Does anyone know why the de-facto standard definition of isapprox intentionally fails when one of the arguments is zero? isapprox(0.0, 0.0 + 1e-10) # false isapprox(1.0, 1.0 + 1e-10) # true It is clear from the formula why this is happening: ||x - y|| \le max(atol, rtol*max(||x||, ||y||)) If we…

[image] stevengj: For example, suppose I’ve worked out a nontrivial formula, like \mathrm{vec}(BCA^T) = (A \otimes B) \mathrm{vec}(C)vec(BCAT)=(A⊗B)vec(C)\mathrm{vec}(BCA^T) = (A \otimes B) \mathrm{vec}(C), and I want to make sure I didn’t make some simple algebra mistake. The first thing I do i…

[image] stevengj: I find it incredibly convenient (and clearer) that I don’t have to write norm(vec(B*C*A') - kron(A, B) * vec(C)) < 1e-8 * norm(kron(A, B) * vec(C)) over and over again for these kinds of things. Aside: one function that I do find myself writing over and over is: relerr(a, b…

[image] Jean_Michel: The first thing I would do is B = randn(Int,10,20); C = randn(Int,20,30); A = randn(Int,40,30); Sure, in this particular example the function maps integers to integers. (I think you mean rand(Int, m, n). Luckily, this particular function is also insensitive to integer o…

There are a couple of different contexts at work here. Maybe you are doing essentially a one-off sanity check, like interactively eyeballing an answer to see if a result is not absurd. But using isapprox() instead of your eyes. Maybe you are about to cement-in a test in a routine in the midst of a…

[image] Richard_Fateman: My thought is that if you use isapprox() in that second context, you should be warned. Do you mean for program validation? Why is calling isapprox (ideally with custom tolerances, at least in tests to validate the precise accuracy as opposed to tests for coarse bugs)…

In brief, anyone reading/ perhaps modifying/ your code will have to know (or ignore) the meaning of isapprox. Also maybe find out where you have set or defined atol, rtol, norm. If you are repeatedly comparing floating-point values for approximate equality with similar but not identical code segme…

[image] Richard_Fateman: In brief, anyone reading/ perhaps modifying/ your code will have to know (or ignore) the meaning of isapprox. I agree, you should understand the functions you call. But the definition of isapprox is not especially complicated (if you know what relative and absolute e…

Just sharing a comment to say that I appreciate the opinion of various experts in the subject. And to say that there are different objectives at play in the arguments. From one side @stevengj seems to promote a deeper understanding of floating point arithmetic. From the other side @Richard_Fateman …

[image] juliohm: From the other side @Richard_Fateman seems to value a friendlier end-user experience that escapes the floating point difficulties. It seems like he’s advocating the opposite? He wants to remove/discourage the isapprox function and tell people to re-implement the desired comp…

My understanding of the comments is a bit different. Maybe I misunderstood the message.

History of `isapprox` in languages

Specific Domains Numerics

Topic		Replies	Views
Approximate equality General Usage question , bug	54	35327	September 29, 2022
Approx with a weird behaviour General Usage	1	380	January 16, 2019
Bug with isapprox? General Usage	6	2629	December 8, 2017
How to compare vectors? General Usage question	10	298	October 14, 2024
How to add a tolerance to isapprox General Usage question	6	337	August 28, 2024

History of `isapprox` in languages

Related topics