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I wanted to write myself a function that makes it possible to Insert several rows into one list.

matrix = Table[i*(j + 2), {i, 3}, {j, 3}];
vector1 = Range[10, 12];
vector2 = Range[20, 22];

This one worked perfectly fine:

Do[matrix = Insert[matrix, {vector1, vector2}[[i]], 1], {i, 2}];

Then I started straightforward with:

InsertRows[vectors_List, matrix_List, position_Integer] :=
Do[
matrix = Insert[matrix, vectors[[i]], position]
, {i, Length@vectors}]

This does not work. After little search I found that I have to force Do[] to return some value. But the same search also highlighted that it is not recommended to use Return[].

So here are my questions:

  1. How to define a function that can insert several rows. If there is an approach without a loop, I was happy to see it.
  2. How to properly define this function with the Do[] Loop.
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  • 1
    $\begingroup$ What error do you get with your version of InsertRows when I copy and paste it into mathematica for vectors_list and matrix_list, "list" I get lower case l's $\endgroup$ – image_doctor Jun 12 '15 at 13:36
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    $\begingroup$ I changed _list to _List. Sorry for the typo. $\endgroup$ – mcocdawc Jun 12 '15 at 14:06
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the main issue is that you cannot (readily*) modify the actual argument to a function Try this:

 InsertRows[vectors_List, matrix0_List,position_Integer] := 
   Module[{matrix},
       matrix = matrix0;
       Do[matrix = Insert[matrix, vectors[[i]], position], {i, 
           Length@vectors}]; matrix]

usage: matrix = InsertRows[{vector1, vector2}, matrix, 1]

*of course it can be done using HoldFirst but its best avoided: (note no _List on matrix )

 InsertRows[matrix_, vectors_List, position_Integer] := Module[{},
      Do[matrix = Insert[matrix, vectors[[i]], position], {i, 
         Length@vectors}]]
 SetAttributes[InsertRows, HoldFirst]

usage: InsertRows[matrix,{vector1, vector2}, 1] modifies the arg and returns Null.

Of course in either case the Do loop is best replaced per @image_doctor's answer -- another variant is Join[matrix[[;; position - 1]], vectors, matrix[[position ;;]]]

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  • $\begingroup$ Thank you very much for both your answers. I gave image_doctor the Question Solved sign since you already have more reputation ;). $\endgroup$ – mcocdawc Jun 12 '15 at 14:43
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Here are a couple of approaches without using a loop, but utilising Flatten and FlattenAt:

FlattenAt[Insert[matrix, {vector1, vector2}, 2], 2]

{{3, 4, 5}, {10, 11, 12}, {20, 21, 22}, {6, 8, 10}, {9, 12, 15}}

ir[vecs_, matrix_, pos_] := Flatten[{matrix[[1 ;; pos - 1]], vecs, matrix[[pos ;; -1]]}, 1]

ir[{vector1, vector2}, matrix, 2]

{{3, 4, 5}, {10, 11, 12}, {20, 21, 22}, {6, 8, 10}, {9, 12, 15}}

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