Re: pure function to generate a list of integrals

*To*: mathgroup at smc.vnet.net*Subject*: [mg77169] Re: [mg77062] pure function to generate a list of integrals*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Tue, 5 Jun 2007 06:39:27 -0400 (EDT)*References*: <26394746.1180984140440.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

Clear[f, g] Block[{k, x, z}, g[k_] = Function[{z}, Evaluate@Integrate[k x, {x, 0, z}]]; f = Function[{k, z}, g[k] /@ z]; ] f[3, {0.1, 0.5, 0.9}] {0.015, 0.375, 1.215} (That version Integrates in advance and may be faster than others.) or f = Function[{k, upper}, NIntegrate[k x, {x, 0, #}] & /@ upper]; f[3, {0.1, 0.5, 0.9}] {0.015, 0.375, 1.215} or Clear[f] f[k_, limits_List] := Block[{x}, NIntegrate[k x, {x, 0, #}] & /@ limits] f[3, {0.1, 0.5, 0.9}] {0.015, 0.375, 1.215} or Clear[f] f[k_, limits_List] := NIntegrate[k x, {x, 0, #}] & /@ limits f[3, {0.1, 0.5, 0.9}] {0.015, 0.375, 1.215} Bobby On Sat, 02 Jun 2007 03:17:59 -0500, <""Ruth Lazkoz Saez"<ruth.lazkoz"@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 > > > > -- DrMajorBob at bigfoot.com