[R] Integrating functions / vector arithmetic

[David Winsemius]

On Nov 15, 2010, at 7:18 PM, Eduardo de Oliveira Horta wrote:

> Hello,
>
> I was trying to build some functions which I would like to integrate  
> over an
> interval using the function 'integrate' from the 'stats' package. As  
> an
> example, please consider the function
>
> h(u)=sin(pi*u) + sqrt(2)*sin(pi*2*u) + sqrt(3)*sin(pi*3*u) +  
> 2*sin(pi*4*u)
>
> Two alternative ways to 'build' this function are as in f and g below:
>
> coeff<-sqrt(1:4)
>
> zeta<-function(i) {force(i); function(u){
>  zeta<-sqrt(2)+sin(pi*i*u)
> }}
>
> f<-function(u){
>  f<-0
>  for (j in 1:4){
>    f<-f+coeff[j]*(zeta(j)(u))
>  }
>  f<-f
> }
>
> g<-function(u){
>  g<-crossprod(coeff,zeta(1:4)(u))
> }
>
> Obviously, f and g are equivalent, but in the actual code I am  
> writing, g is
> much faster. However, I can't seem to integrate (neither to plot) g.  
> In
> fact, these are the error messages I get:
>
>> print(f(.1))
> [1] 4.443642
>> print(g(.1))
>         [,1]
> [1,] 4.443642
>
> Everything ok until here... but...
>
> When using plot(), I get this:
>
>> plot(f) #plots, as expected.
>> plot(g)

Try vectorizing g()


  g<-function(u){
         g<-crossprod(coeff,zeta(1:4)(u))
   }

  gV <- Vectorize(g)

  integrate(gV,0,1)

## 9.696303 with absolute error < 2.5e-13

You didn't say what you thought the analytic answer might be so I  
cannot check it.

-- 
David.

> Error in crossprod(coeff,zeta(1:4)(u)) : arguments not compatible
> Besides that: Warning message:
> In pi * i * u :
>  longer object length is not a multiple of shorter object length
>
> When using integrate(), I get this:
>
>> integrate(f,0,1)
> 1.004172 with absolute error < 2.5e-13
>> integrate(g,0,1)
> Error in crossprod(coeff,zeta(1:4)(u)) : arguments not compatible
> Besides that: Warning message:
> In pi * i * u :
>  longer object length is not a multiple of shorter object length
>>
>
> I have already tried some simple 'solutions', for example to set
> g<-function(u){
>  vec1<-drop(coeff)
>  vec2<-drop(zeta(1:4)(u))
>  g<-drop(crossprod(coeff,zeta(1:4)(u)))
> }
>
> as well as using the %*% operation, but these won't solve my problem.
>
> Any suggestions would be welcome. Thanks in advance,
>
> Eduardo Horta
>
> 	[[alternative HTML version deleted]]

David Winsemius, MD
West Hartford, CT