[Rd] Speeding up transpose

[Radford Neal]

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];
        }

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;
    }