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# cusum

> Compute the cumulative sum along one or more [ndarray][@stdlib/ndarray/ctor] dimensions.

<section class="usage">

## Usage

```javascript
var cusum = require( '@stdlib/blas/ext/cusum' );
```

#### cusum( x\[, initial]\[, options] )

Computes the cumulative sum along one or more [ndarray][@stdlib/ndarray/ctor] dimensions.

```javascript
var array = require( '@stdlib/ndarray/array' );

var x = array( [ -1.0, 2.0, -3.0 ] );

var y = cusum( x );
// returns <ndarray>[ -1.0, 1.0, -2.0 ]
```

The function has the following parameters:

-   **x**: input [ndarray][@stdlib/ndarray/ctor]. Must have a numeric or "generic" [data type][@stdlib/ndarray/dtypes].
-   **initial**: initial value for the cumulative sum (_optional_). May be either a scalar value or an [ndarray][@stdlib/ndarray/ctor] having a [data type][@stdlib/ndarray/dtypes] which [promotes][@stdlib/ndarray/promotion-rules] to the data type of the input [ndarray][@stdlib/ndarray/ctor]. If provided a scalar value, the value is cast to the data type of the input [ndarray][@stdlib/ndarray/ctor]. If provided an [ndarray][@stdlib/ndarray/ctor], the value must have a shape which is [broadcast-compatible][@stdlib/ndarray/base/broadcast-shapes] with the complement of the shape defined by `options.dims`. For example, given the input shape `[2, 3, 4]` and `options.dims=[0]`, an [ndarray][@stdlib/ndarray/ctor] initial value must have a shape which is [broadcast-compatible][@stdlib/ndarray/base/broadcast-shapes] with the shape `[3, 4]`. Similarly, when performing the operation over all elements in a provided input [ndarray][@stdlib/ndarray/ctor], an [ndarray][@stdlib/ndarray/ctor] initial value must be a zero-dimensional [ndarray][@stdlib/ndarray/ctor]. By default, the initial value is the additive identity (i.e., zero).
-   **options**: function options (_optional_).

The function accepts the following options:

-   **dims**: list of dimensions over which to perform operation. If not provided, the function performs the operation over all elements in a provided input [ndarray][@stdlib/ndarray/ctor].
-   **dtype**: output ndarray [data type][@stdlib/ndarray/dtypes]. Must be a numeric or "generic" [data type][@stdlib/ndarray/dtypes].

By default, the function uses the additive identity when computing the cumulative sum. To begin summing from a different value, provide an `initial` argument.

```javascript
var array = require( '@stdlib/ndarray/array' );

var x = array( [ -1.0, 2.0, -3.0 ] );

var y = cusum( x, 10.0 );
// returns <ndarray>[ 9.0, 11.0, 8.0 ]
```

By default, the function performs the operation over all elements in a provided input [ndarray][@stdlib/ndarray/ctor]. To perform the operation over specific dimensions, provide a `dims` option.

```javascript
var array = require( '@stdlib/ndarray/array' );

var x = array( [ -1.0, 2.0, -3.0, 4.0 ], {
    'shape': [ 2, 2 ],
    'order': 'row-major'
});
// returns <ndarray>[ [ -1.0, 2.0 ], [ -3.0, 4.0 ] ]

var y = cusum( x, {
    'dims': [ 0 ]
});
// returns <ndarray>[ [ -1.0, 2.0 ], [ -4.0, 6.0 ] ]

y = cusum( x, {
    'dims': [ 1 ]
});
// returns <ndarray>[ [ -1.0, 1.0 ], [ -3.0, 1.0 ] ]

y = cusum( x, {
    'dims': [ 0, 1 ]
});
// returns <ndarray>[ [ -1.0, 1.0 ], [ -2.0, 2.0 ] ]
```

By default, the function returns an [ndarray][@stdlib/ndarray/ctor] having a [data type][@stdlib/ndarray/dtypes] determined by the function's output data type [policy][@stdlib/ndarray/output-dtype-policies]. To override the default behavior, set the `dtype` option.

```javascript
var dtype = require( '@stdlib/ndarray/dtype' );
var array = require( '@stdlib/ndarray/array' );

var x = array( [ -1.0, 2.0, -3.0 ], {
    'dtype': 'generic'
});

var y = cusum( x, {
    'dtype': 'float64'
});
// returns <ndarray>

var dt = dtype( y );
// returns 'float64'
```

#### cusum.assign( x\[, initial], out\[, options] )

Computes the cumulative sum along one or more [ndarray][@stdlib/ndarray/ctor] dimensions and assigns results to a provided output [ndarray][@stdlib/ndarray/ctor].

```javascript
var array = require( '@stdlib/ndarray/array' );
var zerosLike = require( '@stdlib/ndarray/zeros-like' );

var x = array( [ -1.0, 2.0, -3.0 ] );
var y = zerosLike( x );

var out = cusum.assign( x, y );
// returns <ndarray>[ -1.0, 1.0, -2.0 ]

var bool = ( out === y );
// returns true
```

The method has the following parameters:

-   **x**: input [ndarray][@stdlib/ndarray/ctor]. Must have a numeric or generic [data type][@stdlib/ndarray/dtypes].
-   **initial**: initial value for the cumulative sum (_optional_). May be either a scalar value or an [ndarray][@stdlib/ndarray/ctor] having a [data type][@stdlib/ndarray/dtypes] which [promotes][@stdlib/ndarray/promotion-rules] to the data type of the input [ndarray][@stdlib/ndarray/ctor]. If provided a scalar value, the value is cast to the data type of the input [ndarray][@stdlib/ndarray/ctor]. If provided an [ndarray][@stdlib/ndarray/ctor], the value must have a shape which is [broadcast-compatible][@stdlib/ndarray/base/broadcast-shapes] with the complement of the shape defined by `options.dims`. For example, given the input shape `[2, 3, 4]` and `options.dims=[0]`, an [ndarray][@stdlib/ndarray/ctor] initial value must have a shape which is [broadcast-compatible][@stdlib/ndarray/base/broadcast-shapes] with the shape `[3, 4]`. Similarly, when performing the operation over all elements in a provided input [ndarray][@stdlib/ndarray/ctor], an [ndarray][@stdlib/ndarray/ctor] initial value must be a zero-dimensional [ndarray][@stdlib/ndarray/ctor]. By default, the initial value is the additive identity (i.e., zero).
-   **out**: output [ndarray][@stdlib/ndarray/ctor].
-   **options**: function options (_optional_).

The method accepts the following options:

-   **dims**: list of dimensions over which to perform operation. If not provided, the function performs the operation over all elements in a provided input [ndarray][@stdlib/ndarray/ctor].

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   Both functions iterate over [ndarray][@stdlib/ndarray/ctor] elements according to the memory layout of the input [ndarray][@stdlib/ndarray/ctor]. Accordingly, performance degradation is possible when operating over multiple dimensions of a large non-contiguous multi-dimensional input [ndarray][@stdlib/ndarray/ctor]. In such scenarios, one may want to copy an input [ndarray][@stdlib/ndarray/ctor] to contiguous memory before computing the cumulative sum.
-   The output data type [policy][@stdlib/ndarray/output-dtype-policies] only applies to the main function and specifies that, by default, in order to avoid issues arising from integer overflow, the function must return an [ndarray][@stdlib/ndarray/ctor] having a [data type][@stdlib/ndarray/dtypes] amenable to accumulation. This means that, for integer data types having small value ranges (e.g., `int8`, `uint8`, etc), the main function returns an [ndarray][@stdlib/ndarray/ctor] having at least a 32-bit integer data type. By default, if an input [ndarray][@stdlib/ndarray/ctor] has a floating-point data type, the main function returns an [ndarray][@stdlib/ndarray/ctor] having the same data type. For the `assign` method, the output [ndarray][@stdlib/ndarray/ctor] is allowed to have any supported output [data type][@stdlib/ndarray/dtypes].

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var getDType = require( '@stdlib/ndarray/dtype' );
var ndarray2array = require( '@stdlib/ndarray/to-array' );
var ndarray = require( '@stdlib/ndarray/ctor' );
var cusum = require( '@stdlib/blas/ext/cusum' );

// Generate an array of random numbers:
var xbuf = discreteUniform( 25, 0, 20, {
    'dtype': 'generic'
});

// Wrap in an ndarray:
var x = new ndarray( 'generic', xbuf, [ 5, 5 ], [ 5, 1 ], 0, 'row-major' );
console.log( ndarray2array( x ) );

// Perform operation:
var y = cusum( x, 100.0, {
    'dims': [ 0 ]
});

// Resolve the output array data type:
var dt = getDType( y );
console.log( dt );

// Print the results:
console.log( ndarray2array( y ) );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

</section>

<!-- /.related -->

<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->

<section class="links">

[@stdlib/ndarray/ctor]: https://www.npmjs.com/package/@stdlib/ndarray-ctor

[@stdlib/ndarray/dtypes]: https://www.npmjs.com/package/@stdlib/ndarray-dtypes

[@stdlib/ndarray/promotion-rules]: https://www.npmjs.com/package/@stdlib/ndarray-promotion-rules

[@stdlib/ndarray/output-dtype-policies]: https://www.npmjs.com/package/@stdlib/ndarray-output-dtype-policies

[@stdlib/ndarray/base/broadcast-shapes]: https://www.npmjs.com/package/@stdlib/ndarray-base-broadcast-shapes

</section>

<!-- /.links -->
