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 -------------------------------------------------------------------------------------------------- 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