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gvander

Generate a Vandermonde matrix.

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: storage layout.
  • mode: mode indicating whether to generate increasing (1) or decreasing (-1) powers.
  • M: number of rows in out.
  • N: number of columns in out.
  • x: input Array or typed array.
  • strideX: stride length for x.
  • out: output Array or typed array.
  • LDO: stride length for the leading dimension of out.
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, 4.0, 2.0, 1.0, 9.0, 3.0, 1.0 ]

The M and strideX parameters determine which elements in the input array are accessed at runtime. For example, to use every other element from the input array:

var x = [ 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( 'row-major', 1, 3, 3, x, 2, out, 3 );
// out => [ 1.0, 1.0, 1.0, 1.0, 2.0, 4.0, 1.0, 3.0, 9.0 ]

Note that indexing is relative to the first index. To introduce an offset, use typed array views.

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

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

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

var out = new Float64Array( 9 );

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

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 );