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feat: add math/base/tools/chebyshev-series
PR-URL: #11470 Co-authored-by: Athan Reines <kgryte@gmail.com> Reviewed-by: Athan Reines <kgryte@gmail.com> Co-authored-by: stdlib-bot <noreply@stdlib.io>
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‎lib/node_modules/@stdlib/math/base/tools/chebyshev-series/LICENSE‎

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‎lib/node_modules/@stdlib/math/base/tools/chebyshev-series/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2026 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# Chebyshev Series
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> Evaluate a [Chebyshev series][chebyshev-series] using double-precision floating-point arithmetic.
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<section class="intro">
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A [Chebyshev series][chebyshev-series] in a variable `x` can be expressed as
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<!-- <equation class="equation" label="eq:chebyshev_series" align="center" raw="\sum_{i=0}^{n} c_i T_i(x/2)" alt="Chebyshev series expression."> -->
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```math
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\sum_{i=0}^{n} c_i T_i(x/2)
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```
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<!-- <div class="equation" align="center" data-raw-text="\sum_{i=0}^{n}' c_i T_i(x/2)" data-equation="eq:chebyshev_series">
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<img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@7e0a95722efd9c771b129597380c63dc6715508b/lib/node_modules/@stdlib/math/base/tools/chebyshev-series/docs/img/equation_chebyshev_series.svg" alt="Chebyshev series expression.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `c_n, c_{n-1}, ..., c_0` are constants and `T_i` are Chebyshev polynomials of the first kind.
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var chebyshevSeries = require( '@stdlib/math/base/tools/chebyshev-series' );
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```
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#### chebyshevSeries( x, c )
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Evaluates a [Chebyshev series][chebyshev-series] having coefficients `c` at a value `x`.
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```javascript
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var v = chebyshevSeries( 1.0, [ 1.0, 0.5 ] );
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// returns 0.75
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```
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The function evaluates Chebyshev polynomials at `x/2`.
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#### chebyshevSeries.factory( c )
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Uses code generation to in-line coefficients and return a function for evaluating a [Chebyshev series][chebyshev-series] using double-precision floating-point arithmetic.
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```javascript
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var evaluate = chebyshevSeries.factory( [ 1.0, 0.5 ] );
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// 0.5 * T_0(0.5) + 1.0 * T_1(0.5)
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var v = evaluate( 1.0 );
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// returns 0.75
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```
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The returned function evaluates Chebyshev polynomials at `x/2`.
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- The value at which to evaluate a Chebyshev series is expected to reside on the interval `[-2, 2]`.
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- The coefficients `c` **must be** be ordered in **descending** degree.
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- For hot code paths in which coefficients are invariant, a compiled function will be more performant than `chebyshevSeries()`.
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- While code generation can boost performance, its use may be problematic in browser contexts enforcing a strict [content security policy][mdn-csp] (CSP). If running in or targeting an environment with a CSP, avoid using code generation.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var logEachMap = require( '@stdlib/console/log-each-map' );
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var chebyshevSeries = require( '@stdlib/math/base/tools/chebyshev-series' );
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// Create an array of random coefficients:
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var coef = discreteUniform( 10, -100, 100 );
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// Evaluate the series at random values using the direct function:
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var v = uniform( 100, -2.0, 2.0 );
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var i;
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for ( i = 0; i < v.length; i++ ) {
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console.log( 'f(%d) = %d', v[ i ], chebyshevSeries( v[ i ], coef ) );
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}
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// Generate a chebyshev series evaluation function:
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var evaluate = chebyshevSeries.factory( coef );
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var x = uniform( 100, -2.0, 2.0 );
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logEachMap( 'f(%d) = %d', x, evaluate );
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[chebyshev-series]: https://en.wikipedia.org/wiki/Chebyshev_polynomials#Chebyshev_series
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[mdn-csp]: https://developer.mozilla.org/en-US/docs/Web/HTTP/CSP
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</section>
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<!-- /.links -->

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