feat: add math/array/special/softmax

lib/node_modules/@stdlib/math/array/special/softmax/README.md

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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.
+
+-->
+
+# softmax
+
+> Compute the softmax function for each element in an input array.
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var softmax = require( '@stdlib/math/array/special/softmax' );
+```
+
+#### softmax( x\[, options] )
+
+Computes the softmax function for each element in an input array.
+
+```javascript
+var v = softmax( [ 1.0, 2.0, 3.0 ] );
+// returns [ ~0.090, ~0.245, ~0.665 ]
+```
+
+The function has the following parameters:
+
+-   **x**: input array.
+-   **options**: function options.
+
+The function accepts the following options:
+
+-   **dtype**: output array data type.
+
+To specify the output array data type, set the `dtype` option.
+
+```javascript
+var v = softmax( [ 1.0, 2.0, 3.0 ], {
+    'dtype': 'float64'
+});
+// returns <Float64Array>[ ~0.090, ~0.245, ~0.665 ]
+```
+
+#### softmax.assign( x, out )
+
+Computes the softmax function for each element in an input array and assigns results to a provided output array.
+
+```javascript
+var zeros = require( '@stdlib/array/zeros' );
+
+var out = zeros( 3, 'float64' );
+// returns <Float64Array>[ 0.0, 0.0, 0.0 ]
+
+var v = softmax.assign( [ 1.0, 2.0, 3.0 ], out );
+// returns <Float64Array>[ ~0.090, ~0.245, ~0.665 ]
+
+var bool = ( v === out );
+// returns true
+```
+
+The method has the following parameters:
+
+-   **x**: input array.
+-   **out**: output array.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+-   To improve numerical stability, the function subtracts the maximum input value before exponentiation.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEach = require( '@stdlib/console/log-each' );
+var softmax = require( '@stdlib/math/array/special/softmax' );
+
+// Generate an array of random numbers:
+var x = uniform( 10, -3.0, 3.0, {
+    'dtype': 'generic'
+});
+
+// Perform element-wise computation:
+var y = softmax( x );
+
+// Print the results:
+logEach( 'softmax(%f) = %f', x, y );
+```
+
+</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">
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/math/array/special/softmax/benchmark/benchmark.assign.js

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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.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var softmax = require( './../lib' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var x = [
+		uniform( len, -10.0, 10.0, {
+			'dtype': 'float64'
+		}),
+		uniform( len, -10.0, 10.0, {
+			'dtype': 'float64'
+		})
+	];
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var out;
+		var o;
+		var i;
+
+		out = zeros( len, 'float64' );
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			o = softmax.assign( x[ i%x.length ], out );
+			if ( isNaN( o[ i%len ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isNaN( o[ 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:len=%d', pkg, len ), f );
+	}
+}
+
+main();

lib/node_modules/@stdlib/math/array/special/softmax/benchmark/benchmark.length.js

@@ -0,0 +1,102 @@
+/**
+* @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 pow = require( '@stdlib/math/base/special/pow' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var softmax = require( './../lib' );
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var x = [
+		uniform( len, -10.0, 10.0, {
+			'dtype': 'float64'
+		}),
+		uniform( len, -10.0, 10.0, {
+			'dtype': 'float64'
+		})
+	];
+	return benchmark;
+
+	/**
+	* Benchmark function.
+	*
+	* @private
+	* @param {Benchmark} b - benchmark instance
+	*/
+	function benchmark( b ) {
+		var o;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			o = softmax( x[ i%x.length ] );
+			if ( isNaN( o[ i%len ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isNaN( o[ 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:len=%d', pkg, len ), f );
+	}
+}
+
+main();