Re: pure function to generate a list of integrals

• To: mathgroup at smc.vnet.net
• Subject: [mg77082] Re: [mg77062] pure function to generate a list of integrals
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sun, 3 Jun 2007 06:06:29 -0400 (EDT)
• Reply-to: hanlonr at cox.net

```f[a_, y_List] :=
NIntegrate[a*x, {x, 0, #}] & /@ y;

f[2, {0.1, 0.5, 0.9}] ==
{NIntegrate[2 x, {x, 0, 0.1}], NIntegrate[2 x, {x, 0, 0.5}],
NIntegrate[2 x, {x, 0, 0.9}]}

True

f[3, {0.1, 0.5, 0.9}] ==
{NIntegrate[3 x, {x, 0, 0.1}], NIntegrate[3 x, {x, 0, 0.5}],
NIntegrate[3 x, {x, 0, 0.9}]}

True

Bob Hanlon

---- Ruth Lazkoz Saez <ruth.lazkoz at ehu.es> wrote:
> Hi everyone,
>
> 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}]}
>
> That is, I want to generate a list of numerical integrals of the same
> function but making one of the integration limits change by taking
> values from a list.
>
> I also want my function to admit two arguments (a number and a list)
> because I want to be able to use the same definition to generate the
> same output as for instance
>
>
> {NIntegrate[3x, {x, 0, 0.1}], NIntegrate[3x, {x, 0, 0.5}],
>    NIntegrate[3x, {x, 0, 0.9}]}
>
> by evaluating f[3, {0.1, 0.5, 0.9}] this time.
>
> I tried for quite a while, but I failed. I suspect one of the problems
> is NIntegrate is not listable. I could make some progress with  Map but
> I only what halfway and on top I was not satisfied with the syntax I
> would have to use.
>
> Thanks in advance,
>
> Ruth Lazkoz
>
>
>

```

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