I have needed this in the context of GoogleTest tests so I implemented it like a macro:

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/// Convenience macro to compare two VectorXd
#define EXPECT_VECTORXD_NEAR(first, second, epsilon) \
   ASSERT_EQ(first.rows(), second.rows()); \
   for (int i = 0; i < first.rows(); ++i) { \
      EXPECT_NEAR(first(i), second(i), epsilon); \
   }

but I also need something that simply returns true if two VectorXd are close element-wise to an epsilon. This would be a quick and dirty implementation:

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inline bool is_near(const VectorXd& first, const VectorXd& second, double epsilon) {
   bool result = first.rows() == second.rows();
   for (int i = 0; result && (i < first.rows()); ++i) {
      result = abs(first(i) - second(i)) < epsilon;
   }
   return result;
}


How can I do that in the most succint way?

What about A.isApprox(B), though the comparison is not done the exact same way. See http://eigen.tuxfamily.org/dox/classEig ... 98db8e8966.

Your definition is equivalent to:

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((A-B).array().abs() < epsilon).all()


but that's assuming that the expected magnitudes of A and B elements are always the same.

As usual thank you for the excellent support!