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 > > >