Hi,
I apologize for this repeat posting, which I first posted yesterday. I would
appreciate any hints on solving this problem:
I have two matrices A (m x 2) and B (n x 2), where m and n are large
integers (on the order of 10^4). I am looking for an efficient way to
create another matrix, W (m x n), which can be defined as follows:
for (i in 1:m){
for (j in 1:n) {
W[i,j] <- g(A[i,], B[j,])
} }
where g(x,y) is a function that takes two vectors and returns a scalar.
The following works okay, but is not fast enough for my purpose. I am sure
that I can do better:
for (i in 1:m) {
W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
}
How can I do this in a faster manner? I attempted "outer",
"kronecker",
"expand.grid", etc, but with no success.
Here is an example:
m <- 2000
n <- 5000
A <- matrix(rnorm(2*m),ncol=2)
B <- matrix(rnorm(2*n),ncol=2)
W <- matrix(NA, m, n)
for (i in 1:m) {
W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
}
g <- function(x,y){
theta <- atan((y[2]-x[2]) / (y[1] - x[1]))
theta + 2*pi*(theta < 0)
}
Thanks for any suggestions.
Best,
Ravi.
----------------------------------------------------------------------------
-------
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: rvaradhan@jhmi.edu
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
----------------------------------------------------------------------------
--------
[[alternative HTML version deleted]]
Hi
> A <- matrix(runif(10),ncol=2)
> B <- matrix(runif(10),ncol=2)
> g <- function(i4){theta <- atan2( (i4[4]-i4[2]),(i4[3]-i4[1]))
+ return(theta + 2*pi*(theta<0))}
> apply(A,1,function(x){apply(B,1,function(y){g(c(x,y))})})
[,1] [,2] [,3] [,4] [,5]
[1,] 1.1709326 2.6521457 3.857477 0.219274562 1.2948374
[2,] 1.1770919 4.2109056 4.057313 4.918552967 1.9733967
[3,] 0.9171661 0.6721475 4.193675 0.434253839 0.9781060
[4,] 0.9181475 0.6911804 4.213295 0.455127422 0.9771797
[5,] 1.0467449 4.9263243 3.983248 0.004371504 1.1693707
>
HTH
rksh
On 1 Feb 2007, at 15:10, Ravi Varadhan wrote:
> Hi,
>
>
>
> I apologize for this repeat posting, which I first posted
> yesterday. I would
> appreciate any hints on solving this problem:
>
>
>
> I have two matrices A (m x 2) and B (n x 2), where m and n are large
> integers (on the order of 10^4). I am looking for an efficient way to
> create another matrix, W (m x n), which can be defined as follows:
>
>
>
> for (i in 1:m){
>
> for (j in 1:n) {
>
> W[i,j] <- g(A[i,], B[j,])
>
> } }
>
> where g(x,y) is a function that takes two vectors and returns a
> scalar.
>
>
>
> The following works okay, but is not fast enough for my purpose. I
> am sure
> that I can do better:
>
>
>
> for (i in 1:m) {
>
> W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
>
> }
>
>
>
> How can I do this in a faster manner? I attempted "outer",
> "kronecker",
> "expand.grid", etc, but with no success.
>
>
>
> Here is an example:
>
>
>
> m <- 2000
>
> n <- 5000
>
> A <- matrix(rnorm(2*m),ncol=2)
>
> B <- matrix(rnorm(2*n),ncol=2)
>
> W <- matrix(NA, m, n)
>
>
>
> for (i in 1:m) {
>
> W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
>
> }
>
>
>
> g <- function(x,y){
>
> theta <- atan((y[2]-x[2]) / (y[1] - x[1]))
>
> theta + 2*pi*(theta < 0)
>
> }
>
>
>
> Thanks for any suggestions.
>
>
>
> Best,
>
> Ravi.
>
>
>
>
>
>
>
> ----------------------------------------------------------------------
> ------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/
> Varadhan.html
>
>
>
> ----------------------------------------------------------------------
> ------
> --------
>
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at stat.math.ethz.ch 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.
--
Robin Hankin
Uncertainty Analyst
National Oceanography Centre, Southampton
European Way, Southampton SO14 3ZH, UK
tel 023-8059-7743
--
This e-mail (and any attachments) is confidential and intend...{{dropped}}
the following seems to be a first improvement:
m <- 2000
n <- 5000
A <- matrix(rnorm(2*m), ncol=2)
B <- matrix(rnorm(2*n), ncol=2)
W1 <- W2 <- matrix(0, m, n)
##############################
##############################
g1 <- function(x, y){
theta <- atan((y[2] - x[2]) / (y[1] - x[1]))
theta + 2*pi*(theta < 0)
}
invisible({gc(); gc()})
system.time(for (i in 1:m) {
W1[i, ] <- apply(B, 1, y = A[i,], function(x, y) g1(y, x))
})
##############################
g2 <- function(x){
out <- tB - x
theta <- atan(out[2, ] / out[1, ])
theta + 2*pi*(theta < 0)
}
tB <- t(B)
invisible({gc(); gc()})
system.time(for (i in 1:m) {
W2[i, ] <- g2(A[i, ])
})
## or
invisible({gc(); gc()})
system.time(W3 <- t(apply(A, 1, g2)))
all.equal(W1, W2)
all.equal(W1, W3)
I hope it helps.
Best,
Dimitris
----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven
Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
http://www.student.kuleuven.be/~m0390867/dimitris.htm
----- Original Message -----
From: "Ravi Varadhan" <rvaradhan at jhmi.edu>
To: <r-help at stat.math.ethz.ch>
Sent: Thursday, February 01, 2007 4:10 PM
Subject: [R] Need help writing a faster code
> Hi,
>
>
>
> I apologize for this repeat posting, which I first posted yesterday.
> I would
> appreciate any hints on solving this problem:
>
>
>
> I have two matrices A (m x 2) and B (n x 2), where m and n are large
> integers (on the order of 10^4). I am looking for an efficient way
> to
> create another matrix, W (m x n), which can be defined as follows:
>
>
>
> for (i in 1:m){
>
> for (j in 1:n) {
>
> W[i,j] <- g(A[i,], B[j,])
>
> } }
>
> where g(x,y) is a function that takes two vectors and returns a
> scalar.
>
>
>
> The following works okay, but is not fast enough for my purpose. I
> am sure
> that I can do better:
>
>
>
> for (i in 1:m) {
>
> W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
>
> }
>
>
>
> How can I do this in a faster manner? I attempted "outer",
> "kronecker",
> "expand.grid", etc, but with no success.
>
>
>
> Here is an example:
>
>
>
> m <- 2000
>
> n <- 5000
>
> A <- matrix(rnorm(2*m),ncol=2)
>
> B <- matrix(rnorm(2*n),ncol=2)
>
> W <- matrix(NA, m, n)
>
>
>
> for (i in 1:m) {
>
> W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
>
> }
>
>
>
> g <- function(x,y){
>
> theta <- atan((y[2]-x[2]) / (y[1] - x[1]))
>
> theta + 2*pi*(theta < 0)
>
> }
>
>
>
> Thanks for any suggestions.
>
>
>
> Best,
>
> Ravi.
>
>
>
>
>
>
>
>
----------------------------------------------------------------------------
> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:
> http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
>
----------------------------------------------------------------------------
> --------
>
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at stat.math.ethz.ch 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.
>
Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
Dear Dimitris,
I implemented your solution on my actual problem. I was able to generate my
large transition matrix in 56 seconds, compared to the previous time of
around 27 minutes. Wow!!!
I thank you very much for the help. R and the R-user group are truly
amazing!
Best regards,
Ravi.
----------------------------------------------------------------------------
-------
Ravi Varadhan, Ph.D.
Assistant Professor, The Center on Aging and Health
Division of Geriatric Medicine and Gerontology
Johns Hopkins University
Ph: (410) 502-2619
Fax: (410) 614-9625
Email: rvaradhan at jhmi.edu
Webpage: http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
----------------------------------------------------------------------------
--------
-----Original Message-----
From: Dimitris Rizopoulos [mailto:dimitris.rizopoulos at med.kuleuven.be]
Sent: Thursday, February 01, 2007 10:33 AM
To: Ravi Varadhan
Cc: r-help at stat.math.ethz.ch
Subject: Re: [R] Need help writing a faster code
the following seems to be a first improvement:
m <- 2000
n <- 5000
A <- matrix(rnorm(2*m), ncol=2)
B <- matrix(rnorm(2*n), ncol=2)
W1 <- W2 <- matrix(0, m, n)
##############################
##############################
g1 <- function(x, y){
theta <- atan((y[2] - x[2]) / (y[1] - x[1]))
theta + 2*pi*(theta < 0)
}
invisible({gc(); gc()})
system.time(for (i in 1:m) {
W1[i, ] <- apply(B, 1, y = A[i,], function(x, y) g1(y, x))
})
##############################
g2 <- function(x){
out <- tB - x
theta <- atan(out[2, ] / out[1, ])
theta + 2*pi*(theta < 0)
}
tB <- t(B)
invisible({gc(); gc()})
system.time(for (i in 1:m) {
W2[i, ] <- g2(A[i, ])
})
## or
invisible({gc(); gc()})
system.time(W3 <- t(apply(A, 1, g2)))
all.equal(W1, W2)
all.equal(W1, W3)
I hope it helps.
Best,
Dimitris
----
Dimitris Rizopoulos
Ph.D. Student
Biostatistical Centre
School of Public Health
Catholic University of Leuven
Address: Kapucijnenvoer 35, Leuven, Belgium
Tel: +32/(0)16/336899
Fax: +32/(0)16/337015
Web: http://med.kuleuven.be/biostat/
http://www.student.kuleuven.be/~m0390867/dimitris.htm
----- Original Message -----
From: "Ravi Varadhan" <rvaradhan at jhmi.edu>
To: <r-help at stat.math.ethz.ch>
Sent: Thursday, February 01, 2007 4:10 PM
Subject: [R] Need help writing a faster code
> Hi,
>
>
>
> I apologize for this repeat posting, which I first posted yesterday.
> I would
> appreciate any hints on solving this problem:
>
>
>
> I have two matrices A (m x 2) and B (n x 2), where m and n are large
> integers (on the order of 10^4). I am looking for an efficient way
> to
> create another matrix, W (m x n), which can be defined as follows:
>
>
>
> for (i in 1:m){
>
> for (j in 1:n) {
>
> W[i,j] <- g(A[i,], B[j,])
>
> } }
>
> where g(x,y) is a function that takes two vectors and returns a
> scalar.
>
>
>
> The following works okay, but is not fast enough for my purpose. I
> am sure
> that I can do better:
>
>
>
> for (i in 1:m) {
>
> W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
>
> }
>
>
>
> How can I do this in a faster manner? I attempted "outer",
> "kronecker",
> "expand.grid", etc, but with no success.
>
>
>
> Here is an example:
>
>
>
> m <- 2000
>
> n <- 5000
>
> A <- matrix(rnorm(2*m),ncol=2)
>
> B <- matrix(rnorm(2*n),ncol=2)
>
> W <- matrix(NA, m, n)
>
>
>
> for (i in 1:m) {
>
> W[i,] <- apply(B, 1, y=A[i,], function(x,y) g(y,x))
>
> }
>
>
>
> g <- function(x,y){
>
> theta <- atan((y[2]-x[2]) / (y[1] - x[1]))
>
> theta + 2*pi*(theta < 0)
>
> }
>
>
>
> Thanks for any suggestions.
>
>
>
> Best,
>
> Ravi.
>
>
>
>
>
>
>
>
----------------------------------------------------------------------------> -------
>
> Ravi Varadhan, Ph.D.
>
> Assistant Professor, The Center on Aging and Health
>
> Division of Geriatric Medicine and Gerontology
>
> Johns Hopkins University
>
> Ph: (410) 502-2619
>
> Fax: (410) 614-9625
>
> Email: rvaradhan at jhmi.edu
>
> Webpage:
> http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html
>
>
>
>
----------------------------------------------------------------------------> --------
>
>
>
>
> [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at stat.math.ethz.ch 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.
>
Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
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