Help with multiple use of "quantile"

Hello

I have a matrix aaa like this:

? ? ? ? ? ? aa1? ? ?  aa2? ? ?  aa3
[1,]? 8371.417? 27613.57? 1170.466
[2,] 14317.999? 42421.82? 3423.934
[3,] 22026.466? 59874.14? 8103.084
[4,] 33884.986? 84506.34 19176.764
[5,] 57954.968 129824.30 56097.310

where each column represents an empirical distribution of random variates
(normally the number of rows would be, say, 10,000 or 100,000) and a matrix
bbb of percentiles like this:

bbb

? ? ? ? ? ? [,1]? ? ? [,2]? ? ? [,3]
[1,] 0.70092980 0.8144194 0.6200732
[2,] 0.77968803 0.5804948 0.5463661
[3,] 0.01509415 0.9313509 0.8611973
[4,] 0.22654757 0.6183386 0.4962867
[5,] 0.36548835 0.6608696 0.3062784
What I'd like to do is to apply the quantiles in the three columns of bbb
to the columns of aaa independently, so as to obtain a matrix ccc such
that, for example, ccc[3,1]=quantile(aaa[,1],bbb[3,1]). THe complete matrix
is:


ccc =? ? quantile(aaa[,1],bbb[1,1]), quantile(aaa[,2],bbb[1,2]),
quantile(aaa[,3],bbb[1,3])
? ? ? ? ? ?  quantile(aaa[,1],bbb[2,1]), quantile(aaa[,2],bbb[2,2]),
quantile(aaa[,3],bbb[2,3])
? ? ? ? ? ?  quantile(aaa[,1],bbb[3,1]), quantile(aaa[,2],bbb[3,2]),
quantile(aaa[,3],bbb[3,3])
? ? ? ? ? ?  quantile(aaa[,1],bbb[4,1]), quantile(aaa[,2],bbb[4,2]),
quantile(aaa[,3],bbb[4,3])
? ? ? ? ? ?  quantile(aaa[,1],bbb[5,1]), quantile(aaa[,2],bbb[5,2]),
quantile(aaa[,3],bbb[5,3])



Now if I only two vectors, it would be enough for me to define
ccc=quantile(aaa,bbb). However, if I do this when aaa and bbb are matrix,
quantile(aaa,bbb) does something else -- it gives the percentiles bbb of
the whole set of matrix elements rather than considering separately the
quantiles of the different columns.

I suspect I'll need to use "apply" in some form but have been able to come
up with the correct form.

As you might have imagined, this arises in the? context of simulating
random variables from different distribution in empirical form that are
correlated through a copula.

Thanks in advance for your help!

Pietro
_

HI,
You could also use:

set.seed(24)
aaa <- matrix(rnorm(60), ncol=3)
bbb <- matrix(runif(15), ncol=3)
ccc1<- mapply(quantile,as.data.frame(aaa),as.data.frame(bbb))
ccc <- sapply(1:dim(aaa)[2], function(i) quantile(aaa[, i], bbb[, i])) #Jean's solution

colnames(ccc1)<-NULL

   identical(ccc,ccc1)
#[1] TRUE
A.K.



----- Original Message -----
From: "Adams, Jean" <jvadams at usgs.gov>
To: "Parodi, Pietro" <Pietro.Parodi at willis.com>
Cc: "r-help at r-project.org" <r-help at r-project.org>
Sent: Saturday, June 8, 2013 9:49 AM
Subject: Re: [R] Help with multiple use of "quantile"

Try this, Pietro ...

# example data
aaa <- matrix(rnorm(60), ncol=3)
bbb <- matrix(runif(15), ncol=3)

# calculate quantiles
ccc <- sapply(1:dim(aaa)[2], function(i) quantile(aaa[, i], bbb[, i]))
# change rownames
rownames(ccc) <- seq(dim(ccc)[1])

Jean


On Sat, Jun 8, 2013 at 8:20 AM, Parodi, Pietro <Pietro.Parodi at willis.com>wrote:

Hello

I have a matrix aaa like this:

             aa1       aa2       aa3
[1,]  8371.417  27613.57  1170.466
[2,] 14317.999  42421.82  3423.934
[3,] 22026.466  59874.14  8103.084
[4,] 33884.986  84506.34 19176.764
[5,] 57954.968 129824.30 56097.310

where each column represents an empirical distribution of random variates
(normally the number of rows would be, say, 10,000 or 100,000) and a matrix
bbb of percentiles like this:

bbb

             [,1]      [,2]      [,3]
[1,] 0.70092980 0.8144194 0.6200732
[2,] 0.77968803 0.5804948 0.5463661
[3,] 0.01509415 0.9313509 0.8611973
[4,] 0.22654757 0.6183386 0.4962867
[5,] 0.36548835 0.6608696 0.3062784
What I'd like to do is to apply the quantiles in the three columns of bbb
to the columns of aaa independently, so as to obtain a matrix ccc such
that, for example, ccc[3,1]=quantile(aaa[,1],bbb[3,1]). THe complete matrix
is:


ccc =    quantile(aaa[,1],bbb[1,1]), quantile(aaa[,2],bbb[1,2]),
quantile(aaa[,3],bbb[1,3])
              quantile(aaa[,1],bbb[2,1]), quantile(aaa[,2],bbb[2,2]),
quantile(aaa[,3],bbb[2,3])
              quantile(aaa[,1],bbb[3,1]), quantile(aaa[,2],bbb[3,2]),
quantile(aaa[,3],bbb[3,3])
              quantile(aaa[,1],bbb[4,1]), quantile(aaa[,2],bbb[4,2]),
quantile(aaa[,3],bbb[4,3])
              quantile(aaa[,1],bbb[5,1]), quantile(aaa[,2],bbb[5,2]),
quantile(aaa[,3],bbb[5,3])



Now if I only two vectors, it would be enough for me to define
ccc=quantile(aaa,bbb). However, if I do this when aaa and bbb are matrix,
quantile(aaa,bbb) does something else -- it gives the percentiles bbb of
the whole set of matrix elements rather than considering separately the
quantiles of the different columns.

I suspect I'll need to use "apply" in some form but have been able to come
up with the correct form.

As you might have imagined, this arises in the  context of simulating
random variables from different distribution in empirical form that are
correlated through a copula.

Thanks in advance for your help!

Pietro
_

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