diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md new file mode 100644 index 000000000000..3284513e229e --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/README.md @@ -0,0 +1,155 @@ + + +# chebyshevtpoly + +> [Chebyshev polynomial][chebyshev-polynomial] of the first kind. + +
+ +The [Chebyshev Polynomial][chebyshev-polynomial] of the first kind is defined as + + + +```math +T_n(x) = \cos( n \cos^{-1}(x) ) +``` + + + +where `n` is the polynomial degree. + +The [Chebyshev Polynomial][chebyshev-polynomial] of the first kind is related to the [Gaussian hypergeometric function][@stdlib/math/base/special/hyp2f1] via the following equation + + + +```math +T_n(x) = {}_2F_1\left( -n, n; \frac{1}{2}; \frac{1}{2}(1-x) \right) +``` + + + +
+ + + +
+ +## Usage + +```javascript +var chebyshevtpoly = require( '@stdlib/math/base/special/chebyshev-t-polynomial' ); +``` + +#### chebyshevtpoly( n, x ) + +Evaluates the [Chebyshev Polynomial][chebyshev-polynomial] of the first kind for a degree `n` at a value `x`. + +```javascript +var y = chebyshevtpoly( 0.0, 0.5 ); +// returns 1.0 + +y = chebyshevtpoly( 1.0, -0.5 ); +// returns -0.5 + +y = chebyshevtpoly( 5.0, 0.5 ); +// returns 0.5 +``` + +If provided `NaN` as any argument, the function returns `NaN`. + +```javascript +var y = chebyshevtpoly( NaN, 1.0 ); +// returns NaN + +y = chebyshevtpoly( 0.0, NaN ); +// returns NaN +``` + +If provided a polynomial degree `n < 0`, the function returns `NaN`. + +```javascript +var y = chebyshevtpoly( -2.0, 0.5 ); +// returns NaN + +y = chebyshevtpoly( -4.5, -0.5 ); +// returns NaN +``` + +If provided a polynomial degree `n` which is not a nonnegative number, the function returns `NaN`. + +```javascript +var y = chebyshevtpoly( -2.5, 0.5 ); +// returns NaN + +y = chebyshevtpoly( -1.0, -0.5 ); +// returns NaN +``` + +
+ + + +
+ +## Examples + + + +```javascript +var randu = require( '@stdlib/random/base/randu' ); +var round = require( '@stdlib/math/base/special/round' ); +var chebyshevtpoly = require( '@stdlib/math/base/special/chebyshev-t-polynomial' ); + +var n; +var x; +var y; +var i; + +for ( i = 0; i < 10; i++ ) { + n = round( randu()*10.0 ); + x = ( randu()*2.0 ) - 1.0; + y = chebyshevtpoly( n, x ); + console.log( 'n: %d, x: %d, T_n(x): %d', n.toFixed( 4 ), x.toFixed( 4 ), y.toFixed( 4 ) ); +} +``` + +
+ + + + + +
+ +
+ + + + + +
+ +[chebyshev-polynomial]: https://en.wikipedia.org/wiki/Chebyshev_polynomials +[@stdlib/math/base/special/hyp2f1]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/math/base/special/hyp2f1 + +
+ + diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/benchmark/benchmark.js b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/benchmark/benchmark.js new file mode 100644 index 000000000000..8532b482f525 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/benchmark/benchmark.js @@ -0,0 +1,55 @@ +/** +* @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. +*/ + +'use strict'; + +// MODULES // + +var bench = require( '@stdlib/bench' ); +var uniform = require( '@stdlib/random/array/uniform' ); +var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var pkg = require( './../package.json' ).name; +var chebyshevtpoly = require( './../lib' ); + + +// MAIN // + +bench( pkg, function benchmark( b ) { + var n; + var x; + var y; + var i; + + n = discreteUniform( 100, 0, 50 ); + x = uniform( 100, -1.0, 1.0 ); + + b.tic(); + for ( i = 0; i < b.iterations; i++ ) { + y = chebyshevtpoly( n[ i % n.length ], x[ i % x.length ] ); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + } + b.toc(); + if ( isnan( y ) ) { + b.fail( 'should not return NaN' ); + } + b.pass( 'benchmark finished' ); + b.end(); +}); diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/repl.txt b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/repl.txt new file mode 100644 index 000000000000..cbada92e8a68 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/repl.txt @@ -0,0 +1,38 @@ + +{{alias}}( n, x ) + Evaluates the Chebyshev polynomial of the first kind for + a degree `n` at a value `x`. + + Parameters + ---------- + n: number + Degree of the polynomial. + + x: number + Input value. + + Returns + ------- + out: number + Polynomial value. + + Examples + -------- + > var y = {{alias}}( 0.0, 0.5 ) + 1.0 + > y = {{alias}}( 1.0, -0.5 ) + -0.5 + > y = {{alias}}( 5.0, 0.5 ) + 0.5 + > y = {{alias}}( -2.5, 0.5 ) + NaN + > y = {{alias}}( -1.0, 0.5 ) + NaN + > y = {{alias}}( NaN, 1.0 ) + NaN + > y = {{alias}}( 1.0, NaN ) + NaN + + See Also + -------- + diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/index.d.ts b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/index.d.ts new file mode 100644 index 000000000000..ba3ac6daea16 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/index.d.ts @@ -0,0 +1,61 @@ +/* +* @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. +*/ + +// TypeScript Version: 4.1 + +/** +* Evaluates the Chebyshev polynomial of the first kind for a degree `n` at a value `x`. +* +* @param n - degree of the polynomial +* @param x - input value +* @returns polynomial value +* +* @example +* var y = chebyshevtpoly( 0.0, 0.5 ); +* // returns 1.0 +* +* @example +* var y = chebyshevtpoly( 1.0, -0.5 ); +* // returns -0.5 +* +* @example +* var y = chebyshevtpoly( 5.0, 0.5 ); +* // returns 0.5 +* +* @example +* var y = chebyshevtpoly( -2.5, 0.5 ); +* // returns NaN +* +* @example +* var y = chebyshevtpoly( -1.0, 0.5 ); +* // returns NaN +* +* @example +* var y = chebyshevtpoly( NaN, 1.0 ); +* // returns NaN +* +* @example +* var y = chebyshevtpoly( 1.0, NaN ); +* // returns NaN +*/ +declare function chebyshevtpoly( n: number, x: number ): number; + + +// EXPORTS // + +export = chebyshevtpoly; diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/test.ts b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/test.ts new file mode 100644 index 000000000000..32c58234156a --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/docs/types/test.ts @@ -0,0 +1,56 @@ +/* +* @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. +*/ + +import chebyshevtpoly = require( './index' ); + + +// TESTS // + +// The function returns a number... +{ + chebyshevtpoly( 8.0, 1.0 ); // $ExpectType number +} + +// The compiler throws an error if the function is provided values other than two numbers... +{ + chebyshevtpoly( true, 3 ); // $ExpectError + chebyshevtpoly( false, 2 ); // $ExpectError + chebyshevtpoly( '5', 1 ); // $ExpectError + chebyshevtpoly( [], 1 ); // $ExpectError + chebyshevtpoly( {}, 2 ); // $ExpectError + chebyshevtpoly( ( x: number ): number => x, 2 ); // $ExpectError + + chebyshevtpoly( 9, true ); // $ExpectError + chebyshevtpoly( 9, false ); // $ExpectError + chebyshevtpoly( 5, '5' ); // $ExpectError + chebyshevtpoly( 8, [] ); // $ExpectError + chebyshevtpoly( 9, {} ); // $ExpectError + chebyshevtpoly( 8, ( x: number ): number => x ); // $ExpectError + + chebyshevtpoly( [], true ); // $ExpectError + chebyshevtpoly( {}, false ); // $ExpectError + chebyshevtpoly( false, '5' ); // $ExpectError + chebyshevtpoly( {}, [] ); // $ExpectError + chebyshevtpoly( '5', ( x: number ): number => x ); // $ExpectError +} + +// The compiler throws an error if the function is provided insufficient arguments... +{ + chebyshevtpoly(); // $ExpectError + chebyshevtpoly( 3 ); // $ExpectError +} diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/examples/index.js b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/examples/index.js new file mode 100644 index 000000000000..893bde7affd8 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/examples/index.js @@ -0,0 +1,34 @@ +/** +* @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. +*/ + +'use strict'; + +var logEachMap = require( '@stdlib/console/log-each-map' ); +var randu = require( '@stdlib/random/base/randu' ); +var round = require( '@stdlib/math/base/special/round' ); +var chebyshevtpoly = require( './../lib' ); + +var n; +var x; +var i; + +for ( i = 0; i < 10; i++ ) { + n = round( randu()*10.0 ); + x = ( randu()*2.0 ) - 1.0; + logEachMap( 'n: %d, x: %d, T_n(x): %d', n.toFixed( 4 ), x.toFixed( 4 ), chebyshevtpoly ); +} diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/index.js b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/index.js new file mode 100644 index 000000000000..64bc9e1bc3b1 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/index.js @@ -0,0 +1,58 @@ +/** +* @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. +*/ + +'use strict'; + +/** +* Evaluate the Chebyshev polynomial of the first kind for a degree `n` at a value `x`. +* +* @module @stdlib/math/base/special/chebyshev-t-polynomial +* +* @example +* var chebyshevtpoly = require( '@stdlib/math/base/special/chebyshev-t-polynomial' ); +* +* var y = chebyshevtpoly( 0.0, 0.5 ); +* // returns 1.0 +* +* y = chebyshevtpoly( 1.0, -0.5 ); +* // returns -0.5 +* +* y = chebyshevtpoly( 5.0, 0.5 ); +* // returns 0.5 +* +* y = chebyshevtpoly( -2.5, 0.5 ); +* // returns NaN +* +* y = chebyshevtpoly( -1.0, 0.5 ); +* // returns NaN +* +* y = chebyshevtpoly( NaN, 1.0 ); +* // returns NaN +* +* y = chebyshevtpoly( 1.0, NaN ); +* // returns NaN +*/ + +// MODULES // + +var main = require( './main.js' ); + + +// EXPORTS // + +module.exports = main; diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/main.js b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/main.js new file mode 100644 index 000000000000..0410ae03f2ea --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/lib/main.js @@ -0,0 +1,77 @@ +/** +* @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. +*/ + +'use strict'; + +// MODULES // + +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var hyp2f1 = require( '@stdlib/math/base/special/hyp2f1' ); + + +// MAIN // + +/** +* Evaluates the Chebyshev polynomial of the first kind for a degree `n` at a value `x`. +* +* @param {NonNegativeNumber} n - degree of the polynomial +* @param {number} x - input value +* @returns {number} polynomial value +* +* @example +* var y = chebyshevtpoly( 0.0, 0.5 ); +* // returns 1.0 +* +* @example +* var y = chebyshevtpoly( 1.0, -0.5 ); +* // returns -0.5 +* +* @example +* var y = chebyshevtpoly( 5.0, 0.5 ); +* // returns 0.5 +* +* @example +* var y = chebyshevtpoly( -2.5, 0.5 ); +* // returns NaN +* +* @example +* var y = chebyshevtpoly( -1.0, 0.5 ); +* // returns NaN +* +* @example +* var y = chebyshevtpoly( NaN, 1.0 ); +* // returns NaN +* +* @example +* var y = chebyshevtpoly( 1.0, NaN ); +* // returns NaN +*/ +function chebyshevtpoly( n, x ) { + if ( + isnan( x ) || + n < 0.0 + ) { + return NaN; + } + return hyp2f1( -n, n, 0.5, 0.5*(1.0-x) ); +} + + +// EXPORTS // + +module.exports = chebyshevtpoly; diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/package.json b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/package.json new file mode 100644 index 000000000000..29324e3f9189 --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/package.json @@ -0,0 +1,68 @@ +{ + "name": "@stdlib/math/base/special/chebyshev-t-polynomial", + "version": "0.0.0", + "description": "Evaluate the Chebyshev polynomial of the first kind.", + "license": "Apache-2.0", + "author": { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + }, + "contributors": [ + { + "name": "The Stdlib Authors", + "url": "https://github.com/stdlib-js/stdlib/graphs/contributors" + } + ], + "main": "./lib", + "directories": { + "benchmark": "./benchmark", + "doc": "./docs", + "example": "./examples", + "lib": "./lib", + "test": "./test" + }, + "types": "./docs/types", + "scripts": {}, + "homepage": "https://github.com/stdlib-js/stdlib", + "repository": { + "type": "git", + "url": "git://github.com/stdlib-js/stdlib.git" + }, + "bugs": { + "url": "https://github.com/stdlib-js/stdlib/issues" + }, + "dependencies": {}, + "devDependencies": {}, + "engines": { + "node": ">=0.10.0", + "npm": ">2.7.0" + }, + "os": [ + "aix", + "darwin", + "freebsd", + "linux", + "macos", + "openbsd", + "sunos", + "win32", + "windows" + ], + "keywords": [ + "stdlib", + "stdmath", + "mathematics", + "math", + "special function", + "special", + "function", + "chebyshev", + "polynomial", + "chebyshev-t-polynomial", + "chebyshevtpoly", + "tchebyshev", + "tchebyshev polynomial", + "first kind", + "hypergeometric function" + ] +} diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/large_n.json b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/large_n.json new file mode 100644 index 000000000000..ed39a946a13b --- /dev/null +++ b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/large_n.json @@ -0,0 +1 @@ +{"x": [-1.0, -0.997997997997998, -0.995995995995996, -0.993993993993994, -0.991991991991992, -0.98998998998999, -0.987987987987988, -0.985985985985986, -0.983983983983984, -0.9819819819819819, -0.97997997997998, -0.977977977977978, -0.975975975975976, -0.973973973973974, -0.9719719719719719, -0.96996996996997, -0.967967967967968, -0.965965965965966, -0.963963963963964, -0.9619619619619619, -0.95995995995996, -0.957957957957958, -0.955955955955956, -0.953953953953954, -0.9519519519519519, -0.94994994994995, -0.9479479479479479, -0.9459459459459459, -0.943943943943944, 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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. + +"""Generate fixtures.""" + +import os +import json +import numpy as np +from scipy.special import eval_chebyt + +# Set a seed for reproducibility: +np.random.seed(1234) + +# Get the file path: +FILE = os.path.realpath(__file__) + +# Extract the directory in which this file resides: +DIR = os.path.dirname(FILE) + + +def gen(x, n, name): + """Generate fixture data and write to file. + + # Arguments + + * `x`: domain + * `n`: domain + * `name::str`: output filename + + # Examples + + ``` python + python> x = linspace(0, 1, 2001) + python> n = linspace(0.1, 1000, 2001) + python> gen(x, n, './data.json') + ``` + """ + y = eval_chebyt(n, x) + + # Store data to be written to file as a dictionary: + data = { + "x": x.tolist(), + "n": n.tolist(), + "expected": y.tolist() + } + + # Based on the script directory, create an output filepath: + filepath = os.path.join(DIR, name) + + # Write the data to the output filepath as JSON: + with open(filepath, "w", encoding="utf-8") as outfile: + json.dump(data, outfile) + + +def main(): + """Generate fixture data.""" + x = np.linspace(-1, 1, 1000) + + # Small degree: + n = np.random.randint(0, 10, 1000) + gen(x, n, "small_n.json") + + # Medium degree: + n = np.random.randint(10, 50, 1000) + gen(x, n, "medium_n.json") + + # Large degree: + n = np.random.randint(40, 100, 1000) + gen(x, n, "large_n.json") + + +if __name__ == "__main__": + main() diff --git a/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/small_n.json b/lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/small_n.json new file mode 100644 index 000000000000..544c576cea6c --- /dev/null +++ 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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. +*/ + +'use strict'; + +// MODULES // + +var tape = require( 'tape' ); +var isnan = require( '@stdlib/math/base/assert/is-nan' ); +var abs = require( '@stdlib/math/base/special/abs' ); +var EPS = require( '@stdlib/constants/float64/eps' ); +var chebyshevtpoly = require( './../lib' ); + + +// FIXTURES // + +var smallN = require( './fixtures/python/small_n.json' ); +var mediumN = require( './fixtures/python/medium_n.json' ); +var largeN = require( './fixtures/python/large_n.json' ); + + +// TESTS // + +tape( 'main export is a function', function test( t ) { + t.ok( true, __filename ); + t.strictEqual( typeof chebyshevtpoly, 'function', 'main export is a function' ); + t.end(); +}); + +tape( 'if provided `NaN` for any parameter, the function returns `NaN`', function test( t ) { + var val = chebyshevtpoly( NaN, 2.0 ); + t.ok( isnan( val ), 'returns expected value' ); + val = chebyshevtpoly( 2.0, NaN ); + t.ok( isnan( val ), 'returns expected value' ); + t.end(); +}); + +tape( 'if provided a negative number for `n` and a valid `x`, the function returns `NaN`', function test( t ) { + var val = chebyshevtpoly( -2.0, 0.5 ); + t.ok( isnan( val ), 'returns expected value' ); + val = chebyshevtpoly( -4.0, -0.5 ); + t.ok( isnan( val ), 'returns expected value' ); + val = chebyshevtpoly( -4.5, -0.5 ); + t.ok( isnan( val ), 'returns expected value' ); + t.end(); +}); + +tape( 'if provided a `n` which is not a nonnegative number and a valid `x`, the function returns `NaN`', function test( t ) { + var val = chebyshevtpoly( -2.5, 0.5 ); + t.ok( isnan( val ), 'returns expected value' ); + val = chebyshevtpoly( -1.0, -0.5 ); + + t.ok( isnan( val ), 'returns expected value' ); + t.end(); +}); + +tape( 'the function evaluates the chebyshev polynomial for `x` given small degree `n`', function test( t ) { + var expected; + var delta; + var tol; + var x; + var n; + var y; + var i; + + expected = smallN.expected; + x = smallN.x; + n = smallN.n; + for ( i = 0; i < x.length; i++ ) { + y = chebyshevtpoly( n[i], x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+'. n:'+n[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + + // NOTE: The tolerance is higher due to the numerical differences between the `hyp2f1` implementation in JavaScript and its reference implementation in SciPy. + tol = 755.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. n: '+n[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the chebyshev polynomial for `x` given medium degree `n`', function test( t ) { + var expected; + var delta; + var tol; + var x; + var n; + var y; + var i; + + expected = mediumN.expected; + x = mediumN.x; + n = mediumN.n; + for ( i = 0; i < x.length; i++ ) { + y = chebyshevtpoly( n[i], x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+'. n:'+n[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + + // NOTE: The tolerance is higher due to the numerical differences between the `hyp2f1` implementation in JavaScript and its reference implementation in SciPy. + tol = 5836.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. n: '+n[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +}); + +tape( 'the function evaluates the chebyshev polynomial for `x` given large degree `n`', function test( t ) { + var expected; + var delta; + var tol; + var x; + var n; + var y; + var i; + + expected = largeN.expected; + x = largeN.x; + n = largeN.n; + for ( i = 0; i < x.length; i++ ) { + y = chebyshevtpoly( n[i], x[i] ); + if ( y === expected[i] ) { + t.equal( y, expected[i], 'x: '+x[i]+'. n: '+n[i]+', y: '+y+', expected: '+expected[i] ); + } else { + delta = abs( y - expected[ i ] ); + + // NOTE: The tolerance is higher due to the numerical differences between the `hyp2f1` implementation in JavaScript and its reference implementation in SciPy. + tol = 6591.0 * EPS * abs( expected[ i ] ); + t.ok( delta <= tol, 'within tolerance. x: '+x[ i ]+'. n: '+n[i]+'. y: '+y+'. E: '+expected[ i ]+'. Δ: '+delta+'. tol: '+tol+'.' ); + } + } + t.end(); +});