Function(s) to express nearishness #652

pao · 2012-03-31T21:33:02Z

This is a first shot at expressing nearishness in Julia, taking as inspiration NumPy's allclose() function. It doesn't handle Inf/NaN the same as numpy.allclose(), and doesn't handle all the possible types that R's all.equal() can apparently handle.

So, what is needed from those other functions here (or for specific types), noting that isequal() already exists to express actual equality? The single commit is the simplest thing that could possibly work, but I'll add optimized things (like mapping it to isequal() for integer types) before merge if I'm on the right path and this is something we want.

Whether this belongs in base/ is certainly up for discussion as well.

Input from everyone certainly helpful, but I do want to make sure @dmbates gets to see this, since he got me started thinking about it.

numpy.allclose() is defined at https://github.com/numpy/numpy/blob/master/numpy/core/numeric.py#L1963

timholy · 2012-04-01T11:18:02Z

Nice idea. Two points:

Your expression is not symmetric in x and y. I'd at least change it to

isclose(x, y, rtol, atol) = abs(x-y) <= atol+rtol.*(abs(x)+abs(y))

(Otherwise, you'd get very different behavior for elements where y is zero but x is not.)

In the version that supplies defaults for the two parameters, it won't work well for a Float32. How about

isclose{T}(x::T, y::T) = isclose(x, y, eps(::Type{T})^(1/3), sqrt(eps(::Type{T})))

I'm assuming that the compiler will recognize that the powers-of-eps computations result in constants, so there shouldn't be any overhead.

ViralBShah · 2012-04-01T11:57:13Z

This does require some thought and needs to evolve. Also, support arrays, and be extensible. @pao, can you move it to extras for now?

Preparing for a 1.0 release, I believe we will be moving more stuff out of base in any case...

timholy · 2012-04-01T12:03:47Z

To be fair, his version supported arrays. My "eps cleanup" would need additional specifications for x::Array{T} and x::DArray{T}, however.

pao · 2012-04-01T14:01:44Z

The asymmetry is also present in the NumPy prototype, so I kept it. It's open for discussion, though. I've also considered the relative tolerance expression rtol.*max(abs(x), abs(y)) which would allow for tighter tolerances than simply adding.

As @timholy observed, this does support arrays and scalar/array mixes; I intentionally used .* to ensure that. But if we want the same NaN/Inf handling as NumPy (I'm not sure what R does yet) I can't see how to do that without specializing for arrays.

@ViralBShah extras/nearequal.jl sound good?

ViralBShah · 2012-04-01T14:19:22Z

Location sounds fine.

-viral

On 01-Apr-2012, at 7:31 PM, paoreply@reply.github.com wrote:

The asymmetry is also present in the NumPy prototype, so I kept it. It's open for discussion, though. I've also considered the relative tolerance expression rtol.*max(abs(x), abs(y)) which would allow for tighter tolerances than simply adding.

As @timholy observed, this does support arrays and scalar/array mixes; I intentionally used .* to ensure that. But if we want the same NaN/Inf handling as NumPy (I'm not sure what R does yet) I can't see how to do that without specializing for arrays.

@ViralBShah extras/nearequal.jl sound good?

Reply to this email directly or view it on GitHub:
#652 (comment)

…true

pao · 2012-04-01T20:58:57Z

New version incorporating some of the above suggestions. I'm letting isclose(NaN, NaN) be true, which allows isclose() to be used to check that two similar computations which may result in NaN have the same results. (EDIT: Previous sentence had a misstatement about numpy.allclose().)

Alternatively, I could let isclose(NaN, NaN) be false, and (following MATLAB's isequalwithequalnans()) provide an isclosewithequalnans() or similar.

ViralBShah · 2012-04-02T02:34:54Z

@pao, let me know when you think this is ready for a merge. Would you like the pull request open for some more discussion? I hate those long Matlab function names, but they are actually quite clear about what they do.

ViralBShah · 2012-04-02T02:36:08Z

isclose(nan, nan) ought to be false, but for this purpose, I guess the behaviour you implemented is what we need.

Keno · 2012-04-02T02:42:42Z

How about isclosen following MATLAB's isequaln?

pao · 2012-04-02T03:06:04Z

Agreed on the long function names; I didn't know about isequaln(), which looks like the new name for isequalwithequalnans(). Let's have them both and get MATLAB parity here. I can implement isequaln() while I'm at it.

ViralBShah · 2012-04-02T03:15:37Z

I didn't know that either - must be a new name. I like it better. Perhaps we can dispense with the "withequalnans" names? I don't think that anyone except Matlab geeks like us actually know about such things, but I could be wrong. :-)

-viral

On 02-Apr-2012, at 8:36 AM, pao wrote:

Agreed on the long function names; I didn't know about isequaln(), which looks like the new name for isequalwithequalnans(). Must be newish. Let's have them both and get MATLAB parity here. I can implement isequaln() while I'm at it.

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#652 (comment)

…lementations. Originally, isclose() treated NaNs as equal, but this conflicts with the conventional default. Since treating NaNs as equal is often useful, that ability is preserved by the implementation of isclosen(). Similarly, isequaln() is included as an equal-NaNs version of isequal().

pao · 2012-04-02T03:44:50Z

Viral, let's bake this for a few more hours. I'll see if there are any further comments when I wake up in the morning. And if someone could check that I'm doing the @eval correctly—it does work, so I think I am—that would be great.

UPDATE: I just checked the docs; isequaln() is brand spankin' new in R2012a, so I don't feel bad for not knowing that. :D

pao · 2012-04-02T12:42:09Z

@ViralBShah Go for merge.

ViralBShah · 2012-04-02T17:35:55Z

@JeffBezanson can check the macrology, as he calls it..

Function(s) to express nearishness

This reuses the machinery that gives good stacktraces when a user calls wait on a Task. Since bind internally uses _wait2, this machinery is bypassed currently. Currently, julia throws an uninformative stacktrace in this situation: julia> c = Channel(_ -> error("foo")) Channel{Any}(sz_max:0,sz_curr:0) julia> for i in c end ERROR: foo Stacktrace: [1] iterate(::Channel{Any}) at ./channels.jl:459 [2] top-level scope at ./REPL[2]:1 With this change, the stacktrace is much more informative: julia> for i in c end ERROR: TaskFailedException: foo Stacktrace: [1] error(::String) at ./error.jl:33 [2] (::var"JuliaLang#1#2")(::Channel{Any}) at ./REPL[4]:1 [3] (::Base.var"JuliaLang#652#653"{var"JuliaLang#1#2",Channel{Any}})() at ./channels.jl:129 Stacktrace: [1] check_channel_state at ./channels.jl:167 [inlined] [2] take_unbuffered(::Channel{Any}) at ./channels.jl:405 [3] take! at ./channels.jl:383 [inlined] [4] iterate(::Channel{Any}, ::Nothing) at ./channels.jl:449 [5] iterate(::Channel{Any}) at ./channels.jl:448 [6] top-level scope at ./REPL[5]:1

This reuses the machinery that gives good stacktraces when a user calls wait on a Task. Since bind internally uses _wait2, this machinery is bypassed currently. Currently, julia throws an uninformative stacktrace in this situation: julia> c = Channel(_ -> error("foo")) Channel{Any}(sz_max:0,sz_curr:0) julia> for i in c end ERROR: foo Stacktrace: [1] iterate(::Channel{Any}) at ./channels.jl:459 [2] top-level scope at ./REPL[2]:1 With this change, the stacktrace is much more informative: julia> for i in c end ERROR: TaskFailedException: foo Stacktrace: [1] error(::String) at ./error.jl:33 [2] (::var"#1#2")(::Channel{Any}) at ./REPL[4]:1 [3] (::Base.var"#652#653"{var"#1#2",Channel{Any}})() at ./channels.jl:129 Stacktrace: [1] check_channel_state at ./channels.jl:167 [inlined] [2] take_unbuffered(::Channel{Any}) at ./channels.jl:405 [3] take! at ./channels.jl:383 [inlined] [4] iterate(::Channel{Any}, ::Nothing) at ./channels.jl:449 [5] iterate(::Channel{Any}) at ./channels.jl:448 [6] top-level scope at ./REPL[5]:1

pao added 2 commits April 1, 2012 15:49

extras/nearequal: Provide isclose() to express near-equality

69cd0f9

extras/nearequal: Handle Inf/NaN gracefully, with isclose(NaN, NaN)==…

b4538a9

…true

ViralBShah added a commit that referenced this pull request Apr 2, 2012

Merge pull request #652 from pao/topic/nearish

913171f

Function(s) to express nearishness

ViralBShah merged commit 913171f into JuliaLang:master Apr 2, 2012

pao mentioned this pull request Apr 14, 2012

add isapprox() to base/float and remove approx_eq() from extras/test #716

Closed

pao mentioned this pull request May 13, 2013

RFC: isapprox(n)/isequal -> base #3076

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pao mentioned this pull request Jul 29, 2015

isapprox broken on large numbers #12375

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Function(s) to express nearishness #652

Function(s) to express nearishness #652

pao commented Mar 31, 2012

timholy commented Apr 1, 2012

ViralBShah commented Apr 1, 2012

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pao commented Apr 1, 2012

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pao commented Apr 2, 2012

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ViralBShah commented Apr 2, 2012

Function(s) to express nearishness #652

Function(s) to express nearishness #652

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pao commented Mar 31, 2012

timholy commented Apr 1, 2012

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timholy commented Apr 1, 2012

pao commented Apr 1, 2012

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pao commented Apr 2, 2012

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