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Building a sparse array from given lists


Given some lists


lstRow1 = {{"C1", "C2", "C3"}, {1, 2, 3}};
lstRow2 = {{"C2", "D1", "D2"}, {4, 5, 6}};
lstRow3 = {{"C1", "D2", "D3"}, {7, 8, 9}};
lstRow4 = {{}, {}};
lstRow5 = {{"D1", "D2", "E1"}, {10, 11, 12}};
lstRow6 = {{}, {}};

lstHead = {{"C1", "H1"}, {"C2", "H1"}, {"C3", "H1"}, {"D1", 

    "H2"}, {"D2", "H2"}, {"D3", "H2"}, {"E1", "H3"}};

how to build a sparse arrary like this:


lstSparse = {
   {"H1", "0", "0", "H2", "0", "0", "H3"},
   {"C1", "C2", "C3", "D1", "D2", "D3", "E1"}, {1, 2, 3, 0, 0, 0, 
    0}, {0, 4, 0, 5, 6, 0, 0}, {7, 0, 0, 0, 8, 9, 0}, {0, 0, 0, 0, 0, 
    0, 0}, {0, 0, 0, 10, 11, 0, 12}, {0, 0, 0, 0, 0, 0, 0}};

or ZEROs could be replaced by blank string, to be like this. $$\left( \begin{array}{ccccccc} \text{H1} & \text{0} & \text{0} & \text{H2} & \text{0} & \text{0} & \text{H3} \\ \text{C1} & \text{C2} & \text{C3} & \text{D1} & \text{D2} & \text{D3} & \text{E1} \\ 1 & 2 & 3 & 0 & 0 & 0 & 0 \\ 0 & 4 & 0 & 5 & 6 & 0 & 0 \\ 7 & 0 & 0 & 0 & 8 & 9 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 10 & 11 & 0 & 12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right) \to \left( \begin{array}{ccccccc} \text{H1} & \text{} & \text{} & \text{H2} & \text{} & \text{} & \text{H3} \\ \text{C1} & \text{C2} & \text{C3} & \text{D1} & \text{D2} & \text{D3} & \text{E1} \\ 1 & 2 & 3 & \text{} & \text{} & \text{} & \text{} \\ \text{} & 4 & \text{} & 5 & 6 & \text{} & \text{} \\ 7 & \text{} & \text{} & \text{} & 8 & 9 & \text{} \\ \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ \text{} & \text{} & \text{} & 10 & 11 & \text{} & 12 \\ \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ \end{array} \right)$$




Answer



rows = {lstRow1, lstRow2, lstRow3, lstRow4, lstRow5, lstRow6};
ac = ArrayComponents[rows[[All, 1]]];
sa = SparseArray[Join @@ (Thread /@ Thread[MapIndexed[{#2[[1]], #} &, ac, {2}] -> 
        rows[[All, 2]]]), {Length@rows, Max@ac}];

sa // MatrixForm // TeXForm


$\left( \begin{array}{ccccccc} 1 & 2 & 3 & 0 & 0 & 0 & 0 \\ 0 & 4 & 0 & 5 & 6 & 0 & 0 \\ 7 & 0 & 0 & 0 & 8 & 9 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 10 & 11 & 0 & 12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$




Alternatively, use "" as the background element


sa2 = SparseArray[Join @@ (Thread /@ Thread[MapIndexed[{#2[[1]], #} &, ac, {2}] -> 
            rows[[All, 2]]]), {Length@rows, Max@ac}, ""];
sa2 // MatrixForm // TeXForm


$\left( \begin{array}{ccccccc} 1 & 2 & 3 & \text{} & \text{} & \text{} & \text{} \\ \text{} & 4 & \text{} & 5 & 6 & \text{} & \text{} \\ 7 & \text{} & \text{} & \text{} & 8 & 9 & \text{} \\ \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ \text{} & \text{} & \text{} & 10 & 11 & \text{} & 12 \\ \text{} & \text{} & \text{} & \text{} & \text{} & \text{} & \text{} \\ \end{array} \right)$



headers = Join @@@ Transpose[PadRight /@ MapIndexed[{{"H" <> ToString[#2[[1]]]}, #} &, 

     GatherBy[DeleteDuplicates[Join @@ rows[[All, 1]]], StringTake[#, 1] &]]]


{{0, "H1", 0, 0, "H2", 0, 0, "H3"}, {0, "C1", "C2", "C3", "D1", "D2", "D3", "E1"}}



Join[headers, sa] // TeXForm


$\left( \begin{array}{ccccccc} \text{H1} & 0 & 0 & \text{H2} & 0 & 0 & \text{H3} \\ \text{C1} & \text{C2} & \text{C3} & \text{D1} & \text{D2} & \text{D3} & \text{E1} \\ 1 & 2 & 3 & 0 & 0 & 0 & 0 \\ 0 & 4 & 0 & 5 & 6 & 0 & 0 \\ 7 & 0 & 0 & 0 & 8 & 9 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 10 & 11 & 0 & 12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$




Update: Obtaining header rows from lstHead:


headers2 = {SequenceReplace[#[[1]], {b : (a_String) ..} :> 
     Sequence[a, ## & @@ ConstantArray[0, Length[{b}] - 1]]], #[[2]]} &@
  Reverse[Transpose[lstHead]]


{{"H1", 0, 0, "H2", 0, 0, "H3"}, {"C1", "C2", "C3", "D1", "D2", "D3", "E1"}}



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