Rcpp is a good tool for this kind of problem.
I sort of went overboard here and wrote a very complex function that can find the coordinates of the lowest-index (that would be top-left for matrices) corners of all matches of a smaller array in a larger array, for any dimensionality. If you want to find all the locations of a 9-dimensional array in an 11-dimensional array, this function can do it for you.
Here it is:
library('Rcpp');
cppFunction('
IntegerMatrix findarray(IntegerVector big, IntegerVector small, bool nacmp=true ) {
// debugging macros
#define QUOTEID(...) #__VA_ARGS__
#define QUOTE(...) QUOTEID(__VA_ARGS__)
#define PRINT_VEC(vec,...) Rprintf(QUOTE(vec)"={"); if (vec.size() > 0) { Rprintf("%ld",vec[0]); for (size_t i = 1; i < vec.size(); ++i) Rprintf(",%ld",vec[i]); } Rprintf("}"__VA_ARGS__);
typedef std::vector<size_t> Dims;
// get big dimensions, treating a plain vector as a 1D array
Dims bigdims;
SEXP bigdimsSE = big.attr("dim");
if (Rf_isNull(bigdimsSE)) {
bigdims.push_back(big.size());
} else {
bigdims = as<Dims>(bigdimsSE);
}
//PRINT_VEC(bigdims,"\n");
// now we can use this macro to easily return a result matrix with no matches
#define RES_NOMATCH IntegerMatrix(0,bigdims.size())
// get small dimensions, treating a plain vector as a 1D array
Dims smalldims;
SEXP smalldimsSE = small.attr("dim");
if (Rf_isNull(smalldimsSE)) {
smalldims.push_back(small.size());
} else {
smalldims = as<Dims>(smalldimsSE);
}
//PRINT_VEC(smalldims,"\n");
// trivial case: if small has greater dimensionality than big, just return no matches
// note: we could theoretically support this case, at least when all extra small dimensions have only one index, but whatever
if (smalldims.size() > bigdims.size())
return RES_NOMATCH;
// derive a "bounds" Dims object, which will represent the maximum index plus one in big against which we must compare the first index in small for the corresponding dimension
// if small is greater than big in any dimension, then we can return no matches immediately
Dims bounds(smalldims.size());
for (size_t i = 0; i < smalldims.size(); ++i) {
if (smalldims[i] > bigdims[i])
return RES_NOMATCH;
bounds[i] = bigdims[i]-smalldims[i]+1;
}
// trivial case: if either big or small has any zero-length dimension, then just return no matches, because in that case the offending argument cannot have any actual data in it
// theoretically you can consider such degenerate arrays to match everywhere, sort of like the empty string matching at every position in any given string, but whatever
for (size_t i = 0; i < bigdims.size(); ++i) if (bigdims[i] == 0) return RES_NOMATCH;
for (size_t i = 0; i < smalldims.size(); ++i) if (smalldims[i] == 0) return RES_NOMATCH;
// prepare to build up the result data
// it would not make sense to build up the result data directly in a matrix, because we have to add one row at a time, which does not commute with the internal storage arrangement of matrices
// I then tried to use a data.frame, but the Rcpp DataFrame type is surprisingly light in functionality, seemingly without any provision for adding a row, and requires named columns, so best to avoid that
// instead, we'll just build up the data on a vector of vectors, going all-STL
typedef std::vector<std::vector<int> > ResBuilder;
ResBuilder resBuilder(bigdims.size());
// retrieve raw vector pointers for best performance
int* bigp = INTEGER(big);
int* smallp = INTEGER(small);
// now, iterate through each index of each (big) dimension from zero through the bound for that dimension (which is automatically the big dimension's length if small's dimensionality does not extend to that dimension), and see if small's first element matches
Dims bdis(bigdims.size()); // conveniently, initializes to all zeroes
size_t bvi = 0; // big vector index
while (true) { // big element loop, restricted to bounds
if (bigp[bvi] == smallp[0] && (nacmp || bigp[bvi] != NA_INTEGER)) {
//PRINT_VEC(bdis," ") Rprintf("found first element match at bvi=%ld big=small=%d\n",bvi,bigp[bvi]);
size_t bvi2 = bvi; // don't screw up the original bvi; matches can overlap
// now we need to iterate through each index of each (small) dimension and test if all remaining elements match
Dims sdis(smalldims.size()); // conveniently, initializes to all zeroes
size_t svi = 0;
bool match = true; // assumption
while (true) { // small element loop
// note: once inside this inner loop, we don't have to worry about bounds anymore, because we already enforced that the outer loop will only iterate over indexes within bounds
// increment small and big indexes
++svi; // always increment svi by exactly one; the small array governs this matching loop
//PRINT_VEC(bdis," ") PRINT_VEC(sdis," ") Rprintf("incremented svi=%ld\n",svi);
size_t bm = 1;
size_t d;
for (d = 0; d < sdis.size(); ++d) {
++sdis[d];
++bvi2;
if (sdis[d] == smalldims[d]) {
//PRINT_VEC(bdis," ") PRINT_VEC(sdis," ") Rprintf("reached small end=%ld of dimension d=%ld; bvi2=%ld bm=%ld\n",smalldims[d],d,bvi2,bm);
sdis[d] = 0;
bvi2 += (bigdims[d]-smalldims[d])*bm-1;
bm *= bigdims[d];
//PRINT_VEC(bdis," ") PRINT_VEC(sdis," ") Rprintf("after jumping to next index we have bvi2=%ld bm=%ld\n",bvi2,bm);
} else {
//PRINT_VEC(bdis," ") PRINT_VEC(sdis," ") Rprintf("valid dimension index increment at dimension d=%ld; bvi2=%ld bm=%ld\n",d,bvi2,bm);
break;
}
}
// test if we reached the end of small; then break the inner while loop, and we have a match
if (d == sdis.size())
break;
// at this point, we have a new element to test; if unequal, we have no match
if (bigp[bvi2] != smallp[svi] || !nacmp && bigp[bvi] == NA_INTEGER) {
//PRINT_VEC(bdis," ") PRINT_VEC(sdis," ") Rprintf("match overturned by big=%d != small=%d\n",bigp[bvi2],smallp[svi]);
match = false;
break;
} else {
//PRINT_VEC(bdis," ") PRINT_VEC(sdis," ") Rprintf("match respected by big=small=%d\n",bigp[bvi2]);
}
}
// if we have a match, add it to the result data
if (match) {
//PRINT_VEC(bdis," ") Rprintf("found complete match!\n");
for (size_t bd = 0; bd < bigdims.size(); ++bd)
resBuilder[bd].push_back(bdis[bd]+1); // also add one to convert from C++ zero-based to R one-based indexes
//PRINT_VEC(bdis," ") Rprintf("resBuilder dims = {%ld,%ld}\n",resBuilder[0].size(),resBuilder.size());
}
} else {
//PRINT_VEC(bdis," ") Rprintf("first element mismatch: big=%d != small=%d\n",bigp[bvi],smallp[0]);
}
// increment big index
size_t bm = 1;
size_t d;
for (d = 0; d < bdis.size(); ++d) {
++bdis[d];
++bvi;
size_t bound = bounds.size() > d ? bounds[d] : bigdims[d];
if (bdis[d] >= bound) {
//PRINT_VEC(bdis," ") Rprintf("big index hit bound=%ld of dimension d=%ld; bvi=%ld bm=%ld\n",bound,d,bvi,bm);
bdis[d] = 0;
bvi += (bigdims[d]-bound)*bm-1;
bm *= bigdims[d];
//PRINT_VEC(bdis," ") Rprintf("after advancing big index we have bvi=%ld bm=%ld\n",bvi,bm);
} else {
//PRINT_VEC(bdis," ") Rprintf("valid dimension index increment at dimension d=%ld; bvi=%ld bm=%ld\n",d,bvi,bm);
break;
}
}
// test if we reached the end of big; then break the outer while loop, and we're done
if (d == bdis.size() || bvi >= big.size())
break;
}
// copy to a matrix
IntegerMatrix res(resBuilder[0].size(),resBuilder.size());
int* resp = INTEGER(res);
for (size_t c = 0; c < res.ncol(); ++c)
std::copy(resBuilder[c].begin(),resBuilder[c].end(),resp+c*res.nrow());
// return the matrix
return res;
}
');
Here's some fairly arbitrary testing I did, only up to cube-in-cube (each test prints the big array, then the small array, then the result, and finally a logical vector testing if slices of the size of small extending from each successive match in big are really identical to small):
## testing
slice <- function(arr,is,ls,...) { length(ls) <- length(is); ls[is.na(ls)] <- 1; do.call(`[`,c(list(arr),Map(function(i,l) seq(i,len=l),is,ls),...)); };
printAndTest <- function(big,small) { print(big); print(small); findarray(big,small); };
printAndTestAndSliceIdentical <- function(big,small) { big <- structure(as.integer(big),dim=dim(big)); small <- structure(as.integer(small),dim=dim(small)); res <- printAndTest(big,small); print(res); if (nrow(res) > 0) sapply(1:nrow(res),function(r) identical(structure(slice(big,res[r,],if (is.null(dim(small))) length(small) else dim(small),drop=F),dim=dim(small)),small)) else logical(); };
## one-element match
printAndTestAndSliceIdentical(1,1);
## [1] 1
## [1] 1
## [,1]
## [1,] 1
## [1] TRUE
## vector in vector
printAndTestAndSliceIdentical(1:3,2:3);
## [1] 1 2 3
## [1] 2 3
## [,1]
## [1,] 2
## [1] TRUE
printAndTestAndSliceIdentical(1:3,1:3);
## [1] 1 2 3
## [1] 1 2 3
## [,1]
## [1,] 1
## [1] TRUE
printAndTestAndSliceIdentical(1:3,1:4);
## [1] 1 2 3
## [1] 1 2 3 4
## [,1]
## logical(0)
## vector in matrix
printAndTestAndSliceIdentical(matrix(rep(1:12,2),4),1:2);
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1 5 9 1 5 9
## [2,] 2 6 10 2 6 10
## [3,] 3 7 11 3 7 11
## [4,] 4 8 12 4 8 12
## [1] 1 2
## [,1] [,2]
## [1,] 1 1
## [2,] 1 4
## [1] TRUE TRUE
printAndTestAndSliceIdentical(matrix(rep(1:12,2),4),12);
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1 5 9 1 5 9
## [2,] 2 6 10 2 6 10
## [3,] 3 7 11 3 7 11
## [4,] 4 8 12 4 8 12
## [1] 12
## [,1] [,2]
## [1,] 4 3
## [2,] 4 6
## [1] TRUE TRUE
printAndTestAndSliceIdentical(matrix(rep(1:12,2),4),5:8);
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 1 5 9 1 5 9
## [2,] 2 6 10 2
