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

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

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

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

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

$$\left( \begin{array}{ccccccc} \text{H1} & 0 & 0 & \text{H2} & 0 & 0 & \text{H3} \\ \text{C1} & \text{C2} & \text{C3} & \text{D1} & \text{D2} & \text{D3} & \text{E1} \\ 1 & 2 & 3 & 0 & 0 & 0 & 0 \\ 0 & 4 & 0 & 5 & 6 & 0 & 0 \\ 7 & 0 & 0 & 0 & 8 & 9 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 10 & 11 & 0 & 12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \end{array} \right)$$
• Thanks! could the values H1H2H3 in the head be picked from the original values in lstHead other than generated by codes? – Jerry Nov 28 '18 at 2:55