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edited Aug 1, 2017 at 15:28

kglr

403.4k
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Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer - updated:

ClearAll[aroundF, replaceF] aroundF[m_, t_] := JoinDeleteDuplicates[Join @@ Function[{k}, DeleteDuplicates[Clip[#Clip[#, {1, #2}] & @@@ Transpose[#] & /@ Thread[Transpose[{k + #, Dimensions[m]}] & /@  Tuples[{-1, 0, 1}, {2}], Dimensions[m]}, List,]] 1]]]/@ Position[m, t]t]]  replaceF[old_: 0, new_: 1][m_, t_] := MapAt[If[#===old, new, #] &, m, Join@@aroundF[maroundF[m,t]] replaceF[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

replaceF[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer - updated:

ClearAll[aroundF, replaceF] aroundF[m_, t_] := Join @@ Function[{k}, DeleteDuplicates[Clip[#, {1, #2}] & @@@ Transpose[#] & /@ Thread[{k + # & /@ Tuples[{-1, 0, 1}, {2}], Dimensions[m]}, List, 1]]]/@ Position[m, t] replaceF[old_: 0, new_: 1][m_, t_] := MapAt[If[#===old, new, #] &, m, Join@@aroundF[m,t]] replaceF[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

replaceF[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer - updated:

ClearAll[aroundF, replaceF] aroundF[m_, t_] := DeleteDuplicates[Join @@ Function[{k}, Clip[#, {1, #2}] & @@@ Transpose[{k + #, Dimensions[m]}] & /@  Tuples[{-1, 0, 1}, {2}]] /@ Position[m, t]]  replaceF[old_: 0, new_: 1][m_, t_] := MapAt[If[#===old, new, #] &, m, aroundF[m,t]] replaceF[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

replaceF[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

deleted 61 characters in body

Source Link

edited Aug 1, 2017 at 14:35

kglr

403.4k
18
501
959

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer - updated:

ClearAll[positionsFClearAll[aroundF, setNeighborValues]replaceF] positionsF[{r_aroundF[m_, c_}][pos_]t_] := Join @@ Function[{k},   DeleteDuplicates[Transpose[{Clip[#[[1]]DeleteDuplicates[Clip[#, {1, r#2}], Clip[#[[2]], {1,& c}]}]]@@@ &@ Transpose[#] & /@    Transpose[kThread[{k + # & /@ Tuples[{-1, 0, 1}, {2}]]]], Dimensions[m]}, List, 1]]]/@ posPosition[m, t] setNeighborValues[old_ replaceF[old_: 0, new_: 1][m_, t_] :=  MapAt[If[# === oldMapAt[If[#===old, new, #] &, m, Join @@ positionsF[Dimensions @ m][Position[mJoin@@aroundF[m, t]]]t]] setNeighborValues[][matrix0replaceF[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

setNeighborValues[0replaceF[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer:

ClearAll[positionsF, setNeighborValues] positionsF[{r_, c_}][pos_] := Function[{k},   DeleteDuplicates[Transpose[{Clip[#[[1]], {1, r}], Clip[#[[2]], {1, c}]}]] &@  Transpose[k + # & /@ Tuples[{-1, 0, 1}, {2}]]] /@ pos setNeighborValues[old_: 0, new_: 1][m_, t_] :=  MapAt[If[# === old, new, #] &, m, Join @@ positionsF[Dimensions @ m][Position[m, t]]] setNeighborValues[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

setNeighborValues[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer - updated:

ClearAll[aroundF, replaceF] aroundF[m_, t_] := Join @@ Function[{k}, DeleteDuplicates[Clip[#, {1, #2}] & @@@ Transpose[#] & /@    Thread[{k + # & /@ Tuples[{-1, 0, 1}, {2}], Dimensions[m]}, List, 1]]]/@ Position[m, t]  replaceF[old_: 0, new_: 1][m_, t_] := MapAt[If[#===old, new, #] &, m, Join@@aroundF[m,t]] replaceF[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

replaceF[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

added 241 characters in body

Source Link

edited Aug 1, 2017 at 12:53

kglr

403.4k
18
501
959

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer:

ClearAll[positionsF, setNeighborValues] positionsF[{r_, c_}][pos_] := Function[{k}, DeleteDuplicates[Transpose[{Clip[#[[1]], {1, r}], Clip[#[[2]], {1, c}]}]] &@ Transpose[k + # & /@ Tuples[{-1, 0, 1}, {2}]]] /@ pos setNeighborValues[old_: 0, new_: 1][m_, t_] := MapAt[If[# === old, new, #] &, m, Join @@ positionsF[Dimensions @ m][Position[m, t]]] setNeighborValues[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

setNeighborValues[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

Original answer:

ClearAll[positionsF, setNeighborValues] positionsF[{r_, c_}][pos_] := Function[{k}, DeleteDuplicates[Transpose[{Clip[#[[1]], {1, r}], Clip[#[[2]], {1, c}]}]] &@ Transpose[k + # & /@ Tuples[{-1, 0, 1}, {2}]]] /@ pos setNeighborValues[old_: 0, new_: 1][m_, t_] := MapAt[If[# === old, new, #] &, m, Join @@ positionsF[Dimensions @ m][Position[m, t]]] setNeighborValues[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

setNeighborValues[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $

Update: Re: why my version does not work

Documentation >> ReplacePart:

ReplacePart[expr, i -> new] yields an expression in which the i'th part of expr is replaced by new.

that is, it does not replace expr with the expression it yields.

So, with a small change, namely assigning the value of ReplacePart[...] to matrix0 in each step of the For loop, your version also works:

For[i = 1, i <= Length[around[-2, matrix0]], i++, If[Part[matrix0, around[-2, matrix0][[i, 1]], around[-2, matrix0][[i, 2]]] == 0, matrix0 = ReplacePart[matrix0, around[-2, matrix0][[i]] -> 1], Null]] matrix0 // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

By the way, since

ReplacePart[expr, {i, j, ...} -> new] replaces the part at position {i, j, ...}

you can use much simpler

 matrix0 = ReplacePart[matrix0, around[-2, matrix0] -> 1]

instead of using a For loop.

Original answer:

ClearAll[positionsF, setNeighborValues] positionsF[{r_, c_}][pos_] := Function[{k}, DeleteDuplicates[Transpose[{Clip[#[[1]], {1, r}], Clip[#[[2]], {1, c}]}]] &@ Transpose[k + # & /@ Tuples[{-1, 0, 1}, {2}]]] /@ pos setNeighborValues[old_: 0, new_: 1][m_, t_] := MapAt[If[# === old, new, #] &, m, Join @@ positionsF[Dimensions @ m][Position[m, t]]] setNeighborValues[][matrix0, -2] // TeXForm

$\left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right)$

setNeighborValues[0, aa][matrix0, -2] // TeXForm

$ \left( \begin{array}{cccccccccc} -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -2 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & \text{aa} & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 \\ -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 \\ \end{array} \right) $