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* @license Apache-2.0
*
* Copyright (c) 2026 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/* eslint-disable max-len */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var dfill = require( '@stdlib/blas/ext/base/dfill' ).ndarray;
// MAIN //
/**
* Generates a double-precision floating-point Vandermonde matrix.
*
* ## Notes
*
* - The implementation uses recursive multiplication to generate successive powers, which carries risk of additional accumulated floating-point error; however, for most use cases, such additional error should be negligible and not problematic.
*
* @private
* @param {integer} mode - mode indicating whether to generate increasing or decreasing powers
* @param {NonNegativeInteger} M - number of rows in `out`
* @param {NonNegativeInteger} N - number of columns in `out`
* @param {Float64Array} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} out - output matrix
* @param {integer} strideOut1 - stride length for the first dimension of `out`
* @param {integer} strideOut2 - stride length for the second dimension of `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @returns {Float64Array} output matrix
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
* var out = new Float64Array( 9 );
*
* dvander( -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 ]
*/
function dvander( mode, M, N, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut ) {
var do0;
var do1;
var S0;
var S1;
var io;
var ix;
var i0;
var i1;
// Note on variable naming convention: S#, do#, io, i# where # corresponds to the loop number, with `0` being the innermost loop...
if ( isRowMajor( [ strideOut1, strideOut2 ] ) ) {
S0 = N;
S1 = M;
do0 = strideOut2;
do1 = strideOut1 - ( S0*strideOut2 );
// Increasing: x^0, x^1, ..., x^(N-1)
if ( mode > 0 ) {
io = offsetOut;
ix = offsetX;
for ( i1 = 0; i1 < S1; i1++ ) {
out[ io ] = 1.0;
io += do0;
for ( i0 = 1; i0 < S0; i0++ ) {
out[ io ] = out[ io-do0 ] * x[ ix ];
io += do0;
}
ix += strideX;
io += do1;
}
return out;
}
// Decreasing: x^(N-1), x^(N-2), ..., x^0
io = offsetOut + ( ( S1-1 ) * strideOut1 ) + ( ( S0-1 ) * strideOut2 );
ix = offsetX + ( ( S1-1 ) * strideX );
for ( i1 = S1-1; i1 >= 0; i1-- ) {
out[ io ] = 1.0;
io -= do0;
for ( i0 = 1; i0 < S0; i0++ ) {
out[ io ] = out[ io+do0 ] * x[ ix ];
io -= do0;
}
ix -= strideX;
io -= do1;
}
return out;
}
// Column-major...
S0 = M;
S1 = N;
do0 = strideOut1;
do1 = strideOut2 - ( S0*strideOut1 );
// Increasing: column j contains x^j
if ( mode > 0 ) {
dfill( S0, 1.0, out, strideOut1, offsetOut );
io = offsetOut + strideOut2;
for ( i1 = 1; i1 < S1; i1++ ) {
ix = offsetX;
for ( i0 = 0; i0 < S0; i0++ ) {
out[ io ] = out[ io-strideOut2 ] * x[ ix ];
ix += strideX;
io += do0;
}
io += do1;
}
return out;
}
// Decreasing: column 0 contains x^(N-1), last column all ones
dfill( S0, 1.0, out, strideOut1, offsetOut + ( ( S1-1 ) * strideOut2 ) );
io = offsetOut + ( ( S1-2 ) * strideOut2 ) + ( ( S0-1 ) * strideOut1 );
for ( i1 = S1-2; i1 >= 0; i1-- ) {
ix = offsetX + ( ( S0-1 ) * strideX );
for ( i0 = S0-1; i0 >= 0; i0-- ) {
out[ io ] = out[ io+strideOut2 ] * x[ ix ];
ix -= strideX;
io -= do0;
}
io -= do1;
}
return out;
}
// EXPORTS //
module.exports = dvander;
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