From 6ce2b7d33dcfaf827399269f8dd504be6e68a924 Mon Sep 17 00:00:00 2001
From: gururaj1512 <gururajgurram1512@gmail.com>
Date: Fri, 18 Jul 2025 13:20:05 +0000
Subject: [PATCH 1/6] feat: add `stats/base/ndarray/dcovarmtk`

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---
 .../stats/base/ndarray/dcovarmtk/README.md    | 216 +++++++++++++++
 .../ndarray/dcovarmtk/benchmark/benchmark.js  | 115 ++++++++
 .../base/ndarray/dcovarmtk/docs/repl.txt      |  64 +++++
 .../ndarray/dcovarmtk/docs/types/index.d.ts   |  68 +++++
 .../base/ndarray/dcovarmtk/docs/types/test.ts |  57 ++++
 .../base/ndarray/dcovarmtk/examples/index.js  |  51 ++++
 .../stats/base/ndarray/dcovarmtk/lib/index.js |  57 ++++
 .../stats/base/ndarray/dcovarmtk/lib/main.js  |  91 ++++++
 .../stats/base/ndarray/dcovarmtk/package.json |  67 +++++
 .../stats/base/ndarray/dcovarmtk/test/test.js | 262 ++++++++++++++++++
 10 files changed, 1048 insertions(+)
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/test.ts
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json
 create mode 100644 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
new file mode 100644
index 000000000000..a9a4c1b19d29
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
@@ -0,0 +1,216 @@
+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2025 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.
+
+-->
+
+# dcovarmtk
+
+> Calculate the [covariance][covariance] of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.
+
+<section class="intro">
+
+The population [covariance][covariance] of two finite size populations of size `N` is given by
+
+<!-- <equation class="equation" label="eq:population_covariance" align="center" raw="\operatorname{\mathrm{cov_N}} = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu_x)(y_i - \mu_y)" alt="Equation for the population covariance."> -->
+
+```math
+\mathop{\mathrm{cov_N}} = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu_x)(y_i - \mu_y)
+```
+
+<!-- </equation> -->
+
+where the population means are given by
+
+<!-- <equation class="equation" label="eq:population_mean_for_x" align="center" raw="\mu_x = \frac{1}{N} \sum_{i=0}^{N-1} x_i" alt="Equation for the population mean for first array."> -->
+
+```math
+\mu_x = \frac{1}{N} \sum_{i=0}^{N-1} x_i
+```
+
+<!-- </equation> -->
+
+and
+
+<!-- <equation class="equation" label="eq:population_mean_for_y" align="center" raw="\mu_y = \frac{1}{N} \sum_{i=0}^{N-1} y_i" alt="Equation for the population mean for second array."> -->
+
+```math
+\mu_y = \frac{1}{N} \sum_{i=0}^{N-1} y_i
+```
+
+<!-- </equation> -->
+
+Often in the analysis of data, the true population [covariance][covariance] is not known _a priori_ and must be estimated from samples drawn from population distributions. If one attempts to use the formula for the population [covariance][covariance], the result is biased and yields a **biased sample covariance**. To compute an **unbiased sample covariance** for samples of size `n`,
+
+<!-- <equation class="equation" label="eq:unbiased_sample_covariance" align="center" raw="\operatorname{\mathrm{cov_n}} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)" alt="Equation for computing an unbiased sample variance."> -->
+
+```math
+\mathop{\mathrm{cov_n}} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)
+```
+
+<!-- </equation> -->
+
+where sample means are given by
+
+<!-- <equation class="equation" label="eq:sample_mean_for_x" align="center" raw="\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i" alt="Equation for the sample mean for first array."> -->
+
+```math
+\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
+```
+
+<!-- </equation> -->
+
+and
+
+<!-- <equation class="equation" label="eq:sample_mean_for_y" align="center" raw="\bar{y} = \frac{1}{n} \sum_{i=0}^{n-1} y_i" alt="Equation for the sample mean for second array."> -->
+
+```math
+\bar{y} = \frac{1}{n} \sum_{i=0}^{n-1} y_i
+```
+
+<!-- </equation> -->
+
+The use of the term `n-1` is commonly referred to as Bessel's correction. Depending on the characteristics of the population distributions, other correction factors (e.g., `n-1.5`, `n+1`, etc) can yield better estimators.
+
+</section>
+
+<!-- /.intro -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dcovarmtk = require( '@stdlib/stats/base/ndarray/dcovarmtk' );
+```
+
+#### dcovarmtk( arrays )
+
+Computes the covariance of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+
+var opts = {
+    'dtype': 'float64'
+};
+
+var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+var meanx = scalar2ndarray( 1.0/3.0, opts );
+var meany = scalar2ndarray( 1.0/3.0, opts );
+var correction = scalar2ndarray( 1.0, opts );
+
+var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+// returns ~3.8333
+```
+
+The function has the following parameters:
+
+-   **arrays**: array-like object containing the following ndarrays in order:
+
+    1.  first one-dimensional input ndarray.
+    2.  second one-dimensional input ndarray.
+    3.  a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
+    4.  a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
+    5.  a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [covariance][covariance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population [covariance][covariance], setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample [covariance][covariance], setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+
+</section>
+
+<!-- /.usage -->
+
+<section class="notes">
+
+## Notes
+
+-   If provided an empty one-dimensional ndarray, the function returns `NaN`.
+
+</section>
+
+<!-- /.notes -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var dcovarmtk = require( '@stdlib/stats/base/ndarray/dcovarmtk' );
+
+// Define array options:
+var opts = {
+    'dtype': 'float64'
+};
+
+// Create first one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
+var xbuf = discreteUniform( 10, -50, 50, opts );
+var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( x ) );
+
+// Create second one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
+var ybuf = discreteUniform( 10, -50, 50, opts );
+var y = new ndarray( opts.dtype, ybuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( y ) );
+
+// Specify the known means:
+var meanx = scalar2ndarray( 0.0, opts );
+var meany = scalar2ndarray( 0.0, opts );
+
+// Specify the degrees of freedom adjustment:
+var correction = scalar2ndarray( 1.0, opts );
+
+// Calculate the sample covariance:
+var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+console.log( v );
+```
+
+</section>
+
+<!-- /.examples -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+</section>
+
+<!-- /.links -->
+
+[covariance]: https://en.wikipedia.org/wiki/Covariance
+
+</section>
+
+<!-- /.links -->
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js
new file mode 100644
index 000000000000..378425698d85
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js
@@ -0,0 +1,115 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 The Stdlib Authors.
+*
+* Licensed under the Apache License, Version 2.0 (the "License");
+* you may not use this file except in compliance with the License.
+* You may obtain a copy of the License at
+*
+*    http://www.apache.org/licenses/LICENSE-2.0
+*
+* Unless required by applicable law or agreed to in writing, software
+* distributed under the License is distributed on an "AS IS" BASIS,
+* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+* See the License for the specific language governing permissions and
+* limitations under the License.
+*/
+
+'use strict';
+
+// MODULES //
+
+var bench = require( '@stdlib/bench' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var isnan = require( '@stdlib/math/base/assert/is-nan' );
+var pow = require( '@stdlib/math/base/special/pow' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/base/from-scalar' );
+var pkg = require( './../package.json' ).name;
+var dcovarmtk = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Creates a benchmark function.
+*
+* @private
+* @param {PositiveInteger} len - array length
+* @returns {Function} benchmark function
+*/
+function createBenchmark( len ) {
+	var correction;
+	var meanx;
+	var meany;
+	var xbuf;
+	var ybuf;
+	var x;
+	var y;
+
+	xbuf = uniform( len, -10.0, 10.0, options );
+	x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
+
+	ybuf = uniform( len, -10.0, 10.0, options );
+	y = new ndarray( options.dtype, ybuf, [ len ], [ 1 ], 0, 'row-major' );
+
+	meanx = scalar2ndarray( 0.0, options.dtype, 'row-major' );
+	meany = scalar2ndarray( 0.0, options.dtype, 'row-major' );
+	correction = scalar2ndarray( 1.0, options.dtype, 'row-major' );
+
+	return benchmark;
+
+	function benchmark( b ) {
+		var v;
+		var i;
+
+		b.tic();
+		for ( i = 0; i < b.iterations; i++ ) {
+			v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+			if ( isnan( v ) ) {
+				b.fail( 'should not return NaN' );
+			}
+		}
+		b.toc();
+		if ( isnan( v ) ) {
+			b.fail( 'should not return NaN' );
+		}
+		b.pass( 'benchmark finished' );
+		b.end();
+	}
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+	var len;
+	var min;
+	var max;
+	var f;
+	var i;
+
+	min = 1; // 10^min
+	max = 6; // 10^max
+
+	for ( i = min; i <= max; i++ ) {
+		len = pow( 10, i );
+		f = createBenchmark( len );
+		bench( pkg+':len='+len, f );
+	}
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
new file mode 100644
index 000000000000..3f67b11004d7
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
@@ -0,0 +1,64 @@
+
+{{alias}}( arrays )
+    Computes the covariance of two one-dimensional double-precision
+    floating-point ndarrays provided known means and using a one-pass textbook
+    algorithm.
+
+    If provided an empty ndarray, the function returns `NaN`.
+
+    Parameters
+    ----------
+    arrays: ArrayLikeObject<ndarray>
+        The function expects the following ndarrays in order:
+
+        -   first one-dimensional input ndarray.
+        -   second one-dimensional input ndarray.
+        -   a zero-dimensional ndarray specifying mean of the first
+        one-dimensional ndarray.
+        -   a zero-dimensional ndarray specifying mean of the second
+        one-dimensional ndarray.
+        -   a zero-dimensional ndarray specifying degrees of freedom
+        adjustment. Setting this parameter to a value other than `0` has the
+        effect of adjusting the divisor during the calculation of the
+        covariance according to `N-c` where `c` corresponds to the provided
+        degrees of freedom adjustment. When computing the population
+        covariance, setting this parameter to `0` is the standard choice (i.e.,
+        the provided arrays contain data constituting entire populations). When
+        computing the unbiased sample covariance, setting this parameter to `1`
+        is the standard choice (i.e., the provided arrays contain data sampled
+        from larger populations; this is commonly referred to as Bessel's
+        correction).
+
+    Returns
+    -------
+    out: number
+        The covariance.
+
+    Examples
+    --------
+    // Create the input ndarrays:
+    > var xbuf = new {{alias:@stdlib/array/float64}}( [ 1.0, -2.0, 2.0 ] );
+    > var ybuf = new {{alias:@stdlib/array/float64}}( [ 2.0, -2.0, 1.0 ] );
+    > var dt = 'float64';
+    > var sh = [ xbuf.length ];
+    > var st = [ 1 ];
+    > var oo = 0;
+    > var ord = 'row-major';
+    > var x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, st, oo, ord );
+    > var y = new {{alias:@stdlib/ndarray/ctor}}( dt, ybuf, sh, st, oo, ord );
+
+    // Specify the known means:
+    > var opts = { 'dtype': dt };
+    > var meanx = new {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, opts );
+    > var meany = new {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, opts );
+
+    // Specify the degrees of freedom adjustment:
+    > var correction = new {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts );
+
+    // Calculate the sample covariance:
+    > {{alias}}( [ x, y, meanx, meany, correction ] )
+    ~3.8333
+
+    See Also
+    --------
+
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
new file mode 100644
index 000000000000..91feaa590a3e
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
@@ -0,0 +1,68 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 { float64ndarray } from '@stdlib/types/ndarray';
+
+/**
+* Computes the covariance of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.
+*
+* ## Notes
+*
+* -   The function expects the following ndarrays in order:
+*
+*     -   first one-dimensional input ndarray.
+*     -   second one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+*
+* @param arrays - array-like object containing input ndarrays
+* @returns maximum value
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var ndarray = require( '@stdlib/ndarray/base/ctor' );
+*
+* var opts = {
+*     'dtype': 'float64'
+* };
+*
+* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+* var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+* var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var meanx = scalar2ndarray( 1.0/3.0, opts );
+* var meany = scalar2ndarray( 1.0/3.0, opts );
+* var correction = scalar2ndarray( 1.0, opts );
+*
+* var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+* // returns ~3.8333
+*/
+declare function dcovarmtk( arrays: [ float64ndarray, float64ndarray, float64ndarray, float64ndarray, float64ndarray ] ): number;
+
+
+// EXPORTS //
+
+export = dcovarmtk;
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/test.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/test.ts
new file mode 100644
index 000000000000..89d0b12b302f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/test.ts
@@ -0,0 +1,57 @@
+/*
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 zeros = require( '@stdlib/ndarray/zeros' );
+import dcovarmtk = require( './index' );
+
+
+// TESTS //
+
+// The function returns a number...
+{
+	const x = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+
+	dcovarmtk( [ x, x, x, x, x ] ); // $ExpectType number
+}
+
+// The compiler throws an error if the function is provided a first argument which is not an array of ndarrays...
+{
+	dcovarmtk( '10' ); // $ExpectError
+	dcovarmtk( 10 ); // $ExpectError
+	dcovarmtk( true ); // $ExpectError
+	dcovarmtk( false ); // $ExpectError
+	dcovarmtk( null ); // $ExpectError
+	dcovarmtk( undefined ); // $ExpectError
+	dcovarmtk( [] ); // $ExpectError
+	dcovarmtk( {} ); // $ExpectError
+	dcovarmtk( ( x: number ): number => x ); // $ExpectError
+}
+
+// The compiler throws an error if the function is provided an unsupported number of arguments...
+{
+	const x = zeros( [ 10 ], {
+		'dtype': 'float64'
+	});
+
+	dcovarmtk(); // $ExpectError
+	dcovarmtk( [ x, x, x, x, x ], {} ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
new file mode 100644
index 000000000000..429cf23c92cc
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
@@ -0,0 +1,51 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var dcovarmtk = require( './../lib' );
+
+// Define array options:
+var opts = {
+	'dtype': 'float64'
+};
+
+// Create first one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
+var xbuf = discreteUniform( 10, -50, 50, opts );
+var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( x ) );
+
+// Create second one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
+var ybuf = discreteUniform( 10, -50, 50, opts );
+var y = new ndarray( opts.dtype, ybuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+console.log( ndarray2array( y ) );
+
+// Specify the known means:
+var meanx = scalar2ndarray( 0.0, opts );
+var meany = scalar2ndarray( 0.0, opts );
+
+// Specify the degrees of freedom adjustment:
+var correction = scalar2ndarray( 1.0, opts );
+
+// Calculate the sample covariance:
+var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+console.log( v );
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js
new file mode 100644
index 000000000000..438d87eca1b0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js
@@ -0,0 +1,57 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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';
+
+/**
+* Compute the covariance of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.
+*
+* @module @stdlib/stats/base/ndarray/dcovarmtk
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var ndarray = require( '@stdlib/ndarray/base/ctor' );
+* var dcovarmtk = require( '@stdlib/stats/base/ndarray/dcovarmtk' );
+*
+* var opts = {
+*     'dtype': 'float64'
+* };
+*
+* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+* var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+* var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var meanx = scalar2ndarray( 1.0/3.0, opts );
+* var meany = scalar2ndarray( 1.0/3.0, opts );
+* var correction = scalar2ndarray( 1.0, opts );
+*
+* var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+* // returns ~3.8333
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
new file mode 100644
index 000000000000..7341ef1fd1e0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
@@ -0,0 +1,91 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 numelDimension = require( '@stdlib/ndarray/base/numel-dimension' );
+var getStride = require( '@stdlib/ndarray/base/stride' );
+var getOffset = require( '@stdlib/ndarray/base/offset' );
+var getData = require( '@stdlib/ndarray/base/data-buffer' );
+var ndarraylike2scalar = require( '@stdlib/ndarray/base/ndarraylike2scalar' );
+var strided = require( '@stdlib/stats/strided/dcovarmtk' ).ndarray;
+
+
+// MAIN //
+
+/**
+* Computes the covariance of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.
+*
+* ## Notes
+*
+* -   The function expects the following ndarrays in order:
+*
+*     -   first one-dimensional input ndarray.
+*     -   second one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+*
+* @param {ArrayLikeObject<Object>} arrays - array-like object containing input ndarrays
+* @returns {number} maximum value
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var ndarray = require( '@stdlib/ndarray/base/ctor' );
+*
+* var opts = {
+*     'dtype': 'float64'
+* };
+*
+* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+* var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+* var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var meanx = scalar2ndarray( 1.0/3.0, opts );
+* var meany = scalar2ndarray( 1.0/3.0, opts );
+* var correction = scalar2ndarray( 1.0, opts );
+*
+* var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+* // returns ~3.8333
+*/
+function dcovarmtk( arrays ) {
+	var correction;
+	var meanx;
+	var meany;
+	var x;
+	var y;
+
+	x = arrays[ 0 ];
+	y = arrays[ 1 ];
+
+	meanx = ndarraylike2scalar( arrays[ 2 ] );
+	meany = ndarraylike2scalar( arrays[ 3 ] );
+	correction = ndarraylike2scalar( arrays[ 4 ] );
+
+	return strided( numelDimension( x, 0 ), correction, meanx, getData( x ), getStride( x, 0 ), getOffset( x ), meany, getData( y ), getStride( y, 0 ), getOffset( y ) ); // eslint-disable-line max-len
+}
+
+
+// EXPORTS //
+
+module.exports = dcovarmtk;
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json
new file mode 100644
index 000000000000..52b0d204caa7
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json
@@ -0,0 +1,67 @@
+{
+  "name": "@stdlib/stats/base/ndarray/dcovarmtk",
+  "version": "0.0.0",
+  "description": "Computes the covariance of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.",
+  "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",
+    "statistics",
+    "stats",
+    "mathematics",
+    "math",
+    "covariance",
+    "covar",
+    "sample covariance",
+    "unbiased",
+    "correlation",
+    "variance",
+    "ndarray"
+  ],
+  "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js
new file mode 100644
index 000000000000..8b8c40af84d3
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js
@@ -0,0 +1,262 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2025 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 isnan = require( '@stdlib/math/base/assert/is-nan' );
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var dcovarmtk = require( './../lib' );
+
+
+// VARIABLES //
+
+var options = {
+	'dtype': 'float64'
+};
+
+
+// FUNCTIONS //
+
+/**
+* Returns a one-dimensional ndarray.
+*
+* @private
+* @param {Float64Array} buffer - underlying data buffer
+* @param {NonNegativeInteger} length - number of indexed elements
+* @param {integer} stride - stride length
+* @param {NonNegativeInteger} offset - index offset
+* @returns {ndarray} one-dimensional ndarray
+*/
+function vector( buffer, length, stride, offset ) {
+	return new ndarray( 'float64', buffer, [ length ], [ stride ], offset, 'row-major' );
+}
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+	t.ok( true, __filename );
+	t.strictEqual( typeof dcovarmtk, 'function', 'main export is a function' );
+	t.end();
+});
+
+tape( 'the function has an arity of 1', function test( t ) {
+	t.strictEqual( dcovarmtk.length, 1, 'has expected arity' );
+	t.end();
+});
+
+tape( 'the function calculates the population covariance of two one-dimensional double-precision floating-point ndarrays provided known means', function test( t ) {
+	var correction;
+	var meanx;
+	var meany;
+	var x;
+	var y;
+	var v;
+
+	correction = scalar2ndarray( 0.0, options );
+
+	x = new Float64Array( [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ] );
+	y = new Float64Array( [ -2.0, 1.0, 5.0, -4.0, 3.0, 0.0 ] );
+	meanx = scalar2ndarray( 0.5, options );
+	meany = scalar2ndarray( 0.5, options );
+	v = dcovarmtk( [ vector( x, 6, 1, 0 ), vector( y, 6, 1, 0 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( v, -45.5/x.length, 'returns expected value' );
+
+	x = new Float64Array( [ -4.0, -4.0 ] );
+	meanx = scalar2ndarray( -4.0, options );
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( v, 0.0, 'returns expected value' );
+
+	x = new Float64Array( [ NaN, 4.0 ] );
+	meanx = scalar2ndarray( 4.0, options );
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function calculates the sample covariance of two one-dimensional double-precision floating-point ndarrays provided known means', function test( t ) {
+	var correction;
+	var meanx;
+	var meany;
+	var x;
+	var y;
+	var v;
+
+	correction = scalar2ndarray( 1.0, options );
+
+	x = new Float64Array( [ 1.0, -2.0, -4.0, 5.0, 0.0, 3.0 ] );
+	y = new Float64Array( [ -2.0, 1.0, 5.0, -4.0, 3.0, 0.0 ] );
+	meanx = scalar2ndarray( 0.5, options );
+	meany = scalar2ndarray( 0.5, options );
+	v = dcovarmtk( [ vector( x, 6, 1, 0 ), vector( y, 6, 1, 0 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( v, -45.5/(x.length-1), 'returns expected value' );
+
+	x = new Float64Array( [ -4.0, -4.0 ] );
+	meanx = scalar2ndarray( -4.0, options );
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( v, 0.0, 'returns expected value' );
+
+	x = new Float64Array( [ NaN, 4.0 ] );
+	meanx = scalar2ndarray( 4.0, options );
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'if provided an empty vector, the function returns `NaN`', function test( t ) {
+	var correction;
+	var meanx;
+	var x;
+	var v;
+
+	x = new Float64Array( [] );
+	meanx = scalar2ndarray( 0.5, options );
+	correction = scalar2ndarray( 1.0, options );
+
+	v = dcovarmtk( [ vector( x, 0, 1, 0 ), vector( x, 0, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( isnan( v ), true, 'returns expected value' );
+
+	t.end();
+});
+
+tape( 'the function supports one-dimensional ndarrays having non-unit strides', function test( t ) {
+	var correction;
+	var meanx;
+	var meany;
+	var x;
+	var y;
+	var v;
+
+	correction = scalar2ndarray( 1.0, options );
+
+	x = new Float64Array([
+		1.0,  // 0
+		2.0,
+		2.0,  // 1
+		-7.0,
+		-2.0, // 2
+		3.0,
+		4.0,  // 3
+		2.0
+	]);
+	meanx = scalar2ndarray( 1.25, options );
+
+	y = new Float64Array([
+		2.0,  // 0
+		2.0,
+		1.0,  // 1
+		-7.0,
+		4.0,  // 2
+		3.0,
+		-2.0, // 3
+		2.0
+	]);
+	meany = scalar2ndarray( 1.25, options );
+
+	v = dcovarmtk( [ vector( x, 4, 2, 0 ), vector( y, 4, 2, 0 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+
+	t.strictEqual( v, -18.25/3, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports one-dimensional ndarrays having negative strides', function test( t ) {
+	var correction;
+	var meanx;
+	var meany;
+	var x;
+	var y;
+	var v;
+
+	correction = scalar2ndarray( 1.0, options );
+
+	x = new Float64Array([
+		1.0,  // 3
+		2.0,
+		2.0,  // 2
+		-7.0,
+		-2.0, // 1
+		3.0,
+		4.0,  // 0
+		2.0
+	]);
+	meanx = scalar2ndarray( 1.25, options );
+
+	y = new Float64Array([
+		2.0,  // 3
+		2.0,
+		1.0,  // 2
+		-7.0,
+		4.0,  // 1
+		3.0,
+		-2.0, // 0
+		2.0
+	]);
+	meany = scalar2ndarray( 1.25, options );
+
+	v = dcovarmtk( [ vector( x, 4, -2, 6 ), vector( y, 4, -2, 6 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+
+	t.strictEqual( v, -18.25/3, 'returns expected value' );
+	t.end();
+});
+
+tape( 'the function supports one-dimensional ndarrays having non-zero offsets', function test( t ) {
+	var correction;
+	var meanx;
+	var meany;
+	var x;
+	var y;
+	var v;
+
+	correction = scalar2ndarray( 1.0, options );
+
+	x = new Float64Array([
+		2.0,
+		1.0,  // 0
+		2.0,
+		-2.0, // 1
+		-2.0,
+		2.0,  // 2
+		3.0,
+		4.0   // 3
+	]);
+	meanx = scalar2ndarray( 1.25, options );
+
+	y = new Float64Array([
+		2.0,
+		-2.0, // 0
+		2.0,
+		1.0,  // 1
+		-2.0,
+		4.0,  // 2
+		3.0,
+		2.0   // 3
+	]);
+	meany = scalar2ndarray( 1.25, options );
+
+	v = dcovarmtk( [ vector( x, 4, 2, 1 ), vector( y, 4, 2, 1 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	t.strictEqual( v, 5.75/3, 'returns expected value' );
+
+	t.end();
+});

From b79d0833bbdac1fabd4400c66c30119f0a2efcf8 Mon Sep 17 00:00:00 2001
From: Gururaj Gurram <143020143+gururaj1512@users.noreply.github.com>
Date: Fri, 18 Jul 2025 20:50:19 +0530
Subject: [PATCH 2/6] Update README.md

Signed-off-by: Gururaj Gurram <143020143+gururaj1512@users.noreply.github.com>
---
 lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
index a9a4c1b19d29..1a1c57e092c4 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
@@ -174,7 +174,7 @@ console.log( ndarray2array( x ) );
 
 // Create second one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
 var ybuf = discreteUniform( 10, -50, 50, opts );
-var y = new ndarray( opts.dtype, ybuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( y ) );
 
 // Specify the known means:

From be50f23e1c1536026df117b4f374c0001259927d Mon Sep 17 00:00:00 2001
From: Gururaj Gurram <143020143+gururaj1512@users.noreply.github.com>
Date: Fri, 18 Jul 2025 21:26:30 +0530
Subject: [PATCH 3/6] Update main.js

Signed-off-by: Gururaj Gurram <143020143+gururaj1512@users.noreply.github.com>
---
 .../@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js            | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
index 7341ef1fd1e0..a3675d1e41c0 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
@@ -44,7 +44,7 @@ var strided = require( '@stdlib/stats/strided/dcovarmtk' ).ndarray;
 *     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
 *
 * @param {ArrayLikeObject<Object>} arrays - array-like object containing input ndarrays
-* @returns {number} maximum value
+* @returns {number} covariance
 *
 * @example
 * var Float64Array = require( '@stdlib/array/float64' );

From 0fae24724e5fa4e6c3e7e53b5aaa590d8afe96d2 Mon Sep 17 00:00:00 2001
From: Gururaj Gurram <143020143+gururaj1512@users.noreply.github.com>
Date: Fri, 18 Jul 2025 21:34:48 +0530
Subject: [PATCH 4/6] Update index.d.ts

Signed-off-by: Gururaj Gurram <143020143+gururaj1512@users.noreply.github.com>
---
 .../@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts  | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
index 91feaa590a3e..96f02da9535f 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
@@ -36,7 +36,7 @@ import { float64ndarray } from '@stdlib/types/ndarray';
 *     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
 *
 * @param arrays - array-like object containing input ndarrays
-* @returns maximum value
+* @returns covariance
 *
 * @example
 * var Float64Array = require( '@stdlib/array/float64' );

From f8972d7655b6b66af100cc9c9f43662ac4a7c557 Mon Sep 17 00:00:00 2001
From: gururaj1512 <gururajgurram1512@gmail.com>
Date: Mon, 21 Jul 2025 08:55:56 +0000
Subject: [PATCH 5/6] refactor: update parameter order

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown
    status: passed
  - task: lint_package_json
    status: na
  - task: lint_repl_help
    status: passed
  - task: lint_javascript_src
    status: passed
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: passed
  - task: lint_javascript_tests
    status: passed
  - task: lint_javascript_benchmarks
    status: passed
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---
---
 .../stats/base/ndarray/dcovarmtk/README.md    | 18 ++++++++---------
 .../ndarray/dcovarmtk/benchmark/benchmark.js  |  4 ++--
 .../base/ndarray/dcovarmtk/docs/repl.txt      | 18 ++++++++---------
 .../ndarray/dcovarmtk/docs/types/index.d.ts   |  6 +++---
 .../base/ndarray/dcovarmtk/examples/index.js  |  8 ++++----
 .../stats/base/ndarray/dcovarmtk/lib/index.js |  4 ++--
 .../stats/base/ndarray/dcovarmtk/lib/main.js  | 12 +++++------
 .../stats/base/ndarray/dcovarmtk/test/test.js | 20 +++++++++----------
 8 files changed, 45 insertions(+), 45 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
index 1a1c57e092c4..49e4dbde6545 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
@@ -117,11 +117,11 @@ var x = new ndarray( opts.dtype, xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
 var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
 var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
 
+var correction = scalar2ndarray( 1.0, opts );
 var meanx = scalar2ndarray( 1.0/3.0, opts );
 var meany = scalar2ndarray( 1.0/3.0, opts );
-var correction = scalar2ndarray( 1.0, opts );
 
-var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+var v = dcovarmtk( [ x, y, correction, meanx, meany ] );
 // returns ~3.8333
 ```
 
@@ -131,9 +131,9 @@ The function has the following parameters:
 
     1.  first one-dimensional input ndarray.
     2.  second one-dimensional input ndarray.
-    3.  a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
-    4.  a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
-    5.  a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [covariance][covariance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population [covariance][covariance], setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample [covariance][covariance], setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+    3.  a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [covariance][covariance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population [covariance][covariance], setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample [covariance][covariance], setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+    4.  a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
+    5.  a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
 
 </section>
 
@@ -177,15 +177,15 @@ var ybuf = discreteUniform( 10, -50, 50, opts );
 var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( y ) );
 
+// Specify the degrees of freedom adjustment:
+var correction = scalar2ndarray( 1.0, opts );
+
 // Specify the known means:
 var meanx = scalar2ndarray( 0.0, opts );
 var meany = scalar2ndarray( 0.0, opts );
 
-// Specify the degrees of freedom adjustment:
-var correction = scalar2ndarray( 1.0, opts );
-
 // Calculate the sample covariance:
-var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+var v = dcovarmtk( [ x, y, correction, meanx, meany ] );
 console.log( v );
 ```
 
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js
index 378425698d85..b73104a7edfa 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/benchmark/benchmark.js
@@ -61,9 +61,9 @@ function createBenchmark( len ) {
 	ybuf = uniform( len, -10.0, 10.0, options );
 	y = new ndarray( options.dtype, ybuf, [ len ], [ 1 ], 0, 'row-major' );
 
+	correction = scalar2ndarray( 1.0, options.dtype, 'row-major' );
 	meanx = scalar2ndarray( 0.0, options.dtype, 'row-major' );
 	meany = scalar2ndarray( 0.0, options.dtype, 'row-major' );
-	correction = scalar2ndarray( 1.0, options.dtype, 'row-major' );
 
 	return benchmark;
 
@@ -73,7 +73,7 @@ function createBenchmark( len ) {
 
 		b.tic();
 		for ( i = 0; i < b.iterations; i++ ) {
-			v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+			v = dcovarmtk( [ x, y, correction, meanx, meany ] );
 			if ( isnan( v ) ) {
 				b.fail( 'should not return NaN' );
 			}
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
index 3f67b11004d7..46187dd96f4c 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
@@ -13,10 +13,6 @@
 
         -   first one-dimensional input ndarray.
         -   second one-dimensional input ndarray.
-        -   a zero-dimensional ndarray specifying mean of the first
-        one-dimensional ndarray.
-        -   a zero-dimensional ndarray specifying mean of the second
-        one-dimensional ndarray.
         -   a zero-dimensional ndarray specifying degrees of freedom
         adjustment. Setting this parameter to a value other than `0` has the
         effect of adjusting the divisor during the calculation of the
@@ -28,6 +24,10 @@
         is the standard choice (i.e., the provided arrays contain data sampled
         from larger populations; this is commonly referred to as Bessel's
         correction).
+        -   a zero-dimensional ndarray specifying mean of the first
+        one-dimensional ndarray.
+        -   a zero-dimensional ndarray specifying mean of the second
+        one-dimensional ndarray.
 
     Returns
     -------
@@ -47,16 +47,16 @@
     > var x = new {{alias:@stdlib/ndarray/ctor}}( dt, xbuf, sh, st, oo, ord );
     > var y = new {{alias:@stdlib/ndarray/ctor}}( dt, ybuf, sh, st, oo, ord );
 
-    // Specify the known means:
+    // Specify the degrees of freedom adjustment:
     > var opts = { 'dtype': dt };
+    > var correction = new {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts );
+
+    // Specify the known means:
     > var meanx = new {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, opts );
     > var meany = new {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, opts );
 
-    // Specify the degrees of freedom adjustment:
-    > var correction = new {{alias:@stdlib/ndarray/from-scalar}}( 1.0, opts );
-
     // Calculate the sample covariance:
-    > {{alias}}( [ x, y, meanx, meany, correction ] )
+    > {{alias}}( [ x, y, correction, meanx, meany ] )
     ~3.8333
 
     See Also
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
index 96f02da9535f..d71c36d3a8e9 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
@@ -31,9 +31,9 @@ import { float64ndarray } from '@stdlib/types/ndarray';
 *
 *     -   first one-dimensional input ndarray.
 *     -   second one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
 *     -   a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
 *     -   a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
-*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
 *
 * @param arrays - array-like object containing input ndarrays
 * @returns covariance
@@ -53,11 +53,11 @@ import { float64ndarray } from '@stdlib/types/ndarray';
 * var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
 * var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
 *
+* var correction = scalar2ndarray( 1.0, opts );
 * var meanx = scalar2ndarray( 1.0/3.0, opts );
 * var meany = scalar2ndarray( 1.0/3.0, opts );
-* var correction = scalar2ndarray( 1.0, opts );
 *
-* var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+* var v = dcovarmtk( [ x, y, correction, meanx, meany ] );
 * // returns ~3.8333
 */
 declare function dcovarmtk( arrays: [ float64ndarray, float64ndarray, float64ndarray, float64ndarray, float64ndarray ] ): number;
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
index 429cf23c92cc..f348fa53f761 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
@@ -39,13 +39,13 @@ var ybuf = discreteUniform( 10, -50, 50, opts );
 var y = new ndarray( opts.dtype, ybuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( y ) );
 
+// Specify the degrees of freedom adjustment:
+var correction = scalar2ndarray( 1.0, opts );
+
 // Specify the known means:
 var meanx = scalar2ndarray( 0.0, opts );
 var meany = scalar2ndarray( 0.0, opts );
 
-// Specify the degrees of freedom adjustment:
-var correction = scalar2ndarray( 1.0, opts );
-
 // Calculate the sample covariance:
-var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+var v = dcovarmtk( [ x, y, correction, meanx, meany ] );
 console.log( v );
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js
index 438d87eca1b0..2d68c5efe6bf 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/index.js
@@ -39,11 +39,11 @@
 * var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
 * var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
 *
+* var correction = scalar2ndarray( 1.0, opts );
 * var meanx = scalar2ndarray( 1.0/3.0, opts );
 * var meany = scalar2ndarray( 1.0/3.0, opts );
-* var correction = scalar2ndarray( 1.0, opts );
 *
-* var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+* var v = dcovarmtk( [ x, y, correction, meanx, meany ] );
 * // returns ~3.8333
 */
 
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
index a3675d1e41c0..a04d6a397486 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
@@ -39,9 +39,9 @@ var strided = require( '@stdlib/stats/strided/dcovarmtk' ).ndarray;
 *
 *     -   first one-dimensional input ndarray.
 *     -   second one-dimensional input ndarray.
+*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
 *     -   a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
 *     -   a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
-*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
 *
 * @param {ArrayLikeObject<Object>} arrays - array-like object containing input ndarrays
 * @returns {number} covariance
@@ -61,11 +61,11 @@ var strided = require( '@stdlib/stats/strided/dcovarmtk' ).ndarray;
 * var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
 * var y = new ndarray( opts.dtype, ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
 *
+* var correction = scalar2ndarray( 1.0, opts );
 * var meanx = scalar2ndarray( 1.0/3.0, opts );
 * var meany = scalar2ndarray( 1.0/3.0, opts );
-* var correction = scalar2ndarray( 1.0, opts );
 *
-* var v = dcovarmtk( [ x, y, meanx, meany, correction ] );
+* var v = dcovarmtk( [ x, y, correction, meanx, meany ] );
 * // returns ~3.8333
 */
 function dcovarmtk( arrays ) {
@@ -78,9 +78,9 @@ function dcovarmtk( arrays ) {
 	x = arrays[ 0 ];
 	y = arrays[ 1 ];
 
-	meanx = ndarraylike2scalar( arrays[ 2 ] );
-	meany = ndarraylike2scalar( arrays[ 3 ] );
-	correction = ndarraylike2scalar( arrays[ 4 ] );
+	correction = ndarraylike2scalar( arrays[ 2 ] );
+	meanx = ndarraylike2scalar( arrays[ 3 ] );
+	meany = ndarraylike2scalar( arrays[ 4 ] );
 
 	return strided( numelDimension( x, 0 ), correction, meanx, getData( x ), getStride( x, 0 ), getOffset( x ), meany, getData( y ), getStride( y, 0 ), getOffset( y ) ); // eslint-disable-line max-len
 }
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js
index 8b8c40af84d3..dff8befd10ad 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/test/test.js
@@ -79,17 +79,17 @@ tape( 'the function calculates the population covariance of two one-dimensional
 	y = new Float64Array( [ -2.0, 1.0, 5.0, -4.0, 3.0, 0.0 ] );
 	meanx = scalar2ndarray( 0.5, options );
 	meany = scalar2ndarray( 0.5, options );
-	v = dcovarmtk( [ vector( x, 6, 1, 0 ), vector( y, 6, 1, 0 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 6, 1, 0 ), vector( y, 6, 1, 0 ), correction, meanx, meany ] ); // eslint-disable-line max-len
 	t.strictEqual( v, -45.5/x.length, 'returns expected value' );
 
 	x = new Float64Array( [ -4.0, -4.0 ] );
 	meanx = scalar2ndarray( -4.0, options );
-	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), correction, meanx, meanx ] ); // eslint-disable-line max-len
 	t.strictEqual( v, 0.0, 'returns expected value' );
 
 	x = new Float64Array( [ NaN, 4.0 ] );
 	meanx = scalar2ndarray( 4.0, options );
-	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), correction, meanx, meanx ] ); // eslint-disable-line max-len
 	t.strictEqual( isnan( v ), true, 'returns expected value' );
 
 	t.end();
@@ -109,17 +109,17 @@ tape( 'the function calculates the sample covariance of two one-dimensional doub
 	y = new Float64Array( [ -2.0, 1.0, 5.0, -4.0, 3.0, 0.0 ] );
 	meanx = scalar2ndarray( 0.5, options );
 	meany = scalar2ndarray( 0.5, options );
-	v = dcovarmtk( [ vector( x, 6, 1, 0 ), vector( y, 6, 1, 0 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 6, 1, 0 ), vector( y, 6, 1, 0 ), correction, meanx, meany ] ); // eslint-disable-line max-len
 	t.strictEqual( v, -45.5/(x.length-1), 'returns expected value' );
 
 	x = new Float64Array( [ -4.0, -4.0 ] );
 	meanx = scalar2ndarray( -4.0, options );
-	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), correction, meanx, meanx ] ); // eslint-disable-line max-len
 	t.strictEqual( v, 0.0, 'returns expected value' );
 
 	x = new Float64Array( [ NaN, 4.0 ] );
 	meanx = scalar2ndarray( 4.0, options );
-	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 2, 1, 0 ), vector( x, 2, 1, 0 ), correction, meanx, meanx ] ); // eslint-disable-line max-len
 	t.strictEqual( isnan( v ), true, 'returns expected value' );
 
 	t.end();
@@ -135,7 +135,7 @@ tape( 'if provided an empty vector, the function returns `NaN`', function test(
 	meanx = scalar2ndarray( 0.5, options );
 	correction = scalar2ndarray( 1.0, options );
 
-	v = dcovarmtk( [ vector( x, 0, 1, 0 ), vector( x, 0, 1, 0 ), meanx, meanx, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 0, 1, 0 ), vector( x, 0, 1, 0 ), correction, meanx, meanx ] ); // eslint-disable-line max-len
 	t.strictEqual( isnan( v ), true, 'returns expected value' );
 
 	t.end();
@@ -175,7 +175,7 @@ tape( 'the function supports one-dimensional ndarrays having non-unit strides',
 	]);
 	meany = scalar2ndarray( 1.25, options );
 
-	v = dcovarmtk( [ vector( x, 4, 2, 0 ), vector( y, 4, 2, 0 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 4, 2, 0 ), vector( y, 4, 2, 0 ), correction, meanx, meany ] ); // eslint-disable-line max-len
 
 	t.strictEqual( v, -18.25/3, 'returns expected value' );
 	t.end();
@@ -215,7 +215,7 @@ tape( 'the function supports one-dimensional ndarrays having negative strides',
 	]);
 	meany = scalar2ndarray( 1.25, options );
 
-	v = dcovarmtk( [ vector( x, 4, -2, 6 ), vector( y, 4, -2, 6 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 4, -2, 6 ), vector( y, 4, -2, 6 ), correction, meanx, meany ] ); // eslint-disable-line max-len
 
 	t.strictEqual( v, -18.25/3, 'returns expected value' );
 	t.end();
@@ -255,7 +255,7 @@ tape( 'the function supports one-dimensional ndarrays having non-zero offsets',
 	]);
 	meany = scalar2ndarray( 1.25, options );
 
-	v = dcovarmtk( [ vector( x, 4, 2, 1 ), vector( y, 4, 2, 1 ), meanx, meany, correction ] ); // eslint-disable-line max-len
+	v = dcovarmtk( [ vector( x, 4, 2, 1 ), vector( y, 4, 2, 1 ), correction, meanx, meany ] ); // eslint-disable-line max-len
 	t.strictEqual( v, 5.75/3, 'returns expected value' );
 
 	t.end();

From 478c8efee733fd90e8aa68abb921429642e24731 Mon Sep 17 00:00:00 2001
From: gururaj1512 <gururajgurram1512@gmail.com>
Date: Sat, 26 Jul 2025 18:53:46 +0000
Subject: [PATCH 6/6] chore: clean-up

---
type: pre_commit_static_analysis_report
description: Results of running static analysis checks when committing changes.
report:
  - task: lint_filenames
    status: passed
  - task: lint_editorconfig
    status: passed
  - task: lint_markdown
    status: passed
  - task: lint_package_json
    status: passed
  - task: lint_repl_help
    status: passed
  - task: lint_javascript_src
    status: passed
  - task: lint_javascript_cli
    status: na
  - task: lint_javascript_examples
    status: passed
  - task: lint_javascript_tests
    status: na
  - task: lint_javascript_benchmarks
    status: na
  - task: lint_python
    status: na
  - task: lint_r
    status: na
  - task: lint_c_src
    status: na
  - task: lint_c_examples
    status: na
  - task: lint_c_benchmarks
    status: na
  - task: lint_c_tests_fixtures
    status: na
  - task: lint_shell
    status: na
  - task: lint_typescript_declarations
    status: passed
  - task: lint_typescript_tests
    status: na
  - task: lint_license_headers
    status: passed
---
---
 .../stats/base/ndarray/dcovarmtk/README.md    | 12 +++++-----
 .../base/ndarray/dcovarmtk/docs/repl.txt      | 22 ++++++++++---------
 .../ndarray/dcovarmtk/docs/types/index.d.ts   |  6 ++---
 .../base/ndarray/dcovarmtk/examples/index.js  |  5 ++---
 .../stats/base/ndarray/dcovarmtk/lib/main.js  |  6 ++---
 .../stats/base/ndarray/dcovarmtk/package.json |  2 +-
 6 files changed, 27 insertions(+), 26 deletions(-)

diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
index 49e4dbde6545..f9756931994e 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/README.md
@@ -131,9 +131,9 @@ The function has the following parameters:
 
     1.  first one-dimensional input ndarray.
     2.  second one-dimensional input ndarray.
-    3.  a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [covariance][covariance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population [covariance][covariance], setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample [covariance][covariance], setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
-    4.  a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
-    5.  a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
+    3.  a zero-dimensional ndarray specifying the degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the [covariance][covariance] according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment and `N` corresponds to the number of elements in each input ndarray. When computing the population [covariance][covariance], setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample [covariance][covariance], setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+    4.  a zero-dimensional ndarray specifying the mean of the first one-dimensional ndarray.
+    5.  a zero-dimensional ndarray specifying the mean of the second one-dimensional ndarray.
 
 </section>
 
@@ -143,7 +143,8 @@ The function has the following parameters:
 
 ## Notes
 
--   If provided an empty one-dimensional ndarray, the function returns `NaN`.
+-   Both input ndarrays should have the same number of elements.
+-   If provided empty one-dimensional ndarrays, the function returns `NaN`.
 
 </section>
 
@@ -167,12 +168,11 @@ var opts = {
     'dtype': 'float64'
 };
 
-// Create first one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
+// Create one-dimensional ndarrays containing pseudorandom numbers:
 var xbuf = discreteUniform( 10, -50, 50, opts );
 var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( x ) );
 
-// Create second one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
 var ybuf = discreteUniform( 10, -50, 50, opts );
 var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( y ) );
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
index 46187dd96f4c..8ce72f1b7055 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/repl.txt
@@ -1,10 +1,11 @@
 
 {{alias}}( arrays )
-    Computes the covariance of two one-dimensional double-precision
-    floating-point ndarrays provided known means and using a one-pass textbook
-    algorithm.
+    Computes the covariance of two one-dimensional double-precision floating-
+    point ndarrays provided known means and using a one-pass textbook algorithm.
 
-    If provided an empty ndarray, the function returns `NaN`.
+    Both input ndarrays should have the same number of elements.
+
+    If provided empty one-dimensional ndarrays, the function returns `NaN`.
 
     Parameters
     ----------
@@ -13,21 +14,22 @@
 
         -   first one-dimensional input ndarray.
         -   second one-dimensional input ndarray.
-        -   a zero-dimensional ndarray specifying degrees of freedom
+        -   a zero-dimensional ndarray specifying the degrees of freedom
         adjustment. Setting this parameter to a value other than `0` has the
         effect of adjusting the divisor during the calculation of the
         covariance according to `N-c` where `c` corresponds to the provided
-        degrees of freedom adjustment. When computing the population
+        degrees of freedom adjustment and `N` corresponds to the number of
+        elements in each input ndarray. When computing the population
         covariance, setting this parameter to `0` is the standard choice (i.e.,
         the provided arrays contain data constituting entire populations). When
         computing the unbiased sample covariance, setting this parameter to `1`
         is the standard choice (i.e., the provided arrays contain data sampled
         from larger populations; this is commonly referred to as Bessel's
         correction).
-        -   a zero-dimensional ndarray specifying mean of the first
-        one-dimensional ndarray.
-        -   a zero-dimensional ndarray specifying mean of the second
-        one-dimensional ndarray.
+        -   a zero-dimensional ndarray specifying the mean of the first one-
+        dimensional ndarray.
+        -   a zero-dimensional ndarray specifying the mean of the second one-
+        dimensional ndarray.
 
     Returns
     -------
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
index d71c36d3a8e9..eeadddfde502 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/docs/types/index.d.ts
@@ -31,9 +31,9 @@ import { float64ndarray } from '@stdlib/types/ndarray';
 *
 *     -   first one-dimensional input ndarray.
 *     -   second one-dimensional input ndarray.
-*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
-*     -   a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
-*     -   a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying the degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment and `N` corresponds to the number of elements in each input ndarray. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+*     -   a zero-dimensional ndarray specifying the mean of the first one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying the mean of the second one-dimensional ndarray.
 *
 * @param arrays - array-like object containing input ndarrays
 * @returns covariance
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
index f348fa53f761..c06e5bc0572c 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/examples/index.js
@@ -29,14 +29,13 @@ var opts = {
 	'dtype': 'float64'
 };
 
-// Create first one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
+// Create one-dimensional ndarrays containing pseudorandom numbers:
 var xbuf = discreteUniform( 10, -50, 50, opts );
 var x = new ndarray( opts.dtype, xbuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( x ) );
 
-// Create second one-dimensional ndarray containing pseudorandom integers drawn from a discrete uniform distribution:
 var ybuf = discreteUniform( 10, -50, 50, opts );
-var y = new ndarray( opts.dtype, ybuf, [ xbuf.length ], [ 1 ], 0, 'row-major' );
+var y = new ndarray( opts.dtype, ybuf, [ ybuf.length ], [ 1 ], 0, 'row-major' );
 console.log( ndarray2array( y ) );
 
 // Specify the degrees of freedom adjustment:
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
index a04d6a397486..66f89996c544 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/lib/main.js
@@ -39,9 +39,9 @@ var strided = require( '@stdlib/stats/strided/dcovarmtk' ).ndarray;
 *
 *     -   first one-dimensional input ndarray.
 *     -   second one-dimensional input ndarray.
-*     -   a zero-dimensional ndarray specifying degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
-*     -   a zero-dimensional ndarray specifying mean of the first one-dimensional ndarray.
-*     -   a zero-dimensional ndarray specifying mean of the second one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying the degrees of freedom adjustment. Setting this parameter to a value other than `0` has the effect of adjusting the divisor during the calculation of the covariance according to `N-c` where `c` corresponds to the provided degrees of freedom adjustment and `N` corresponds to the number of elements in each input ndarray. When computing the population covariance, setting this parameter to `0` is the standard choice (i.e., the provided arrays contain data constituting entire populations). When computing the unbiased sample covariance, setting this parameter to `1` is the standard choice (i.e., the provided arrays contain data sampled from larger populations; this is commonly referred to as Bessel's correction).
+*     -   a zero-dimensional ndarray specifying the mean of the first one-dimensional ndarray.
+*     -   a zero-dimensional ndarray specifying the mean of the second one-dimensional ndarray.
 *
 * @param {ArrayLikeObject<Object>} arrays - array-like object containing input ndarrays
 * @returns {number} covariance
diff --git a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json
index 52b0d204caa7..32030201d611 100644
--- a/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json
+++ b/lib/node_modules/@stdlib/stats/base/ndarray/dcovarmtk/package.json
@@ -1,7 +1,7 @@
 {
   "name": "@stdlib/stats/base/ndarray/dcovarmtk",
   "version": "0.0.0",
-  "description": "Computes the covariance of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.",
+  "description": "Compute the covariance of two one-dimensional double-precision floating-point ndarrays provided known means and using a one-pass textbook algorithm.",
   "license": "Apache-2.0",
   "author": {
     "name": "The Stdlib Authors",