Error using Eigen: invalid use of incomplete type ‘const class Eigen

Question

I have the following code that works:

Matrix <float, ny+1, nx> eXX;
eXX.setZero();

Eigen::Matrix< double, (ny+1), (ny)> u; 
    u.setZero(); 
    for(int i = 0; i< nx; i++){
        for(int j = 0; j< ny+1; j++){
            eXX(j + (ny+1)*i) = (i)*2*EIGEN_PI/nx; 
            u(j + (ny+1)*i) = cos(eXX(j + (ny+1)*i));
        }
    }

But when I write the following it doesn't work:

Matrix <float, ny+1, nx> eXX;
eXX.setZero();

Eigen::Matrix< double, (ny+1), (ny)> u; 
    u.setZero(); 
    for(int i = 0; i< nx; i++){
        for(int j = 0; j< ny+1; j++){
            eXX(j + (ny+1)*i) = (i)*2*EIGEN_PI/nx; 
        }
    }
u = eXX.matrix().cos();// -or- std::cos(eXX.array());
    std::cout << u << "\n"; //error

The full error message:

Test.cpp:418:23: error: invalid use of incomplete type ‘const class Eigen::MatrixFunctionReturnValue<Eigen::Matrix<float, 11, 10> >’
  418 |  u = eXX.matrix().cos();
      |                       ^
In file included from /mnt/c/Users/eigen-3.4.0/eigen-3.4.0/Eigen/Core:163,
                 from /mnt/c/Users/eigen-3.4.0/eigen-3.4.0/Eigen/Dense:1,
                 from Test.cpp:21:
/mnt/c/Users/eigen-3.4.0/eigen-3.4.0/Eigen/src/Core/util/ForwardDeclarations.h:305:34: note: declaration of ‘class Eigen::MatrixFunctionReturnValue<Eigen::Matrix<float, 11, 10> >’
  305 | template<typename Derived> class MatrixFunctionReturnValue;

I guess I could try rewriting eXX without the use of for loop and pass it but that also doesn't work. Also, I read someone recommending adding something like #include <MatrixFunctionReturnValue> which made things a lot worse actually. Thanks.

I am adding my includes as well here:

#define _USE_MATH_DEFINES 
#include <cmath>
#include<math.h>
#include<stdio.h>
#include "fftw3.h"
#include <cstring>
#include <sstream>
#include <string>
#include <sys/resource.h>
#include <iostream> 
#include <vector>
#include <fstream> 
#include <iomanip>
#include <numeric>
#include <assert.h>
#include <Eigen/Dense>
#include <unsupported/Eigen/FFT>
#include <Eigen/SparseCore> 
#include <Eigen/Sparse>

Answer 1

The Matrix class is built for linear algebra. When you want to operate over the elements of a matrix you need to the use the Array class instead. See Eigen documentation on Array . The other way to do this is to use the unaryExpr to take each element of the matrix as an input.

Here are both methods:

#include <iostream>
#include <Eigen/Dense>
....
Eigen::Matrix<double, 3, 3> vals;
vals.setZero();
std::cout << vals << '\n';
std::cout << "******\n";
std::cout << vals.array().cos() << '\n';
std::cout << vals << '\n';
std::cout << "******\n";
Eigen::Matrix<double, 3, 3> res = vals.unaryExpr([](double a) { return cos(a); });
std::cout << res << '\n';
std::cout << vals << '\n';

Take note of how vals changes (and doesn't change) with the various operations.