feat: add ml/base/loss/float64/epsilon-insensitive-gradient

lib/node_modules/@stdlib/ml/base/loss/float64/epsilon-insensitive-gradient/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.
+
+-->
+
+# epsilonInsensitiveGradient
+
+> Compute the [epsilon insensitive loss gradient][epsilon-insensitive-loss-gradient] with respect to a model parameter.
+
+<section class="intro">
+
+The [epsilon insensitive loss gradient][epsilon-insensitive-loss-gradient] is defined as
+
+<!-- <equation class="equation" label="eq:epsilon_insensitive_loss_gradient" align="center" raw="\frac{\partial \ell}{\partial w_i} =\begin{cases}-x_i & \text{if } y - p > \epsilon, \\x_i & \text{if } p - y > \epsilon, \\0 & \text{otherwise.}\end{cases}" alt="Equation for the epsilon insensitive loss gradient."> -->
+
+```math
+\frac{\partial \ell}{\partial w_i} =
+\begin{cases}
+-x_i & \text{if } y - p > \epsilon, \\
+x_i & \text{if } p - y > \epsilon, \\
+0 & \text{otherwise.}
+\end{cases}
+```
+
+<!-- </equation> -->
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+<!-- eslint-disable id-length -->
+
+```javascript
+var epsilonInsensitiveGradient = require( '@stdlib/ml/base/loss/float64/epsilon-insensitive-gradient' );
+```
+
+#### epsilonInsensitiveGradient( x, e, y, p )
+
+Computes the [epsilon insensitive loss gradient][epsilon-insensitive-loss-gradient] with respect to a model parameter.
+
+<!-- eslint-disable id-length -->
+
+```javascript
+var v = epsilonInsensitiveGradient( 3.0, 5.0, 10.2, 0.782 );
+// returns -3.0
+
+v = epsilonInsensitiveGradient( -1.3, 1.0, 23.2, -0.999 );
+// returns 1.3
+```
+
+If any argument is `NaN`, the function returns `NaN`.
+
+<!-- eslint-disable id-length -->
+
+```javascript
+var v = epsilonInsensitiveGradient( NaN, 1.0, 1.0, 0.782 );
+// returns NaN
+
+v = epsilonInsensitiveGradient( 1.0, 1.0, NaN, 0.782 );
+// returns NaN
+
+v = epsilonInsensitiveGradient( NaN, NaN, 1.0, 0.782 );
+// returns NaN
+
+v = epsilonInsensitiveGradient( NaN, NaN, NaN, NaN );
+// returns NaN
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint-disable id-length -->
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var logEachMap = require( '@stdlib/console/log-each-map' );
+var epsilonInsensitiveGradient = require( '@stdlib/ml/base/loss/float64/epsilon-insensitive-gradient' );
+
+var x = uniform( 100, -100.0, 100.0, {
+    'dtype': 'float64'
+});
+var e = uniform( 100, 0.0, 5.0, {
+    'dtype': 'float64'
+});
+var y = uniform( 100, -100.0, 100.0, {
+    'dtype': 'float64'
+});
+var p = uniform( 100, -5.0, 5.0, {
+    'dtype': 'float64'
+});
+
+logEachMap( 'epsilonInsensitiveGradient(%0.4f, %0.4f, %0.4f, %0.4f) = %0.4f', x, e, y, p, epsilonInsensitiveGradient );
+
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- C interface documentation. -->
+
+* * *
+
+<section class="c">
+
+## C APIs
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- C usage documentation. -->
+
+<section class="usage">
+
+### Usage
+
+```c
+#include "stdlib/ml/base/loss/float64/epsilon_insensitive_gradient.h"
+```
+
+#### stdlib_base_float64_epsilon_insensitive_gradient( x, e, y, p )
+
+Computes the [epsilon insensitive loss gradient][epsilon-insensitive-loss-gradient] with respect to a model parameter.
+
+```c
+double out = stdlib_base_float64_epsilon_insensitive_gradient( 3.0, 5.0, 10.2, 0.782 );
+// returns -3.0
+```
+
+The function accepts the following arguments:
+
+-   **x**: `[in] double` input value.
+-   **e**: `[in] double` insensitivity parameter.
+-   **y**: `[in] double` true target value.
+-   **p**: `[in] double` predicted value.
+
+```c
+double stdlib_base_float64_epsilon_insensitive_gradient( const double x, const double e, const double y, const double p );
+```
+
+</section>
+
+<!-- /.usage -->
+
+<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+</section>
+
+<!-- /.notes -->
+
+<!-- C API usage examples. -->
+
+<section class="examples">
+
+### Examples
+
+```c
+#include "stdlib/ml/base/loss/float64/epsilon_insensitive_gradient.h"
+#include <stdio.h>
+
+int main( void ) {
+    const double x[] = { -10.0, -9.56, -8.67, -7.78, -6.89, 6.89, 7.78, 8.67, 9.56, 10.0 };
+    const double e[] = { 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 };
+    const double y[] = { -9.9, -7.7, -5.5, -3.3, -1.1, 1.1, 3.3, 5.5, 7.7, 9.9 };
+    const double p[] = { -5.0, -3.89, -2.78, -1.67, -0.56, 0.56, 1.67, 2.78, 3.89, 5.0 };
+
+    double v;
+    int i;
+    for ( i = 0; i < 10; i++ ) {
+        v = stdlib_base_float64_epsilon_insensitive_gradient( x[ i ], e[ i ], y[ i ], p[ i ] );
+        printf( "epsilonInsensitiveGradient(%lf, %lf, %lf, %lf) = %lf\n", x[ i ], e[ i ], y[ i ], p[ i ], v );
+    }
+}
+```
+
+</section>
+
+<!-- /.examples -->
+
+</section>
+
+<!-- /.c -->
+
+<!-- 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">
+
+[epsilon-insensitive-loss-gradient]: https://en.wikipedia.org/wiki/Support_vector_machine#Regression
+
+<!-- <related-links> -->
+
+
+<!-- </related-links> -->
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/ml/base/loss/float64/epsilon-insensitive-gradient/benchmark/benchmark.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 uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pkg = require( './../package.json' ).name;
+var epsilonInsensitiveGradient = require( './../lib' );
+
+
+// MAIN //
+
+bench( pkg, function benchmark( b ) {
+	var len;
+	var x;
+	var y;
+	var p;
+	var v;
+	var i;
+
+	len = 100;
+	x = uniform( len, -100.0, 100.0 );
+	y = uniform( len, -100.0, 100.0 );
+	p = uniform( len, -100.0, 100.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = epsilonInsensitiveGradient( x[ i%x.length ], 1.0, y[ i%y.length ], p[ i%p.length ] );
+		if ( isnan( v ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( v ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});

lib/node_modules/@stdlib/ml/base/loss/float64/epsilon-insensitive-gradient/benchmark/benchmark.native.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 resolve = require( 'path' ).resolve;
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var tryRequire = require( '@stdlib/utils/try-require' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+
+
+// VARIABLES //
+
+var epsilonInsensitiveGradient = tryRequire( resolve( __dirname, './../lib/native.js' ) );
+var opts = {
+	'skip': ( epsilonInsensitiveGradient instanceof Error )
+};
+
+
+// MAIN //
+
+bench( format( '%s::native', pkg ), opts, function benchmark( b ) {
+	var len;
+	var x;
+	var y;
+	var p;
+	var v;
+	var i;
+
+	len = 100;
+	x = uniform( len, -100.0, 100.0 );
+	y = uniform( len, -100.0, 100.0 );
+	p = uniform( len, -100.0, 100.0 );
+
+	b.tic();
+	for ( i = 0; i < b.iterations; i++ ) {
+		v = epsilonInsensitiveGradient( x[ i%x.length ], 1.0, y[ i%y.length ], p[ i%p.length ] );
+		if ( isnan( v ) ) {
+			b.fail( 'should not return NaN' );
+		}
+	}
+	b.toc();
+	if ( isnan( v ) ) {
+		b.fail( 'should not return NaN' );
+	}
+	b.pass( 'benchmark finished' );
+	b.end();
+});