Constructing diagonal matrix in eigen

Question

In eigen, we can create a matrix as

Matrix3f m;
m << 1, 2, 3,
     4, 5, 6,
     7, 8, 9;

How can I create a diagonal matrix like the one below

 3, 0, 0,
 0, 8, 0,
 0, 0, 6;

I don't understand how Eigen handle diagonal matrix? Only the diagonal elements are important here. So does Eigen save all 9 elements from above example or Eigen just save only 3 elements 3,8,6. Also, if eigen save all 9 elements then is it necessary to define the matrix as diagonal or is it the same as defining normal 3*3 matrix?

Bedmate

Answer 1

If you want a standalone diagonal matrix, construct a DiagonalMatrix.

DiagonalMatrix<double, 3> m(3, 8, 6);

// Input after construction
m.diagonal() << 3, 8, 6;

A DiagonalMatrix works like a normal matrix but stores only the diagonal.

Vector3d v(1, 2, 3);
m * v;  // 3 16 18

If you want to make a diagonal matrix out of an existing vector, call .asDiagonal(). Note that .diagonal() returns the diagonal as a vector, so .diagonal().asDiagonal() extract the diagonal part of a matrix and regard it as a diagonal matrix.

Rogatory

what if the size of the diagonal matrix is a variable? – Anguished

Answer 2

Here's a code and its output :

Code:

#include <iostream>
#include "Eigen/Dense"

int main()
{
    Eigen::Matrix< double, 3, 1> v ;
    v << 1, 2, 3;
    Eigen::Matrix< double, 3, 3> m = v.array().sqrt().matrix().asDiagonal();

    std::cout << m << "\n";

    return 0;
}

Output :

  1       0       0
  0 1.41421       0
  0       0 1.73205

As you can see, the output created asDiagonal() from a (31) vector is a normal (33) matrix (that you have to define first), meaning that Eigen holds the 9 elements not just the diagonal ones.

Golgotha

so basically there is no difference between Diagonal matrix and normal matrix? Is there any special optimization done for diagonal one? – Bedmate

Fixed-size matrices are fully optimized: dynamic memory allocation is avoided, and the loops are unrolled when that makes sense. So, whenever you know the size to be, specify it. After all, diagonal matrix is not that special. – Golgotha

please, consider accepting the answer if it solved your original question. cheers. – Golgotha

MatrixBase::asDiagonal() returns a DiagonalWrapper, which holds only the diagonal. The zeros are generated when evaluating into the general matrix m. – Rogatory