Hi Radford,
On 08/25/2010 07:50 PM, Radford Neal wrote:
I've looked at how to speed up the transpose function in R
(ie, t(X)).
The existing code does the work with loops like the following:
for (i = 0; i< len; i++)
REAL(r)[i] = REAL(a)[(i / ncol) + (i % ncol) * nrow];
It seems a bit optimistic to expect a compiler to produce good code
from this. I've re-written these loops as follows:
for (i = 0, j = 0; i<len; i += 1, j += nrow) {
if (j>=len) j -= (len-1);
REAL(r)[i] = REAL(a)[j];
}
You can even avoid the j>=len test within the loop by using 2 nested
loops:
dest = REAL(r);
src = REAL(a);
// walk the dest col by col (i.e. linearly)
// walk the src row by row (i.e. not linearly)
for (i = 0; i < nrow; i++, src++)
for (j = 0; j < len; j += nrow, dest++)
*dest = src[j];
1 test, 3 additions (src[j] being equiv to *(src + j)), 1 assignment
in the inner loop. I wonder if it's possible to get rid of one of the
additions.
This gives me another 10% gain in speed (on my 64-bit Ubuntu laptop),
not that much, but still...
BTW isn't that surprising that using div() is actually slower than using
of / and %, at least on Linux? Since div() is kind of the atomic version
of it, I would have expected it to be slightly faster :-/
Cheers,
H.
The resulting improvement is sometimes dramatic. Here's a test
program:
M<- matrix(seq(0,1,12000),200,60)
print(system.time({for (i in 1:10000) S<- t(M)}))
print(system.time({for (i in 1:10000) R<- t(S)}))
v<- seq(0,2,12000)
print(system.time({for (i in 1:100000) u<- t(v)}))
print(system.time({for (i in 1:100000) w<- t(u)}))
Here are the times on an Intel Linux system:
R version 2.11.1: Modified version:
user system elapsed user system elapsed
1.190 0.040 1.232 0.610 0.010 0.619
user system elapsed user system elapsed
1.200 0.020 1.226 0.610 0.000 0.616
user system elapsed user system elapsed
0.800 0.010 0.813 0.750 0.000 0.752
user system elapsed user system elapsed
0.910 0.010 0.921 0.860 0.000 0.864
Here are the times on a SPARC Solaris system:
R version 2.11.1: Modified version:
user system elapsed user system elapsed
18.643 0.041 18.685 2.994 0.039 3.033
user system elapsed user system elapsed
18.574 0.041 18.616 3.123 0.039 3.163
user system elapsed user system elapsed
3.803 0.271 4.075 3.868 0.296 4.163
user system elapsed user system elapsed
4.184 0.273 4.457 4.238 0.302 4.540
So with the modification, transpose for a 60x200 or 200x60 matrix is
about a factor of two faster on the Intel system, and a factor of six
faster on the SPARC system. There is little or no gain from the
modification when transposing a row or column vector, however. (I
think it must be that on these machines multiplies and divides do not
take constant time, but are faster when, for instance, dividing by 1.)
I've appended below the new version of the modified part of the
do_transpose function in src/main/array.c.
Radford Neal
----------------------------------------------------------------------
PROTECT(r = allocVector(TYPEOF(a), len));
switch (TYPEOF(a)) {
case LGLSXP:
case INTSXP:
for (i = 0, j = 0; i<len; i += 1, j += nrow) {
if (j>=len) j -= (len-1);
INTEGER(r)[i] = INTEGER(a)[j];
}
case REALSXP:
for (i = 0, j = 0; i<len; i += 1, j += nrow) {
if (j>=len) j -= (len-1);
REAL(r)[i] = REAL(a)[j];
}
break;
case CPLXSXP:
for (i = 0, j = 0; i<len; i += 1, j += nrow) {
if (j>=len) j -= (len-1);
COMPLEX(r)[i] = COMPLEX(a)[j];
}
break;
case STRSXP:
for (i = 0, j = 0; i<len; i += 1, j += nrow) {
if (j>=len) j -= (len-1);
SET_STRING_ELT(r, i, STRING_ELT(a,j));
}
break;
case VECSXP:
for (i = 0, j = 0; i<len; i += 1, j += nrow) {
if (j>=len) j -= (len-1);
SET_VECTOR_ELT(r, i, VECTOR_ELT(a,j));
}
break;
case RAWSXP:
for (i = 0, j = 0; i<len; i += 1, j += nrow) {
if (j>=len) j -= (len-1);
RAW(r)[i] = RAW(a)[j];
}
break;
default:
UNPROTECT(1);
goto not_matrix;
}
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Program in Computational Biology
Division of Public Health Sciences
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