Comparing matrices and vectors is a topic that I have had to deal with. An important issue here is that there are different ways of comparing that are appropriate for different cases. It really depends on the computation that produced the vector or matrix. For instance, say we have a matrix and we do an FFT along each rows (a common case in signal processing). One way to compare the result against a reference matrix is to compute an RMS error for each row and take the maximum of the row errors for the overall error. Note that a simple maximum of the element-wise errors doesn't work well in practice since elements with very small values can have large errors (percentage wise) with respect to the reference value but will not be significant within the context of the values in the row. Also, a full matrix technique (e.g. comparing eigenvalues and eigenvectors) wouldn't be appropriate either since each row is the result of a separate FFT and the errors will be be correlated across rows. Actually, similar problems crop up when comparing individual complex values (i.e. values that have both a real and a complex component). The three basic patterns that come to mind are element-wise comparison (good for either vectors or matrices), vector-wise comparison (good for either vectors or along the rows / columns of a matrix), and matrix-wises comparison. If you just need a simple element-wise comparison then thats fine but it would be good if the framework is extensible enough to handle more complex cases. Glenn Schrader Dave Steffen wrote:
Fine. Now, we want to be able to compare more complicated mathematical objects, such as vectors and matrices.
After some thought, we decided the responsibility for providing such functions is the responsibility of the mathematical object, not the unit test framework. That is to say, a function "relative difference between matrices" should be in Matrix.h, not some unit test thing.
Which leads to the idea of Matrix.h #including "boost/test/floating_point_comparison.hpp", which strikes me as rather odd. My first impulse was to copy/pull the relevent code out of floating_point_comparison.hpp and stick it in some more convenient place, where mathematical objects could use those functions to implement their own comparision functions.
Might this be a common idiom? Might we consider factoring these floating point comparison functions (not the BOOST_CHECK_CLOSE macro, but the functions it uses) out into a separate library? Any comments on my approach?
Any and all thoughts, comments, or complaints welcome. Thanks!
---------------------------------------------------------------------- Dave Steffen, Ph.D. Disobey this command! Software Engineer IV - Douglas Hofstadter Numerica Corporation dg@steffen a@t numerica d@ot us (remove @'s to email me)
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