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To best explain my problem, I will take the following example:

Consider the following matrix :

A = {{1, 2, 3, 4, ""}, {"", 2, 3, 4, ""}, {"", "", 3, 4, ""}, {"", "", "", 4, 5}}

I designed the following two algorithms :

ProjVt[x_, y_, pat_] :=
     Block[
                {X = x, Y = y, Grid11, Grid21, Resvf1},

                Grid11 = PosGrid[X, pat];

                Grid21 = ConstantArray["", 10000];

                Table[
                      Table[
                            Grid21[[ Grid11[[i, j]] ]] = X[[i, Grid11[[i, j]] [[1]]  ]],
                            {j, 1, Length[Grid11[[i]]], 1}
                           ],
                            {i, 1, Length[X], 1}
                    ];

                 Resvf1 =  Grid21[[1 ;; Length[Y]]]

            ];

and

ProjHt[x_, y_, pat_] :=
Block[
               {X = x, Y = y, Grid12, Grid22, Resvf2},

                Grid12 = PosGrid[X, pat];

                Grid22 = ConstantArray["", 10000];

                Table[
                       Grid22[[i]] = X[[ i , Grid12[[i, 1, 1]] ;; Grid12[[i, -1, 1]] ]],
                       {i, 1, Length[X], 1}
                     ];

                Resvf2 = DeleteCases[Grid22, ""]

            ];

The results provided by ProjVt and ProjHt in the case of matrix A are :

Resvf1 = {1,2,3,4,5}
Resvf2 = {{1, 2, 3, 4}, {2, 3, 4}, {3, 4}, {4, 5}}


Best known optimization :

ProjHt[X_]:= Map[Select[#, NumberQ] &, X]

ProjVt[X_]:=
Block[
      {step1, Res},
       step1 = Tranpose[x];
       Res = ProjHt[step1][[All,1]]
     ]

.

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5
  • $\begingroup$ DeleteDuplicates@Cases[A, _?NumberQ, {2}] and as you have already written: Map[Select[#, NumberQ] &, A]? $\endgroup$
    – Öskå
    Commented May 14, 2014 at 17:30
  • $\begingroup$ Hey Doedalos. Note that I fixed Tr(X) to Tr[X]. Please try making code blocks using the shortcut control/command + k, rather than using ` (backtick) for large code blocks. $\endgroup$
    – Jacob Akkerboom
    Commented May 14, 2014 at 18:49
  • $\begingroup$ @Doedalos Well, replace A with X? :) And then ProjVtalt1[A] :) So you would need ProjVtalt1[mat_]:=DeleteDuplicates[Cases[mat,_?NumberQ,{2}]] $\endgroup$
    – Öskå
    Commented May 17, 2014 at 9:53
  • $\begingroup$ @Doedalos If you wish you can answer your own question :) That would be great :) $\endgroup$
    – Öskå
    Commented May 17, 2014 at 11:21
  • $\begingroup$ @Doedalos Please answer your own question with the informations provided in the comments. $\endgroup$
    – Öskå
    Commented May 17, 2014 at 16:16

2 Answers 2

Reset to default
2
$\begingroup$ 
A /. "" -> Sequence[]

{{1, 2, 3, 4}, {2, 3, 4}, {3, 4}, {4, 5}}

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0
$\begingroup$

Best known optimization :

A = {{1, 2, 3, 4, ""}, {"", 2, 3, 4, ""}, {"", "", 3, 4, ""}, {"", "","", 4, 5}}

ProjHt[X_]:= Map[Select[#, NumberQ] &, X]

ProjVt[X_]:=
Block[
      {step1, Res},
       step1 = Transpose[x];
       Res = ProjHt[step1][[All,1]]
     ]

ProjHt[A]

{{1, 2, 3, 4}, {2, 3, 4}, {3, 4}, {4, 5}}
Improve this answer
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