inverted axis

(X,BR2) is plotted with X on horizontal and BR2 on vertical axis
(X, BR1) is plotted with X on vertical axis and BR1 on horizontal axis.

On Wed, Mar 20, 2002 at 09:41:04AM +0200, Juhana Vartiainen wrote:

(X,BR2) is plotted with X on horizontal and BR2 on vertical axis
(X, BR1) is plotted with X on vertical axis and BR1 on horizontal axis.

help(plot)
help(points)

as in

plot(X,BR2)
points(BR1,X)

help(par), with attention to "pch" would also probably help.

This, and more, is all in "An Introduction to R" - $RHOME/doc/R-intro.pdf

Hello everybody!

Spse I have the following

X <- seq(1:100)     #(a dim(100) sequence of integers 1:100 representing
the possible actions of player 1 and player2 in a game)
BR2X<- br2(X)      #(a dim(100) sequence of points on range (1,100)
representing the best response function of player 2 to player 1:s
actions)
BR1X<- br1(X)      #(a dim(100) sequence of points on range (1,100)
representing the best response function of player 1 to player 2:s
actions)

To illustrate Nash equilibrium , I would like to plot these  in the same
picture, with inverted axes, so that

(X,BR2) is plotted with X on horizontal and BR2 on vertical axis
(X, BR1) is plotted with X on vertical axis and BR1 on horizontal axis.

How can I do that ?

Juhana Vartiainen
juhana.vartiainen at labour.fi

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prov(2)$counts

I want to maximise a function using 'optim' with a method that requires
the gradient, so I supply two functions, 'fun' for the function value
and 'd.fun' for its gradient. My question is: Since some calculations are
common to the two functions, is it possible to save time by feeding
'd.fun' with some of the calculations made in 'fun'? That would require
(at least) that it is guaranteed that each time 'd.fun' is evaluated, it
is done immediately after a call to 'fun' at the same parameter value.
The help page says:

"It is guaranteed that `gr' will be called immediately after a
call to `fn' at the same parameter values."

which is not exactly the same. However, look at this trivial example:

prov <- function(x.start = 0){
  fun <- function(x) {
    e.x <- exp(-x)
    x * e.x
  }
  d.fun <- function(x) {
    e.x <- exp(-x)
    e.x * (1 - x)
  }
  optim(x.start, fun, d.fun, method = "BFGS",
     control = list(fnscale = -1))
}

prov(2)$counts

function gradient
      19        9

This contradicts the help page info, since that implies that the gradient
is called at least as many times as the function.

Q1: What is the correct guarantee? Is it what I need?

Q2: If so, How do I share calculations between the two functions? In my
    trivial example, exp(-x) is calculated in both.

Thanks for any enlightenment! (Brian?)

Göran
--
 Göran Broström                      tel: +46 90 786 5223
 professor                           fax: +46 90 786 6614
 Department of Statistics            http://www.stat.umu.se/egna/gb/
 Umeå University
 SE-90187 Umeå, Sweden             e-mail: gb at stat.umu.se

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On Wed, 20 Mar 2002, [iso-8859-1] G?ran Brostr?m wrote:

I want to maximise a function using 'optim' with a method that requires
the gradient, so I supply two functions, 'fun' for the function value
and 'd.fun' for its gradient. My question is: Since some calculations are
common to the two functions, is it possible to save time by feeding
'd.fun' with some of the calculations made in 'fun'? That would require
(at least) that it is guaranteed that each time 'd.fun' is evaluated, it
is done immediately after a call to 'fun' at the same parameter value.
The help page says:

"It is guaranteed that `gr' will be called immediately after a
call to `fn' at the same parameter values."

Only if hessian=FALSE, and that phrase is now removed.

which is not exactly the same. However, look at this trivial example:

prov <- function(x.start = 0){
  fun <- function(x) {
    e.x <- exp(-x)
    x * e.x
  }
  d.fun <- function(x) {
    e.x <- exp(-x)
    e.x * (1 - x)
  }
  optim(x.start, fun, d.fun, method = "BFGS",
     control = list(fnscale = -1))
}

prov(2)$counts

function gradient
      19        9

This contradicts the help page info, since that implies that the gradient
is called at least as many times as the function.

No, the other way around.  It meant `if gr is called, it will be called
...'

You need to cache the par values and the results you need, and test both.

I want to maximise a function using 'optim' with a method that requires 
the gradient, so I supply two functions, 'fun' for the function value
and 'd.fun' for its gradient. My question is: Since some calculations are 
common to the two functions, is it possible to save time by feeding 
'd.fun' with some of the calculations made in 'fun'? That would require
(at least) that it is guaranteed that each time 'd.fun' is evaluated, it 
is done immediately after a call to 'fun' at the same parameter value.
The help page says:  

"It is guaranteed that `gr' will be called immediately after a
call to `fn' at the same parameter values."

which is not exactly the same. However, look at this trivial example:

prov <- function(x.start = 0){
  fun <- function(x) {
    e.x <- exp(-x)
    x * e.x
  }
  d.fun <- function(x) {
    e.x <- exp(-x)
    e.x * (1 - x)
  }
  optim(x.start, fun, d.fun, method = "BFGS", 
     control = list(fnscale = -1))
}

prov(2)$counts

function gradient 
      19        9 

This contradicts the help page info, since that implies that the gradient 
is called at least as many times as the function. 

Q1: What is the correct guarantee? Is it what I need?

Q2: If so, How do I share calculations between the two functions? In my 
    trivial example, exp(-x) is calculated in both.

Thanks for any enlightenment! (Brian?)

G?ran 
-- 
 G?ran Brostr?m                      tel: +46 90 786 5223
 professor                           fax: +46 90 786 6614
 Department of Statistics            http://www.stat.umu.se/egna/gb/
 Ume? University
 SE-90187 Ume?, Sweden             e-mail: gb at stat.umu.se

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Send "info", "help", or "[un]subscribe"
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Hi G?ran,

Q1: first, it seems that the validity of this guarantee depends on the "method" used. Using method="L-BFGS-B", I found that that guarantee seemed to hold for the iterations towards the optimum, but was violated for the final evaluation of the hessian. After submitting a bug report it appears  that the documentation will be updated in version 1.5.

Q2: You can use e.g. a variable local to prov() which is visible both to 
fun() and d.fun(),   manipulating it with "<<-" in fun(). Given the 
uncertainty about this guarantee, it seems advisable to also store the 
fun() parameters in there, and explicitely verify in d.fun() whether the 
parameters are really the same...     

Best regards,
Wolfgang.



Dr. Wolfgang Huber
DKFZ 
Dep. Molecular Genome Analysis 
69120 Heidelberg 
Germany