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dvander

Generate a double-precision floating-point Vandermonde matrix.

Installation

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

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

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

Generates a double-precision floating-point Vandermonde matrix.

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

var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
var out = new Float64Array( 9 );

dvander( 'row-major', -1, 3, 3, x, 1, out, 3 );
// out => <Float64Array>[ 1.0, 1.0, 1.0, 4.0, 2.0, 1.0, 9.0, 3.0, 1.0 ]

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.
• N: number of columns in out.
• x: input Float64Array.
• strideX: stride length for x.
• out: output matrix stored in linear memory as a Float64Array.
• 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( 10 );

// 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

dvander( '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.

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

Generates a double-precision floating-point Vandermonde matrix using alternative indexing semantics.

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

var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
var out = new Float64Array( 9 );

dvander.ndarray( -1, 3, 3, x, 1, 0, out, 3, 1, 0 );
// out => <Float64Array>[ 1.0, 1.0, 1.0, 4.0, 2.0, 1.0, 9.0, 3.0, 1.0 ]

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 Float64Array = require( '@stdlib/array-float64' );

var x = new Float64Array( [ 0.0, 1.0, 0.0, 2.0, 0.0, 3.0 ] );
var out = new Float64Array( 9 );

dvander.ndarray( 1, 3, 3, x, 2, 1, out, 3, 1, 0 );
// out => <Float64Array>[ 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 the output matrix unchanged.

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var Float64Array = require( '@stdlib/array-float64' );
var dvander = require( '@stdlib/blas-ext-base-dvander' );

var M = 3;
var N = 4;

var x = discreteUniform( M, 0, 10, {
    'dtype': 'float64'
});
var out = new Float64Array( M*N );

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

---

C APIs

Usage

#include "stdlib/blas/ext/base/dvander.h"

stdlib_strided_dvander( order, mode, M, N, *X, strideX, *Out, LDO )

Generates a double-precision floating-point Vandermonde matrix.

#include "stdlib/blas/base/shared.h"

const double x[ 3 ] = { 1.0, 2.0, 3.0 };
double Out[ 3*3 ] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_dvander( CblasRowMajor, -1.0, 3, 3, x, 1, Out, 3 );

The function accepts the following arguments:

• order: [in] CBLAS_LAYOUT storage layout.
• mode: [in] double mode. If mode < 0, the function generates decreasing powers. If mode > 0, the function generates increasing powers.
• M: [in] CBLAS_INT number of rows in Out.
• N: [in] CBLAS_INT number of columns in Out.
• X: [in] double* input array.
• strideX: [in] CBLAS_INT stride length for X.
• Out: [out] double* output matrix.
• LDO: [in] CBLAS_INT stride between successive contiguous vectors of the matrix Out (a.k.a., leading dimension of the matrix Out).

void API_SUFFIX(stdlib_strided_dvander)( const CBLAS_LAYOUT order, const double mode, const CBLAS_INT M, const CBLAS_INT N, const double *X, const CBLAS_INT strideX, double *Out, const CBLAS_INT LDO );

stdlib_strided_dvander_ndarray( mode, M, N, *X, strideX, offsetX, *Out, strideOut1, strideOut2, offsetOut )

Generates a double-precision floating-point Vandermonde matrix using alternative indexing semantics.

#include "stdlib/blas/base/shared.h"

const double x[ 3 ] = { 1.0, 2.0, 3.0 };
double Out[ 3*3 ] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

stdlib_strided_dvander_ndarray( -1.0, 3, 3, x, 1, 0, Out, 3, 1, 0 );

The function accepts the following arguments:

• mode: [in] double mode. If mode < 0, the function generates decreasing powers. If mode > 0, the function generates increasing powers.
• M: [in] CBLAS_INT number of rows in Out.
• N: [in] CBLAS_INT number of columns in Out.
• X: [in] double* input array.
• strideX: [in] CBLAS_INT stride length for X.
• offsetX: [in] CBLAS_INT starting index for X.
• Out: [out] double* output matrix.
• strideOut1: [in] CBLAS_INT stride length for the first dimension of Out.
• strideOut2: [in] CBLAS_INT stride length for the second dimension of Out.
• offsetOut: [in] CBLAS_INT starting index for Out.

void API_SUFFIX(stdlib_strided_dvander_ndarray)( const double mode, const CBLAS_INT M, const CBLAS_INT N, const double *X, const CBLAS_INT strideX, const CBLAS_INT offsetX, double *Out, const CBLAS_INT strideOut1, const CBLAS_INT strideOut2, const CBLAS_INT offsetOut );

Examples

#include "stdlib/blas/ext/base/dvander.h"
#include "stdlib/blas/base/shared.h"
#include <stdio.h>

int main( void ) {
    // Define the input array:
    const double x[ 3 ] = { 1.0, 2.0, 3.0 };

    // Define a 3x3 output array stored in row-major order:
    double Out[ 3*3 ] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 };

    // Specify the number of rows and columns:
    const int M = 3;
    const int N = 3;

    // Perform operation:
    stdlib_strided_dvander( CblasRowMajor, -1.0, M, N, x, 1, Out, N );

    // Print the result:
    for ( int i = 0; i < M; i++ ) {
        for ( int j = 0; j < N; j++ ) {
            printf( "Out[%i,%i] = %lf\n", i, j, Out[ (i*N)+j ] );
        }
    }
}

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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.