Re: replace with closest value

• To: mathgroup at smc.vnet.net
• Subject: [mg119548] Re: replace with closest value
• From: Stefan Salanski <wutchamacallit27 at gmail.com>
• Date: Wed, 8 Jun 2011 07:16:39 -0400 (EDT)
• References: <iskvgs\$5nt\$1@smc.vnet.net>

```On Jun 7, 6:45 am, graser <gra... at gmail.com> wrote:
> Hi
>
> I have a some question for you!
>
> Let's say there is a list like that
> AA={1.3, 1.5, 1.6, 1.8, 2.1, 2.3, 2.6, 2.9, 3.3, 3.7, 4.2, 4.7, 5.2,
> 5.9, 6.6, 7.4, 8.3, 9.4, 10.6, 11.8, 13.1, 14.8, 16.9, 19., 21.5,
> 23.6}.
> Length[AA]=26
> I want to replace the element in the list with a closest number I
> specify in my list  BB,
> BB={1.2, 1.4, 1.6, 1.8, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 5,
> 6, 8 , 10 , 15, 20, 25, 40, 60, 100},
> Length[BB]=23
> so that the list AA after I replace will be
>
> AA={1.2, 1.5, 1.6, 1.8, 2. 2.25, 2.5,3.........20, 25}
> Length[AA]=26.
>
> I wonder if anyone can help me to solve this problem!

So there's a function called Nearest, which sounds like it fits your
situation pretty well. However I think we might need some
clarification on what exactly you want. First of all, your very first
element in AA is 1.3, which is equally close to 1.2 and 1.4 in BB. And
the next one 1.5 is equally close to 1.4 and 1.6. Do you care which
one gets chosen?

A short bit of code to do this using Nearest would be
First@Nearest[BB, #] & /@ AA
{1.4, 1.4, 1.6, 1.8, 2, 2.25, 2.5, 3, 3.25, 3.75, 4, 5, 5, 6, 6, 8, 8,
10, 10, 10, 15, 15, 15, 20, 20, 25}
I threw the 'First' on there to specify that in a tie, to just pick
the first one. You could of course pick the last one, or some specific
one based on other rules you define.

As a side note, I just realized that it seems like Nearest didnt
actually work consistently. When there are multiple elements in the
list that are 'closest' to your element, its supposed to return a list
of those elements, like this:
In[12] := Nearest[{1.4, 1.6}, 1.5]
Out[12] = {1.4, 1.6}
but it didnt do that in this case:
In[13] := Nearest[{1.2, 1.4}, 1.3]
Out[13] = {1.4}

??? I ran a high precision thing and the cutoff point is somewhere
random, and I obviously didnt do it to high enough precision to find
the point where it returns {1.2,1.4}
ne[1.299999999999999933386618522490607574582099914550781] = {1.2}
ne[1.299999999999999933386618522490607574582099914550782] = {1.4}
Does anyone have thoughts on this? (I'm running 8.0.1 on 64 bit
windows)

-Stefan S

```

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