From a581550f0197c21610288c148d2a15a743f0ad89 Mon Sep 17 00:00:00 2001
From: headlessNode <harriskhan047@outlook.com>
Date: Sat, 17 Oct 2026 15:18:51 +0500
Subject: [PATCH 1/4] feat: add blas/ext/base/ghelmert

---
 .../@stdlib/blas/ext/base/ghelmert/README.md  | 180 ++++
 .../ext/base/ghelmert/benchmark/benchmark.js  | 103 ++
 .../ghelmert/benchmark/benchmark.ndarray.js   | 103 ++
 .../blas/ext/base/ghelmert/docs/repl.txt      |  96 ++
 .../ext/base/ghelmert/docs/types/index.d.ts   | 112 +++
 .../blas/ext/base/ghelmert/docs/types/test.ts | 212 +++++
 .../blas/ext/base/ghelmert/examples/index.js  |  34 +
 .../blas/ext/base/ghelmert/lib/accessors.js   |  88 ++
 .../blas/ext/base/ghelmert/lib/index.js       |  73 ++
 .../blas/ext/base/ghelmert/lib/main.js        |  91 ++
 .../blas/ext/base/ghelmert/lib/ndarray.js     |  98 ++
 .../blas/ext/base/ghelmert/package.json       |  70 ++
 .../blas/ext/base/ghelmert/test/test.js       |  38 +
 .../blas/ext/base/ghelmert/test/test.main.js  | 843 +++++++++++++++++
 .../ext/base/ghelmert/test/test.ndarray.js    | 888 ++++++++++++++++++
 15 files changed, 3029 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/README.md
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.ndarray.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/index.d.ts
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/test.ts
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/examples/index.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/index.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/main.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/package.json
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.main.js
 create mode 100644 lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.ndarray.js

diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/README.md b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/README.md
new file mode 100644
index 000000000000..7568ebe9161f
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/README.md
@@ -0,0 +1,180 @@
+<!--
+
+@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.
+
+-->
+
+# ghelmert
+
+> Generate a Helmert matrix.
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var ghelmert = require( '@stdlib/blas/ext/base/ghelmert' );
+```
+
+#### ghelmert( order, full, N, out, ldo )
+
+Generates a Helmert matrix.
+
+```javascript
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ghelmert( 'row-major', true, 3, out, 3 );
+// out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+```
+
+The function has the following parameters:
+
+-   **order**: row-major (C-style) or column-major (Fortran-style) order.
+-   **full**: boolean indicating whether to include the first row of `1/√N` values.
+-   **N**: order of the Helmert matrix.
+-   **out**: output matrix.
+-   **ldo**: stride between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of the matrix `out`).
+
+To exclude the constant first row and retain only the `N-1` orthogonal contrast rows, set `full` to `false`, resulting in an `(N-1)`-by-`N` matrix:
+
+```javascript
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ghelmert( 'row-major', false, 3, out, 3 );
+// out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable stdlib/capitalized-comments, max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+
+// Initial array:
+var out0 = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0 ] );
+
+// Create an offset view:
+var out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 );
+
+ghelmert( 'row-major', true, 2, out1, 2 );
+// out0 => <Float64Array>[ 0.0, ~0.707, ~0.707, ~0.707, ~-0.707 ]
+```
+
+#### ghelmert.ndarray( full, N, out, strideOut1, strideOut2, offsetOut )
+
+Generates a Helmert matrix using alternative indexing semantics.
+
+```javascript
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ghelmert.ndarray( true, 3, out, 3, 1, 0 );
+// out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+```
+
+The function has the following additional parameters:
+
+-   **strideOut1**: stride length for the first dimension of `out`.
+-   **strideOut2**: stride length for the second dimension of `out`.
+-   **offsetOut**: starting index for `out`.
+
+While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameter supports indexing semantics based on a starting index. For example, to start writing matrix elements from the second element of the output array:
+
+```javascript
+var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+
+ghelmert.ndarray( false, 3, out, 3, 1, 1 );
+// out => [ 0.0, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+```
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If the number of output rows is less than or equal to `0`, both functions return `out` unchanged.
+-   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 ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var zeros = require( '@stdlib/array/zeros' );
+var ghelmert = require( '@stdlib/blas/ext/base/ghelmert' );
+
+var N = 4;
+var order = 'row-major';
+var shape = [ N, N ];
+var strides = shape2strides( shape, order );
+
+var out = zeros( N*N, 'generic' );
+
+ghelmert( order, true, N, out, N );
+console.log( ndarray2array( out, shape, strides, 0, order ) );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="references">
+
+</section>
+
+<!-- /.references -->
+
+<!-- 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-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 -->
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.js
new file mode 100644
index 000000000000..326eb9b25354
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.js
@@ -0,0 +1,103 @@
+/**
+* @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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var zeros = require( '@stdlib/array/zeros' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var ghelmert = require( './../lib/main.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var out = zeros( len * len, options.dtype );
+	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 = ghelmert( 'row-major', true, len, out, len );
+			if ( isnan( v[ i%v.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( v[ i%v.length ] ) ) {
+			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 = 2; // 2^min
+	max = 10; // 2^max
+
+	for ( i = min; i <= max; i += 2 ) {
+		len = pow( 2, i );
+		f = createBenchmark( len );
+		bench( format( '%s:len=%d', pkg, len ), f );
+	}
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.ndarray.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.ndarray.js
new file mode 100644
index 000000000000..0244dada5770
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/benchmark/benchmark.ndarray.js
@@ -0,0 +1,103 @@
+/**
+* @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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var zeros = require( '@stdlib/array/zeros' );
+var format = require( '@stdlib/string/format' );
+var pkg = require( './../package.json' ).name;
+var ghelmert = require( './../lib/ndarray.js' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'generic'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var out = zeros( len * len, options.dtype );
+	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 = ghelmert( true, len, out, len, 1, 0 );
+			if ( isnan( v[ i%v.length ] ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( v[ i%v.length ] ) ) {
+			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 = 2; // 2^min
+	max = 10; // 2^max
+
+	for ( i = min; i <= max; i += 2 ) {
+		len = pow( 2, i );
+		f = createBenchmark( len );
+		bench( format( '%s:ndarray:len=%d', pkg, len ), f );
+	}
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
new file mode 100644
index 000000000000..e6b538bfb8ab
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
@@ -0,0 +1,96 @@
+{{alias}}( order, full, N, out, ldo )
+    Generates a Helmert matrix.
+
+    To exclude the constant first row and retain only the `N-1` orthogonal
+    contrast rows, set `full` to `false`, resulting in an `(N-1)xN` matrix.
+
+    If the number of output rows is less than or equal to `0`, the function
+    returns `out` unchanged.
+
+    Parameters
+    ----------
+    order: string
+        Storage layout.
+
+    full: boolean
+        Boolean indicating whether to include the first row of `1/sqrt(N)`
+        values.
+
+    N: integer
+        Order of the Helmert matrix.
+
+    out: ArrayLikeObject
+        Output array.
+
+    ldo: integer
+        Stride length between successive contiguous vectors of the matrix
+        `out` (a.k.a., leading dimension of `out`).
+
+    Returns
+    -------
+    out: ArrayLikeObject
+        Output array.
+
+    Examples
+    --------
+    // Standard usage:
+    > var out = new {{alias:@stdlib/array/float64}}( 9 );
+    > {{alias}}( 'row-major', true, 3, out, 3 )
+    <Float64Array>[ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+
+    // Excluding the first row:
+    > out = new {{alias:@stdlib/array/float64}}( 6 );
+    > {{alias}}( 'row-major', false, 3, out, 3 )
+    <Float64Array>[ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+
+
+{{alias}}.ndarray( full, N, out, so1, so2, oo )
+    Generates a Helmert matrix using alternative indexing semantics.
+
+    To exclude the constant first row and retain only the `N-1` orthogonal
+    contrast rows, set `full` to `false`, resulting in an `(N-1)xN` matrix.
+
+    While typed array views mandate a view offset based on the underlying
+    buffer, the offset parameter supports indexing semantics based on a starting
+    index.
+
+    Parameters
+    ----------
+    full: boolean
+        Boolean indicating whether to include the first row of `1/sqrt(N)`
+        values.
+
+    N: integer
+        Order of the Helmert matrix.
+
+    out: ArrayLikeObject
+        Output array.
+
+    so1: integer
+        Stride length for the first dimension of `out`.
+
+    so2: integer
+        Stride length for the second dimension of `out`.
+
+    oo: integer
+        Starting index for `out`.
+
+    Returns
+    -------
+    out: ArrayLikeObject
+        Output array.
+
+    Examples
+    --------
+    // Standard Usage:
+    > var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+    > {{alias}}.ndarray( true, 3, out, 3, 1, 0 )
+    [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+
+    // Using an index offset:
+    > out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+    > {{alias}}.ndarray( true, 3, out, 3, 1, 1 )
+    [ 0.0, ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+
+    See Also
+    --------
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/index.d.ts b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/index.d.ts
new file mode 100644
index 000000000000..585c44c0bdae
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/index.d.ts
@@ -0,0 +1,112 @@
+/*
+* @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 { Collection, AccessorArrayLike } from '@stdlib/types/array';
+import { Layout } from '@stdlib/types/blas';
+
+/**
+* Output array.
+*/
+type OutputArray<T> = Collection<T> | AccessorArrayLike<T>;
+
+/**
+* Interface describing `ghelmert`.
+*/
+interface Routine {
+	/**
+	* Generates a Helmert matrix.
+	*
+	* @param order - storage layout
+	* @param full - boolean indicating whether to include the first row
+	* @param N - order of the Helmert matrix
+	* @param out - output array
+	* @param ldo - stride length between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of `out`)
+	* @returns output array
+	*
+	* @example
+	* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+	*
+	* ghelmert( 'row-major', true, 3, out, 3 );
+	* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+	*
+	* @example
+	* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+	*
+	* ghelmert( 'row-major', false, 3, out, 3 );
+	* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+	*/
+	<T = unknown, V extends OutputArray<T> = OutputArray<T>>( order: Layout, full: boolean, N: number, out: V, ldo: number ): V;
+
+	/**
+	* Generates a Helmert matrix using alternative indexing semantics.
+	*
+	* @param full - boolean indicating whether to include the first row
+	* @param N - order of the Helmert matrix
+	* @param out - output array
+	* @param strideOut1 - stride length for the first dimension of `out`
+	* @param strideOut2 - stride length for the second dimension of `out`
+	* @param offsetOut - starting index for `out`
+	* @returns output array
+	*
+	* @example
+	* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+	*
+	* ghelmert.ndarray( true, 3, out, 3, 1, 0 );
+	* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+	*
+	* @example
+	* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+	*
+	* ghelmert.ndarray( false, 3, out, 3, 1, 0 );
+	* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+	*/
+	ndarray<T = unknown, V extends OutputArray<T> = OutputArray<T>>( full: boolean, N: number, out: V, strideOut1: number, strideOut2: number, offsetOut: number ): V;
+}
+
+/**
+* Generates a Helmert matrix.
+*
+* @param order - storage layout
+* @param full - boolean indicating whether to include the first row
+* @param N - order of the Helmert matrix
+* @param out - output array
+* @param ldo - stride length between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of `out`)
+* @returns output array
+*
+* @example
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( 'row-major', true, 3, out, 3 );
+* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*
+* @example
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert.ndarray( false, 3, out, 3, 1, 0 );
+* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*/
+declare var ghelmert: Routine;
+
+
+// EXPORTS //
+
+export = ghelmert;
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/test.ts b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/test.ts
new file mode 100644
index 000000000000..9d8919c06745
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/types/test.ts
@@ -0,0 +1,212 @@
+/*
+* @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.
+*/
+
+/* eslint-disable space-in-parens */
+
+import AccessorArray = require( '@stdlib/array/base/accessor' );
+import ghelmert = require( './index' );
+
+
+// TESTS //
+
+// The function returns a collection...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert( 'row-major', true, 4, out, 4 ); // $ExpectType Float64Array
+	ghelmert( 'row-major', true, 4, new AccessorArray( out ), 4 ); // $ExpectType AccessorArray<number>
+}
+
+// The compiler throws an error if the function is provided a first argument which is not a valid order...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert( 10, true, 4, out, 4 ); // $ExpectError
+	ghelmert( true, true, 4, out, 4 ); // $ExpectError
+	ghelmert( false, true, 4, out, 4 ); // $ExpectError
+	ghelmert( null, true, 4, out, 4 ); // $ExpectError
+	ghelmert( undefined, true, 4, out, 4 ); // $ExpectError
+	ghelmert( [], true, 4, out, 4 ); // $ExpectError
+	ghelmert( {}, true, 4, out, 4 ); // $ExpectError
+	ghelmert( ( x: number ): number => x, true, 4, out, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a second argument which is not a boolean...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert( 'row-major', '10', 4, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', 10, 4, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', null, 4, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', undefined, 4, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', [], 4, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', {}, 4, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', ( x: number ): number => x, 4, out, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a third argument which is not a number...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert( 'row-major', true, '10', out, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, true, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, false, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, null, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, undefined, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, [], out, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, {}, out, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, ( x: number ): number => x, out, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fourth argument which is not a collection...
+{
+	ghelmert( 'row-major', true, 4, 10, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, 4, true, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, 4, false, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, 4, null, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, 4, undefined, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, 4, {}, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, 4, ( x: number ): number => x, 4 ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided a fifth argument which is not a number...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert( 'row-major', true, 4, out, '10' ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, true ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, false ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, null ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, undefined ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, [] ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, {} ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert(); // $ExpectError
+	ghelmert( 'row-major' ); // $ExpectError
+	ghelmert( 'row-major', true ); // $ExpectError
+	ghelmert( 'row-major', true, 4 ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out ); // $ExpectError
+	ghelmert( 'row-major', true, 4, out, 4, 10 ); // $ExpectError
+}
+
+// Attached to the main export is an `ndarray` method which returns a collection...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert.ndarray( true, 4, out, 4, 1, 0 ); // $ExpectType Float64Array
+	ghelmert.ndarray( true, 4, new AccessorArray( out ), 4, 1, 0 ); // $ExpectType AccessorArray<number>
+}
+
+// The compiler throws an error if the `ndarray` method is provided a first argument which is not a boolean...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert.ndarray( '10', 4, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( 10, 4, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( null, 4, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( undefined, 4, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( [], 4, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( {}, 4, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( ( x: number ): number => x, 4, out, 4, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a second argument which is not a number...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert.ndarray( true, '10', out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, true, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, false, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, null, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, undefined, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, [], out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, {}, out, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, ( x: number ): number => x, out, 4, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a third argument which is not a collection...
+{
+	ghelmert.ndarray( true, 4, 10, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, true, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, false, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, null, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, undefined, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, {}, 4, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, ( x: number ): number => x, 4, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a fourth argument which is not a number...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert.ndarray( true, 4, out, '10', 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, true, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, false, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, null, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, undefined, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, [], 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, {}, 1, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, ( x: number ): number => x, 1, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a fifth argument which is not a number...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert.ndarray( true, 4, out, 4, '10', 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, true, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, false, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, null, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, undefined, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, [], 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, {}, 0 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, ( x: number ): number => x, 0 ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided a sixth argument which is not a number...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert.ndarray( true, 4, out, 4, 1, '10' ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, true ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, false ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, null ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, undefined ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, [] ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, {} ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the `ndarray` method is provided an unsupported number of arguments...
+{
+	const out = new Float64Array( 16 );
+
+	ghelmert.ndarray(); // $ExpectError
+	ghelmert.ndarray( true ); // $ExpectError
+	ghelmert.ndarray( true, 4 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1 ); // $ExpectError
+	ghelmert.ndarray( true, 4, out, 4, 1, 0, 10 ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/examples/index.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/examples/index.js
new file mode 100644
index 000000000000..e2e2656ef598
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/examples/index.js
@@ -0,0 +1,34 @@
+/**
+* @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';
+
+var ndarray2array = require( '@stdlib/ndarray/base/to-array' );
+var shape2strides = require( '@stdlib/ndarray/base/shape2strides' );
+var zeros = require( '@stdlib/array/zeros' );
+var ghelmert = require( './../lib' );
+
+var N = 4;
+var order = 'row-major';
+var shape = [ N, N ];
+var strides = shape2strides( shape, order );
+
+var out = zeros( N*N, 'generic' );
+
+ghelmert( order, true, N, out, N );
+console.log( ndarray2array( out, shape, strides, 0, order ) );
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js
new file mode 100644
index 000000000000..3797f1f6fd23
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js
@@ -0,0 +1,88 @@
+/**
+* @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 sqrt = require( '@stdlib/math/base/special/sqrt' );
+
+
+// MAIN //
+
+/**
+* Generates a Helmert matrix using accessor arrays.
+*
+* @private
+* @param {boolean} full - boolean indicating whether to include the first row
+* @param {NonNegativeInteger} N - order of the Helmert matrix
+* @param {Object} out - output array object
+* @param {integer} strideOut1 - stride length for the first dimension of `out`
+* @param {integer} strideOut2 - stride length for the second dimension of `out`
+* @param {NonNegativeInteger} offsetOut - starting index for `out`
+* @returns {Object} output array object
+*
+* @example
+* var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
+* var arraylike2object = require( '@stdlib/array/base/arraylike2object' );
+*
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( true, 3, arraylike2object( toAccessorArray( out ) ), 3, 1, 0 );
+* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*/
+function ghelmert( full, N, out, strideOut1, strideOut2, offsetOut ) {
+	var obuf;
+	var oset;
+	var io;
+	var v;
+	var i;
+	var j;
+
+	obuf = out.data;
+	oset = out.accessors[ 1 ];
+
+	io = offsetOut;
+
+	// If full, write the first row with all elements equal to 1/sqrt(N)...
+	if ( full ) {
+		v = 1.0 / sqrt( N );
+		for ( j = 0; j < N; j++ ) {
+			oset( obuf, io + (j*strideOut2), v );
+		}
+		io += strideOut1;
+	}
+	// For the remaining rows, compute the sub-diagonal Helmert rows...
+	for ( i = 1; i < N; i++ ) {
+		v = 1.0 / sqrt( i * (i+1) );
+		for ( j = 0; j < i; j++ ) {
+			oset( obuf, io + (j*strideOut2), v );
+		}
+		oset( obuf, io + (i*strideOut2), -i * v );
+		for ( j = i + 1; j < N; j++ ) {
+			oset( obuf, io + (j*strideOut2), 0.0 );
+		}
+		io += strideOut1;
+	}
+	return out;
+}
+
+
+// EXPORTS //
+
+module.exports = ghelmert;
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/index.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/index.js
new file mode 100644
index 000000000000..1f59cbdcfdf4
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/index.js
@@ -0,0 +1,73 @@
+/**
+* @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';
+
+/**
+* Generate a Helmert matrix.
+*
+* @module @stdlib/blas/ext/base/ghelmert
+*
+* @example
+* var ghelmert = require( '@stdlib/blas/ext/base/ghelmert' );
+*
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( 'row-major', true, 3, out, 3 );
+* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*
+* @example
+* var ghelmert = require( '@stdlib/blas/ext/base/ghelmert' );
+*
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( 'row-major', false, 3, out, 3 );
+* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*
+* @example
+* var ghelmert = require( '@stdlib/blas/ext/base/ghelmert' );
+*
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert.ndarray( true, 3, out, 3, 1, 0 );
+* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*
+* @example
+* var ghelmert = require( '@stdlib/blas/ext/base/ghelmert' );
+*
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert.ndarray( false, 3, out, 3, 1, 0 );
+* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*/
+
+// MODULES //
+
+var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
+var main = require( './main.js' );
+var ndarray = require( './ndarray.js' );
+
+
+// MAIN //
+
+setReadOnly( main, 'ndarray', ndarray );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/main.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/main.js
new file mode 100644
index 000000000000..3b2b5451f555
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/main.js
@@ -0,0 +1,91 @@
+/**
+* @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 isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' );
+var resolveLayout = require( '@stdlib/blas/base/layout-resolve-str' );
+var max = require( '@stdlib/math/base/special/fast/max' );
+var format = require( '@stdlib/string/format' );
+var ndarray = require( './ndarray.js' );
+
+
+// MAIN //
+
+/**
+* Generates a Helmert matrix.
+*
+* @param {(integer|string)} order - storage layout
+* @param {boolean} full - boolean indicating whether to include the first row
+* @param {NonNegativeInteger} N - order of the Helmert matrix
+* @param {Collection} out - output array
+* @param {PositiveInteger} ldo - stride between successive contiguous vectors of the matrix `out` (a.k.a., leading dimension of the matrix `out`)
+* @throws {TypeError} first argument must be a valid order
+* @throws {RangeError} fifth argument must be a valid stride
+* @returns {Collection} output matrix
+*
+* @example
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( 'row-major', true, 3, out, 3 );
+* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*
+* @example
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( 'row-major', false, 3, out, 3 );
+* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*/
+function ghelmert( order, full, N, out, ldo ) {
+	var iscm;
+	var sa1;
+	var sa2;
+	var M;
+	var l;
+
+	l = resolveLayout( order );
+	if ( l === null ) {
+		throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
+	}
+	M = ( full ) ? N : N - 1;
+	iscm = isColumnMajor( l );
+	if ( iscm ) {
+		if ( ldo < max( 1, M ) ) {
+			throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to max(1,%d). Value: `%d`.', M, ldo ) );
+		}
+		sa1 = 1;
+		sa2 = ldo;
+	} else { // order === 'row-major'
+		if ( ldo < max( 1, N ) ) {
+			throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to max(1,%d). Value: `%d`.', N, ldo ) );
+		}
+		sa1 = ldo;
+		sa2 = 1;
+	}
+	if ( M <= 0 ) {
+		return out;
+	}
+	return ndarray( full, N, out, sa1, sa2, 0 );
+}
+
+
+// EXPORTS //
+
+module.exports = ghelmert;
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js
new file mode 100644
index 000000000000..31d151d1e1bc
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js
@@ -0,0 +1,98 @@
+/**
+* @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 arraylike2object = require( '@stdlib/array/base/arraylike2object' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var accessors = require( './accessors.js' );
+
+
+// MAIN //
+
+/**
+* Generates a Helmert matrix using alternative indexing semantics.
+*
+* @param {boolean} full - boolean indicating whether to include the first row
+* @param {NonNegativeInteger} N - order of the Helmert matrix
+* @param {Collection} out - output array
+* @param {integer} strideOut1 - stride length for the first dimension of `out`
+* @param {integer} strideOut2 - stride length for the second dimension of `out`
+* @param {NonNegativeInteger} offsetOut - starting index for `out`
+* @returns {Collection} output matrix
+*
+* @example
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( true, 3, out, 3, 1, 0 );
+* // out => [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*
+* @example
+* var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
+*
+* ghelmert( false, 3, out, 3, 1, 0 );
+* // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+*/
+function ghelmert( full, N, out, strideOut1, strideOut2, offsetOut ) {
+	var oo;
+	var io;
+	var v;
+	var M;
+	var i;
+	var j;
+
+	M = ( full ) ? N : N - 1;
+	if ( M <= 0 ) {
+		return out;
+	}
+	oo = arraylike2object( out );
+	if ( oo.accessorProtocol ) {
+		accessors( full, N, oo, strideOut1, strideOut2, offsetOut );
+		return out;
+	}
+	io = offsetOut;
+
+	// If full, write the first row with all elements equal to 1/sqrt(N)...
+	if ( full ) {
+		v = 1.0 / sqrt( N );
+		for ( j = 0; j < N; j++ ) {
+			out[ io + (j*strideOut2) ] = v;
+		}
+		io += strideOut1;
+	}
+	// For the remaining rows, compute the sub-diagonal Helmert rows...
+	for ( i = 1; i < N; i++ ) {
+		v = 1.0 / sqrt( i * (i+1) );
+		for ( j = 0; j < i; j++ ) {
+			out[ io + (j*strideOut2) ] = v;
+		}
+		out[ io + (i*strideOut2) ] = -i * v;
+		for ( j = i + 1; j < N; j++ ) {
+			out[ io + (j*strideOut2) ] = 0.0;
+		}
+		io += strideOut1;
+	}
+	return out;
+}
+
+
+// EXPORTS //
+
+module.exports = ghelmert;
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/package.json b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/package.json
new file mode 100644
index 000000000000..2585a5f5dd0b
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/package.json
@@ -0,0 +1,70 @@
+{
+  "name": "@stdlib/blas/ext/base/ghelmert",
+  "version": "0.0.0",
+  "description": "Generate a Helmert matrix.",
+  "license": "Apache-2.0",
+  "author": {
+    "name": "The Stdlib Authors",
+    "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+  },
+  "contributors": [
+    {
+      "name": "The Stdlib Authors",
+      "url": "https://github.com/stdlib-js/stdlib/graphs/contributors"
+    }
+  ],
+  "main": "./lib",
+  "directories": {
+    "benchmark": "./benchmark",
+    "doc": "./docs",
+    "example": "./examples",
+    "lib": "./lib",
+    "test": "./test"
+  },
+  "types": "./docs/types",
+  "scripts": {},
+  "homepage": "https://github.com/stdlib-js/stdlib",
+  "repository": {
+    "type": "git",
+    "url": "git://github.com/stdlib-js/stdlib.git"
+  },
+  "bugs": {
+    "url": "https://github.com/stdlib-js/stdlib/issues"
+  },
+  "dependencies": {},
+  "devDependencies": {},
+  "engines": {
+    "node": ">=0.10.0",
+    "npm": ">2.7.0"
+  },
+  "os": [
+    "aix",
+    "darwin",
+    "freebsd",
+    "linux",
+    "macos",
+    "openbsd",
+    "sunos",
+    "win32",
+    "windows"
+  ],
+  "keywords": [
+    "stdlib",
+    "stdmath",
+    "mathematics",
+    "math",
+    "blas",
+    "extended",
+    "helmert",
+    "matrix",
+    "strided",
+    "strided array",
+    "typed",
+    "array",
+    "ndarray",
+    "vector",
+    "ghelmert",
+    "orthogonal"
+  ],
+  "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.js
new file mode 100644
index 000000000000..bd940dc10f51
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.js
@@ -0,0 +1,38 @@
+/**
+* @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 tape = require( 'tape' );
+var ghelmert = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof ghelmert, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'attached to the main export is a method providing an ndarray interface', function test( t ) {
+	t.strictEqual( typeof ghelmert.ndarray, 'function', 'method is a function' );
+	t.end();
+});
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.main.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.main.js
new file mode 100644
index 000000000000..8eba85a56d63
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.main.js
@@ -0,0 +1,843 @@
+/**
+* @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 tape = require( 'tape' );
+var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
+var Float64Array = require( '@stdlib/array/float64' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var ghelmert = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof ghelmert, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function has an arity of 5', function test( t ) {
+	t.strictEqual( ghelmert.length, 5, 'has expected arity' );
+	t.end();
+});
+
+tape( 'the function throws an error if provided an invalid first argument', function test( t ) {
+	var values;
+	var i;
+
+	values = [
+		'foo',
+		'bar',
+		'beep',
+		'boop'
+	];
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			ghelmert( value, true, 2, [ 0.0, 0.0, 0.0, 0.0 ], 2 );
+		};
+	}
+});
+
+tape( 'the function throws an error if provided an invalid first argument (accessors)', function test( t ) {
+	var values;
+	var i;
+
+	values = [
+		'foo',
+		'bar',
+		'beep',
+		'boop'
+	];
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), TypeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			ghelmert( value, true, 2, toAccessorArray( [ 0.0, 0.0, 0.0, 0.0 ] ), 2 ); // eslint-disable-line max-len
+		};
+	}
+});
+
+tape( 'the function throws an error if provided an invalid fifth argument (row-major)', function test( t ) {
+	var values;
+	var i;
+
+	values = [
+		-2,
+		-1,
+		0,
+		1
+	];
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			ghelmert( 'row-major', true, 2, [ 0.0, 0.0, 0.0, 0.0 ], value );
+		};
+	}
+});
+
+tape( 'the function throws an error if provided an invalid fifth argument (row-major, accessors)', function test( t ) {
+	var values;
+	var i;
+
+	values = [
+		-2,
+		-1,
+		0,
+		1
+	];
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			ghelmert( 'row-major', true, 2, toAccessorArray( [ 0.0, 0.0, 0.0, 0.0 ] ), value );
+		};
+	}
+});
+
+tape( 'the function throws an error if provided an invalid fifth argument (column-major)', function test( t ) {
+	var values;
+	var i;
+
+	values = [
+		-2,
+		-1,
+		0,
+		1
+	];
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			ghelmert( 'column-major', true, 2, [ 0.0, 0.0, 0.0, 0.0 ], value );
+		};
+	}
+});
+
+tape( 'the function throws an error if provided an invalid fifth argument (column-major, accessors)', function test( t ) {
+	var values;
+	var i;
+
+	values = [
+		-2,
+		-1,
+		0,
+		1
+	];
+
+	for ( i = 0; i < values.length; i++ ) {
+		t.throws( badValue( values[ i ] ), RangeError, 'throws an error when provided ' + values[ i ] );
+	}
+	t.end();
+
+	function badValue( value ) {
+		return function badValue() {
+			ghelmert( 'column-major', true, 2, toAccessorArray( [ 0.0, 0.0, 0.0, 0.0 ] ), value );
+		};
+	}
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( 'row-major', true, 0, out, 1 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( 'row-major', true, 0, toAccessorArray( out ), 1 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( 'row-major', false, 1, out, 1 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=false, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( 'row-major', false, 1, toAccessorArray( out ), 1 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function returns the output matrix', function test( t ) {
+	var out;
+	var v;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	v = ghelmert( 'row-major', true, 2, out, 2 );
+
+	t.strictEqual( v, out, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function returns the output matrix (accessors)', function test( t ) {
+	var out;
+	var v;
+
+	out = toAccessorArray( [ 0.0, 0.0, 0.0, 0.0 ] );
+
+	v = ghelmert( 'row-major', true, 2, out, 2 );
+
+	t.strictEqual( v, out, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'row-major', true, 4, out, 4 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'row-major', true, 4, toAccessorArray( out ), 4 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'row-major', false, 4, out, 4 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=false, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'row-major', false, 4, toAccessorArray( out ), 4 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'column-major', true, 4, out, 4 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'column-major', true, 4, toAccessorArray( out ), 4 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'column-major', false, 4, out, 3 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=false, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'column-major', false, 4, toAccessorArray( out ), 3 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports a leading dimension for the output matrix (row-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'row-major', true, 2, out, 3 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports a leading dimension for the output matrix (row-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'row-major', true, 2, toAccessorArray( out ), 3 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports a leading dimension for the output matrix (column-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'column-major', true, 2, out, 3 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports a leading dimension for the output matrix (column-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'column-major', true, 2, toAccessorArray( out ), 3 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports a leading dimension for the output matrix (row-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'row-major', false, 3, out, 5 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports a leading dimension for the output matrix (column-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( 'column-major', false, 3, out, 4 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		0.0,
+		0.0,
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		0.0,
+		0.0,
+		0.0,
+		-2.0 / sqrt( 6 ),
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports view offsets (full=true)', function test( t ) {
+	var expected;
+	var out0;
+	var out1;
+
+	out0 = new Float64Array( 5 );
+	out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 );
+
+	ghelmert( 'row-major', true, 2, out1, 2 );
+
+	expected = new Float64Array([
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 )
+	]);
+
+	t.deepEqual( out1, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports view offsets (full=false)', function test( t ) {
+	var expected;
+	var out0;
+	var out1;
+
+	out0 = new Float64Array( 7 );
+	out1 = new Float64Array( out0.buffer, out0.BYTES_PER_ELEMENT*1 );
+
+	ghelmert( 'row-major', false, 3, out1, 3 );
+
+	expected = new Float64Array([
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 )
+	]);
+
+	t.deepEqual( out1, expected, 'returns expected value' );
+	t.end();
+});
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.ndarray.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.ndarray.js
new file mode 100644
index 000000000000..996f591a9068
--- /dev/null
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/test/test.ndarray.js
@@ -0,0 +1,888 @@
+/**
+* @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 tape = require( 'tape' );
+var toAccessorArray = require( '@stdlib/array/base/to-accessor-array' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var ghelmert = require( './../lib/ndarray.js' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof ghelmert, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function has an arity of 6', function test( t ) {
+	t.strictEqual( ghelmert.length, 6, 'has expected arity' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 4, out, 4, 1, 0 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 4, toAccessorArray( out ), 4, 1, 0 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( false, 4, out, 4, 1, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (row-major, full=false, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( false, 4, toAccessorArray( out ), 4, 1, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 12 ),
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 4, out, 1, 4, 0 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 4, toAccessorArray( out ), 1, 4, 0 );
+
+	expected = [
+		1.0 / sqrt( 4 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		1.0 / sqrt( 4 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( false, 4, out, 1, 3, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function generates a Helmert matrix (column-major, full=false, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( false, 4, toAccessorArray( out ), 1, 3, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		-2.0 / sqrt( 6 ),
+		1.0 / sqrt( 12 ),
+		0.0,
+		0.0,
+		-3.0 * ( 1.0 / sqrt( 12 ) )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( true, 0, out, 0, 1, 0 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( true, 0, toAccessorArray( out ), 0, 1, 0 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( false, 1, out, 0, 1, 0 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'if the number of output rows is less than or equal to `0`, the function returns the output array unchanged (full=false, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	ghelmert( false, 1, toAccessorArray( out ), 0, 1, 0 );
+
+	expected = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function returns the output matrix', function test( t ) {
+	var out;
+	var v;
+
+	out = [ 0.0, 0.0, 0.0, 0.0 ];
+
+	v = ghelmert( true, 2, out, 2, 1, 0 );
+
+	t.strictEqual( v, out, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function returns the output matrix (accessors)', function test( t ) {
+	var out;
+	var v;
+
+	out = toAccessorArray( [ 0.0, 0.0, 0.0, 0.0 ] );
+
+	v = ghelmert( true, 2, out, 2, 1, 0 );
+
+	t.strictEqual( v, out, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying output strides (row-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, out, 5, 1, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying output strides (row-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, toAccessorArray( out ), 5, 1, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying output strides (column-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, out, 1, 5, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying output strides (column-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, toAccessorArray( out ), 1, 5, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying output strides (row-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( false, 3, out, 5, 1, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		0.0,
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 ),
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying output strides (column-major, full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( false, 3, out, 1, 5, 0 );
+
+	expected = [
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		0.0,
+		0.0,
+		0.0,
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 6 ),
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		-2.0 / sqrt( 6 ),
+		0.0,
+		0.0,
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying an offset for `out` (full=false)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( false, 3, out, 3, 1, 1 );
+
+	expected = [
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 6 ),
+		1.0 / sqrt( 6 ),
+		-2.0 / sqrt( 6 )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying negative output strides (row-major, full=true)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, out, -2, -1, 3 );
+
+	expected = [
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying negative output strides (row-major, full=true, accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, toAccessorArray( out ), -2, -1, 3 );
+
+	expected = [
+		-1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying an offset for `out`', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, out, 2, 1, 1 );
+
+	expected = [
+		0.0,
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports specifying an offset for `out` (accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, toAccessorArray( out ), 2, 1, 1 );
+
+	expected = [
+		0.0,
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 )
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports complex access patterns', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, out, 3, 1, 1 );
+
+	expected = [
+		0.0,
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports complex access patterns (accessors)', function test( t ) {
+	var expected;
+	var out;
+
+	out = [
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0,
+		0.0
+	];
+
+	ghelmert( true, 2, toAccessorArray( out ), 3, 1, 1 );
+
+	expected = [
+		0.0,
+		1.0 / sqrt( 2 ),
+		1.0 / sqrt( 2 ),
+		0.0,
+		1.0 / sqrt( 2 ),
+		-1.0 / sqrt( 2 ),
+		0.0
+	];
+
+	t.deepEqual( out, expected, 'returns expected value' );
+	t.end();
+});

From f1298644a5b2aa659f5a873e2b7923f6dacdd7ca Mon Sep 17 00:00:00 2001
From: headlessNode <harriskhan047@outlook.com>
Date: Sat, 17 Oct 2026 15:25:44 +0500
Subject: [PATCH 2/4] fix: lint err

---
 .../@stdlib/blas/ext/base/ghelmert/docs/repl.txt          | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
index e6b538bfb8ab..cd0c070711ed 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
@@ -34,14 +34,14 @@
     Examples
     --------
     // Standard usage:
-    > var out = new {{alias:@stdlib/array/float64}}( 9 );
+    > var out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
     > {{alias}}( 'row-major', true, 3, out, 3 )
-    <Float64Array>[ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+    [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
 
     // Excluding the first row:
-    > out = new {{alias:@stdlib/array/float64}}( 6 );
+    > out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
     > {{alias}}( 'row-major', false, 3, out, 3 )
-    <Float64Array>[ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+    [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
 
 
 {{alias}}.ndarray( full, N, out, so1, so2, oo )

From 2e0d983c6342ff21b931e5904471b8b7f4da2fe4 Mon Sep 17 00:00:00 2001
From: headlessNode <harriskhan047@outlook.com>
Date: Sat, 17 Oct 2026 15:33:59 +0500
Subject: [PATCH 3/4] fix: lint err

---
 .../@stdlib/blas/ext/base/ghelmert/docs/repl.txt            | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
index cd0c070711ed..9acabe021492 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/docs/repl.txt
@@ -88,9 +88,9 @@
     [ ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
 
     // Using an index offset:
-    > out = [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ];
-    > {{alias}}.ndarray( true, 3, out, 3, 1, 1 )
-    [ 0.0, ~0.577, ~0.577, ~0.577, ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
+    > out = [ 0.0, 0.0, 0.0, 0.0, 0.0 ];
+    > {{alias}}.ndarray( true, 2, out, 2, 1, 1 )
+    [ 0.0, ~0.707, ~0.707, ~0.707, ~-0.707 ]
 
     See Also
     --------

From 71af9ea9f7d3c4829aef7393b27229f0a8649aea Mon Sep 17 00:00:00 2001
From: headlessNode <harriskhan047@outlook.com>
Date: Sun, 18 Oct 2026 18:13:47 +0500
Subject: [PATCH 4/4] refactor: implementation

---
 .../blas/ext/base/ghelmert/lib/accessors.js   | 18 ++++++++++-----
 .../blas/ext/base/ghelmert/lib/ndarray.js     | 22 +++++++++++--------
 2 files changed, 25 insertions(+), 15 deletions(-)

diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js
index 3797f1f6fd23..fc8e5e3725d0 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/accessors.js
@@ -49,6 +49,7 @@ var sqrt = require( '@stdlib/math/base/special/sqrt' );
 function ghelmert( full, N, out, strideOut1, strideOut2, offsetOut ) {
 	var obuf;
 	var oset;
+	var do1;
 	var io;
 	var v;
 	var i;
@@ -57,27 +58,32 @@ function ghelmert( full, N, out, strideOut1, strideOut2, offsetOut ) {
 	obuf = out.data;
 	oset = out.accessors[ 1 ];
 
+	do1 = strideOut1 - ( N*strideOut2 );
 	io = offsetOut;
 
 	// If full, write the first row with all elements equal to 1/sqrt(N)...
 	if ( full ) {
 		v = 1.0 / sqrt( N );
 		for ( j = 0; j < N; j++ ) {
-			oset( obuf, io + (j*strideOut2), v );
+			oset( obuf, io, v );
+			io += strideOut2;
 		}
-		io += strideOut1;
+		io += do1;
 	}
 	// For the remaining rows, compute the sub-diagonal Helmert rows...
 	for ( i = 1; i < N; i++ ) {
 		v = 1.0 / sqrt( i * (i+1) );
 		for ( j = 0; j < i; j++ ) {
-			oset( obuf, io + (j*strideOut2), v );
+			oset( obuf, io, v );
+			io += strideOut2;
 		}
-		oset( obuf, io + (i*strideOut2), -i * v );
+		oset( obuf, io, -i * v );
+		io += strideOut2;
 		for ( j = i + 1; j < N; j++ ) {
-			oset( obuf, io + (j*strideOut2), 0.0 );
+			oset( obuf, io, 0.0 );
+			io += strideOut2;
 		}
-		io += strideOut1;
+		io += do1;
 	}
 	return out;
 }
diff --git a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js
index 31d151d1e1bc..0cc78474f3ba 100644
--- a/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js
+++ b/lib/node_modules/@stdlib/blas/ext/base/ghelmert/lib/ndarray.js
@@ -51,15 +51,14 @@ var accessors = require( './accessors.js' );
 * // out => [ ~0.707, ~-0.707, 0.0, ~0.408, ~0.408, ~-0.816 ]
 */
 function ghelmert( full, N, out, strideOut1, strideOut2, offsetOut ) {
+	var do1;
 	var oo;
 	var io;
 	var v;
-	var M;
 	var i;
 	var j;
 
-	M = ( full ) ? N : N - 1;
-	if ( M <= 0 ) {
+	if ( N <= 0 || ( !full && N <= 1 ) ) {
 		return out;
 	}
 	oo = arraylike2object( out );
@@ -67,27 +66,32 @@ function ghelmert( full, N, out, strideOut1, strideOut2, offsetOut ) {
 		accessors( full, N, oo, strideOut1, strideOut2, offsetOut );
 		return out;
 	}
+	do1 = strideOut1 - ( N*strideOut2 );
 	io = offsetOut;
 
 	// If full, write the first row with all elements equal to 1/sqrt(N)...
 	if ( full ) {
 		v = 1.0 / sqrt( N );
 		for ( j = 0; j < N; j++ ) {
-			out[ io + (j*strideOut2) ] = v;
+			out[ io ] = v;
+			io += strideOut2;
 		}
-		io += strideOut1;
+		io += do1;
 	}
 	// For the remaining rows, compute the sub-diagonal Helmert rows...
 	for ( i = 1; i < N; i++ ) {
 		v = 1.0 / sqrt( i * (i+1) );
 		for ( j = 0; j < i; j++ ) {
-			out[ io + (j*strideOut2) ] = v;
+			out[ io ] = v;
+			io += strideOut2;
 		}
-		out[ io + (i*strideOut2) ] = -i * v;
+		out[ io ] = -i * v;
+		io += strideOut2;
 		for ( j = i + 1; j < N; j++ ) {
-			out[ io + (j*strideOut2) ] = 0.0;
+			out[ io ] = 0.0;
+			io += strideOut2;
 		}
-		io += strideOut1;
+		io += do1;
 	}
 	return out;
 }