I'm trying to get the upper and lower bound vectors of the objective vector that will keep the same optimal solution of a linear program. I am using gurobi in R to solve my LP. The gurobi reference manual says that the attributes SAObjLow and SAObjUP will give you these bounds, but I cannot find them in the output of my gurobi call.
Is there a special way to tell the solver to return these vectors?
The only values that I see in the output of my gurobi call are status, runtime, itercount, baritercount, nodecount, objval, x, slack, rc, pi, vbasis, cbasis, objbound. The dual variables and reduced costs are returned in pi and rc, but not bounds on the objective vector.
I have tried forcing all 6 different 'methods' but none of them return what I'm looking for.
I know I can get these easily using the lpsolve R package, but I'm solving a relatively large problem and I trust gurobi more than this package.
Here's a reproducible example...
library(gurobi)
model = list()
model$obj = c(500,450)
model$modelsense = 'max'
model$A = matrix(c(6,10,1,5,20,0),3,2)
model$rhs = c(60,150,8)
model$sense = '<'
sol = gurobi(model)
names(sol)
Ideally something like SAObjLow would be one of the possible entries in sol.
Not all attributes are available in the Gurobi R interface - this includes the ones for sensitivity analysis.
You may find this example helpful.
Alternatively, you can use a different API, like Python, to query all available information.
In my program, I need to have a function, that makes continuous density estimate (defined everywhere on reals) from arbitrary sample. So I've chosen the library(ks) and found that it sometimes produces buggy object, and other functions (e.g. plot) crash R session while accessing it.
Please, I want someone else to check whether it is a bug in the package, my R build, (or even I'm doing something wrong).
So, the code to reproduce the crash :
library(ks)
set.seed(8192)
density_generator<-function(s)
{
# this function returns kernel density estimate built on sample 's'
hpi1 <- hpi(x=s) # calculating h parameter for kernel estimation
fhat.pi1 <- kde(x=s, H=hpi1) # generating density object
fhat.pi1
}
## testing the density generator
conditional_density_object<-density_generator(c(1,2,3,4,5))
foo<-function(z){predict(conditional_density_object,x=z)}
y<-seq(from=-7,to=11, by=0.01) # R session fails for some of the parameters
plot(y,sapply(y,foo),pch=".")
Other parameters, e.g. y<-seq(from=-7,to=5, by=0.01) do not crash the R session:
If everything works Ok for the range (-7,11) - please, check other (large) numbers, maybe this is system-specific.
I am using the R function expect_equal to test if two large vectors are equal (almost) up to a certain tolerance. I was wondering if there was a way to only print the cases where expect_equal breaks the tolerance.
For example
a <- c(2.001, 3.5)
b <- c(2,3)
expect_equal(object=a,expected=b,tolerance=0.015, scale=1).
This prints the error:
Error: c(2, 3) not equal to c(2.001, 3.5)
2/2 mismatches (average diff: 0.25).
First 2:
pos x y diff
1 2 2.0 -0.001
2 3 3.5 -0.500
Even though case 1 "passes" my test. Is it possible to only print the cases that break the tolerance level? And even better would be if I could then store and refer to cases which fail so that I can route out the errors quicker.
The quick answer is "no". You can't only show the values that break the tolerance. The reason is that equality is tested using the "all.equal" function which doesn't have that option (to see this, you can look at the function "compare.numeric" in testthat via
testthat:::compare.numeric
at the R command prompt.
The longer answer depends how hard you want to work to get your answer and how often you will reuse the method. The simplest is to do as #VermillionAzure mentioned, manually generate the vector out of tolerance and check for its length to be 0 (or a similar test). For that test, you could use the expect_true function. A more complex method would be to create your own data class (other than numeric) and then make your own compare method for that class. If you really need the result to be summarized your way, you may have to go down the path of creating your own compare function.
For the second part of your question (storing to refer to tests that failed later), you can store the results of the test() function call from testthat, and from that, you can find what function had the errors.
results <- test()
I'm trying to use user defined kernel. I know that kernlab offer user defined kernel(custom kernel functions) in R. I used data spam including package kernlab.
(number of variables=57 number of examples =4061)
I'm defined kernel's form,
kp=function(d,e){
as=v*d
bs=v*e
cs=as-bs
cs=as.matrix(cs)
exp(-(norm(cs,"F")^2)/2)
}
class(kp)="kernel"
It is the transformed kernel for gaussian kernel, where v is the continuously changed values that are inverse of standard deviation vector about each variables, for example:
v=(0.1666667,........0.1666667)
The training set defined 60% of spam data (preserving the proportions of the different classes).
if data's type is spam, than data's type = 1 for train svm
m=ksvm(xtrain,ytrain,type="C-svc",kernel=kp,C=10)
But this step is not working. It's always waiting for a response.
So, I ask you this problem, why? Is it because the number of examples are too big? Is there any other R package that can train SVMs for user defined kernel?
First, your kernel looks like a classic RBF kernel, with v = 1/sigma, so why do you use it? You can use a built-in RBF kernel and simply set the sigma parameter. In particular - instead of using frobenius norm on matrices you could use classic euclidean on the vectorized matrices.
Second - this is working just fine.
> xtrain = as.matrix( c(1,2,3,4) )
> ytrain = as.factor( c(0,0,1,1) )
> v= 0.01
> m=ksvm(xtrain,ytrain,type="C-svc",kernel=kp,C=10)
> m
Support Vector Machine object of class "ksvm"
SV type: C-svc (classification)
parameter : cost C = 10
Number of Support Vectors : 4
Objective Function Value : -39.952
Training error : 0
There are at least two reasons for you still waiting for results:
RBF kernels induce the most hard problem to optimize for SVM (especially for large C)
User defined kernels are far less efficient then builtin
As I am not sure, whether ksvm actually optimizes the user-defined kernel computation (in fact I'm pretty sure it does not), you could try to build the kernel matrix ( K[i,j] = K(x_i,x_j) where x_i is i'th training vector) and provide ksvm with it. You can achieve this by
K <- kernelMatrix(kp,xtrain)
m <- ksvm(K,ytrain,type="C-svc",kernel='matrix',C=10)
Precomputing kernel matrix can be quite long process, but then optimization itself will be much faster, so it is a good method if you want to test many different C values (which you for sure should do). Unfortunately this requires O(n^2) memory, so if you use more then 100 000 vectors, you will need really great amount of RAM.
In recent conversations with fellow students, I have been advocating for avoiding globals except to store constants. This is a sort of typical applied statistics-type program where everyone writes their own code and project sizes are on the small side, so it can be hard for people to see the trouble caused by sloppy habits.
In talking about avoidance of globals, I'm focusing on the following reasons why globals might cause trouble, but I'd like to have some examples in R and/or Stata to go with the principles (and any other principles you might find important), and I'm having a hard time coming up with believable ones.
Non-locality: Globals make debugging harder because they make understanding the flow of code harder
Implicit coupling: Globals break the simplicity of functional programming by allowing complex interactions between distant segments of code
Namespace collisions: Common names (x, i, and so forth) get re-used, causing namespace collisions
A useful answer to this question would be a reproducible and self-contained code snippet in which globals cause a specific type of trouble, ideally with another code snippet in which the problem is corrected. I can generate the corrected solutions if necessary, so the example of the problem is more important.
Relevant links:
Global Variables are Bad
Are global variables bad?
I also have the pleasure of teaching R to undergraduate students who have no experience with programming. The problem I found was that most examples of when globals are bad, are rather simplistic and don't really get the point across.
Instead, I try to illustrate the principle of least astonishment. I use examples where it is tricky to figure out what was going on. Here are some examples:
I ask the class to write down what they think the final value of i will be:
i = 10
for(i in 1:5)
i = i + 1
i
Some of the class guess correctly. Then I ask should you ever write code like this?
In some sense i is a global variable that is being changed.
What does the following piece of code return:
x = 5:10
x[x=1]
The problem is what exactly do we mean by x
Does the following function return a global or local variable:
z = 0
f = function() {
if(runif(1) < 0.5)
z = 1
return(z)
}
Answer: both. Again discuss why this is bad.
Oh, the wonderful smell of globals...
All of the answers in this post gave R examples, and the OP wanted some Stata examples, as well. So let me chime in with these.
Unlike R, Stata does take care of locality of its local macros (the ones that you create with local command), so the issue of "Is this this a global z or a local z that is being returned?" never comes up. (Gosh... how can you R guys write any code at all if locality is not enforced???) Stata has a different quirk, though, namely that a non-existent local or global macro is evaluated as an empty string, which may or may not be desirable.
I have seen globals used for several main reasons:
Globals are often used as shortcuts for variable lists, as in
sysuse auto, clear
regress price $myvars
I suspect that the main usage of such construct is for someone who switches between interactive typing and storing the code in a do-file as they try multiple specifications. Say they try regression with homoskedastic standard errors, heteroskedastic standard errors, and median regression:
regress price mpg foreign
regress price mpg foreign, robust
qreg price mpg foreign
And then they run these regressions with another set of variables, then with yet another one, and finally they give up and set this up as a do-file myreg.do with
regress price $myvars
regress price $myvars, robust
qreg price $myvars
exit
to be accompanied with an appropriate setting of the global macro. So far so good; the snippet
global myvars mpg foreign
do myreg
produces the desirable results. Now let's say they email their famous do-file that claims to produce very good regression results to collaborators, and instruct them to type
do myreg
What will their collaborators see? In the best case, the mean and the median of mpg if they started a new instance of Stata (failed coupling: myreg.do did not really know you meant to run this with a non-empty variable list). But if the collaborators had something in the works, and too had a global myvars defined (name collision)... man, would that be a disaster.
Globals are used for directory or file names, as in:
use $mydir\data1, clear
God only knows what will be loaded. In large projects, though, it does come handy. You would want to define global mydir somewhere in your master do-file, may be even as
global mydir `c(pwd)'
Globals can be used to store an unpredictable crap, like a whole command:
capture $RunThis
God only knows what will be executed; let's just hope it is not ! format c:\. This is the worst case of implicit strong coupling, but since I am not even sure that RunThis will contain anything meaningful, I put a capture in front of it, and will be prepared to treat the non-zero return code _rc. (See, however, my example below.)
Stata's own use of globals is for God settings, like the type I error probability/confidence level: the global $S_level is always defined (and you must be a total idiot to redefine this global, although of course it is technically doable). This is, however, mostly a legacy issue with code of version 5 and below (roughly), as the same information can be obtained from less fragile system constant:
set level 90
display $S_level
display c(level)
Thankfully, globals are quite explicit in Stata, and hence are easy to debug and remove. In some of the above situations, and certainly in the first one, you'd want to pass parameters to do-files which are seen as the local `0' inside the do-file. Instead of using globals in the myreg.do file, I would probably code it as
unab varlist : `0'
regress price `varlist'
regress price `varlist', robust
qreg price `varlist'
exit
The unab thing will serve as an element of protection: if the input is not a legal varlist, the program will stop with an error message.
In the worst cases I've seen, the global was used only once after having been defined.
There are occasions when you do want to use globals, because otherwise you'd have to pass the bloody thing to every other do-file or a program. One example where I found the globals pretty much unavoidable was coding a maximum likelihood estimator where I did not know in advance how many equations and parameters I would have. Stata insists that the (user-supplied) likelihood evaluator will have specific equations. So I had to accumulate my equations in the globals, and then call my evaluator with the globals in the descriptions of the syntax that Stata would need to parse:
args lf $parameters
where lf was the objective function (the log-likelihood). I encountered this at least twice, in the normal mixture package (denormix) and confirmatory factor analysis package (confa); you can findit both of them, of course.
One R example of a global variable that divides opinion is the stringsAsFactors issue on reading data into R or creating a data frame.
set.seed(1)
str(data.frame(A = sample(LETTERS, 100, replace = TRUE),
DATES = as.character(seq(Sys.Date(), length = 100, by = "days"))))
options("stringsAsFactors" = FALSE)
set.seed(1)
str(data.frame(A = sample(LETTERS, 100, replace = TRUE),
DATES = as.character(seq(Sys.Date(), length = 100, by = "days"))))
options("stringsAsFactors" = TRUE) ## reset
This can't really be corrected because of the way options are implemented in R - anything could change them without you knowing it and thus the same chunk of code is not guaranteed to return exactly the same object. John Chambers bemoans this feature in his recent book.
A pathological example in R is the use of one of the globals available in R, pi, to compute the area of a circle.
> r <- 3
> pi * r^2
[1] 28.27433
>
> pi <- 2
> pi * r^2
[1] 18
>
> foo <- function(r) {
+ pi * r^2
+ }
> foo(r)
[1] 18
>
> rm(pi)
> foo(r)
[1] 28.27433
> pi * r^2
[1] 28.27433
Of course, one can write the function foo() defensively by forcing the use of base::pi but such recourse may not be available in normal user code unless packaged up and using a NAMESPACE:
> foo <- function(r) {
+ base::pi * r^2
+ }
> foo(r = 3)
[1] 28.27433
> pi <- 2
> foo(r = 3)
[1] 28.27433
> rm(pi)
This highlights the mess you can get into by relying on anything that is not solely in the scope of your function or passed in explicitly as an argument.
Here's an interesting pathological example involving replacement functions, the global assign, and x defined both globally and locally...
x <- c(1,NA,NA,NA,1,NA,1,NA)
local({
#some other code involving some other x begin
x <- c(NA,2,3,4)
#some other code involving some other x end
#now you want to replace NAs in the the global/parent frame x with 0s
x[is.na(x)] <<- 0
})
x
[1] 0 NA NA NA 0 NA 1 NA
Instead of returning [1] 1 0 0 0 1 0 1 0, the replacement function uses the index returned by the local value of is.na(x), even though you're assigning to the global value of x. This behavior is documented in the R Language Definition.
One quick but convincing example in R is to run the line like:
.Random.seed <- 'normal'
I chose 'normal' as something someone might choose, but you could use anything there.
Now run any code that uses generated random numbers, for example:
rnorm(10)
Then you can point out that the same thing could happen for any global variable.
I also use the example of:
x <- 27
z <- somefunctionthatusesglobals(5)
Then ask the students what the value of x is; the answer is that we don't know.
Through trial and error I've learned that I need to be very explicit in naming my function arguments (and ensure enough checks at the start and along the function) to make everything as robust as possible. This is especially true if you have variables stored in global environment, but then you try to debug a function with a custom valuables - and something doesn't add up! This is a simple example that combines bad checks and calling a global variable.
glob.arg <- "snake"
customFunction <- function(arg1) {
if (is.numeric(arg1)) {
glob.arg <- "elephant"
}
return(strsplit(glob.arg, "n"))
}
customFunction(arg1 = 1) #argument correct, expected results
customFunction(arg1 = "rubble") #works, but may have unexpected results
An example sketch that came up while trying to teach this today. Specifically, this focuses on trying to give intuition as to why globals can cause problems, so it abstracts away as much as possible in an attempt to state what can and cannot be concluded just from the code (leaving the function as a black box).
The set up
Here is some code. Decide whether it will return an error or not based on only the criteria given.
The code
stopifnot( all( x!=0 ) )
y <- f(x)
5/x
The criteria
Case 1: f() is a properly-behaved function, which uses only local variables.
Case 2: f() is not necessarily a properly-behaved function, which could potentially use global assignment.
The answer
Case 1: The code will not return an error, since line one checks that there are no x's equal to zero and line three divides by x.
Case 2: The code could potentially return an error, since f() could e.g. subtract 1 from x and assign it back to the x in the parent environment, where any x element equal to 1 could then be set to zero and the third line would return a division by zero error.
Here's one attempt at an answer that would make sense to statisticsy types.
Namespace collisions: Common names (x, i, and so forth) get re-used, causing namespace collisions
First we define a log likelihood function,
logLik <- function(x) {
y <<- x^2+2
return(sum(sqrt(y+7)))
}
Now we write an unrelated function to return the sum of squares of an input. Because we're lazy we'll do this passing it y as a global variable,
sumSq <- function() {
return(sum(y^2))
}
y <<- seq(5)
sumSq()
[1] 55
Our log likelihood function seems to behave exactly as we'd expect, taking an argument and returning a value,
> logLik(seq(12))
[1] 88.40761
But what's up with our other function?
> sumSq()
[1] 633538
Of course, this is a trivial example, as will be any example that doesn't exist in a complex program. But hopefully it'll spark a discussion about how much harder it is to keep track of globals than locals.
In R you may also try to show them that there is often no need to use globals as you may access the variables defined in the function scope from within the function itself by only changing the enviroment. For example the code below
zz="aaa"
x = function(y) {
zz="bbb"
cat("value of zz from within the function: \n")
cat(zz , "\n")
cat("value of zz from the function scope: \n")
with(environment(x),cat(zz,"\n"))
}