Randy,
Raul was pointing out that assuming 4&$. refers to all 1s is not enough.
This is because in a sparse array, not every axis has
to be sparse. Look at Roger's first two examples:
(2;0)$.4 5$1
0 | 1 1 1 1 1
1 | 1 1 1 1 1
2 | 1 1 1 1 1
3 | 1 1 1 1 1
(2;0)$.4 7$1
0 | 1 1 1 1 1 1 1
1 | 1 1 1 1 1 1 1
2 | 1 1 1 1 1 1 1
3 | 1 1 1 1 1 1 1
The 4&$. are exactly the same, and both refer to all 1s, but the arrays are
different. So the "all ones" assumption is
insufficient: you'd have to know the shape of the original array, and which
axes were specified to be sparse.
But, if I understand you correctly, you're suggesting Roger assume 4&$.
refers to all SCALAR 1s; i.e., 4&$.^:_1 should
produce a two dimensional boolean array, and both axes should be sparse.
Maybe that assumption is too restrictive to be useful, especially given that
1&$. already provides a more general mechanism?
In any case, Raul's post was relevant because:
RM> #(,m)-.0 1
RM> 0
proves that the array contains only 0s and 1s, and
RM> 3 $.m
RM> 0
proves that the sparse element is zero. So if the sparse element is 0, and the
array only contains 0 and 1, then 4&$. only
refers to 1s [A].
Raul was demonstrating that even if you know that, you still can't recover s
:
test =: ('passed'"_) @: (verb define) :: ('failed'"_)
assert. 0 -: #(,y)-.0 1
assert. 84 -: +/,y
assert. 105 -: */$y
assert. 0 -: 3 $. y
assert. (i.4 1) -: 4 $. y
)
m0 =. 1 (i.4) } 1 $. (5 21 ) ; (,0) ; 0
m1 =. 1 (i.4) } 1 $. (5 3 7) ; (,0) ; 0
test m0
passed
test m1
passed
m0 -: m1
0
The arrays are different (in shape), yet 4&$. is the same, and refers to all
1s in each case.
-Dan
[A] Actually, these two tests don't prove that 4&$. refers to all 1s, c.f.
Roger's s4 :
s4
0 | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
1 | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
2 | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
3 | 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ...
----------------------------------------------------------------------
For information about J forums see http://www.jsoftware.com/forums.htm
