Re: pure function to generate a list of integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg77100] Re: pure function to generate a list of integrals*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sun, 3 Jun 2007 06:15:49 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <f3r9er$19e$1@smc.vnet.net>

Ruth Lazkoz Saez 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 What about the following? In[1]:= f[(n_)?NumericQ, lst_List] := (NIntegrate[n*x, {x, 0, #1}] & ) /@ lst f[2, {0.1, 0.5, 0.9}] f[3, {0.1, 0.5, 0.9}] Out[2]= {0.01, 0.25, 0.81} Out[3]= {0.015, 0.375, 1.215} Regards, Jean-Marc