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# gvander

> Generate a Vandermonde matrix.

<section class="intro">

</section>

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<section class="usage">

## Usage

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

#### gvander( order, mode, M, N, x, strideX, out, ldo )

Generates a Vandermonde matrix.

```javascript
var x = [ 1.0, 2.0, 3.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

gvander( 'row-major', 1, 3, 3, x, 1, out, 3 );
// out => [ 1.0, 1.0, 1.0, 1.0, 2.0, 4.0, 1.0, 3.0, 9.0 ]
```

The function has the following parameters:

-   **order**: row-major (C-style) or column-major (Fortran-style) order.
-   **mode**: mode. If `mode < 0`, the function generates decreasing powers. If `mode > 0`, the function generates increasing powers.
-   **M**: number of rows in `out` and number of indexed elements in `x`.
-   **N**: number of columns in `out`.
-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
-   **strideX**: stride length for `x`.
-   **out**: output matrix.
-   **ldo**: stride between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of the matrix `out`).

Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.

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

// Initial arrays:
var x0 = new Float64Array( [ 999.0, 1.0, 2.0, 3.0 ] );
var out0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );

// Create offset views:
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 );       // start at 2nd element
var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 ); // start at 2nd element

gvander( 'row-major', 1, 3, 3, x1, 1, out1, 3 );
// out0 => <Float64Array>[ 0.0, 1.0, 1.0, 1.0, 1.0, 2.0, 4.0, 1.0, 3.0, 9.0 ]
```

When the mode is positive, the matrix is generated such that

```text
[
    1   x_0^1   x_0^2   ...   x_0^(N-1)
    1   x_1^1   x_1^2   ...   x_1^(N-1)
    ...
]
```

with increasing powers along the rows.

When the mode is negative, the matrix is generated such that

```text
[
    x_0^(N-1)   ...   x_0^2   x_0^1   1
    x_1^(N-1)   ...   x_1^2   x_1^1   1
    ...
]
```

with decreasing powers along the rows.

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#### gvander.ndarray( mode, M, N, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut )

<!-- lint enable maximum-heading-length -->

Generates a Vandermonde matrix using alternative indexing semantics.

```javascript
var x = [ 1.0, 2.0, 3.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

gvander.ndarray( 1, 3, 3, x, 1, 0, out, 3, 1, 0 );
// out => [ 1.0, 1.0, 1.0, 1.0, 2.0, 4.0, 1.0, 3.0, 9.0 ]
```

The function has the following additional parameters:

-   **offsetX**: starting index for `x`.
-   **strideOut1**: stride length for the first dimension of `out`.
-   **strideOut2**: stride length for the second dimension of `out`.
-   **offsetOut**: starting index for `out`.

While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, offset parameters support indexing semantics based on starting indices. For example, to use every other element from the input array starting from the second element:

```javascript
var x = [ 0.0, 1.0, 0.0, 2.0, 0.0, 3.0 ];
var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];

gvander.ndarray( 1, 3, 3, x, 2, 1, out, 3, 1, 0 );
// out => [ 1.0, 1.0, 1.0, 1.0, 2.0, 4.0, 1.0, 3.0, 9.0 ]
```

</section>

<!-- /.usage -->

<section class="notes">

## Notes

-   If `M <= 0` or `N <= 0`, both functions return `out` unchanged.
-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
-   Depending on the environment, the typed versions ([`dvander`][@stdlib/blas/ext/base/dvander], [`svander`][@stdlib/blas/ext/base/svander], etc.) are likely to be significantly more performant.

</section>

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<section class="examples">

## Examples

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

```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var zeros = require( '@stdlib/array/zeros' );
var gvander = require( '@stdlib/blas/ext/base/gvander' );

var M = 3;
var N = 4;

var x = discreteUniform( M, 0, 10, {
    'dtype': 'generic'
});
var out = zeros( M*N, 'generic' );
console.log( x );

gvander( 'row-major', -1, M, N, x, 1, out, N );
console.log( out );
```

</section>

<!-- /.examples -->

<section class="references">

</section>

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<section class="related">

</section>

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<section class="links">

[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array

[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray

[@stdlib/array/base/accessor]: https://www.npmjs.com/package/@stdlib/array-base-accessor

[@stdlib/blas/ext/base/dvander]: https://github.com/stdlib-js/blas/tree/main/ext/base/dvander

[@stdlib/blas/ext/base/svander]: https://github.com/stdlib-js/blas/tree/main/ext/base/svander

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</section>

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