Re: How to apply a list of functions

• To: mathgroup at smc.vnet.net
• Subject: [mg112892] Re: How to apply a list of functions
• From: Leonid Shifrin <lshifr at gmail.com>
• Date: Tue, 5 Oct 2010 05:33:36 -0400 (EDT)

```Vince,

My feeling is that Inner is in principle a little faster, since it is more
specialized. For
example, here it is true (although the difference is not at all dramatic):

In[67]:=
Do[Inner[Rule,Range[100000],Range[100001,200000],List],{10}]//Timing
Out[67]= {0.797,Null}

In[68]:=
Out[68]= {0.922,Null}

But this seems to show up only in the most trivial cases like this one
above. Perhaps, the
overhead of Compose is sufficient to hide this effect. Besides,  I just  did
a few benchmarks,
and indeed using Hold instead of List slows Inner down somewhat, so all in
all it is not worth the
trouble, I agree.

Regards,
Leonid

On Mon, Oct 4, 2010 at 10:02 PM, Vincent N. Virgilio <virgilio at ieee.org>wrote:

> Leonid,
>
> Certainly.
>
> (The timing difference between MapThread and Inner/Hold appears to be in
> the noise. I didn't look at Inner/List as closely.)
>
> Vince
>
>
> On Mon, Oct 4, 2010 at 1:46 PM, Leonid Shifrin <lshifr at gmail.com> wrote:
>
>> Vince,
>>
>>
>> In[51]:=
>> Inner[Compose,Hold[f1,f2,f3],Hold[{{1,2},{3,4}},{{5,6},{7,8}},{{9,10},{11,12}}],List]
>>
>> Out[51]= {f1[{{1,2},{3,4}}],f2[{{5,6},{7,8}}],f3[{{9,10},{11,12}}]}
>>
>> Basically, wrap your arguments in Hold rather than List, and you don't
>> have this problem.
>>
>> Regards,
>> Leonid
>>
>> On Mon, Oct 4, 2010 at 9:37 PM, Vincent N. Virgilio <virgilio at ieee.org>wrote:
>>
>>> Leonid,
>>>
>>> I notice that Inner/Compose is a little fragile if x is, say, a list of
>>> matrices, and the goal is to apply each f to each whole matrix.
>>>
>>> Thanks again,
>>>
>>> Vince
>>>
>>> On Mon, Oct 4, 2010 at 1:07 PM, Leonid Shifrin <lshifr at gmail.com> wrote:
>>>
>>>> Hi Vince,
>>>>
>>>> First, you could use Compose in your code - perhaps it is a little
>>>> faster:
>>>>
>>>>
>>>> Out[2]= {f1[x1],f2[x2],f3[x3]}
>>>>
>>>> Using Inner can be a bit faster still:
>>>>
>>>> In[4]:= Inner[Compose,{f1,f2,f3},{x1,x2,x3},List]
>>>>
>>>> Out[4]= {f1[x1],f2[x2],f3[x3]}
>>>>
>>>> In most cases, you probably won't see the difference in performance,
>>>> do very little and you have lots of them.
>>>>
>>>> Regards,
>>>> Leonid
>>>>
>>>>
>>>>
>>>>
>>>> On Mon, Oct 4, 2010 at 2:06 PM, Vince Virgilio <blueschi at gmail.com>wrote:
>>>>
>>>>> On Oct 3, 3:39 am, Sam Takoy <sam.ta... at yahoo.com> wrote:
>>>>> > Hi,
>>>>> >
>>>>> > As a follow up to my question about apply {Sin, Cos} to x, I came up
>>>>> > with the tasteless
>>>>> >
>>>>> > Map[Apply[#, {x}] &, {Sin, Cos}]
>>>>> >
>>>>> > but I expect that the pros in this ng will be able to improve upon
>>>>> it.
>>>>> >
>>>>> > Thanks,
>>>>> >
>>>>> > Sam
>>>>>
>>>>> Tangentially,
>>>>>
>>>>> I've always wondered if there was a better way to apply a list of
>>>>> functions to a list of arguments. Here's how I do it, where f and x
>>>>> are the respective lists.
>>>>>
>>>>>
>>>>> Seems performant.
>>>>>
>>>>> Anyone?
>>>>>
>>>>> Vince
>>>>>
>>>>>
>>>>
>>>
>>
>

```

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