Re: pure function to generate a list of integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg77331] Re: pure function to generate a list of integrals
• From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
• Date: Thu, 7 Jun 2007 03:37:55 -0400 (EDT)
• Organization: The Open University, Milton Keynes, UK
• References: <f43gpj\$2k7\$1@smc.vnet.net>

```Ruth wrote:
> Thanks to everyone. Bill's was the purest solution of them all (if I
> understand correctly the meaning of purity). However, my example was to
> naive (linear).
>
> I would like to have a new function with basically the same purity as
> Bill's solution
>
> f = #1 Block[{x}, NIntegrate[x, {x, 0, #}] & /@ #2] &;
>
> but this time to be able to produce the equivalent of
>
> {NIntegrate[Sqrt[2x+3], {x, 0, 0.1}], NIntegrate[Sqrt[2x+3], {x, 0, 0.5}],
> NIntegrate[Sqrt[2x+3], {x, 0, 0.9}]}
>
> when evaluating f[2,3,{0.1,0.5,0.9}]
>
> Thanks again.

In[1]:= f = Block[{x, a = #1, b = #2},
(NIntegrate[Sqrt[a*x + b], {x, 0, #1}] & ) /@ #3] & ;
f[2, 3, {0.1, 0.5, 0.9}]

Out[2]= {0.17606053323094345, 0.9346158590977903, 1.7733735604641878}

Regards,
Jean-Marc

> Bill Rowe escribiÃ³:
>> On 6/2/07 at 4:17 AM, ruth.lazkoz at ehu.es (Ruth Lazkoz Saez) wrote:
>>
>>
>>> I am trying to brush up a long code I have to make it more compliant
>>> with the spirit of functional programming. I do not like to hear
>>> that the kind of calculations I do should run faster in C, because I
>>> suspect that if I managed to write good code in Mathematica it
>>> should be as fast. So I have to go and improve my code chunk by
>>> chunk.
>>>
>>
>>> My first problem is that I want to generate a pure function say f,
>>> which, so that f[2, {0.1, 0.5, 0.9}] gives me the same output as
>>>
>>
>>> {NIntegrate[2x, {x, 0, 0.1}], NIntegrate[2x, {x, 0, 0.5}],
>>> NIntegrate[2x, {x, 0, 0.9}]}
>>>
>> This will do the trick
>>
>> f = #1 Block[{x}, NIntegrate[x, {x, 0, #}] & /@ #2] &;
>>
>> Checking:
>>
>> In[14]:= f[2, {0.1, 0.5, 0.9}]
>>
>> Out[14]= {0.01,0.25,0.81}
>>
>> In[15]:= f[3, {0.1, 0.5, 0.9}]
>>
>> Out[15]= {0.015,0.375,1.215}
>> --
>> To reply via email subtract one hundred and four
>>
>>
>>
>
>
>
>

```

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