Skip to main content

list manipulation - Building matrices by attaching vectors (columns) and matrices



Having the need to attach a column to a matrix or to join matrices to make longer rows is an operation that I use very frequently and I find the Join function ideal for these cases.


m1 = {{10, 11, 12}, {21, 22, 23}};
m2 = {100, 101};

(* Join matrices to make longer rows: *)
Join[m1, m1, 2]
(* --> {{10, 11, 12, 10, 11, 12}, {21, 22, 23, 21, 22, 23}} *)

(* Attach a column to a matrix *)
Join[m1, List /@ m2, 2]

(* --> {{10, 11, 12, 100}, {21, 22, 23, 101}} *)

(* Join two columns to make a matrix *)
Join[List /@ m2, List /@ m2, 2]
(* --> {{100, 100}, {101, 101}} *)

However, I wanted to define my own function that would simplify the notation needed to reach my goal:


columnAttach[a1_List, a2_List] := 
Join[If[VectorQ[a1], List /@ a1, a1],
If[VectorQ[a2], List /@ a2, a2], 2]


columnAttach[m1, m1]
(* --> {{10, 11, 12, 10, 11, 12}, {21, 22, 23, 21, 22, 23}} *)
columnAttach[m1, m2]
(* --> {{10, 11, 12, 100}, {21, 22, 23, 101}} *)
columnAttach[m2, m2]
(* --> {{100, 100}, {101, 101}} *)

This works as expected, but I would like to generalize it a bit. For instance, Join can take a list of vectors/matrices of any length:


Join[m1, m1, List /@ m2, List /@ m2, 2]

(* --> {{10, 11, 12, 10, 11, 12, 100, 100},
{21, 22, 23, 21, 22, 23, 101, 101}} *)

How can I adapt my columnAttach function to achieve the same flexibility?



Answer



One possibility:


columnAttach[ak__List] := Join[##, 2] & @@ Replace[{ak}, v_?VectorQ :> List /@ v, 1]

columnAttach[{{10, 11, 12}, {21, 22, 23}}, {100, 101}, {{10, 11, 12}, {21, 22, 23}},
{100, 101}, {100, 101}]

{{10, 11, 12, 100, 10, 11, 12, 100, 100},
{21, 22, 23, 101, 21, 22, 23, 101, 101}}



Alternatively:


columnAttach[ak__List] := ArrayFlatten[{Replace[{ak}, v_?VectorQ :> List /@ v, 1]}]

Comments

Popular posts from this blog

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

list manipulation - Selecting multiple columns from a matrix?

Sample data: data = { {{2013, 1, 1}, 24.13, 167.67, 231.82}, {{2013, 1, 2}, 32.15, 170.92, 225.99}, {{2013, 1, 3}, 35.43, 172.68, 221.67}, {{2013, 1, 4}, 36.73, 173.05, 218.32}, {{2013, 1, 5}, 58.19, 165.96, 197.05}, {{2013, 1, 6}, 69.99, 163.50, 187.52}, {{2013, 1, 7}, 71.37, 154.21, 175.58}, {{2013, 1, 8}, 72.51, 149.66, 163.25}}; I want a DateListPlot with three graphs, so for a matrix formed by columns 1 and 2, one for columns 1 and 3, and 1 for columns 1 and 4. At the moment I'm using this code: data2 = Transpose[{data[[All, 1]], data[[All, 2]]}]; data3 = Transpose[{data[[All, 1]], data[[All, 3]]}]; data4 = Transpose[{data[[All, 1]], data[[All, 4]]}]; DateListPlot[{data2, data3, data4}, Joined -> True, Filling -> {3 -> {1}}] but I have a hunch that this can be done more efficiently. I don't like the Transpose s in particular. Any ideas? edit (for extra credit) What if I need to multiply the second column by 2, which in my solution is simp...