test: add tests and its fixtures

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---

Author: anandkaranubc

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/large_n.json

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+#!/usr/bin/env python
+#
+# @license Apache-2.0
+#
+# Copyright (c) 2025 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.
+
+"""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(50, 100, 1000)
+    gen(x, n, "large_n.json")
+
+
+if __name__ == "__main__":
+    main()

lib/node_modules/@stdlib/math/base/special/chebyshev-t-polynomial/test/fixtures/python/medium_n.json

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+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 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 integer 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( 0.5, -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();
+});