Compare Eigen matrices in Google Test or Google Mock

Question

I was wondering if there is a good way to test two Eigen matrices for approximate equality using Google Test, or Google Mock.

Take the following test-case as a simplified example: I am multiplying two complex valued matrices A, and B, and expect a certain result C_expect. I calculate the numerical result C_actual = A * B, using Eigen. Now, I want to compare C_expect, and C_actual. Right now, the corresponding code looks like this:

#include <complex>
#include <Eigen/Dense>
#include <gtest/gtest.h>
#include <gmock/gmock.h>

typedef std::complex<double> Complex;
typedef Eigen::Matrix2cd Matrix;

TEST(Eigen, MatrixMultiplication) {
    Matrix A, B, C_expect, C_actual;

    A << Complex(1, 1), Complex(2, 3),
         Complex(3, 2), Complex(4, 4);
    B << Complex(4, 4), Complex(3, 2),
         Complex(2, 3), Complex(1, 1);
    C_expect << Complex(-5, 20), Complex(0, 10),
                Complex(0, 40), Complex(5, 20);

    C_actual = A * B;

    // !!! These are the lines that bother me.
    for (int j = 0; j < C_actual.cols(); ++j) {
        for (int i = 0; i < C_actual.rows(); ++i) {
            EXPECT_NEAR(C_expect(i, j).real(), C_actual(i, j).real(), 1e-7)
                << "Re(" << i << "," << j << ")";
            EXPECT_NEAR(C_expect(i, j).imag(), C_actual(i, j).imag(), 1e-7)
                << "Im(" << i << "," << j << ")";
        }
    }
}

What's wrong with this? Well, I have to manually iterate through all indices of the matrix, and then compare the real-part and imaginary-part individually. I would much prefer something along the lines of Google Mock's ElementsAreArray matcher. E.g.

EXPECT_THAT(C_actual, ElementsAreArray(C_expect));
// or
EXPECT_THAT(C_actual, Pointwise(MyComplexNear(1e-7), C_expect));

Unfortunately, the built-in capabilities of Google Mock only seem to work on 1-dimensional C-style, or STL-type containers. Furthermore, I need an approximate comparison for the complex values of my matrix.

My question: Do you know if (and how) it is possible to teach Google Mock to iterate over multiple dimensions, and compare complex floating point numbers to approximate equality?

Please note, that I cannot just handle the data-pointers as C-style arrays, because the storage layout might differ between C_expect, and C_actual. Also, in reality, the matrices are larger than just 2x2 matrices. I.e. some sort of loop is definitely necessary.

Answer 1

Why not use the isApprox or isMuchSmallerThan member functions of Eigen Matrix types?

The documentation of these above functions are available here

So for most cases ASSERT_TRUE(C_actual.isApprox(C_expect)); is what you need. You can also provide a precision parameter as the second arguement to isApprox.

Answer 2

A simplified solution would be to compare the norm of the difference with some epsilon, i.e.

(C_expect - C_actual).norm() < 1e-6 

In a vector space || X - Y || == 0 if and only if X == Y, and the norm is always non-negative (real). This way, you won't have to manually do the loop and compare element-wise (of course the norm will perform more calculations in the background than simple element-wise comparisons)

PS: the Matrix::norm() implemented in Eigen is the Frobenius norm, which is computationally very fast to evaluate, see http://mathworld.wolfram.com/FrobeniusNorm.html

Answer 3

EXPECT_PRED2 from GoogleTest can be used for this.

Under C++11 using a lambda works fine but looks unseemly:

  ASSERT_PRED2([](const MatrixXf &lhs, const MatrixXf &rhs) {
                  return lhs.isApprox(rhs, 1e-4);
               },
               C_expect, C_actual);

If that fails, you get a print-out of the input arguments.

Instead of using a lambda, a normal predicate function can be defined like this:

bool MatrixEquality(const MatrixXf &lhs, const MatrixXf &rhs) {
  return lhs.isApprox(rhs, 1e-4);
}

TEST(Eigen, MatrixMultiplication) {
  ...

  ASSERT_PRED2(MatrixEquality, C_expected, C_actual);
}

The later version also works on pre-C++11.