Accumulate

The running sums of a list.

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Accumulate(list)

\{a_1, a_1+a_2, a_1+a_2+a_3, \ldots\}

Typed signatures

Type	Package	Applies
`(collection<any>) -> collection`	`combinatorics`	always

Domain: Collections

Details

The first element is kept as-is; each later element is the sum of everything up to and including it.
Equivalent to $FoldList(Add, list)$ — see FoldList.

Examples

Basic #

\mathrm{Accumulate}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack)

Out

\bigl\lbrack1, 3, 6, 10\bigr\rbrack

Running sums with symbolic entries

\mathrm{Accumulate}(\bigl\lbrack a, b, c, d\bigr\rbrack)

Out

\bigl\lbrack a, a+b, a+b+c, a+b+c+d\bigr\rbrack

\mathrm{Accumulate}(\bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack c, d\bigr\rbrack, \bigl\lbrack k, f\bigr\rbrack\bigr\rbrack)

Out

\bigl\lbrack\bigl\lbrack a, b\bigr\rbrack, \bigl\lbrack a+c, b+d\bigr\rbrack, \bigl\lbrack a+c+k, b+d+f\bigr\rbrack\bigr\rbrack

Scope #

The running sum of the empty list is empty

\mathrm{Accumulate}(\bigl\lbrack\bigr\rbrack)

Out

\bigl\lbrack\bigr\rbrack

\mathrm{Accumulate}(\mathrm{data})

Out

\mathrm{Accumulate}(\mathrm{data})

\mathrm{Accumulate}(v)

Out

\mathrm{Accumulate}(v)

Applications #

Running sums of $1..10$ give the triangular numbers

\mathrm{Accumulate}(1..10)

Out

\bigl\lbrack1, 3, 6, 10, 15, 21, 28, 36, 45, 55\bigr\rbrack

Properties #

The last element is the sum of the whole list

\mathrm{Last}(\mathrm{Accumulate}(\bigl\lbrack1, 2, 3, 4, 5\bigr\rbrack))=1+2+3+4+5

Out

\mathrm{True}

Neat examples #

Repeated accumulation builds columns of binomial coefficients

\mathrm{NestList}(\mathrm{Accumulate}, 1..5, 5)^T

Out

\bigl\lbrack\bigl\lbrack1, 1, 1, 1, 1, 1\bigr\rbrack, \bigl\lbrack2, 3, 4, 5, 6, 7\bigr\rbrack, \bigl\lbrack3, 6, 10, 15, 21, 28\bigr\rbrack, \bigl\lbrack4, 10, 20, 35, 56, 84\bigr\rbrack, \bigl\lbrack5, 15, 35, 70, 126, 210\bigr\rbrack\bigr\rbrack

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