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# linspace

> Generate a linearly spaced array over a specified interval.

<section class="usage">

## Usage

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

#### linspace( start, stop, length\[, options] )

Generates a linearly spaced array over a specified interval.

```javascript
var arr = linspace( 0.0, 100.0, 6 );
// returns <Float64Array>[ 0.0, 20.0, 40.0, 60.0, 80.0, 100.0 ]
```

If `length` is `0`, the function returns an empty array.

```javascript
var arr = linspace( 0.0, 100.0, 0 );
// returns <Float64Array>[]
```

If `length` is `1`, the function returns an array containing `stop`, but not `start`, when `endpoint` is `true`; otherwise, the function returns an array containing `start`, but not `stop`.

```javascript
var arr = linspace( 0.0, 100.0, 1 );
// returns <Float64Array>[ 100.0 ]

arr = linspace( 0.0, 100.0, 1, {
    'endpoint': true
});
// returns <Float64Array>[ 100.0 ]

arr = linspace( 0.0, 100.0, 1, {
    'endpoint': false
});
// returns <Float64Array>[ 0.0 ]
```

For real-valued `start` and `stop`, if `start` is less than `stop`, the output array will contain ascending values, and, if `start` is greater than `stop`, the output array will contain descending values.

```javascript
var arr = linspace( 0.0, -100.0, 6 );
// returns <Float64Array>[ 0.0, -20.0, -40.0, -60.0, -80.0, -100.0 ]
```

The function accepts the following `options`:

-   **dtype**: output array data type. Must be a [floating-point data type][@stdlib/array/typed-float-dtypes] or `'generic'`. If both `start` and `stop` are the same type (either `'float64'`, `'complex64'`, or `'complex128'`), the default output array data type is the same type as the input values (either `'float64'`, `'complex64'`, or `'complex128'`, respectively). Otherwise, the default output array data type is `'complex128'`.
-   **endpoint**: `boolean` indicating whether to include the `stop` value in the output array. If `false`, the function generates `length + 1` linearly spaced values over the interval `[start, stop]` and only writes `length` values to the output array, thus excluding `stop` from the output array. Accordingly, for a fixed `length`, the spacing between adjacent values in the output array changes depending on the value of `endpoint`. Default: `true`.

By default, the function generates a linearly spaced array over the closed interval `[start, stop]`. To generate linearly spaced values over the half-open interval `[start, stop)`, set the `endpoint` option to `false`.

```javascript
var opts = {
    'endpoint': false
};
var arr = linspace( 0.0, 100.0, 5, opts );
// returns <Float64Array>[ 0.0, 20.0, 40.0, 60.0, 80.0 ]
```

When both `start` and `stop` are real-valued, the default output array data type is `'float64'`. To return an output array having a different data type, set the `dtype` option.

```javascript
var opts = {
    'dtype': 'generic'
};
var arr = linspace( 0, 100, 6, opts );
// returns [ 0, 20, 40, 60, 80, 100 ]
```

When either `start` or `stop` is a complex number, the default output array data type is `'complex128'`. To return an output array having a different data type, set the `dtype` option.

<!-- eslint-disable stdlib/no-redeclare -->

```javascript
var Complex128 = require( '@stdlib/complex/float64/ctor' );
var real = require( '@stdlib/complex/float64/real' );
var imag = require( '@stdlib/complex/float64/imag' );

var opts = {
    'dtype': 'generic'
};

var start = new Complex128( 0.0, 0.0 );
var stop = new Complex128( 100.0, 10.0 );

var arr = linspace( start, stop, 6, opts );
// returns [ <Complex128>, <Complex128>, <Complex128>, <Complex128>, <Complex128>, <Complex128> ]

var z = arr[ 0 ];
// returns <Complex128>

var re = real( z );
// returns 0.0

var im = imag( z );
// returns 0.0

z = arr[ 1 ];
// returns <Complex128>

re = real( z );
// returns 20.0

im = imag( z );
// returns 2.0

// ...
```

#### linspace.assign( start, stop, out\[, options] )

Generates a linearly spaced sequence over a specified interval and assigns the results to a provided output array.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var out = new Float64Array( 6 );
var arr = linspace.assign( 0.0, 100.0, out );
// returns <Float64Array>[ 0.0, 20.0, 40.0, 60.0, 80.0, 100.0 ]

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

If the provided output array is empty, the function returns the provided output array unchanged.

```javascript
var arr = linspace.assign( 0.0, 100.0, [] );
// returns []
```

If the provided output array contains a single element, the function writes the `stop` value, but not `start`, when `endpoint` is `true`; otherwise, the function writes the `start` value, but not `stop`.

```javascript
var arr = linspace.assign( 0.0, 100.0, [ -10.0 ] );
// returns [ 100.0 ]

arr = linspace.assign( 0.0, 100.0, [ -10.0 ], {
    'endpoint': true
});
// returns [ 100.0 ]

arr = linspace.assign( 0.0, 100.0, [ -10.0 ], {
    'endpoint': false
});
// returns [ 0.0 ]
```

For real-valued `start` and `stop`, if `start` is less than `stop`, the output array will contain ascending values, and, if `start` is greater than `stop`, the output array will contain descending values.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var out = new Float64Array( 6 );
var arr = linspace.assign( 0.0, -100.0, out );
// returns <Float64Array>[ 0.0, -20.0, -40.0, -60.0, -80.0, -100.0 ]
```

The function accepts the following `options`:

-   **endpoint**: `boolean` indicating whether to include the `stop` value in the output array. If `false`, the function generates `N + 1` linearly spaced values (where `N` is the length of the provided output array) over the interval `[start, stop]` and only writes `N` values to the output array, thus excluding `stop` from the output array. Accordingly, for a fixed `N`, the spacing between adjacent values in the output array changes depending on the value of `endpoint`. Default: `true`.

By default, the function generates a linearly spaced array over the closed interval `[start, stop]`. To generate linearly spaced values over the half-open interval `[start, stop)`, set the `endpoint` option to `false`.

```javascript
var Float64Array = require( '@stdlib/array/float64' );

var opts = {
    'endpoint': false
};

var out = new Float64Array( 5 );
var arr = linspace.assign( 0.0, 100.0, out, opts );
// returns <Float64Array>[ 0.0, 20.0, 40.0, 60.0, 80.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   For `M >= 2`, the spacing between values is computed as

    ```text
    delta = (stop-start) / (M-1)
    ```

    where `M` is the number of values to generate. Accordingly, values may not be evenly spaced due to floating-point rounding errors.

-   When the output array length is greater than `1` and `endpoint` is `true`, the output array is guaranteed to include the `start` and `stop` values. Beware, however, that values between `start` and `stop` are subject to floating-point rounding errors. Hence,

    ```javascript
    var arr = linspace( 0.0, 1.0, 3 );
    // returns <Float64Array>[ 0.0, ~0.5, 1.0 ]
    ```

    where `arr[1]` is only guaranteed to be approximately equal to `0.5`. If you desire more control over element precision, consider using [`roundn`][@stdlib/math/base/special/roundn]:

    ```javascript
    var roundn = require( '@stdlib/math/base/special/roundn' );

    // Create an array subject to floating-point rounding errors:
    var arr = linspace( 0.0, 1.0, 3, {
        'dtype': 'generic'
    });

    // Round each value to the nearest hundredth:
    var i;
    for ( i = 0; i < arr.length; i++ ) {
        arr[ i ] = roundn( arr[ i ], -2 );
    }
    console.log( arr );
    // => [ 0.0, 0.5, 1.0 ]
    ```

-   For both functions, if both `start` and `stop` are real-valued, the output array data type may be any [floating-point data type][@stdlib/array/typed-float-dtypes] or `'generic'`. However, if either `start` or `stop` are complex numbers, the output array type must be a [complex floating-point data type][@stdlib/array/typed-complex-dtypes] or `'generic'`.

-   While the `assign` method accepts any array-like object for the output array when both `start` and `stop` are real-valued, providing an integer-valued typed array (e.g., [`Int32Array`][@stdlib/array/int32], etc) is not encouraged due to potential rounding errors during value generation and assignment and, thus, irregular spacing between adjacent values. Instead, consider using [`incrspace`][@stdlib/array/incrspace].

-   When writing to a complex floating-point output array, real-valued `start` and `stop` values are treated as complex numbers having a real component equaling the provided value and having an imaginary component equaling `0`.

-   When generating linearly spaced complex floating-point numbers, the real and imaginary components are generated separately (i.e., real components are generated over the interval `[real(start), real(stop)]` and imaginary components are generated over the interval `[imag(start), imag(stop)]`).

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

// Define function options:
var opts = {
    'dtype': 'generic'
};

// Create arrays of varying lengths...
var out = linspace( 0, 10, 10, opts );
console.log( out );

out = linspace( 0, 10, 11, opts );
console.log( out );

out = linspace( 0, 10, 21, opts );
console.log( out );

// Create an array with decremented values:
out = linspace( 10, 0, 11, opts );
console.log( out );
```

</section>

<!-- /.examples -->

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

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/array/incrspace`][@stdlib/array/incrspace]</span><span class="delimiter">: </span><span class="description">generate a linearly spaced numeric array using a provided increment.</span>
-   <span class="package-name">[`@stdlib/array/logspace`][@stdlib/array/logspace]</span><span class="delimiter">: </span><span class="description">generate a logarithmically spaced numeric array.</span>

</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/math/base/special/roundn]: https://github.com/stdlib-js/math-base-special-roundn

[@stdlib/array/typed-float-dtypes]: https://github.com/stdlib-js/array/tree/main/typed-float-dtypes

[@stdlib/array/typed-complex-dtypes]: https://github.com/stdlib-js/array/tree/main/typed-complex-dtypes

[@stdlib/array/int32]: https://github.com/stdlib-js/array/tree/main/int32

[@stdlib/array/incrspace]: https://github.com/stdlib-js/array/tree/main/incrspace

<!-- <related-links> -->

[@stdlib/array/logspace]: https://github.com/stdlib-js/array/tree/main/logspace

<!-- </related-links> -->

</section>

<!-- /.links -->
