R help - Aug 2011 - Efficient way to Calculate the squared distances for a set of vectors to a fixed vector

I am pretty new to R. So this may be an easy question for most of you.
?
I would like to calculate the squared distances of a large set (let's say
20000) of vectors (let's say dimension of 5) to a fixed vector.
?
Say I have a data frame MY_VECTORS with 20000 rows and 5 columns, and one 5x1
vector y. I would like to efficiently calculate the squared distances?between
each of the 20000 vectors in MY_VECTORS and y.
?
The squared distance between two vectors x and y can be calculated:
distance <- crossprod(x-y)
?
Without looping, what is?the efficient code to achieve this?
?
Thanks.

Let's say your fixed vector is x, and y is the list of vectors that you want
to create the squared distance to x with, then:

x<-c(1:5)
y<-list()
y[[1]]<-sample(c(1:5),5)
y[[2]]<-sample(c(1:5),5)
y[[3]]<-sample(c(1:5),5)
y

distances<-lapply(y,function(a,b) crossprod(a-b), b=x) 

#lapply goes over the list elements of y and executes the function for each
of these list elements
#the current list element of "y" is plugged in for "a" and
"x" is plugged in
for "b" and the crossproduct is formed

distances<-unlist(distances)

HTH,
Daniel





Wei Wu wrote:
> 
> I am pretty new to R. So this may be an easy question for most of you.
> ?
> I would like to calculate the squared distances of a large set (let's
say
> 20000) of vectors (let's say dimension of 5) to a fixed vector.
> ?
> Say I have a data frame MY_VECTORS with 20000 rows and 5 columns, and one
> 5x1 vector y. I would like to efficiently calculate the squared
> distances?between each of the 20000 vectors in MY_VECTORS and y.
> ?
> The squared distance between two vectors x and y can be calculated:
> distance <- crossprod(x-y)
> ?
> Without looping, what is?the efficient code to achieve this?
> ?
> Thanks.
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> 
--
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You could do something like this:

# data
nrows <- 20000L
ncols <- 5L
myVec <- array(rnorm(nrows * ncols), dim = c(nrows, ncols))
y <- rnorm(ncols)

temp <- t(myVec) - y
result <- colSums(temp * temp)

# check
all.equal(as.numeric(crossprod(myVec[1L, ] - y)), result[1L])
#...

(And don't use a data.frame, but a matrix.)

regards,
Enrico
> -----Urspr?ngliche Nachricht-----
> Von: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] Im Auftrag von Wei Wu
> Gesendet: Mittwoch, 24. August 2011 07:18
> An: r-help at r-project.org
> Betreff: [R] Efficient way to Calculate the squared distances 
> for a set ofvectors to a fixed vector
> 
> I am pretty new to R. So this may be an easy question for most of you.
> ?
> I would like to calculate the squared distances of a large 
> set (let's say 20000) of vectors (let's say dimension of 5) 
> to a fixed vector.
> ?
> Say I have a data frame MY_VECTORS with 20000 rows and 5 
> columns, and one 5x1 vector y. I would like to efficiently 
> calculate the squared distances?between each of the 20000 
> vectors in MY_VECTORS and y.
> ?
> The squared distance between two vectors x and y can be calculated:
> distance <- crossprod(x-y)
> ?
> Without looping, what is?the efficient code to achieve this?
> ?
> Thanks.
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

Yes, sorry, so the distance is

colSums((t(x)-y)**2)

(I knew that) :S

Tsjerk

On Wed, Aug 24, 2011 at 9:19 AM, Enrico Schumann
<enricoschumann at yahoo.de> wrote:
> R will subtract the vector columnwise from the matrix (so the vectors need
> be the columns).
>
> x <- matrix(0, nrow = 10L, ncol = 5L)
> y <- 1:5
> x - y
>
> ? ? ?[,1] [,2] [,3] [,4] [,5]
> ?[1,] ? -1 ? -1 ? -1 ? -1 ? -1
> ?[2,] ? -2 ? -2 ? -2 ? -2 ? -2
> ?[3,] ? -3 ? -3 ? -3 ? -3 ? -3
> ?[4,] ? -4 ? -4 ? -4 ? -4 ? -4
> ?[5,] ? -5 ? -5 ? -5 ? -5 ? -5
> ?[6,] ? -1 ? -1 ? -1 ? -1 ? -1
> ?[7,] ? -2 ? -2 ? -2 ? -2 ? -2
> ?[8,] ? -3 ? -3 ? -3 ? -3 ? -3
> ?[9,] ? -4 ? -4 ? -4 ? -4 ? -4
> [10,] ? -5 ? -5 ? -5 ? -5 ? -5
>
>
>
>
>> -----Urspr?ngliche Nachricht-----
>> Von: Tsjerk Wassenaar [mailto:tsjerkw at gmail.com]
>> Gesendet: Mittwoch, 24. August 2011 09:02
>> An: Enrico Schumann
>> Cc: Wei Wu; r-help at r-project.org
>> Betreff: Re: [R] Efficient way to Calculate the squared
>> distances for a set ofvectors to a fixed vector
>>
>> Hi Wei Wu,
>>
>> What about:
>>
>> x <- matrix(rnorm(20000*5),ncol=5)
>> y <- rnorm(5)
>> distances <- rowSums((x-y)**2)
>>
>> Cheers,
>>
>> Tsjerk
>>
>> On Wed, Aug 24, 2011 at 8:43 AM, Enrico Schumann
>> <enricoschumann at yahoo.de> wrote:
>> >
>> > You could do something like this:
>> >
>> > # data
>> > nrows <- 20000L
>> > ncols <- 5L
>> > myVec <- array(rnorm(nrows * ncols), dim = c(nrows, ncols)) y
<-
>> > rnorm(ncols)
>> >
>> > temp <- t(myVec) - y
>> > result <- colSums(temp * temp)
>> >
>> > # check
>> > all.equal(as.numeric(crossprod(myVec[1L, ] - y)), result[1L]) #...
>> >
>> > (And don't use a data.frame, but a matrix.)
>> >
>> > regards,
>> > Enrico
>> >> -----Urspr?ngliche Nachricht-----
>> >> Von: r-help-bounces at r-project.org
>> >> [mailto:r-help-bounces at r-project.org] Im Auftrag von Wei Wu
>> >> Gesendet: Mittwoch, 24. August 2011 07:18
>> >> An: r-help at r-project.org
>> >> Betreff: [R] Efficient way to Calculate the squared
>> distances for a
>> >> set ofvectors to a fixed vector
>> >>
>> >> I am pretty new to R. So this may be an easy question for
>> most of you.
>> >>
>> >> I would like to calculate the squared distances of a large
>> set (let's
>> >> say 20000) of vectors (let's say dimension of 5) to a
fixed vector.
>> >>
>> >> Say I have a data frame MY_VECTORS with 20000 rows and 5
>> columns, and
>> >> one 5x1 vector y. I would like to efficiently calculate
>> the squared
>> >> distances?between each of the 20000 vectors in MY_VECTORS and
y.
>> >>
>> >> The squared distance between two vectors x and y can be
calculated:
>> >> distance <- crossprod(x-y)
>> >>
>> >> Without looping, what is?the efficient code to achieve this?
>> >>
>> >> Thanks.
>> >>
>> >> ______________________________________________
>> >> R-help at r-project.org mailing list
>> >> https://stat.ethz.ch/mailman/listinfo/r-help
>> >> PLEASE do read the posting guide
>> >> http://www.R-project.org/posting-guide.html
>> >> and provide commented, minimal, self-contained, reproducible
code.
>> >
>> > ______________________________________________
>> > R-help at r-project.org mailing list
>> > https://stat.ethz.ch/mailman/listinfo/r-help
>> > PLEASE do read the posting guide
>> > http://www.R-project.org/posting-guide.html
>> > and provide commented, minimal, self-contained, reproducible code.
>> >
>>
>>
>>
>> --
>> Tsjerk A. Wassenaar, Ph.D.
>>
>> post-doctoral researcher
>> Molecular Dynamics Group
>> * Groningen Institute for Biomolecular Research and Biotechnology
>> * Zernike Institute for Advanced Materials University of
>> Groningen The Netherlands
>
>


-- 
Tsjerk A. Wassenaar, Ph.D.

post-doctoral researcher
Molecular Dynamics Group
* Groningen Institute for Biomolecular Research and Biotechnology
* Zernike Institute for Advanced Materials
University of Groningen
The Netherlands