feat: add differentiate/strided/ggradient

lib/node_modules/@stdlib/differentiate/strided/ggradient/README.md

@@ -0,0 +1,194 @@
+<!--
+
+@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.
+
+-->
+
+# ggradient
+
+> Compute the gradient of a strided array.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ggradient = require( '@stdlib/differentiate/strided/ggradient' );
+```
+
+#### ggradient( N, edgeOrder, x, strideX, h, strideH, out, strideOut )
+
+Computes the gradient of a strided array.
+
+```javascript
+var x = [ 0.0, 1.0, 9.0, 36.0, 100.0 ];
+var h = [ 1.0, 2.0, 3.0, 4.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ggradient( x.length, 1, x, 1, h, 1, out, 1 );
+// out => [ 1.0, 2.0, 6.0, 12.0, 16.0 ]
+```
+
+The function has the following parameters:
+
+-   **N**: number of indexed elements.
+-   **edgeOrder**: approximation order at the boundaries.
+-   **x**: input [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **strideX**: stride length for `x`.
+-   **h**: spacing [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **strideH**: stride length for `h`.
+-   **out**: output [`Array`][mdn-array] or [`typed array`][mdn-typed-array].
+-   **strideOut**: stride length for `out`.
+
+The `N` and stride parameters determine which elements in the strided arrays are accessed at runtime. For example, to compute the gradient of every other element:
+
+```javascript
+var x = [ 0.0, -1.0, 1.0, -1.0, 4.0, -1.0, 9.0, -1.0, 16.0 ];
+var h = [ 1.0 ];
+var out = [ 0.0, -1.0, 0.0, -1.0, 0.0, -1.0, 0.0, -1.0, 0.0 ];
+
+ggradient( 5, 2, x, 2, h, 0, out, 2 );
+// out => [ 0.0, -1.0, 2.0, -1.0, 4.0, -1.0, 6.0, -1.0, 8.0 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial arrays:
+var xbuf = new Float64Array( [ -1.0, -1.0, 0.0, 1.0, 9.0, 36.0, 100.0 ] );
+var hbuf = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0 ] );
+var obuf = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+// Create offset views:
+var x1 = new Float64Array( xbuf.buffer, xbuf.BYTES_PER_ELEMENT*2 ); // start at 3rd element
+var h1 = new Float64Array( hbuf.buffer, hbuf.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+var out1 = new Float64Array( obuf.buffer, obuf.BYTES_PER_ELEMENT*2 );
+
+// Compute the gradient of the last 5 elements:
+ggradient( 5, 1, x1, 1, h1, 1, out1, 1 );
+// obuf => <Float64Array>[ 0.0, 0.0, 1.0, 2.0, 6.0, 12.0, 16.0 ]
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### ggradient.ndarray( N, edgeOrder, x, strideX, offsetX, h, strideH, offsetH, out, strideOut, offsetOut )
+
+<!-- lint enable maximum-heading-length -->
+
+Computes the gradient of a strided array using alternative indexing semantics.
+
+```javascript
+var x = [ 0.0, 1.0, 9.0, 36.0, 100.0 ];
+var h = [ 1.0, 2.0, 3.0, 4.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ggradient.ndarray( x.length, 1, x, 1, 0, h, 1, 0, out, 1, 0 );
+// out => [ 1.0, 2.0, 6.0, 12.0, 16.0 ]
+```
+
+The function has the following additional parameters:
+
+-   **offsetX**: starting index for `x`.
+-   **offsetH**: starting index for `h`.
+-   **offsetOut**: starting index for `out`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example, to compute the gradient of the last five elements:
+
+```javascript
+var x = [ -1.0, -1.0, 0.0, 1.0, 9.0, 36.0, 100.0 ];
+var h = [ 1.0, 2.0, 3.0, 4.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ggradient.ndarray( 5, 1, x, 1, 2, h, 1, 0, out, 1, 2 );
+// out => [ 0.0, 0.0, 1.0, 2.0, 6.0, 12.0, 16.0 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If `N <= 0` or `N === 1`, both functions return `out` unchanged.
+-   Both functions support first-order (i.e., `edgeOrder = 1`) and second-order (i.e., `edgeOrder = 2`) finite-difference approximations at the boundaries.
+-   Both functions support array-like objects having getter and setter accessors for array element access (e.g., [`@stdlib/array/base/accessor`][@stdlib/array/base/accessor]).
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var ggradient = require( '@stdlib/differentiate/strided/ggradient' );
+
+// Approximate the gradient of f(t) = 3t^2 at t = 0, 1, 2, 3, 4 with uniform spacing...
+var x = [ 0.0, 3.0, 12.0, 27.0, 48.0 ];
+var h = [ 1.0 ];
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ggradient( x.length, 2, x, 1, h, 0, out, 1 );
+console.log( out );
+// => [ 0.0, 6.0, 12.0, 18.0, 24.0 ]
+
+// Approximate the gradient of f(t) = 3t^2 at t = 0, 1, 3, 4, 7 with non-uniform spacing...
+x = [ 0.0, 3.0, 27.0, 48.0, 147.0 ];
+h = [ 1.0, 2.0, 1.0, 3.0 ];
+out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ggradient( x.length, 2, x, 1, h, 1, out, 1 );
+console.log( out );
+// => [ 0.0, 6.0, 18.0, 24.0, 42.0 ]
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/base/accessor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/base/accessor
+
+<!-- <related-links> -->
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/differentiate/strided/ggradient/benchmark/benchmark.non_uniform_spacing.js

@@ -0,0 +1,109 @@
+/**
+* @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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var ggradient = require( './../lib/main.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Create a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var out;
+	var h;
+	var x;
+
+	x = uniform( len, -100.0, 100.0, options );
+	h = uniform( len-1, 0.1, 2.0, options );
+	out = uniform( len, -100.0, 100.0, options );
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = ggradient( x.length, 2, x, 1, h, 1, out, 1 );
+			if ( typeof v !== 'object' ) {
+				b.fail( 'should return an object' );
+			}
+		}
+		b.toc();
+		if ( isnan( out[ i%len ] ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( format( '%s::non_uniform_spacing:len=%d', pkg, len ), f );
+	}
+}
+
+main();