Differences among norm, normalize and normalized in eigen

Eigen in norm、normalize、normalized The difference between

norm()

about Vector,norm Returns the second norm of the vector , namely

for example ：

Vector2d vec(3.0,4.0);
cout << vec.norm() << endl;	// Output 5

about Matrix,norm The Frobenius norm of the matrix is returned （Frobenius Norm）, namely

for example ：

Matrix2d mat;
mat << 1,2
    3,4;
cout << mat.norm() << endl;    // Output sqrt(1*1+2*2+3*3+4*4), namely sqrt(30) = 5.47723

normalize()

It's clear norm() After the definition of ,normalize() In fact, it is to divide each element of itself by its norm . The return value is void.

for example ：

vec.normalize();
cout << vec << endl;    // Output ：      0.6
                       //            0.8

mat.normalize();        //mat Each element divided by mat.norm()
cout << mat << endl;    

normalized()

and normalized() And normalize() similar , It's just normalize() Is to make changes to itself , and normalized() It's a new Vector/Matrix, Does not change the original matrix .