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Optimize sorting

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Optimize _sort_general and change  accordingly sort and sortidx.
Introduce _valid_idx() to simplify teh validations of arg idx.
Add input validation to subindex().
This commit is contained in:
RonaldoCMP 2020-08-05 06:16:48 +01:00
parent e06519bbfb
commit c6b472318f
1 changed files with 53 additions and 68 deletions
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121
arrays.scad
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@ -709,40 +709,36 @@ function _sort_vectors4(arr) =
) concat( _sort_vectors4(lesser), equal, _sort_vectors4(greater) ); ) concat( _sort_vectors4(lesser), equal, _sort_vectors4(greater) );
// when idx==undef, returns the sorted array
// otherwise, returns the indices of the sorted array
function _sort_general(arr, idx=undef) = function _sort_general(arr, idx=undef) =
(len(arr)<=1) ? arr : (len(arr)<=1) ? arr :
is_undef(idx)
? _sort_scalar(arr)
: let( arrind=[for(k=[0:len(arr)-1], ark=[arr[k]]) [ k, [for (i=idx) ark[i]] ] ] )
_indexed_sort(arrind);
// given a list of pairs, return the first element of each pair of the list sorted by the second element of the pair
// the sorting is done using compare_vals()
function _indexed_sort(arrind) =
arrind==[] ? [] : len(arrind)==1? [arrind[0][0]] :
let( pivot = arrind[floor(len(arrind)/2)][1] )
let( let(
pivot = arr[floor(len(arr)/2)], lesser = [ for (entry=arrind) if (compare_vals(entry[1], pivot) <0 ) entry ],
pivotval = idx==undef? pivot : [for (i=idx) pivot[i]], equal = [ for (entry=arrind) if (compare_vals(entry[1], pivot)==0 ) entry[0] ],
compare = greater = [ for (entry=arrind) if (compare_vals(entry[1], pivot) >0 ) entry ]
is_undef(idx) ? [for(entry=arr) compare_vals(entry, pivotval) ] : )
[ for (entry = arr) concat(_indexed_sort(lesser), equal, _indexed_sort(greater));
let( val = [for (i=idx) entry[i] ] )
compare_vals(val, pivotval) ] ,
lesser = [ for (i = [0:1:len(arr)-1]) if (compare[i] < 0) arr[i] ],
equal = [ for (i = [0:1:len(arr)-1]) if (compare[i] ==0) arr[i] ],
greater = [ for (i = [0:1:len(arr)-1]) if (compare[i] > 0) arr[i] ]
)
concat(_sort_general(lesser,idx), equal, _sort_general(greater,idx));
function _sort_general(arr, idx=undef) = // returns true for valid index specifications idx in the interval [imin, imax)
(len(arr)<=1) ? arr : // note that idx can't have any value greater or EQUAL to imax
let( function _valid_idx(idx,imin,imax) =
pivot = arr[floor(len(arr)/2)], is_undef(idx)
pivotval = idx==undef? pivot : [for (i=idx) pivot[i]], || ( is_finite(idx) && idx>=imin && idx< imax )
compare = [ || ( is_list(idx) && min(idx)>=imin && max(idx)< imax )
for (entry = arr) let( || ( valid_range(idx) && idx[0]>=imin && idx[2]< imax );
val = idx==undef? entry : [for (i=idx) entry[i]],
cmp = compare_vals(val, pivotval)
) cmp
],
lesser = [ for (i = [0:1:len(arr)-1]) if (compare[i] < 0) arr[i] ],
equal = [ for (i = [0:1:len(arr)-1]) if (compare[i] ==0) arr[i] ],
greater = [ for (i = [0:1:len(arr)-1]) if (compare[i] > 0) arr[i] ]
)
concat(_sort_general(lesser,idx), equal, _sort_general(greater,idx));
// Function: sort() // Function: sort()
// Usage: // Usage:
@ -761,19 +757,21 @@ function _sort_general(arr, idx=undef) =
// sorted = sort(l); // Returns [2,3,8,9,12,16,23,34,37,45,89] // sorted = sort(l); // Returns [2,3,8,9,12,16,23,34,37,45,89]
function sort(list, idx=undef) = function sort(list, idx=undef) =
!is_list(list) || len(list)<=1 ? list : !is_list(list) || len(list)<=1 ? list :
assert( is_undef(idx) || is_finite(idx) || is_vector(idx) || is_range(idx) , "Invalid indices.") is_def(idx)
is_def(idx) ? _sort_general(list,idx) : ? assert( _valid_idx(idx,0,len(list)) , "Invalid indices.")
let(size = array_dim(list)) let( sarr = _sort_general(list,idx) )
len(size)==1 ? _sort_scalars(list) : [for(i=[0:len(sarr)-1]) list[sarr[i]] ]
len(size)==2 && size[1] <=4 : let(size = array_dim(list))
? ( len(size)==1 ? _sort_scalars(list) :
size[1]==0 ? list : len(size)==2 && size[1] <=4
size[1]==1 ? _sort_vectors1(list) : ? (
size[1]==2 ? _sort_vectors2(list) : size[1]==0 ? list :
size[1]==3 ? _sort_vectors3(list) size[1]==1 ? _sort_vectors1(list) :
/*size[1]==4*/ : _sort_vectors4(list) size[1]==2 ? _sort_vectors2(list) :
) size[1]==3 ? _sort_vectors3(list)
: _sort_general(list); /*size[1]==4*/ : _sort_vectors4(list)
)
: _sort_general(list);
// Function: sortidx() // Function: sortidx()
@ -799,13 +797,13 @@ function sort(list, idx=undef) =
// idxs3 = sortidx(lst, idx=[1,3]); // Returns: [3,0,2,1] // idxs3 = sortidx(lst, idx=[1,3]); // Returns: [3,0,2,1]
function sortidx(list, idx=undef) = function sortidx(list, idx=undef) =
assert( is_list(list) || is_string(list) , "Invalid input to sort." ) assert( is_list(list) || is_string(list) , "Invalid input to sort." )
assert( is_undef(idx) || is_finite(idx) || is_vector(idx) , "Invalid indices.") assert( _valid_idx(idx,0,len(list)) , "Invalid indices.")
list==[] ? [] : list==[] ? [] :
let( let(
size = array_dim(list), size = array_dim(list),
aug = is_undef(idx) && (len(size) == 1 || (len(size) == 2 && size[1]<=4)) aug = is_undef(idx) && (len(size) == 1 || (len(size) == 2 && size[1]<=4))
? zip(list, list_range(len(list))) ? zip(list, list_range(len(list)))
: enumerate(list,idx=idx) : 0
) )
is_undef(idx) && len(size) == 1? subindex(_sort_vectors1(aug),1) : is_undef(idx) && len(size) == 1? subindex(_sort_vectors1(aug),1) :
is_undef(idx) && len(size) == 2 && size[1] <=4 is_undef(idx) && len(size) == 2 && size[1] <=4
@ -817,27 +815,9 @@ function sortidx(list, idx=undef) =
/*size[1]==4*/ : subindex(_sort_vectors4(aug),4) /*size[1]==4*/ : subindex(_sort_vectors4(aug),4)
) )
: // general case : // general case
subindex(_sort_general(aug, idx=list_range(s=1,n=len(aug)-1)), 0); _sort_general(list,idx);
function sortidx(list, idx=undef) =
list==[] ? [] : let(
size = array_dim(list),
aug = is_undef(idx) && (len(size) == 1 || (len(size) == 2 && size[1]<=4))?
zip(list, list_range(len(list))) :
enumerate(list,idx=idx)
)
is_undef(idx) && len(size) == 1? subindex(_sort_vectors1(aug),1) :
is_undef(idx) && len(size) == 2 && size[1] <=4? (
size[1]==0? list_range(len(arr)) :
size[1]==1? subindex(_sort_vectors1(aug),1) :
size[1]==2? subindex(_sort_vectors2(aug),2) :
size[1]==3? subindex(_sort_vectors3(aug),3) :
/*size[1]==4*/ subindex(_sort_vectors4(aug),4)
) :
// general case
subindex(_sort_general(aug, idx=list_range(s=1,n=len(aug)-1)), 0);
// sort() does not accept strings but sortidx does; isn't inconsistent ? // sort() does not accept strings but sortidx does; isn't inconsistent ?
@ -911,10 +891,10 @@ function idx(list, step=1, end=-1,start=0) =
// for (p=enumerate(colors)) right(20*p[0]) color(p[1]) circle(d=10); // for (p=enumerate(colors)) right(20*p[0]) color(p[1]) circle(d=10);
function enumerate(l,idx=undef) = function enumerate(l,idx=undef) =
assert(is_list(l)||is_string(list), "Invalid input." ) assert(is_list(l)||is_string(list), "Invalid input." )
assert(is_undef(idx)||is_finite(idx)||is_vector(idx) ||is_range(idx), "Invalid index/indices." ) assert( _valid_idx(idx,0,len(l)), "Invalid index/indices." )
(idx==undef) (idx==undef)
? [for (i=[0:1:len(l)-1]) [i,l[i]]] ? [for (i=[0:1:len(l)-1]) [i,l[i]]]
: [for (i=[0:1:len(l)-1]) concat([i], [for (j=idx) l[i][j]])]; : [for (i=[0:1:len(l)-1]) [ i, for (j=idx) l[i][j]] ];
// Function: force_list() // Function: force_list()
@ -1130,8 +1110,9 @@ function add_scalar(v,s) =
// subindex(M, idx) // subindex(M, idx)
// Description: // Description:
// Extracts the entries listed in idx from each entry in M. For a matrix this means // Extracts the entries listed in idx from each entry in M. For a matrix this means
// selecting a specified set of columsn. If idx is a number the return is a vector, otherwise // selecting a specified set of columns. If idx is a number the return is a vector,
// it is a list of lists (the submatrix). // otherwise it is a list of lists (the submatrix).
// This function will return `undef` at all entry positions indexed by idx not found in the input list M.
// Arguments: // Arguments:
// M = The given list of lists. // M = The given list of lists.
// idx = The index, list of indices, or range of indices to fetch. // idx = The index, list of indices, or range of indices to fetch.
@ -1141,8 +1122,12 @@ function add_scalar(v,s) =
// subindex(M,[2]); // Returns [[3], [7], [11], [15]] // subindex(M,[2]); // Returns [[3], [7], [11], [15]]
// subindex(M,[2,1]); // Returns [[3, 2], [7, 6], [11, 10], [15, 14]] // subindex(M,[2,1]); // Returns [[3, 2], [7, 6], [11, 10], [15, 14]]
// subindex(M,[1:3]); // Returns [[2, 3, 4], [6, 7, 8], [10, 11, 12], [14, 15, 16]] // subindex(M,[1:3]); // Returns [[2, 3, 4], [6, 7, 8], [10, 11, 12], [14, 15, 16]]
// N = [ [1,2], [3], [4,5], [6,7,8] ];
// subindex(N,[0,1]); // Returns [ [1,2], [3,undef], [4,5], [6,7] ]
function subindex(M, idx) = function subindex(M, idx) =
is_num(idx) assert( is_list(M), "The input is not a list." )
assert( !is_undef(idx) && _valid_idx(idx,0,1/0), "Invalid index input." )
is_finite(idx)
? [for(row=M) row[idx]] ? [for(row=M) row[idx]]
: [for(row=M) [for(i=idx) row[i]]]; : [for(row=M) [for(i=idx) row[i]]];