Recenty,I encounter a problem described as below:
I have a table that owns many boxes,and each box has a sequence like 1,2,3,4,etc.In addition,every box has a value.
Now I want to make the value of a box become the average of the values of boxes that arounding it.
For example,
the value of box 1become the average ofthe values of box 2,11,12,
the value of box 11become the average ofthe values of box 1,2,12,22,21
the value of box 14become the average ofthe values of box 3,4,5,13,15,23,24,25
Grid[Reverse@Partition[Range[80], 10], Frame -> All]
sequenceValue = Thread@List[Range[80], RandomInteger[{0, 1}, 80]];
Reverse@Partition[sequenceValue, 10] // Grid[#, Frame -> All] &
My trial
Extract the sequence of the boundary of table
ExtractBoundarySequence[length_, width_] := Block[
{bottomData, topData, leftData, rightData, cornerData},
bottomData = Range[2, length - 1];
topData = Range[2 + (width - 1) length, width*length - 1];
leftData = Range[1 + length, 1 + (width - 2) length, length];
rightData = Range[2 length, (width - 1) length, length];
cornerData = {1, length, 1 + (width - 1) length, width*length};
List[cornerData, bottomData, topData, leftData, rightData]
]
Extract the sequence of the innerior of table
ExtractInteriorSequence[length_, width_] := Block[
{},
DeleteCases[
Flatten@Table[{# - 1, #, # + 1} + i *length, {i, -1, 1}], #] & /@
Flatten@Table[Range[2 + length, 2 length - 1]+(i - 1)length , {i, 1, width - 2}]
]
Caculate the value of the boundary of table
CalculateBoundaryValue[SequenceValue_, length_, width_] := Block[
{corner, bottom, top, left, right,
cornerSequence, bottomSequence, topSequence, leftSequence, rightSequence,
value1, value2},
{corner, bottom, top, left, right} =ExtractBoundarySequence[length, width];
bottomSequence = DeleteCases[
Flatten@Table[{# - 1, #, # + 1} + i *length, {i, 0, 1}], #] & /@bottom;
topSequence = DeleteCases[
Flatten@Table[{# - 1, #, # + 1} + i *length, {i, -1, 0}], #] & /@top;
leftSequence = DeleteCases[
Flatten@Table[{#, # + 1} + i *length, {i, -1, 1}], #] & /@ left;
rightSequence = DeleteCases[
Flatten@Table[{# - 1, #} + i *length, {i, -1, 1}], #] & /@ right;
value1 =
Mean /@ (Flatten[
Map[Part[SequenceValue[[All, 2]], #] &,
{bottomSequence, topSequence, leftSequence,
rightSequence}, {2}], 1]);
cornerSequence =
{
DeleteCases[
Flatten@Table[{#, # + 1} + i*length, {i, 0, 1}], #] &[corner[[1]]],
DeleteCases[
Flatten@Table[{# - 1, #} + i *length, {i, 0, 1}], #] &[corner[[2]]],
DeleteCases[
Flatten@Table[{#, # + 1} + i *length, {i, -1, 0}], #] &[corner[[3]]],
DeleteCases[
Flatten@Table[{# - 1, #} + i *length, {i, -1, 0}], #] &[corner[[4]]]
};
value2 =
Mean /@ (Part[SequenceValue[[All, 2]], #] & /@ cornerSequence);
Thread@List[Flatten@{corner, bottom, top, left, right}, Join[value2, value1]]
]
Caculate the value of the innerior of table
CalculateInteriorValue[SequenceValue_, length_, width_] := Block[
{interiorSequence, interiorNumber, value},
interiorSequence =
ExtractInteriorSequence[length, width];
interiorNumber =
Flatten@Table[Range[2 + length, 2 length - 1]+(i - 1)length, {i, 1, width - 2}];
value =
Mean /@ ((Part[SequenceValue[[All, 2]], #] &) /@ interiorSequence);
Thread@List[interiorNumber, value]
]
Final sequence-v-alue
NewSequenceValue[SequenceValue_, length_, width_] := Block[
{NewBoundaryData, NewInteriorData},
NewBoundaryData =
CalculateBoundaryValue[SequenceValue, length, width];
NewInteriorData =
CalculateInteriorValue[SequenceValue, length, width];
SortBy[Join[NewBoundaryData, NewInteriorData], First]
]
Using my function:
Reverse@Partition[NewSequenceValue[sequenceValue, 10, 8], 10] //Grid[#, Frame -> All] &
and it can achieve the result.
However, I think my method is a little tedious, so my question: is there a better algorithm (method) to solve my problem?
0or1) to all boxes and you are done. – Artes Jul 18 '14 at 08:12