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feat: add stats/base/ndarray/dsem
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‎lib/node_modules/@stdlib/stats/base/ndarray/dsem/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dsem
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> Calculate the [standard error of the mean][standard-error] of a one-dimensional double-precision floating-point ndarray.
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<section class="intro">
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The [standard error of the mean][standard-error] of a finite size sample of size `n` is given by
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<!-- <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."> -->
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```math
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\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}
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```
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<!-- <div class="equation" align="center" data-raw-text="\sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}}" data-equation="eq:standard_error_of_the_mean">
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<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.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `σ` is the population [standard deviation][standard-deviation].
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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]
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<!-- <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."> -->
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```math
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\sigma_{\bar{x}} \approx \frac{s}{\sqrt{n}}
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```
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<!-- <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">
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<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.">
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<br>
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</div> -->
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<!-- </equation> -->
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where `s` is the sample [standard deviation][standard-deviation].
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</section>
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<!-- /.intro -->
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<section class="usage">
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## Usage
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```javascript
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var dsem = require( '@stdlib/stats/base/ndarray/dsem' );
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```
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#### dsem( arrays )
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Computes the [standard error of the mean][standard-error] of a one-dimensional double-precision floating-point ndarray.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var ndarray = require( '@stdlib/ndarray/ctor' );
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var opts = {
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'dtype': 'float64'
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};
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var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
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var correction = scalar2ndarray( 1.0, opts );
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var v = dsem( [ x, correction ] );
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// returns ~1.20185
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```
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The function accepts the following arguments:
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- **arrays**: array-like object containing a one-dimensional input ndarray and a zero-dimensional ndarray specifying a degrees of freedom adjustment.
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</section>
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<!-- /.usage -->
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<section class="examples">
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## Examples
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var ndarray = require( '@stdlib/ndarray/ctor' );
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var dsem = require( '@stdlib/stats/base/ndarray/dsem' );
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var opts = {
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'dtype': 'float64'
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};
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var xbuf = new Float64Array( [ 2.0, 1.0, 2.0, -2.0, -2.0, 2.0, 3.0, 4.0 ] );
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var x = new ndarray( opts.dtype, xbuf, [ 4 ], [ 2 ], 1, 'row-major' );
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var correction = scalar2ndarray( 1.0, opts );
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var v = dsem( [ x, correction ] );
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// returns 1.25
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```
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</section>
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<!-- /.examples -->
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<!-- Section for related `stdlib` packages. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[standard-error]: https://en.wikipedia.org/wiki/Standard_error
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[standard-deviation]: https://en.wikipedia.org/wiki/Standard_deviation
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/stats/base/ndarray/dsem/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var uniform = require( '@stdlib/random/array/uniform' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var ndarray = require( '@stdlib/ndarray/base/ctor' );
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var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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var format = require( '@stdlib/string/format' );
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var pkg = require( './../package.json' ).name;
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var dsem = require( './../lib' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} len - array length
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* @returns {Function} benchmark function
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*/
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function createBenchmark( len ) {
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var correction;
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var xbuf;
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var x;
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xbuf = uniform( len, -10.0, 10.0, options );
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x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
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correction = scalar2ndarray( 1.0, options );
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return benchmark;
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function benchmark( b ) {
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var v;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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v = dsem( [ x, correction ] );
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( v ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var len;
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var min;
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var max;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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len = pow( 10, i );
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f = createBenchmark( len );
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bench( format( '%s::len=%d', pkg, len ), f );
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}
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}
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main();

‎lib/node_modules/@stdlib/stats/base/ndarray/dsem/docs/repl.txt‎

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

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/*
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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// TypeScript Version: 4.1
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/// <reference types="@stdlib/types"/>
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import { typedndarray } from '@stdlib/types/ndarray';
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/**
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* Computes the standard error of the mean of a one-dimensional double-precision floating-point ndarray.
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*
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* @param arrays - array-like object containing a one-dimensional input ndarray and a zero-dimensional ndarray specifying a degrees of freedom adjustment
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* @returns standard error of the mean
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*
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* @example
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* var ndarray = require( '@stdlib/ndarray/base/ctor' );
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* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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* var opts = {
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* 'dtype': 'float64'
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* };
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*
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* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
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* var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
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* var correction = scalar2ndarray( 1.0, opts );
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*
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* var v = dsem( [ x, correction ] );
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* // returns ~1.20185
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*/
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declare function dsem<T extends typedndarray<number> = typedndarray<number>>( arrays: [ T, T ] ): number;
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// EXPORTS //
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export = dsem;

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