Orsdxy

Is there a way to display matrices in a shorter form similar to Short or Shallow?

I find that I very often want to inspect the initial and final rows and columns of matrices just to make sure I didn't do something completely silly when generating it. For matrices larger than the truncation size (say Partition[Range[10^6], 1000], Mathematica outputs (...1...) in a box with the options "show less", "show more", "show all", and "set size limit...".

I don't know if "show more" is supposed to do something similar to what I want, but clicking it doesn't do anything. I also don't really want to see the entire matrix. I'd like functionality similar to what Short does for 1D lists (i.e. Range[10^6]//Short produces something like:

{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,<<999966>>,999984,999985,999986,999987,999988,999989,999990,999991,999992,999993,999994,999995,999996,999997,999998,999999,1000000}

Ideally, I'd like something nearly as easy to read as the TableForm or MatrixForm of the full matrix, just with fewer lines. I realize I could do something like:

matrix[[Flatten[{Range[10], Range[-10, -1]}], Flatten[{Range[10], Range[-10, -1]}]]]

each time, but that seems tedious.

I haven't seen anything come up in my Google and MMA.SE searches, so perhaps this isn't a problem other people worry about. I've created my own code to deal with this in a way that's pleasing to my eye, so I'll post the code as an answer in case it helps anyone else. However, if anyone else has a better or more robust way please post an answer and I'll be glad to accept it!

Here is my answer:

myshallow[mat_List, dims_: {20, 20}] :=

 Module[{matrix, rows, cols, matrows, matcols, splitrow, splitcol},

  If[! And @@ IntegerQ /@ dims, 

   Return[HoldForm[myshallow[mat, dims]]]];

  If[Length[Dimensions[mat]] == 1, matrix = {mat}, matrix = mat];

  Switch[

   Length[dims],

   0,

   rows = dims; cols = 20,

   1,

   cols = dims[[1]]; rows = 20,

   2,

   {rows, cols} = dims

   ];

  {matrows, matcols} = Dimensions[matrix][[;; 2]];

  {splitrow, splitcol} = {Ceiling[rows/2], Ceiling[cols/2]};

  Which[

   matrows <= rows [And] matcols <= cols,

   Grid[

    matrix,

    Alignment -> {Center, Center}],

   matrows <= rows [And] matcols > cols,

   Grid[

    Table[

     Which[

      row == 1 [And] col == splitcol + 1,

      Skeleton[matcols - cols],

      row > 1 [And] col == splitcol + 1,

      SpanFromAbove,

      col <= splitcol,

      matrix[[row, col]],

      col >= splitcol + 2,

      matrix[[row, col - (cols + 2)]]],

     {row, matrows}, {col, cols + 1}],

    Alignment -> {Center, Center}],

   matrows > rows [And] matcols <= cols,

   Grid[

    Table[

     Which[

      row == splitrow + 1 [And] col == 1,

      Skeleton[matrows - rows],

      row == splitrow + 1 [And] col > 1,

      SpanFromLeft,

      row <= splitrow,

      matrix[[row, col]],

      row >= splitrow + 2,

      matrix[[row - (rows + 2), col]]],

     {row, rows + 1}, {col, matcols}],

    Alignment -> {Center, Center}],

   matrows > rows [And] matcols > cols,

   Grid[

    Table[

     Which[

      row <= splitrow [And] col <= splitcol,

      matrix[[row, col]],

      row == 1 [And] col == splitcol + 1,

      Skeleton[matcols - cols],

      row <= splitrow [And] col == splitcol + 1,

      SpanFromAbove,

      row <= splitrow [And] col >= splitcol + 2,

      matrix[[row, col - (cols + 2)]],

      row == splitrow + 1 [And] col == 1,

      Skeleton[matrows - rows],

      row == splitrow + 1 [And] col <= splitcol,

      SpanFromLeft,

      row == splitrow + 1 [And] col == splitcol + 1,

      "",

      row == splitrow + 1 [And] col == splitcol + 2,

      Skeleton[matrows - rows],

      row == splitrow + 1 [And] col > splitcol + 2,

      SpanFromLeft,

      row >= splitrow + 2 [And] col <= splitcol,

      matrix[[row - (rows + 2), col]],

      row == splitrow + 2 [And] col == splitcol + 1,

      Skeleton[matcols - cols],

      row > splitrow + 2 [And] col == splitcol + 1,

      SpanFromAbove,

      row >= splitrow + 2 [And] col >= splitcol + 2,

      matrix[[row - (rows + 2), col - (cols + 2)]]],

     {row, rows + 1}, {col, cols + 1}],

    Alignment -> {Center, Center}]

   ]

  ]

Essentially, I take any 1D or higher list followed by an optional number of dimensions. Based on other Mathematica functions, if you input 5 for the dimensions it specifies the number of rows and {5} specifies 5 columns. My plan is to place it in $UserBaseDirectory/Kernel/init.m to make it available for every session.

With the following test cases:

matrixhuge = Partition[Range[5*10^6], 1000];

matrixsmall = Partition[Range[25], 5];

matrixwide = Partition[Range[1000], 100];

matrixlong = Partition[Range[1000], 2];

matrixhuge // myshallow

matrixsmall // myshallow

matrixwide // myshallow

matrixlong // myshallow

I get the following:

Short/@Partition[Range[10^6], 1000]



Shallow/@Partition[Range[10^6], 1000]