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gvander

Generate a Vandermonde matrix.

Installation

npm install @stdlib/blas-ext-base-gvander

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

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

Generates a Vandermonde matrix.

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 or 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 views.

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

[
    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

[
    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.

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

Generates a Vandermonde matrix using alternative indexing semantics.

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 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:

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 ]

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).
• Depending on the environment, the typed versions (dvander, svander, etc.) are likely to be significantly more performant.

Examples

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 );

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Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

Community

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License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.