R help - Oct 2004 - cumsum over a list or an array

Hello list,

my question is related to svd of a matrix:

b=matrix(rnorm(50),10,5)
mysvd=svd(b)

I would like to compute each xi where xi = di* ui %*% t(vi). I do it by :

xlist=sapply(1:ncol(b), function(x1,y) 
y$d[x1]*y$u[,x1]%*%t(y$v[,x1]),y=mysvd,simplify=F) # result is a list

xarray=array(sapply(1:ncol(b), function(x1,y) 
y$d[x1]*y$u[,x1]%*%t(y$v[,x1]),y=mysvd),c(nrow(b),ncol(b),ncol(b))) # 
result is an array

Now i would like to compute cumulative sum:

y1=x1 # y[,,1]
y2=x1+x2 # y[,,2]
...

I have try to do it with apply without succes:

y=apply(xarray,c(1,2),cumsum)

The results are good but not in the format that I want. I could modify the 
results to modify the format but I am sure that it exists another faster way.

Is it possible to do the same on the list ?

Thanks in advance

Sincerely



St??phane DRAY
--------------------------------------------------------------------------------------------------

D??partement des Sciences Biologiques
Universit?? de Montr??al, C.P. 6128, succursale centre-ville
Montr??al, Qu??bec H3C 3J7, Canada

Tel : (514) 343-6111 poste 1233         Fax : (514) 343-2293
E-mail : stephane.dray at umontreal.ca
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Web                                          http://www.steph280.freesurf.fr/

Stephane DRAY <stephane.dray <at> umontreal.ca> writes:

: 
: Hello list,
: 
: my question is related to svd of a matrix:
: 
: b=matrix(rnorm(50),10,5)
: mysvd=svd(b)
: 
: I would like to compute each xi where xi = di* ui %*% t(vi). I do it by :
: 
: xlist=sapply(1:ncol(b), function(x1,y) 
: y$d[x1]*y$u[,x1]%*%t(y$v[,x1]),y=mysvd,simplify=F) # result is a list
: 
: xarray=array(sapply(1:ncol(b), function(x1,y) 
: y$d[x1]*y$u[,x1]%*%t(y$v[,x1]),y=mysvd),c(nrow(b),ncol(b),ncol(b))) # 
: result is an array
: 
: Now i would like to compute cumulative sum:
: 
: y1=x1 # y[,,1]
: y2=x1+x2 # y[,,2]
: ...
: 
: I have try to do it with apply without succes:
: 
: y=apply(xarray,c(1,2),cumsum)
: 
: The results are good but not in the format that I want. I could modify the 
: results to modify the format but I am sure that it exists another faster way.
: 
: Is it possible to do the same on the list ?
: 
: Thanks in advance

I assume the format you want is a list in which the ith
element is the approximation to b formed from the first i
singular values and the associated spaces.

Its actually pretty straighforward and short to simply use a 
for loop:

   z1 <- xlist
   for(i in 2:length(mysvd$d)) z1[[i]] <- z1[[i-1]] + xlist[[i]]

or one can do it directly from the output of the svd
without using xlist or xarray by simply zeroing all but
the first i singular values in udv' in the ith iteration 
within lapply:

   z2 <- with(mysvd, {
      idx <- seq(along = d)
      lapply(idx, function(i) u %*% diag(d*(idx<=i)) %*% t(v))
   })

   all.equal(z1, z2) # TRUE