[R] Find maxima of a function

[David Winsemius]

> On Aug 26, 2017, at 12:13 PM, Ismail SEZEN <sezenismail at gmail.com> wrote:
> 
> 
>> On 26 Aug 2017, at 16:39, niharika singhal <niharikasinghal1990 at gmail.com> wrote:
>> 
>> Hi,
>> 
>> Thanks for your mail, and time
>> 
>> It is not working for some arguments, when mean value is like >6.
>> 
>> 
>> case
>> 
>> mc0 <- c(0.08844446,0.1744455,0.1379778,0.1209769,0.1573065,0.
>> 1134463,0.2074027)
>> 
>> rv <-UnivarMixingDistribution(Norm(486.4255, 53.24133),
>> 
>>                             Norm(664.0713, 3.674773),
>> 
>>                             Norm(669.0484, 4.101381),
>> 
>>                             Norm(677.1753, 4.869985),
>> 
>>                             Norm(683.2635, 7.288175),
>> 
>>                             Norm(727.6229, 37.64198),
>> 
>>                             Norm(819.2011, 57.06655),
>> 
>>                             mixCoeff=mc0/sum(mc0))
>> 
>> plot(rv, to.draw.arg="d")
>> 
>> 
>> I am getting 731.1345 from the code you have provide
>> 
>> 
>> It is part of a code, so it was difficult to write a reproducible code
>> 
>> I have tried to use optimr but it gives me the local maxima, now I am
>> struck with the problem of how to get the global maxima
>> 
> 
> This is basically an optimization problem so it’s nothing to do with distr package and UnivarMixingDistribution function. Also I’m not able to install distr package because of an error.

> str(rv)
Formal class 'AbscontDistribution' [package "distr"] with 12 slots
  ..@ gaps       : num [1:2, 1:2] 259 1037 295 1063
  ..@ img        :Formal class 'Reals' [package "distr"] with 2 slots
  .. .. ..@ dimension: num 1
  .. .. ..@ name     : chr "Real Space"
  ..@ param      : NULL
  ..@ r          :function (n)  
  ..@ d          :function (x, log = FALSE)  
  ..@ p          :function (q, lower.tail = TRUE, log.p = FALSE)  
  ..@ q          :function (p, lower.tail = TRUE, log.p = FALSE)  
  ..@ .withSim   : logi FALSE
  ..@ .withArith : logi TRUE
  ..@ .logExact  : logi FALSE
  ..@ .lowerExact: logi FALSE
  ..@ Symmetry   :Formal class 'NoSymmetry' [package "distr"] with 2 slots
  .. .. ..@ type      : chr "non-symmetric distribution"
  .. .. ..@ SymmCenter: NULL
> str(density(rv))
Error in density.default(rv) : argument 'x' must be numeric
> str(density(rv at r(1000))
+ )
List of 7
 $ x        : num [1:512] 297 298 300 301 302 ...
 $ y        : num [1:512] 4.39e-07 6.40e-07 9.15e-07 1.29e-06 1.78e-06 ...
 $ bw       : num 10.5
 $ n        : int 1000
 $ call     : language density.default(x = rv at r(1000))
 $ data.name: chr "rv at r(1000)"
 $ has.na   : logi FALSE
 - attr(*, "class")= chr "density"


> max( density(rv at r(10000))$y )
[1] 0.02133529
> which.max( density(rv at r(10000))$y )
[1] 259


> my.instance <- rv at r(10000)  # need to creat an immutable value since this is a pseuado-random number series.
> which.max( density(my.instance)$y )  # location of x and y values for global max
[1] 263
> density(my.instance)$x[ which.max( density(my.instance)$y )] # x value that yields global max
[1] 669.8586
> density(my.instance)$y[ which.max( density(my.instance)$y )]  value at max.
[1] 0.02035133

> 


> an you create an example by rnorm function? or use dput to share x and y outputs of UnivarMixingDistribution function and I can look for the issue.
> 
> Also You might have multiple maximas has same maximum y-values (for instance, y = sin(x)) and this definition is relevant to defined interval. For instance again, we can talk about a global extremum for a function like y = ax^2+bx + c. We know we will have only a single extremum point (maxima or minima). For higher order functions, we can talk about only local maximas. So, I assume you want to obtain maximum one of this local maximas, right?
> 
> If yes, why don’t we find the maximum y-value and corresponding x-value as follows?
> 
> y <- c(1,2,3,4,3,2,3,4,5,6,7,8,9,8,7,6,5,6,7,6,5)
> x <- 1:length(y)
> 
> fun <- splinefun(x = x, y = y, method = "n")
> x2 <- seq(1, max(x), 0.1)
> y2 <- fun(x2)
> plot(x, y, type = "l")
> lines(x2, y2, col = "red")
> 
> max.x <- optimize(fun, interval = range(x), maximum = TRUE)
> print(max.x) # x coordinate of global maximum of y by spline and optimize
> x[which(y == max(y))] # global maximum of dicrete x-y vectors
> 
> 
> spline function uses cubic spline method to obtain the undefined values in a discrete series and optimize function calculates EXACT LOCATION of the extremum. I suspect we have a communication failure :)
> 
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David Winsemius
Alameda, CA, USA

'Any technology distinguishable from magic is insufficiently advanced.'   -Gehm's Corollary to Clarke's Third Law