Built-in Mathematica Symbol

Flatten

Flatten[list]
flattens out nested lists.

Flatten[list, n]
flattens to level n.

Flatten[list, n, h]
flattens subexpressions with head h.

Flatten[list, {{s₁₁, s₁₂, ...}, {s₂₁, s₂₂, ...}, ...}]
flattens list by combining all levels s_ij to make each level i in the result.

MORE INFORMATION

Flatten "unravels" lists, effectively just deleting inner braces.

Flatten[list, n] effectively flattens the top level in list n times.

Flatten[f[e, ...]] flattens out subexpressions with head f.

If the m_ij are matrices, Flatten[{{m₁₁, m₁₂}, {m₂₁, m₂₂}}, {{1, 3}, {2, 4}}] effectively constructs a single matrix from the "blocks" m_ij.

Flatten[list, {{i₁}, {i₂}, ...}] effectively transposes levels in list, putting level i_k in list at level k in the result. Note that the function Transpose in effect uses an inverse of this specification.

Flatten flattens out levels in SparseArray objects just as in the corresponding ordinary arrays. »

EXAMPLES

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Basic Examples (2)

Flatten out lists at all levels:

Flatten only at level 1:

Flatten out lists at all levels:

In[1]:=

Out[1]=

Flatten only at level 1:

In[1]:=

Out[1]=

Scope (5)

No flattening:

Flatten to level 1:

Flatten to level 2:

Flatten to level 3:

Flatten to level 4:

This is the same as using level

:

And the same as not specifying a level:

Generalizations & Extensions (4)

Flatten a sparse array:

Flatten works with any head:

Flatten all levels with respect to g:

Flatten all levels with respect to f:

Here is a matrix:

Flatten an array of blocks with the shape of u into a single matrix.

Flatten into a single matrix effectively using the transpose of the blocks:

Applications (4)

Join lists and individual elements:

Unravel a matrix:

Make a flattened list of rules:

Do a "transpose" on a ragged array:

Properties & Relations (3)

Flatten acts as an inverse of Partition:

Flatten effectively arranges elements in the lexicographic order of their indices:

For a permutation p with inverse

, Flatten[a, List/@p^-1]

Transpose[a, p]:

A random permutation:

Get its inverse:

Neat Examples (1)

Peel off successive layers of Framed: