Flatten a four dimensional array into a matrix

Question

What is the simplest way to transform an array of the form

{{{{a11, a12}, {a21, a22}}, 
{{a13, a14}, {a23, a24}}}, 
{{{a31, a32}, {a41, a42}}, 
{{a33, a34}, {a43, a44}}}}

To the matrix

{{a11,a12,a13,a14},
{a21,a22,a23,a24},
{a31,a32,a33,a34},
{a41,a42,a43,a44}}

I understand I should use Flatten, but I cannot figure out how to denote the levels.

score 6 · Accepted Answer · answered May 09 '19 at 20:40

ArrayFlatten is the ticket:

a = {{{{a11, a12}, {a21, a22}}, {{a13, a14}, {a23, a24}}}, {{{a31, a32}, {a41, a42}}, {{a33, a34}, {a43, a44}}}};
b = {{a11, a12, a13, a14}, {a21, a22, a23, a24}, {a31, a32, a33, a34}, {a41, a42, a43, a44}};

ArrayFlatten[a] == b
(* True *)

score 4 · Answer 2 · answered May 09 '19 at 21:10

4

As Roman says, ArrayFlatten is the simplest, but you could use Flatten as well:

Flatten[
    {
    {{{a11,a12},{a21,a22}},{{a13,a14},{a23,a24}}},
    {{{a31,a32},{a41,a42}},{{a33,a34},{a43,a44}}}
    },
    {{1,3}, {2,4}}
] //TeXForm

$\left( \begin{array}{cccc} \text{a11} & \text{a12} & \text{a13} & \text{a14} \\ \text{a21} & \text{a22} & \text{a23} & \text{a24} \\ \text{a31} & \text{a32} & \text{a33} & \text{a34} \\ \text{a41} & \text{a42} & \text{a43} & \text{a44} \\ \end{array} \right)$

answered May 09 '19 at 21:10

Carl Woll

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Is there any simple explanation why {{1,3},{2,4}} works? – tst May 09 '19 at 21:19
@tst: If you don't feel like dealing with the Flatten[] levels, you can also Flatten it "all the way" and then Partition it back into 4-element lists, e.g., {{{{a11, a12}, {a21, a22}}, {{a13, a14}, {a23, a24}}}, {{{a31, a32}, {a41, a42}}, {{a33, a34}, {a43, a44}}}} // Flatten // Partition[#, 4]& – Joshua Schrier May 09 '19 at 21:24
1

@tst Explanations about {{1,3},{2,4}} can be found in Flatten command: matrix as second argument. Not sure about "simple", however :) – WReach May 09 '19 at 21:41

Flatten a four dimensional array into a matrix

2 Answers2