Using setIdentity() on a sparse matrix leads to incorrect result if there are off-trace terms, i.e. there are still off-trace non-zero terms after setIdentity(). The setIdentity() function does not check if the matrix is in compressed form. Compressing the matrix seems to fix this issue on the test below.

MWE:

#include <iostream>
#define EIGEN_DONT_PARALLELIZE
#include <Eigen/Sparse>

using namespace std;
using namespace Eigen;

int main()
{
    //Create 5x5 identity matrix
    SparseMatrix<float> tmp(5,5);
    tmp.setIdentity();
    cout<<"Correct 5x5 identity:\n\n"<<tmp<<endl;        // CORRECT

    //Add a value off the trace
    tmp.coeffRef(3,1) = 5.0;
    //tmp.makeCompressed();                              // UNCOMMENT TO FIX
    cout<<"5x5 identity with additional off-trace value:\n\n"<<tmp<<endl;

    //Reset to the identity
    tmp.setIdentity();
    cout<<"Incorrect 5x5 identity:\n\n"<<tmp<<endl;      // INCORRECT !!!!!!

    return 0;
}