R help - Oct 2004 - How to calculate a double integral ...?

Dear R-Friends, 

How can I calculate a double integral like

  \int_a^b \int_c^y g(x, y) dx dy

where a, b, c are constants, g(x, y), e.g.,
g(x, y) = tan(x + y).

I tried to nested integrate() and adapt(),
but none of them working, seemingly due to the 
limits can not be specified constants.


Best regards,

C. Joseph Lu
Department of Statistics
National Cheng-Kung University
Voice: (886)-6-275-7575 Ext. 53638
  Fax: (886)-6-234-2469

cjlu <cjlu <at> mail.ncku.edu.tw> writes:

: 
: Dear R-Friends, 
: 
: How can I calculate a double integral like
: 
:   \int_a^b \int_c^y g(x, y) dx dy
: 
: where a, b, c are constants, g(x, y), e.g.,
: g(x, y) = tan(x + y).
: 
: I tried to nested integrate() and adapt(),
: but none of them working, seemingly due to the 
: limits can not be specified constants.
: 

Integrate

   g2 <- function(x, y) g(x, y) * (x > y)

over (a,b) x (a,c).

Gabor Grothendieck <ggrothendieck at myway.com>
writes:
> cjlu <cjlu <at> mail.ncku.edu.tw> writes:
> : How can I calculate a double integral like
> : 
> :   \int_a^b \int_c^y g(x, y) dx dy
> : 
> : where a, b, c are constants, g(x, y), e.g.,
> : g(x, y) = tan(x + y).
> :  
> Integrate
> 
>    g2 <- function(x, y) g(x, y) * (x > y)
> 
> over (a,b) x (a,c).
> 
Thanks Gabor for your prompt and helpful response!

Later on, I realized that such an integration can be done by
the following way, provided function g(x, y) takes vector input, e.g.,
g(x, y) = tan(x + y)
> integrate(function(y) {
+   sapply(y, function(y) {
+     integrate(function(x) tan(x + y), -.5, y)$value
+   })
+ }, 0, .5)
0.07238855 with absolute error < 1.1e-15

if g(x, y) can only take scalar input, we can do
> integrate(function(y) {
+   sapply(y, function(y) {
+     integrate(function(x) {
+       sapply(x, function(x) tan(x + y))
+     }, -.5, y)$value
+   })
+ }, 0, .5)
0.07238855 with absolute error < 1.1e-15

Best regards,

C. Joseph Lu
Department of Statistics
National Cheng-Kung University
Tainan
Taiwan, ROC

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