## 19.2 Slicing with range indexes

Slicing returns a contiguous slice of a one-dimensional array, a contiguous sub-block of a two-dimensional array, and so on. Semantically, it is just a special form of multiple indexing.

### Lower and upper bound indexes

For instance, consider supplying an upper and lower bound for an index.

array[7] int c;
// ...
array[4] int d;
d = c[3:6];  // result: d == (c[3], c[4], c[5], c[6])

The range index 3:6 behaves semantically just like the multiple index (3, 4, 5, 6). In terms of implementation, the sliced upper and/or lower bounded indices are faster and use less memory because they do not explicitly create a multiple index, but rather use a direct loop. They are also easier to read, so should be preferred over multiple indexes where applicable.

### Lower or upper bound indexes

It is also possible to supply just a lower bound, or just an upper bound. Writing c[3:] is just shorthand for c[3:size(c)]. Writing c[:5] is just shorthand for c[1:5].

### Full range indexes

Finally, it is possible to write a range index that covers the entire range of an array, either by including just the range symbol (:) as the index or leaving the index position empty. In both cases, c[] and c[:] are equal to c[1:size(c)], which in turn is just equal to c.

### Slicing functions

Stan provides head and tail functions that pull out prefixes or suffixes of vectors, row vectors, and one-dimensional arrays. In each case, the return type is the same as the argument type. For example,

vector[M] a = ...;
vector[N] b = head(a, N);

assigns b to be a vector equivalent to the first N elements of the vector a. The function tail works the same way for suffixes, with

array[M] a = ...;
array[N] b = tail(a, N);

Finally, there is a segment function, which specifies a first element and number of elements. For example,

array[15] a = ...;
array[3] b = segment(a, 5, 3);

will set b to be equal to { a[5], a[6], a[7] }, so that it starts at element 5 of a and includes a total of 3 elements.