Built-in Mathematica Symbol

Partition

Partition[list, n]
partitions list into non-overlapping sublists of length n.

Partition[list, n, d]
generates sublists with offset d.

Partition[list, {n₁, n₂, ...}]
partitions a nested list into blocks of size

.

Partition[list, {n₁, n₂, ...}, {d₁, d₂, ...}]
uses offset d_i at level i in list.

Partition[list, n, d, {k_L, k_R}]
specifies that the first element of list should appear at position k_L in the first sublist, and the last element of list should appear at or after position k_R in the last sublist. If additional elements are needed, Partition fills them in by treating list as cyclic.

Partition[list, n, d, {k_L, k_R}, x]
pads if necessary by repeating the element x.

Partition[list, n, d, {k_L, k_R}, {x₁, x₂, ...}]
pads if necessary by cyclically repeating the elements x_i.

Partition[list, n, d, {k_L, k_R}, {}]
uses no padding, and so can yield sublists of different lengths.

Partition[list, nlist, dlist, {klist_L, klist_R}, padlist]
specifies alignments and padding in a nested list.

MORE INFORMATION

All the sublists generated by Partition[list, n, d] are of length n. Some elements at the end of list may therefore not appear in any sublist.

All elements of list appear in the sublists generated by Partition[list, n, 1].

If d is greater than n in Partition[list, n, d], then elements in the middle of list are skipped. »

Partition[list, n, d, {k_L, k_R}] effectively allows sublists that have overhangs that extend past the beginning or end of list.

Partition[list, n, d, k] is equivalent to Partition[list, n, d, {k, k}].

Common settings for {k_L, k_R} are:

	{1,-1}	allow no overhangs
	{1,1}	allow maximal overhang at the end
	{-1,-1}	allow maximal overhang at the beginning
	{-1,1}	allow maximal overhangs at both beginning and end

Partition[list, n, d, {k_L, k_R}, padlist] effectively lays down repeated copies of padlist, then superimposes one copy of list on them, and partitions the result. »

Common settings for padlist are:

	x	pad with repetitions of a single element
	{x₁,x₂,...}	pad with cyclic repetitions of a sequence of elements
	list	pad by treating list as cyclic (default)
	{}	do no padding, potentially leaving sublists of different lengths

If list has length s, then Partition[list, n, d] yields Max[0, Floor[(s+d-n)/d]] sublists.

Partition[list, {n₁, n₂, ..., n_r}] effectively replaces blocks of elements at level r in list by depth-r nested lists of neighboring elements. »

If no offsets are specified, the neighborhoods are adjacent and non-overlapping.

Partition[list, {n₁, n₂, ...}, d] uses offset d at every level.

Partition[list, nlist, dlist, {{k_L1, k_L2, ...}, {k_R1, k_R2, ...}}] specifies that element {1, 1, ...} of list should appear at position {k_L1, k_L2, ...} in the {1, 1, ...} block of the result, while element {-1, -1, ...} of list should appear at or after position {k_R1, k_R2, ...} in the {-1, -1, ...} block of the result.

{k_L, k_R} is taken to be equivalent to {{k_L, k_L, ...}, {k_R, k_R, ...}}.

{{k₁, k₂, ...}} is taken to be equivalent to {{k₁, k₂, ...}, {k₁, k₂, ...}}.

Partition[list, {n₁, n₂, ..., n_r}, klist, padlist] effectively makes a depth-r array of copies of padlist, then superimposes list on them, and partitions the result.

If list has dimensions {s₁, s₂, ..., s_r} then Partition[list, {n₁, n₂, ..., n_r}] will have dimensions {q₁, q₂, ..., q_r, n₁, n₂, ..., n_r} where q_i is given by Floor[s_i/n_i].