Next: Utility Functions, Previous: Trigonometry, Up: Arithmetic

### 17.4 Sums and Products

— Built-in Function: sum (x)
— Built-in Function: sum (x, dim)
— Built-in Function: sum (..., 'native')
— Built-in Function: sum (..., 'double')
— Built-in Function: sum (..., 'extra')

> Sum of elements along dimension dim. If dim is omitted, it defaults to the first non-singleton dimension.

> If the optional argument 'native' is given, then the sum is performed in the same type as the original argument, rather than in the default double type. For example:

>               sum ([true, true])
>                 ⇒ 2
>               sum ([true, true], 'native')
>                 ⇒ true

> On the contrary, if 'double' is given, the sum is performed in double precision even for single precision inputs.

> For double precision inputs, 'extra' indicates that a more accurate algorithm than straightforward summation is to be used. For single precision inputs, 'extra' is the same as 'double'. Otherwise, 'extra' has no effect.

> See also: cumsum, sumsq, prod.

— Built-in Function: prod (x)
— Built-in Function: prod (x, dim)

> Product of elements along dimension dim. If dim is omitted, it defaults to the first non-singleton dimension.

> See also: cumprod, sum.

— Built-in Function: cumsum (x)
— Built-in Function: cumsum (x, dim)
— Built-in Function: cumsum (..., 'native')
— Built-in Function: cumsum (..., 'double')
— Built-in Function: cumsum (..., 'extra')

> Cumulative sum of elements along dimension dim. If dim is omitted, it defaults to the first non-singleton dimension.

> See `sum` for an explanation of the optional parameters 'native', 'double', and 'extra'.

> See also: sum, cumprod.

— Built-in Function: cumprod (x)
— Built-in Function: cumprod (x, dim)

> Cumulative product of elements along dimension dim. If dim is omitted, it defaults to the first non-singleton dimension.

> See also: prod, cumsum.

— Built-in Function: sumsq (x)
— Built-in Function: sumsq (x, dim)

> Sum of squares of elements along dimension dim. If dim is omitted, it defaults to the first non-singleton dimension.

> This function is conceptually equivalent to computing

>               sum (x .* conj (x), dim)

> but it uses less memory and avoids calling `conj` if x is real.

> See also: sum.