;
}
1 1 2 2
1 1 2 2
3 3 4 4
3 3 4 4

• 也可以直接用block拼接

int main()
{
	Eigen::MatrixXf m1(4,3);
	m1.fill(1);
	auto m2 = m1.col(1)*2;
	Eigen::MatrixXf res(4, 4);
	res << m1, m2;
	std::cout << res << std::endl;
	return 0;
}
1 1 1 2
1 1 1 2
1 1 1 2
1 1 1 2

Eigen::VectorXf::LinSpaced可以同时赋值行或列，但是直接赋值给矩阵后，就是变成1列了。需要使用reshaped()

int main()
{
    Eigen::MatrixXf res(4, 4);
    res.fill(1);
    res.row(0) = Eigen::VectorXf::LinSpaced(4, 2, 5); //正确赋值
    res.col(0) = Eigen::VectorXf::LinSpaced(4, 2, 5); //正确赋值
    //res = Eigen::VectorXf::LinSpaced(16, 2, 17); //这个会导致res变成1列的
    res.reshaped() = Eigen::VectorXf::LinSpaced(16, 2, 17); //正确赋值
    std::cout << res << std::endl;
	return 0;
}
 2  6 10 14
 3  7 11 15
 4  8 12 16
 5  9 13 17

resize会在保持内存顺序不变的情况下，变换行列

int main()
{
	Eigen::MatrixXf res(4, 4);
    res.reshaped() = Eigen::VectorXf::LinSpaced(16, 1, 16);
    res.resize(8, 2);
    std::cout << res << std::endl;
	return 0;
}
1  9
 2 10
 3 11
 4 12
 5 13
 6 14
 7 15
 8 16

两个动态类型可以直接赋值

int main()
{
	MatrixXf a(2,2);
	std::cout << "a is of size " << a.rows() << "x" << a.cols() << std::endl;
	MatrixXf b(3,3);
	a = b;
	std::cout << "a is now of size " << a.rows() << "x" << a.cols() << std::endl;
	return 0;
}
a is of size 2x2
a is now of size 3x3

• array()方法的逐值运算

int main()
{
	Eigen::Vector2f v1;
	v1 << 1, 2;
	auto v2 = v1;
	v2.array() += 2;
	std::cout << v2 << std::endl;
	return 0;
}
3
4

• 一个矩阵倒序

A.colwise().reverseInPlace();

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

• 输出格式设置

std::string sep = "\n----------------------------------------\n";
Matrix3d m1;
m1 << 1.111111, 2, 3.33333, 4, 5, 6, 7, 8.888888, 9;
 
IOFormat CommaInitFmt(StreamPrecision, DontAlignCols, ", ", ", ", "", "", " << ", ";");
IOFormat CleanFmt(4, 0, ", ", "\n", "[", "]");
IOFormat OctaveFmt(StreamPrecision, 0, ", ", ";\n", "", "", "[", "]");
IOFormat HeavyFmt(FullPrecision, 0, ", ", ";\n", "[", "]", "[", "]");
 
std::cout << m1 << sep;
std::cout << m1.format(CommaInitFmt) << sep;
std::cout << m1.format(CleanFmt) << sep;
std::cout << m1.format(OctaveFmt) << sep;
std::cout << m1.format(HeavyFmt) << sep;

• 每列中的数乘不同的元素

int main()
{
	Eigen::Matrix2f m;
	m << 1, 2,
		3, 4;
	Eigen::Vector2f v;
	v << 2, 3;
	m.array().colwise() *=  v.array();
	std::cout << m << std::endl;
	return 0;
}
 2  4
 9 12

• opengl

• 旋转

using namespace Eigen;
	Vector2f v;
	v << 1.0, 2.0;
	auto v1 = Eigen::Rotation2Df(M_PI/2) * v;
	std::cout << v1 << std::endl;

• 缩放

using namespace Eigen;
	Vector2f v;
	v << 1.0, 2.0;
	auto v1 = Eigen::Scaling(2.0) * v;
	std::cout << v1 << std::endl;

• 平移

using namespace Eigen;
	Vector2f v;
	v << 1.0, 2.0;
	auto v1 = Eigen::Translation2f(1.0,3.0) * v;
	std::cout << v1 << std::endl;

• 三维向量的旋转矩阵

Eigen::Vector3d v1{ 0,0,1 };

	Eigen::Vector3d v2{ 0,1,0 };

	Eigen::Matrix3d R;

	//R = Eigen::Quaterniond::FromTwoVectors(v1, v2).toRotationMatrix();
	//std::cout << R << std::endl;
	std::cout << Eigen::Quaterniond::FromTwoVectors(v1, v2) * v1 << std::endl;

• 旋转

逆时针旋转

Vector2f v(1,0);
	auto v1 = Rotation2Df(M_PI / 2) * v;
	std::cout << v1 << std::endl;