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## 17.4 Sums and Products

__Built-in Function:__**sum***(*`x`)__Built-in Function:__**sum***(*`x`,`dim`)__Built-in Function:__**sum***(…, 'native')*Sum of elements along dimension

`dim`. If`dim`is omitted, it defaults to 1 (column-wise sum).As a special case, if

`x`is a vector and`dim`is omitted, return the sum of the elements.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

__Built-in Function:__**prod***(*`x`)__Built-in Function:__**prod***(*`x`,`dim`)Product of elements along dimension

`dim`. If`dim`is omitted, it defaults to 1 (column-wise products).As a special case, if

`x`is a vector and`dim`is omitted, return the product of the elements.

__Built-in Function:__**cumsum***(*`x`)__Built-in Function:__**cumsum***(*`x`,`dim`)__Built-in Function:__**cumsum***(…, 'native')*Cumulative sum of elements along dimension

`dim`. If`dim`is omitted, it defaults to 1 (column-wise cumulative sums).As a special case, if

`x`is a vector and`dim`is omitted, return the cumulative sum of the elements as a vector with the same orientation as`x`.The "native" argument implies the summation is performed in native type. See

`sum`

for a complete description and example of the use of "native".

__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 1 (column-wise cumulative products).As a special case, if

`x`is a vector and`dim`is omitted, return the cumulative product of the elements as a vector with the same orientation as`x`.

__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 1 (column-wise sum of squares).As a special case, if

`x`is a vector and`dim`is omitted, return the sum of squares of the elements.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.

__Function File:__**accumarray***(*`subs`,`vals`,`sz`,`func`,`fillval`,`issparse`)__Function File:__**accumarray***(*`csubs`,`vals`, …)Create an array by accumulating the elements of a vector into the positions defined by their subscripts. The subscripts are defined by the rows of the matrix

`subs`and the values by`vals`. Each row of`subs`corresponds to one of the values in`vals`.The size of the matrix will be determined by the subscripts themselves. However, if

`sz`is defined it determines the matrix size. The length of`sz`must correspond to the number of columns in`subs`.The default action of

`accumarray`

is to sum the elements with the same subscripts. This behavior can be modified by defining the`func`function. This should be a function or function handle that accepts a column vector and returns a scalar. The result of the function should not depend on the order of the subscripts.The elements of the returned array that have no subscripts associated with them are set to zero. Defining

`fillval`to some other value allows these values to be defined.By default

`accumarray`

returns a full matrix. If`issparse`is logically true, then a sparse matrix is returned instead.An example of the use of

`accumarray`

is:accumarray ([1,1,1;2,1,2;2,3,2;2,1,2;2,3,2], 101:105) ⇒ ans(:,:,1) = [101, 0, 0; 0, 0, 0] ans(:,:,2) = [0, 0, 0; 206, 0, 208]

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