How to delete certain elements from a list?

Question

consider a list as follows:

list = {{{{{{{1, 1}, {1, 1}}, 0.}, {{{1, 1}, {1, 2}}, 
  29.7586}}, {{{{1, 1}, {2, 1}}, 0.165637}, {{{1, 1}, {2, 2}}, 
  37.2042}}}, {{{{{1, 2}, {1, 1}}, 29.7586}, {{{1, 2}, {1, 2}}, 
  0.}}, {{{{1, 2}, {2, 1}}, 29.7492}, {{{1, 2}, {2, 2}}, 
  32.2175}}}}, {{{{{{2, 1}, {1, 1}}, 0.165637}, {{{2, 1}, {1, 2}},
   29.7492}}, {{{{2, 1}, {2, 1}}, 0.}, {{{2, 1}, {2, 2}}, 
  37.2055}}}, {{{{{2, 2}, {1, 1}}, 37.2042}, {{{2, 2}, {1, 2}}, 
  32.2175}}, {{{{2, 2}, {2, 1}}, 37.2055}, {{{2, 2}, {2, 2}}, 
  0.}}}}};

I want to delete the elements {{{1, 1}, {1, 1}}, 0.}, {{{1, 2}, {1, 2}}, 0.},{{{2, 1}, {2, 1}}, 0.} and {{{2, 2}, {2, 2}}, 0.}

How can I do this?

Edit 1

Let me breakdown the problem. Consider,

val = {{0., 29.7586, 0.165637, 37.2042}, {29.7586, 0., 29.7492, 
    32.2175}, {0.165637, 29.7492, 0., 37.2055}, {37.2042, 32.2175, 
    37.2055, 0.}};
coordpair = 
  Table[{{i, j}, {k, l}}, {i, 1, 2, 1}, {j, 1, 2, 1}, {k, 1, 2, 
    1}, {l, 1, 2, 1}];

I have constructed the list by combining val and coordpair. Is it possible to delete the cases in coordpair where {i, j} == {k, l}?

Answer 1

DeleteCases[list, {{{i_, j_}, {i_, j_}}, _}, Infinity] 
Pick[list, Map[Unequal @@ First[#] &, list, {-4}]] 
Pick[list, Map[#[[1, 1]] =!= #[[1, 2]] &, list, {-4}]] 
Delete[list, Position[list, {{a_, a_}, _}, {4}]]

all give

{{{{{{{1, 1}, {1, 2}}, 29.7586}}, {{{{1, 1}, {2, 1}}, 0.165637},
{{{1, 1}, {2, 2}}, 37.2042}}}, {{{{{1, 2}, {1, 1}}, 29.7586}},
{{{{1, 2}, {2, 1}}, 29.7492}, {{{1, 2}, {2, 2}}, 32.2175}}}},
{{{{{{2, 1}, {1, 1}}, 0.165637}, {{{2, 1}, {1, 2}}, 29.7492}},
{{{{2, 1}, {2, 2}}, 37.2055}}}, {{{{{2, 2}, {1, 1}}, 37.2042},
{{{2, 2}, {1, 2}}, 32.2175}}, {{{{2, 2}, {2, 1}}, 37.2055}}}}}

And

to delete the cases in coordpair where {i, j} == {k, l}

DeleteCases[coordpair, {{i_, j_}, {i_, j_}}, Infinity] 
Pick[coordpair, Map[Unequal @@ # &, coordpair, {-3}]]  
Pick[coordpair, Map[#[[1]] =!= #[[2]] &, coordpair, {-3}]] 
Delete[coordpair, Position[coordpair, {a_, a_}, {4}]]

{{{{{{1, 1}, {1, 2}}}, {{{1, 1}, {2, 1}}, {{1, 1}, {2, 2}}}},
{{{{1, 2}, {1, 1}}}, {{{1, 2}, {2, 1}}, {{1, 2}, {2, 2}}}}},
{{{{{2, 1}, {1, 1}}, {{2, 1}, {1, 2}}}, {{{2, 1}, {2, 2}}}},
{{{{2, 2}, {1, 1}}, {{2, 2}, {1, 2}}}, {{{2, 2}, {2, 1}}}}}}

Answer 2

list = {{{{{{{1, 1}, {1, 1}}, 0.}, {{{1, 1}, {1, 2}}, 
       29.7586}}, {{{{1, 1}, {2, 1}}, 0.165637}, {{{1, 1}, {2, 2}}, 
       37.2042}}}, {{{{{1, 2}, {1, 1}}, 29.7586}, {{{1, 2}, {1, 2}}, 
       0.}}, {{{{1, 2}, {2, 1}}, 29.7492}, {{{1, 2}, {2, 2}}, 
       32.2175}}}}, {{{{{{2, 1}, {1, 1}}, 
       0.165637}, {{{2, 1}, {1, 2}}, 29.7492}}, {{{{2, 1}, {2, 1}}, 
       0.}, {{{2, 1}, {2, 2}}, 37.2055}}}, {{{{{2, 2}, {1, 1}}, 
       37.2042}, {{{2, 2}, {1, 2}}, 32.2175}}, {{{{2, 2}, {2, 1}}, 
       37.2055}, {{{2, 2}, {2, 2}}, 0.}}}}};

list2 = DeleteCases[list, _?(#[[1, 1]] == #[[1, 2]] &), {4}]

(* {{{{{{{1, 1}, {1, 2}}, 29.7586}}, {{{{1, 1}, {2, 1}}, 
     0.165637}, {{{1, 1}, {2, 2}}, 37.2042}}}, {{{{{1, 2}, {1, 1}}, 
     29.7586}}, {{{{1, 2}, {2, 1}}, 29.7492}, {{{1, 2}, {2, 2}}, 
     32.2175}}}}, {{{{{{2, 1}, {1, 1}}, 0.165637}, {{{2, 1}, {1, 2}}, 
     29.7492}}, {{{{2, 1}, {2, 2}}, 37.2055}}}, {{{{{2, 2}, {1, 1}}, 
     37.2042}, {{{2, 2}, {1, 2}}, 32.2175}}, {{{{2, 2}, {2, 1}}, 
     37.2055}}}}} *)

Complement[Flatten[list, 3], Flatten[list2, 3]]

(* {{{{1, 1}, {1, 1}}, 0.}, {{{1, 2}, {1, 2}}, 0.}, {{{2, 1}, {2, 1}}, 
  0.}, {{{2, 2}, {2, 2}}, 0.}} *)

Answer 3

Assuming you constructed it similarly to this

list = Join[
        ArrayReshape[coordpair, Insert[Dimensions[coordpair], 1, 5]],
        ArrayReshape[val, Append[Dimensions[coordpair][[;; 4]], 1]], 5]

Then the deletion is:

MapIndexed[If[#2[[1]] =!= #2[[3]] || #2[[2]] =!= #2[[4]], #, Nothing] &, list, {4}]