R help - Nov 2010 - Integrating functions / vector arithmetic

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)
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]]

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

Some remarks:
Why are you using assignments to indicate the return values of functions?
This is R idiom:
> f<-function(u){
>  f<-0
>  for (j in 1:4){
>    f<-f+coeff[j]*(zeta(j)(u))
>  }
>  f
> }
> 
If you only want the inner product of 2 vector, "outer" probably is an
overkill.

g <- function(u){
 sum(coeff * zeta(1:4)(u))
}

should be enough.

And plot(g) does not work because g is not vectorized.

plot(Vectorize(g))

will work

On Nov 16, 2010, at 1:18 AM, 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)
> 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]]
> 
> ______________________________________________
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> 
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