feat: add stats/base/ndarray/dsem

lib/node_modules/@stdlib/stats/base/ndarray/dsem/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.
+
+-->
+
+# dsem
+
+> Calculate the [standard error of the mean][standard-error] of a one-dimensional double-precision floating-point ndarray.
+
+<section class="intro">
+
+The [standard error of the mean][standard-error] of a finite size sample of size `n` is given by
+
+<!-- <equation class="equation" label="eq:standard_error_of_the_mean" align="center" raw="\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}" alt="Equation for the standard error of the mean."> -->
+
+```math
+\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}" data-equation="eq:standard_error_of_the_mean">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@227a94a6f2e49efe65e814f2da7bc9b9c2bec9b9/lib/node_modules/@stdlib/stats/strided/dsem/docs/img/equation_standard_error_of_the_mean.svg" alt="Equation for the standard error of the mean.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `σ` is the population [standard deviation][standard-deviation].
+
+Often in the analysis of data, the true population [standard deviation][standard-deviation] is not known _a priori_ and must be estimated from a sample drawn from the population distribution. In this scenario, one must use a sample [standard deviation][standard-deviation] to compute an estimate for the [standard error of the mean][standard-error]
+
+<!-- <equation class="equation" label="eq:standard_error_of_the_mean_estimate" align="center" raw="\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}}" alt="Equation for estimating the standard error of the mean."> -->
+
+```math
+\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}}
+```
+
+<!-- <div class="equation" align="center" data-raw-text="\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}}" data-equation="eq:standard_error_of_the_mean_estimate">
+    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@227a94a6f2e49efe65e814f2da7bc9b9c2bec9b9/lib/node_modules/@stdlib/stats/strided/dsem/docs/img/equation_standard_error_of_the_mean_estimate.svg" alt="Equation for estimating the standard error of the mean.">
+    <br>
+</div> -->
+
+<!-- </equation> -->
+
+where `s` is the sample [standard deviation][standard-deviation].
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dsem = require( '@stdlib/stats/base/ndarray/dsem' );
+```
+
+#### dsem( arrays )
+
+Computes the [standard error of the mean][standard-error] of a one-dimensional double-precision floating-point ndarray.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+
+var opts = {
+    'dtype': 'float64'
+};
+
+var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+var correction = scalar2ndarray( 1.0, opts );
+
+var v = dsem( [ x, correction ] );
+// returns ~1.20185
+```
+
+The function accepts the following arguments:
+
+-   **arrays**: array-like object containing a one-dimensional input ndarray and a zero-dimensional ndarray specifying a degrees of freedom adjustment.
+
+</section>
+
+<!-- /.usage -->
+
+<section class="examples">
+
+## Examples
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var dsem = require( '@stdlib/stats/base/ndarray/dsem' );
+
+var opts = {
+    'dtype': 'float64'
+};
+
+var xbuf = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
+var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 2 ], 1, 'row-major' );
+
+var correction = scalar2ndarray( 1.0, opts );
+
+var v = dsem( [ x, correction ] );
+// returns 1.25
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. -->
+
+<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">
+
+[standard-error]: https://en.wikipedia.org/wiki/Standard_error
+
+[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
+
+</section>
+
+<!-- /.links -->

lib/node_modules/@stdlib/stats/base/ndarray/dsem/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 pow = require( '@stdlib/math/base/special/pow' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var dsem = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var correction;
+	var xbuf;
+	var x;
+
+	xbuf = uniform( len, -10.0, 10.0, options );
+	x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
+	correction = scalar2ndarray( 1.0, options );
+
+	return benchmark;
+
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = dsem( [ x, correction ] );
+			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();
+	}
+}
+
+
+// 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/stats/base/ndarray/dsem/docs/repl.txt

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+
+{{alias}}( arrays )
+    Computes the standard error of the mean of a one-dimensional
+    double-precision floating-point ndarray.
+
+    If provided an empty one-dimensional ndarray, the function returns `NaN`.
+
+    Parameters
+    ----------
+    arrays: ArrayLikeObject<ndarray>
+        Array-like object containing a one-dimensional input ndarray and a
+        zero-dimensional ndarray specifying a degrees of freedom adjustment.
+
+    Returns
+    -------
+    out: number
+        The standard error of the mean.
+
+    Examples
+    --------
+    // Create input ndarray:
+    > var Float64Array = require( '@stdlib/array/float64' );
+    > var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+    > var dt = 'float64';
+    > var sh = [ xbuf.length ];
+    > var st = [ 1 ];
+    > var oo = 0;
+    > var ord = 'row-major';
+    > var x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, st, oo, ord );
+
+    // Create correction ndarray:
+    > var opts = { 'dtype': dt };
+    > var correction = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts );
+
+    // Compute the standard error of the mean:
+    > {{alias}}( [ x, correction ] )
+    ~1.20185
+
+    See Also
+    --------
+

lib/node_modules/@stdlib/stats/base/ndarray/dsem/docs/types/index.d.ts

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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.
+*/
+
+// TypeScript Version: 4.1
+
+/// <reference types="@stdlib/types"/>
+
+import { typedndarray } from '@stdlib/types/ndarray';
+
+/**
+* Computes the standard error of the mean of a one-dimensional double-precision floating-point ndarray.
+*
+* @param arrays - array-like object containing a one-dimensional input ndarray and a zero-dimensional ndarray specifying a degrees of freedom adjustment
+* @returns standard error of the mean
+*
+* @example
+* var ndarray = require( '@stdlib/ndarray/base/ctor' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var opts = {
+*     'dtype': 'float64'
+* };
+*
+* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+* var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+* var correction = scalar2ndarray( 1.0, opts );
+*
+* var v = dsem( [ x, correction ] );
+* // returns ~1.20185
+*/
+declare function dsem<T extends typedndarray<number> = typedndarray<number>>( arrays: [ T, T ] ): number;
+
+
+// EXPORTS //
+
+export = dsem;