Scan

The running combination of $f$ over a collection, one result per element.

Scan(xs, f)$[f(x_1), f(f(x_1), x_2), \ldots]$ — same length as $xs$, the partial folds of $f$ with no seed.

Scan(xs, f, init)as above, but folding from $init$ — still same length as $xs$ (the seed is not itself an output element).

Typed signatures

Type	Package	Applies
(indexed_collection<T>, reducer: (unknown, T) any -> unknown, initial: value?) -> indexed_collection where T	compute-engine	always

Domain: Collections

Examples

Basic #

live ↗

In$\mathrm{Scan}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \mathrm{Add})$Out$\bigl\lbrack1, 3, 6, 10\bigr\rbrack$

The shape of a running fold

live ↗

In$\mathrm{Scan}(\bigl\lbrack a, b, c\bigr\rbrack, f)$Out$\bigl\lbrack a, f(a, b), f(f(a, b), c)\bigr\rbrack$

Scope #

The running maximum

live ↗

In$\mathrm{Scan}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, \mathrm{Max})$Out$\bigl\lbrack1, 2, 3, 4\bigr\rbrack$

Running products: the factorials

live ↗

In$\mathrm{Scan}(\bigl\lbrack1, 2, 3, 4, 5\bigr\rbrack, \mathrm{Multiply})$Out$\bigl\lbrack1, 2, 6, 24, 120\bigr\rbrack$

Running sums of symbolic elements -- Wolfram's Accumulate

live ↗

In$\mathrm{Scan}(\bigl\lbrack a, b, c\bigr\rbrack, \mathrm{Add})$Out$\bigl\lbrack a, a+b, a+b+c\bigr\rbrack$

The running minimum

live ↗

In$\mathrm{Scan}(\bigl\lbrack3, 1, 4, 1, 5\bigr\rbrack, \mathrm{Min})$Out$\bigl\lbrack3, 1, 1, 1, 1\bigr\rbrack$

An empty list scans to an empty list

live ↗

In$\mathrm{Scan}(\bigl\lbrack\bigr\rbrack, \mathrm{Add})$Out$\bigl\lbrack\bigr\rbrack$

Applications #

The values of every prefix of the binary digits 1011

live ↗

In$\mathrm{Scan}(\bigl\lbrack1, 0, 1, 1\bigr\rbrack, (\operatorname{\_1}, \operatorname{\_2})↦2\operatorname{\_1}+\operatorname{\_2})$Out$\bigl\lbrack1, 2, 5, 11\bigr\rbrack$

Possible issues #

The seeded form is still the same length as $xs$ — the seed isn't an output element

live ↗

In$\mathrm{Scan}(\bigl\lbrack1, 2, 3\bigr\rbrack, \mathrm{Add}, 10)$Out$\bigl\lbrack11, 13, 16\bigr\rbrack$

About

Examples	9
Checked against	Wolfram Language 8 agree1 differ

See also: Fold