diff --git a/lib/node_modules/@stdlib/stats/covarmtk/README.md b/lib/node_modules/@stdlib/stats/covarmtk/README.md
new file mode 100644
index 000000000000..91c25d2a787f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/README.md
@@ -0,0 +1,308 @@
+
+
+# covarmtk
+
+> Compute the [covariance][covariance] of two ndarrays provided known means and using a one-pass textbook algorithm.
+
+
+
+The population [covariance][covariance] of two finite size populations of size `N` is given by
+
+
+
+```math
+\mathop{\mathrm{cov_N}} = \frac{1}{N} \sum_{i=0}^{N-1} (x_i - \mu_x)(y_i - \mu_y)
+```
+
+
+
+where the population means are given by
+
+
+
+```math
+\mu_x = \frac{1}{N} \sum_{i=0}^{N-1} x_i
+```
+
+
+
+and
+
+
+
+```math
+\mu_y = \frac{1}{N} \sum_{i=0}^{N-1} y_i
+```
+
+
+
+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`,
+
+
+
+```math
+\mathop{\mathrm{cov_n}} = \frac{1}{n-1} \sum_{i=0}^{n-1} (x_i - \bar{x}_n)(y_i - \bar{y}_n)
+```
+
+
+
+where sample means are given by
+
+
+
+```math
+\bar{x} = \frac{1}{n} \sum_{i=0}^{n-1} x_i
+```
+
+
+
+and
+
+
+
+```math
+\bar{y} = \frac{1}{n} \sum_{i=0}^{n-1} y_i
+```
+
+
+
+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.
+
+
+
+
+
+
+
+## Usage
+
+```javascript
+var covarmtk = require( '@stdlib/stats/covarmtk' );
+```
+
+#### covarmtk( x, y, correction, meanx, meany\[, options] )
+
+Computes the [covariance][covariance] of two ndarrays provided known means and using a one-pass textbook algorithm.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+
+var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+
+var x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+var y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+var correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+});
+var meanx = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+});
+var meany = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+});
+
+var out = covarmtk( x, y, correction, meanx, meany );
+// returns [ ~3.8333 ]
+```
+
+The function has the following parameters:
+
+- **x**: first input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or "generic" [data type][@stdlib/ndarray/dtypes].
+- **y**: second input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or "generic" [data type][@stdlib/ndarray/dtypes].
+- **correction**: zero-dimensional [ndarray][@stdlib/ndarray/ctor] 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][@stdlib/ndarray/ctor]. 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).
+- **meanx**: zero-dimensional [ndarray][@stdlib/ndarray/ctor] specifying the mean of the first input [ndarray][@stdlib/ndarray/ctor].
+- **meany**: zero-dimensional [ndarray][@stdlib/ndarray/ctor] specifying the mean of the second input [ndarray][@stdlib/ndarray/ctor].
+- **options**: function options (_optional_).
+
+The function accepts the following options:
+
+- **dims**: list of dimensions over which to perform a reduction. If not provided, the function performs a reduction over all elements in a provided input [ndarray][@stdlib/ndarray/ctor].
+- **dtype**: output ndarray [data type][@stdlib/ndarray/dtypes]. Must be a real-valued floating-point or "generic" [data type][@stdlib/ndarray/dtypes].
+- **keepdims**: boolean indicating whether the reduced dimensions should be included in the returned [ndarray][@stdlib/ndarray/ctor] as singleton dimensions. Default: `false`.
+
+By default, the function performs a reduction over all elements in the provided input ndarrays. To perform a reduction over specific dimensions, provide a `dims` option.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+
+var xbuf = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
+var ybuf = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
+
+var x = new ndarray( 'float64', xbuf, [ 2, 2, 2 ], [ 4, 2, 1 ], 0, 'row-major' );
+var y = new ndarray( 'float64', ybuf, [ 2, 2, 2 ], [ 4, 2, 1 ], 0, 'row-major' );
+
+var correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+});
+var meanx = scalar2ndarray( 1.25, {
+ 'dtype': 'float64'
+});
+var meany = scalar2ndarray( 1.25, {
+ 'dtype': 'float64'
+});
+
+var out = covarmtk( x, y, correction, meanx, meany, {
+ 'dims': [ 2 ]
+});
+// returns
+```
+
+#### covarmtk.assign( x, y, correction, meanx, meany, out\[, options] )
+
+Computes the [covariance][covariance] of two ndarrays provided known means and using a one-pass textbook algorithm and assigns results to a provided output [ndarray][@stdlib/ndarray/ctor].
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+
+var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+
+var x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+var y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+var correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+});
+var meanx = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+});
+var meany = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+});
+
+var z = zeros( [], {
+ 'dtype': 'float64'
+});
+
+var out = covarmtk.assign( x, y, correction, meanx, meany, z );
+// returns [ ~3.8333 ]
+
+var bool = ( out === z );
+// returns true
+```
+
+The method has the following parameters:
+
+- **x**: first input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or "generic" [data type][@stdlib/ndarray/dtypes].
+- **y**: second input [ndarray][@stdlib/ndarray/ctor]. Must have a real-valued or "generic" [data type][@stdlib/ndarray/dtypes].
+- **correction**: zero-dimensional [ndarray][@stdlib/ndarray/ctor] specifying the degrees of freedom adjustment.
+- **meanx**: zero-dimensional [ndarray][@stdlib/ndarray/ctor] specifying the mean of the first input [ndarray][@stdlib/ndarray/ctor].
+- **meany**: zero-dimensional [ndarray][@stdlib/ndarray/ctor] specifying the mean of the second input [ndarray][@stdlib/ndarray/ctor].
+- **out**: output [ndarray][@stdlib/ndarray/ctor].
+- **options**: function options (_optional_).
+
+The method accepts the following options:
+
+- **dims**: list of dimensions over which to perform a reduction. If not provided, the function performs a reduction over all elements in the provided input ndarrays.
+
+
+
+
+
+
+
+## Notes
+
+- Both input ndarrays must have the same shape.
+- Setting the `keepdims` option to `true` can be useful when wanting to ensure that the output [ndarray][@stdlib/ndarray/ctor] is [broadcast-compatible][@stdlib/ndarray/base/broadcast-shapes] with ndarrays having the same shape as the input ndarrays.
+- The output data type [policy][@stdlib/ndarray/output-dtype-policies] only applies to the main function and specifies that, by default, the function must return an [ndarray][@stdlib/ndarray/ctor] having a real-valued floating-point or "generic" [data type][@stdlib/ndarray/dtypes]. For the `assign` method, the output [ndarray][@stdlib/ndarray/ctor] is allowed to have any supported output [data type][@stdlib/ndarray/dtypes].
+
+
+
+
+
+
+
+## Examples
+
+
+
+```javascript
+var uniform = require( '@stdlib/random/array/uniform' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var covarmtk = require( '@stdlib/stats/covarmtk' );
+
+var opts = {
+ 'dtype': 'float64'
+};
+
+var xbuf = uniform( 40, -50.0, 50.0, opts );
+var x = new ndarray( opts.dtype, xbuf, [ 5, 2, 4 ], [ 8, 4, 1 ], 0, 'row-major' );
+
+var ybuf = uniform( 40, -50.0, 50.0, opts );
+var y = new ndarray( opts.dtype, ybuf, [ 5, 2, 4 ], [ 8, 4, 1 ], 0, 'row-major' );
+
+var correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+});
+var meanx = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+});
+var meany = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+});
+
+var out = covarmtk( x, y, correction, meanx, meany, {
+ 'dims': [ 2 ]
+});
+console.log( ndarray2array( out ) );
+```
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+[covariance]: https://en.wikipedia.org/wiki/Covariance
+
+[@stdlib/ndarray/ctor]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/ctor
+
+[@stdlib/ndarray/dtypes]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/dtypes
+
+[@stdlib/ndarray/output-dtype-policies]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/output-dtype-policies
+
+[@stdlib/ndarray/base/broadcast-shapes]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/ndarray/base/broadcast-shapes
+
+
+
+
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/benchmark/benchmark.assign.js b/lib/node_modules/@stdlib/stats/covarmtk/benchmark/benchmark.assign.js
new file mode 100644
index 000000000000..eb3c1fec7573
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/benchmark/benchmark.assign.js
@@ -0,0 +1,126 @@
+/**
+* @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 format = require( '@stdlib/string/format' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var zeros = require( '@stdlib/array/zeros' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var pkg = require( './../package.json' ).name;
+var covarmtk = 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 out;
+ var x;
+ var y;
+
+ xbuf = uniform( len, -50.0, 50.0, options );
+ x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
+
+ ybuf = uniform( len, -50.0, 50.0, options );
+ y = new ndarray( options.dtype, ybuf, [ len ], [ 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, options );
+ meanx = scalar2ndarray( 0.0, options );
+ meany = scalar2ndarray( 0.0, options );
+
+ out = new ndarray( options.dtype, zeros( 1, options.dtype ), [], [ 0 ], 0, 'row-major' );
+
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var o;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ o = covarmtk.assign( x, y, correction, meanx, meany, out );
+ if ( typeof o !== 'object' ) {
+ b.fail( 'should return an ndarray' );
+ }
+ }
+ b.toc();
+ if ( isnan( o.get() ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var len;
+ var min;
+ var max;
+ var f;
+ var i;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( i = min; i <= max; i++ ) {
+ len = pow( 10, i );
+ f = createBenchmark( len );
+ bench( format( '%s:assign:dtype=%s,len=%d', pkg, options.dtype, len ), f );
+ }
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/benchmark/benchmark.js b/lib/node_modules/@stdlib/stats/covarmtk/benchmark/benchmark.js
new file mode 100644
index 000000000000..94c7b1198d53
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/benchmark/benchmark.js
@@ -0,0 +1,122 @@
+/**
+* @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 format = require( '@stdlib/string/format' );
+var uniform = require( '@stdlib/random/array/uniform' );
+var ndarray = require( '@stdlib/ndarray/base/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var pkg = require( './../package.json' ).name;
+var covarmtk = 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, -50.0, 50.0, options );
+ x = new ndarray( options.dtype, xbuf, [ len ], [ 1 ], 0, 'row-major' );
+
+ ybuf = uniform( len, -50.0, 50.0, options );
+ y = new ndarray( options.dtype, ybuf, [ len ], [ 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, options );
+ meanx = scalar2ndarray( 0.0, options );
+ meany = scalar2ndarray( 0.0, options );
+
+ return benchmark;
+
+ /**
+ * Benchmark function.
+ *
+ * @private
+ * @param {Benchmark} b - benchmark instance
+ */
+ function benchmark( b ) {
+ var o;
+ var i;
+
+ b.tic();
+ for ( i = 0; i < b.iterations; i++ ) {
+ o = covarmtk( x, y, correction, meanx, meany );
+ if ( typeof o !== 'object' ) {
+ b.fail( 'should return an ndarray' );
+ }
+ }
+ b.toc();
+ if ( isnan( o.get() ) ) {
+ b.fail( 'should not return NaN' );
+ }
+ b.pass( 'benchmark finished' );
+ b.end();
+ }
+}
+
+
+// MAIN //
+
+/**
+* Main execution sequence.
+*
+* @private
+*/
+function main() {
+ var len;
+ var min;
+ var max;
+ var f;
+ var i;
+
+ min = 1; // 10^min
+ max = 6; // 10^max
+
+ for ( i = min; i <= max; i++ ) {
+ len = pow( 10, i );
+ f = createBenchmark( len );
+ bench( format( '%s:dtype=%s,len=%d', pkg, options.dtype, len ), f );
+ }
+}
+
+main();
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/docs/repl.txt b/lib/node_modules/@stdlib/stats/covarmtk/docs/repl.txt
new file mode 100644
index 000000000000..93a7a80a495f
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/docs/repl.txt
@@ -0,0 +1,117 @@
+
+{{alias}}( x, y, correction, meanx, meany[, options] )
+ Computes the covariance of two ndarrays provided known means and using a
+ one-pass textbook algorithm.
+
+ Parameters
+ ----------
+ x: ndarray
+ First input array. Must have a real-valued or "generic" data type.
+
+ y: ndarray
+ Second input array. Must have a real-valued or "generic" data type.
+
+ correction: ndarray
+ Zero-dimensional ndarray specifying the degrees of freedom adjustment.
+
+ meanx: ndarray
+ Zero-dimensional ndarray specifying the mean of the first input
+ ndarray.
+
+ meany: ndarray
+ Zero-dimensional ndarray specifying the mean of the second input
+ ndarray.
+
+ options: Object (optional)
+ Function options.
+
+ options.dtype: string|DataType (optional)
+ Output array data type. Must be a real-valued floating-point or
+ "generic" data type.
+
+ options.dims: Array (optional)
+ List of dimensions over which to perform a reduction. If not provided,
+ the function performs a reduction over all elements in provided input
+ ndarrays.
+
+ options.keepdims: boolean (optional)
+ Boolean indicating whether the reduced dimensions should be included in
+ the returned ndarray as singleton dimensions. Default: false.
+
+ Returns
+ -------
+ out: ndarray
+ Output array.
+
+ Examples
+ --------
+ > var x = {{alias:@stdlib/ndarray/array}}( [ 1.0, -2.0, 2.0 ] );
+ > var y = {{alias:@stdlib/ndarray/array}}( [ 2.0, -2.0, 1.0 ] );
+ > var c = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, { 'dtype': 'float64' } );
+ > var mx = {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, { 'dtype': 'float64' } );
+ > var my = {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, { 'dtype': 'float64' } );
+ > var out = {{alias}}( x, y, c, mx, my )
+
+
+ > var x = {{alias:@stdlib/ndarray/array}}( [ [ 1.0, 2.0 ], [ 3.0, 4.0 ] ] );
+ > var y = {{alias:@stdlib/ndarray/array}}( [ [ 4.0, 3.0 ], [ 2.0, 1.0 ] ] );
+ > var out = {{alias}}( x, y, c, mx, my, { 'dims': [ 0 ] } )
+
+
+
+{{alias}}.assign( x, y, correction, meanx, meany, out[, options] )
+ Computes the covariance of two ndarrays provided known means and using a
+ one-pass textbook algorithm and assigns results to a provided output
+ ndarray.
+
+ Parameters
+ ----------
+ x: ndarray
+ First input array. Must have a real-valued or "generic" data type.
+
+ y: ndarray
+ Second input array. Must have a real-valued or "generic" data type.
+
+ correction: ndarray
+ Zero-dimensional ndarray specifying the degrees of freedom adjustment.
+
+ meanx: ndarray
+ Zero-dimensional ndarray specifying the mean of the first input
+ ndarray.
+
+ meany: ndarray
+ Zero-dimensional ndarray specifying the mean of the second input
+ ndarray.
+
+ out: ndarray
+ Output array.
+
+ options: Object (optional)
+ Function options.
+
+ options.dims: Array (optional)
+ List of dimensions over which to perform a reduction. If not provided,
+ the function performs a reduction over all elements in provided input
+ ndarrays.
+
+ Returns
+ -------
+ out: ndarray
+ Output array.
+
+ Examples
+ --------
+ > var x = {{alias:@stdlib/ndarray/array}}( [ 1.0, -2.0, 2.0 ] );
+ > var y = {{alias:@stdlib/ndarray/array}}( [ 2.0, -2.0, 1.0 ] );
+ > var c = {{alias:@stdlib/ndarray/from-scalar}}( 1.0, { 'dtype': 'float64' } );
+ > var mx = {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, { 'dtype': 'float64' } );
+ > var my = {{alias:@stdlib/ndarray/from-scalar}}( 1.0/3.0, { 'dtype': 'float64' } );
+ > var out = {{alias:@stdlib/ndarray/zeros}}( [] );
+ > var z = {{alias}}.assign( x, y, c, mx, my, out )
+
+ > var bool = ( out === z )
+ true
+
+ See Also
+ --------
+
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/docs/types/index.d.ts b/lib/node_modules/@stdlib/stats/covarmtk/docs/types/index.d.ts
new file mode 100644
index 000000000000..a55970e7e529
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/docs/types/index.d.ts
@@ -0,0 +1,193 @@
+/*
+* @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
+
+///
+
+import { ArrayLike } from '@stdlib/types/array';
+import { RealFloatingPointAndGenericDataType as DataType, typedndarray } from '@stdlib/types/ndarray';
+
+/**
+* Input array.
+*/
+type InputArray = typedndarray;
+
+/**
+* Output array.
+*/
+type OutputArray = typedndarray;
+
+/**
+* Interface defining "base" options.
+*/
+interface BaseOptions {
+ /**
+ * List of dimensions over which to perform a reduction.
+ */
+ dims?: ArrayLike;
+}
+
+/**
+* Interface defining options.
+*/
+interface Options extends BaseOptions {
+ /**
+ * Output array data type.
+ */
+ dtype?: DataType;
+
+ /**
+ * Boolean indicating whether the reduced dimensions should be included in the returned array as singleton dimensions. Default: `false`.
+ */
+ keepdims?: boolean;
+}
+
+/**
+* Interface for performing a reduction on two ndarrays.
+*/
+interface Binary {
+ /**
+ * Computes the covariance of two ndarrays provided known means and using a one-pass textbook algorithm.
+ *
+ * @param x - first input ndarray
+ * @param y - second input ndarray
+ * @param correction - zero-dimensional ndarray specifying the degrees of freedom adjustment
+ * @param meanx - zero-dimensional ndarray specifying the mean of the first input ndarray
+ * @param meany - zero-dimensional ndarray specifying the mean of the second input ndarray
+ * @param options - function options
+ * @returns output ndarray
+ *
+ * @example
+ * var Float64Array = require( '@stdlib/array/float64' );
+ * var ndarray = require( '@stdlib/ndarray/ctor' );
+ * var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+ *
+ * var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ * var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+ *
+ * var x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ * var y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ *
+ * var correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ * var meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ * var meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ *
+ * var out = covarmtk( x, y, correction, meanx, meany );
+ * // returns [ ~3.8333 ]
+ */
+ ( x: InputArray, y: InputArray, correction: InputArray, meanx: InputArray, meany: InputArray, options?: Options ): OutputArray;
+
+ /**
+ * Computes the covariance of two ndarrays provided known means and using a one-pass textbook algorithm and assigns results to a provided output ndarray.
+ *
+ * @param x - first input ndarray
+ * @param y - second input ndarray
+ * @param correction - zero-dimensional ndarray specifying the degrees of freedom adjustment
+ * @param meanx - zero-dimensional ndarray specifying the mean of the first input ndarray
+ * @param meany - zero-dimensional ndarray specifying the mean of the second input ndarray
+ * @param out - output ndarray
+ * @param options - function options
+ * @returns output ndarray
+ *
+ * @example
+ * var Float64Array = require( '@stdlib/array/float64' );
+ * var ndarray = require( '@stdlib/ndarray/ctor' );
+ * var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+ * var zeros = require( '@stdlib/ndarray/zeros' );
+ *
+ * var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ * var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+ *
+ * var x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ * var y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ *
+ * var correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ * var meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ * var meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ *
+ * var z = zeros( [], { 'dtype': 'float64' } );
+ *
+ * var out = covarmtk.assign( x, y, correction, meanx, meany, z );
+ * // returns [ ~3.8333 ]
+ *
+ * var bool = ( out === z );
+ * // returns true
+ */
+ assign = OutputArray, V = unknown>( x: InputArray, y: InputArray, correction: InputArray, meanx: InputArray, meany: InputArray, out: U, options?: BaseOptions ): U;
+}
+
+/**
+* Computes the covariance of two ndarrays provided known means and using a one-pass textbook algorithm.
+*
+* @param x - first input ndarray
+* @param y - second input ndarray
+* @param correction - zero-dimensional ndarray specifying the degrees of freedom adjustment
+* @param meanx - zero-dimensional ndarray specifying the mean of the first input ndarray
+* @param meany - zero-dimensional ndarray specifying the mean of the second input ndarray
+* @param options - function options
+* @returns output ndarray
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var ndarray = require( '@stdlib/ndarray/ctor' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+*
+* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+* var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+*
+* var x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+* var y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+* var meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+* var meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+*
+* var out = covarmtk( x, y, correction, meanx, meany );
+* // returns [ ~3.8333 ]
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var ndarray = require( '@stdlib/ndarray/ctor' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var zeros = require( '@stdlib/ndarray/zeros' );
+*
+* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+* var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+*
+* var x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+* var y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+*
+* var correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+* var meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+* var meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+*
+* var z = zeros( [], { 'dtype': 'float64' } );
+*
+* var out = covarmtk.assign( x, y, correction, meanx, meany, z );
+* // returns [ ~3.8333 ]
+*
+* var bool = ( out === z );
+* // returns true
+*/
+declare const covarmtk: Binary;
+
+
+// EXPORTS //
+
+export = covarmtk;
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/docs/types/test.ts b/lib/node_modules/@stdlib/stats/covarmtk/docs/types/test.ts
new file mode 100644
index 000000000000..4b49d5b1efc0
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/docs/types/test.ts
@@ -0,0 +1,294 @@
+/*
+* @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.
+*/
+
+import ndarray = require( '@stdlib/ndarray/ctor' );
+import scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+import zeros = require( '@stdlib/ndarray/zeros' );
+import covarmtk = require( './index' );
+
+
+// TESTS //
+
+// The main function returns an ndarray...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+
+ covarmtk( x, y, correction, meanx, meany ); // $ExpectType OutputArray
+ covarmtk( x, y, correction, meanx, meany, { 'dims': [ 0 ] } ); // $ExpectType OutputArray
+ covarmtk( x, y, correction, meanx, meany, { 'dtype': 'float64' } ); // $ExpectType OutputArray
+ covarmtk( x, y, correction, meanx, meany, { 'keepdims': true } ); // $ExpectType OutputArray
+}
+
+// The main function throws an error if provided arguments which are not ndarrays...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+
+ covarmtk( '5', x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, '5', correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, '5', meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, '5', meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, '5' ); // $ExpectError
+
+ covarmtk( 5, x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, 5, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, 5, meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, 5, meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, 5 ); // $ExpectError
+
+ covarmtk( true, x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, true, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, true, meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, true, meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, true ); // $ExpectError
+
+ covarmtk( false, x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, false, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, false, meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, false, meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, false ); // $ExpectError
+
+ covarmtk( null, x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, null, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, null, meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, null, meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, null ); // $ExpectError
+
+ covarmtk( undefined, x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, undefined, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, undefined, meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, undefined, meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, undefined ); // $ExpectError
+
+ covarmtk( [ 1, 2, 3 ], x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, [ 1, 2, 3 ], correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, [ 1, 2, 3 ], meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, [ 1, 2, 3 ], meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, [ 1, 2, 3 ] ); // $ExpectError
+
+ covarmtk( {}, x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, {}, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, {}, meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, {}, meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, {} ); // $ExpectError
+
+ covarmtk( ( x: number ) => x, x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, ( x: number ) => x, correction, meanx, meany ); // $ExpectError
+ covarmtk( x, x, ( x: number ) => x, meanx, meany ); // $ExpectError
+ covarmtk( x, x, correction, ( x: number ) => x, meany ); // $ExpectError
+ covarmtk( x, x, correction, meanx, ( x: number ) => x ); // $ExpectError
+}
+
+// The main function throws an error if provided an options argument which is not an object...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+
+ covarmtk( x, x, correction, meanx, meany, '5' ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, 5 ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, true ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, false ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, null ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, [] ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, ( x: number ) => x ); // $ExpectError
+}
+
+// The main function throws an error if provided a `dims` option which is not an array-like object of numbers...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+
+ covarmtk( x, x, correction, meanx, meany, { 'dims': '5' } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dims': 5 } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dims': true } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dims': false } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dims': null } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dims': {} } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dims': ( x: number ) => x } ); // $ExpectError
+}
+
+// The main function throws an error if provided a `dtype` option which is not a supported data type...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': '5' } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': 5 } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': true } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': false } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': null } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': [] } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': {} } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'dtype': ( x: number ) => x } ); // $ExpectError
+}
+
+// The main function throws an error if provided a `keepdims` option which is not a boolean...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+
+ covarmtk( x, x, correction, meanx, meany, { 'keepdims': '5' } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'keepdims': 5 } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'keepdims': null } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'keepdims': [] } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'keepdims': {} } ); // $ExpectError
+ covarmtk( x, x, correction, meanx, meany, { 'keepdims': ( x: number ) => x } ); // $ExpectError
+}
+
+// The `assign` method returns an ndarray...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const z = zeros( [], { 'dtype': 'float64' } );
+
+ covarmtk.assign( x, x, correction, meanx, meany, z ); // $ExpectType float64ndarray
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': [ 0 ] } ); // $ExpectType float64ndarray
+}
+
+// The `assign` method throws an error if provided arguments which are not ndarrays...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const z = zeros( [], { 'dtype': 'float64' } );
+
+ covarmtk.assign( '5', x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, '5', correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, '5', meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, '5', meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, '5', z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, '5' ); // $ExpectError
+
+ covarmtk.assign( 5, x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, 5, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, 5, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, 5, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, 5, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, 5 ); // $ExpectError
+
+ covarmtk.assign( true, x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, true, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, true, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, true, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, true, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, true ); // $ExpectError
+
+ covarmtk.assign( false, x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, false, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, false, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, false, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, false, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, false ); // $ExpectError
+
+ covarmtk.assign( null, x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, null, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, null, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, null, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, null, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, null ); // $ExpectError
+
+ covarmtk.assign( undefined, x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, undefined, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, undefined, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, undefined, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, undefined, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, undefined ); // $ExpectError
+
+ covarmtk.assign( [ 1, 2, 3 ], x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, [ 1, 2, 3 ], correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, [ 1, 2, 3 ], meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, [ 1, 2, 3 ], meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, [ 1, 2, 3 ], z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, [ 1, 2, 3 ] ); // $ExpectError
+
+ covarmtk.assign( {}, x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, {}, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, {}, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, {}, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, {}, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, {} ); // $ExpectError
+
+ covarmtk.assign( ( x: number ) => x, x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, ( x: number ) => x, correction, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, ( x: number ) => x, meanx, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, ( x: number ) => x, meany, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, ( x: number ) => x, z ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, ( x: number ) => x ); // $ExpectError
+}
+
+// The `assign` method throws an error if provided an options argument which is not an object...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const z = zeros( [], { 'dtype': 'float64' } );
+
+ covarmtk.assign( x, x, correction, meanx, meany, z, '5' ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, 5 ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, true ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, false ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, null ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, [] ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, ( x: number ) => x ); // $ExpectError
+}
+
+// The `assign` method throws an error if provided a `dims` option which is not an array-like object of numbers...
+{
+ const xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ const x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ const correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+ const meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+ const z = zeros( [], { 'dtype': 'float64' } );
+
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': '5' } ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': 5 } ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': true } ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': false } ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': null } ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': {} } ); // $ExpectError
+ covarmtk.assign( x, x, correction, meanx, meany, z, { 'dims': ( x: number ) => x } ); // $ExpectError
+}
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/examples/index.js b/lib/node_modules/@stdlib/stats/covarmtk/examples/index.js
new file mode 100644
index 000000000000..9819ffb31e1a
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/examples/index.js
@@ -0,0 +1,44 @@
+/**
+* @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 uniform = require( '@stdlib/random/array/uniform' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var covarmtk = require( './../lib' );
+
+var opts = {
+ 'dtype': 'float64'
+};
+
+var xbuf = uniform( 40, -50.0, 50.0, opts );
+var x = new ndarray( opts.dtype, xbuf, [ 5, 2, 4 ], [ 8, 4, 1 ], 0, 'row-major' );
+
+var ybuf = uniform( 40, -50.0, 50.0, opts );
+var y = new ndarray( opts.dtype, ybuf, [ 5, 2, 4 ], [ 8, 4, 1 ], 0, 'row-major' );
+
+var correction = scalar2ndarray( 1.0, opts );
+var meanx = scalar2ndarray( 0.0, opts );
+var meany = scalar2ndarray( 0.0, opts );
+
+var out = covarmtk( x, y, correction, meanx, meany, {
+ 'dims': [ 2 ]
+});
+console.log( ndarray2array( out ) );
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/lib/index.js b/lib/node_modules/@stdlib/stats/covarmtk/lib/index.js
new file mode 100644
index 000000000000..4a92b896d9bf
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/lib/index.js
@@ -0,0 +1,70 @@
+/**
+* @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';
+
+/**
+* Compute the covariance of two ndarrays provided known means and using a one-pass textbook algorithm.
+*
+* @module @stdlib/stats/covarmtk
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+* var ndarray = require( '@stdlib/ndarray/ctor' );
+* var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+* var covarmtk = require( '@stdlib/stats/covarmtk' );
+*
+* // Create data buffers:
+* var xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+* var ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+*
+* // Define the shape of the input arrays:
+* var sh = [ 3 ];
+*
+* // Define the array strides:
+* var sx = [ 1 ];
+* var sy = [ 1 ];
+*
+* // Define the index offsets:
+* var ox = 0;
+* var oy = 0;
+*
+* // Create input ndarrays:
+* var x = new ndarray( 'float64', xbuf, sh, sx, ox, 'row-major' );
+* var y = new ndarray( 'float64', ybuf, sh, sy, oy, 'row-major' );
+*
+* // Define correction and means:
+* var correction = scalar2ndarray( 1.0, { 'dtype': 'float64' } );
+* var meanx = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+* var meany = scalar2ndarray( 1.0/3.0, { 'dtype': 'float64' } );
+*
+* // Perform reduction:
+* var out = covarmtk( x, y, correction, meanx, meany );
+* // returns [ ~3.8333 ]
+*/
+
+// MODULES //
+
+var main = require( './main.js' );
+
+
+// EXPORTS //
+
+module.exports = main;
+
+// exports: { "assign": "main.assign" }
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/lib/main.js b/lib/node_modules/@stdlib/stats/covarmtk/lib/main.js
new file mode 100644
index 000000000000..c523c5d1d06b
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/lib/main.js
@@ -0,0 +1,168 @@
+/**
+* @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 dtypes = require( '@stdlib/ndarray/dtypes' );
+var gcovarmtk = require( '@stdlib/stats/base/ndarray/covarmtk' );
+var dcovarmtk = require( '@stdlib/stats/base/ndarray/dcovarmtk' );
+var scovarmtk = require( '@stdlib/stats/base/ndarray/scovarmtk' );
+var factory = require( '@stdlib/ndarray/base/binary-reduce-strided1d-dispatch-factory' );
+var isObject = require( '@stdlib/assert/is-object' );
+var getShape = require( '@stdlib/ndarray/shape' );
+var indicesComplement = require( '@stdlib/array/base/indices-complement' );
+var takeIndexed = require( '@stdlib/array/base/take-indexed' );
+var zeroTo = require( '@stdlib/array/base/zero-to' );
+var broadcast = require( '@stdlib/ndarray/base/broadcast-array' );
+var setReadOnly = require( '@stdlib/utils/define-nonenumerable-read-only-property' );
+
+
+// VARIABLES //
+
+var idtypes = dtypes( 'real_and_generic' );
+var odtypes = dtypes( 'real_floating_point_and_generic' );
+var policies = {
+ 'output': 'real_floating_point_and_generic',
+ 'casting': 'none'
+};
+var table = {
+ 'types': [
+ 'float64',
+ 'float64',
+ 'float32',
+ 'float32'
+ ],
+ 'fcns': [
+ dcovarmtk,
+ scovarmtk
+ ],
+ 'default': gcovarmtk
+};
+var itypes = [ idtypes, idtypes, idtypes, idtypes, idtypes ];
+var dispatcher = factory( table, itypes, odtypes, policies );
+
+
+// FUNCTIONS //
+
+/**
+* Broadcasts arguments to a loop shape.
+*
+* @private
+* @param {Array} args - arguments to broadcast
+* @param {ndarray} x - reference ndarray for shape
+* @param {Object} [options] - function options
+* @returns {Array} broadcasted arguments
+*/
+function broadcastArgs( args, x, options ) {
+ var loopShape;
+ var sh;
+ var d;
+ var i;
+
+ sh = getShape( x );
+ if ( isObject( options ) && options.dims ) {
+ d = options.dims;
+ } else {
+ d = zeroTo( sh.length );
+ }
+ loopShape = takeIndexed( sh, indicesComplement( sh.length, d ) );
+ for ( i = 0; i < args.length; i++ ) {
+ args[ i ] = broadcast( args[ i ], loopShape );
+ }
+ return args;
+}
+
+
+// MAIN //
+
+/**
+* Computes the covariance of two ndarrays provided known means and using a one-pass textbook algorithm.
+*
+* @name covarmtk
+* @type {Function}
+* @param {ndarray} x - first input ndarray
+* @param {ndarray} y - second input ndarray
+* @param {ndarray} correction - zero-dimensional ndarray specifying the degrees of freedom adjustment
+* @param {ndarray} meanx - zero-dimensional ndarray specifying the mean of the first input ndarray
+* @param {ndarray} meany - zero-dimensional ndarray specifying the mean of the second input ndarray
+* @param {Options} [options] - function options
+* @param {IntegerArray} [options.dims] - list of dimensions over which to perform a reduction
+* @param {boolean} [options.keepdims=false] - boolean indicating whether the reduced dimensions should be included in the returned ndarray as singleton dimensions
+* @param {*} [options.dtype] - output ndarray data type
+* @throws {TypeError} first argument must be an ndarray-like object
+* @throws {TypeError} second argument must be an ndarray-like object
+* @throws {TypeError} third argument must be an ndarray-like object
+* @throws {TypeError} fourth argument must be an ndarray-like object
+* @throws {TypeError} fifth argument must be an ndarray-like object
+* @throws {TypeError} options argument must be an object
+* @throws {RangeError} dimension indices must not exceed input ndarray bounds
+* @throws {RangeError} number of dimension indices must not exceed the number of input ndarray dimensions
+* @throws {Error} must provide valid options
+* @returns {ndarray} output ndarray
+*/
+function covarmtk( x, y, correction, meanx, meany, options ) {
+ var args = broadcastArgs( [ correction, meanx, meany ], x, options );
+ if ( arguments.length < 6 ) {
+ return dispatcher( x, y, args[ 0 ], args[ 1 ], args[ 2 ] );
+ }
+ return dispatcher( x, y, args[ 0 ], args[ 1 ], args[ 2 ], options );
+}
+
+/**
+* Computes the covariance of two ndarrays provided known means and using a one-pass textbook algorithm and assigns results to a provided output ndarray.
+*
+* @private
+* @name assign
+* @memberof covarmtk
+* @type {Function}
+* @param {ndarray} x - first input ndarray
+* @param {ndarray} y - second input ndarray
+* @param {ndarray} correction - zero-dimensional ndarray specifying the degrees of freedom adjustment
+* @param {ndarray} meanx - zero-dimensional ndarray specifying the mean of the first input ndarray
+* @param {ndarray} meany - zero-dimensional ndarray specifying the mean of the second input ndarray
+* @param {ndarray} out - output ndarray
+* @param {Options} [options] - function options
+* @throws {TypeError} first argument must be an ndarray-like object
+* @throws {TypeError} second argument must be an ndarray-like object
+* @throws {TypeError} third argument must be an ndarray-like object
+* @throws {TypeError} fourth argument must be an ndarray-like object
+* @throws {TypeError} fifth argument must be an ndarray-like object
+* @throws {TypeError} sixth argument must be an ndarray-like object
+* @throws {TypeError} options argument must be an object
+* @throws {RangeError} dimension indices must not exceed input ndarray bounds
+* @throws {RangeError} number of dimension indices must not exceed the number of input ndarray dimensions
+* @throws {Error} must provide valid options
+* @returns {ndarray} output ndarray
+*/
+function assign( x, y, correction, meanx, meany, out, options ) {
+ var args = broadcastArgs( [ correction, meanx, meany ], x, options );
+ if ( arguments.length < 7 ) {
+ return dispatcher.assign( x, y, args[ 0 ], args[ 1 ], args[ 2 ], out );
+ }
+ return dispatcher.assign( x, y, args[ 0 ], args[ 1 ], args[ 2 ], out, options ); // eslint-disable-line max-len
+}
+
+// Set the `assign` method:
+setReadOnly( covarmtk, 'assign', assign );
+
+
+// EXPORTS //
+
+module.exports = covarmtk;
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/package.json b/lib/node_modules/@stdlib/stats/covarmtk/package.json
new file mode 100644
index 000000000000..4269be7e22c1
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/package.json
@@ -0,0 +1,65 @@
+{
+ "name": "@stdlib/stats/covarmtk",
+ "version": "0.0.0",
+ "description": "Compute the covariance of two 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",
+ "cov",
+ "textbook",
+ "one-pass",
+ "ndarray"
+ ],
+ "__stdlib__": {}
+}
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/test/test.assign.js b/lib/node_modules/@stdlib/stats/covarmtk/test/test.assign.js
new file mode 100644
index 000000000000..9a5705d837e6
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/test/test.assign.js
@@ -0,0 +1,227 @@
+/**
+* @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 Float64Array = require( '@stdlib/array/float64' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
+var covarmtk = require( './../lib' ).assign;
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof covarmtk, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function throws an error if provided a first argument which is not an ndarray-like object', function test( t ) {
+ var correction;
+ var values;
+ var meanx;
+ var meany;
+ var out;
+ var x;
+ var i;
+
+ x = zeros( [ 3 ], {
+ 'dtype': 'float64'
+ });
+ out = zeros( [], {
+ 'dtype': 'float64'
+ });
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+
+ values = [
+ '5',
+ 5,
+ NaN,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+ 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() {
+ covarmtk( value, x, correction, meanx, meany, out );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a sixth argument which is not an ndarray-like object', function test( t ) {
+ var correction;
+ var values;
+ var meanx;
+ var meany;
+ var x;
+ var i;
+
+ x = zeros( [ 3 ], {
+ 'dtype': 'float64'
+ });
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+
+ values = [
+ '5',
+ 5,
+ NaN,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+ 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() {
+ covarmtk( x, x, correction, meanx, meany, value );
+ };
+ }
+});
+
+tape( 'the function performs a reduction on an ndarray (default, row-major)', function test( t ) {
+ var correction;
+ var expected;
+ var actual;
+ var meanx;
+ var meany;
+ var xbuf;
+ var ybuf;
+ var out;
+ var x;
+ var y;
+
+ xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+
+ x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+
+ out = zeros( [], {
+ 'dtype': 'float64'
+ });
+
+ actual = covarmtk( x, y, correction, meanx, meany, out );
+ expected = 3.8333333333333335;
+
+ t.strictEqual( actual, out, 'returns expected value' );
+ t.strictEqual( isAlmostSameValue( actual.get(), expected, 5 ), true, 'returns expected value' );
+
+ t.end();
+});
+
+tape( 'the function supports specifying reduction dimensions (row-major)', function test( t ) {
+ var correction;
+ var expected;
+ var actual;
+ var meanx;
+ var meany;
+ var xbuf;
+ var ybuf;
+ var out;
+ var x;
+ var y;
+ var i;
+ var j;
+
+ xbuf = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
+ ybuf = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
+
+ x = new ndarray( 'float64', xbuf, [ 2, 2, 2 ], [ 4, 2, 1 ], 0, 'row-major' );
+ y = new ndarray( 'float64', ybuf, [ 2, 2, 2 ], [ 4, 2, 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 1.25, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 1.25, {
+ 'dtype': 'float64'
+ });
+
+ out = zeros( [ 2, 2 ], {
+ 'dtype': 'float64'
+ });
+
+ actual = covarmtk( x, y, correction, meanx, meany, out, {
+ 'dims': [ 2 ]
+ });
+
+ expected = [
+ [ -0.375, 2.625 ],
+ [ 11.875, 6.875 ]
+ ];
+ t.strictEqual( actual, out, 'returns output array' );
+
+ actual = ndarray2array( out );
+ for ( i = 0; i < 2; i++ ) {
+ for ( j = 0; j < 2; j++ ) {
+ t.strictEqual( actual[ i ][ j ], expected[ i ][ j ], 'returns expected value' );
+ }
+ }
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/test/test.js b/lib/node_modules/@stdlib/stats/covarmtk/test/test.js
new file mode 100644
index 000000000000..9d5778c80f78
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/test/test.js
@@ -0,0 +1,39 @@
+/**
+* @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 isMethod = require( '@stdlib/assert/is-method' );
+var covarmtk = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof covarmtk, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'attached to the main export is an `assign` method', function test( t ) {
+ t.strictEqual( isMethod( covarmtk, 'assign' ), true, 'returns expected value' );
+ t.end();
+});
diff --git a/lib/node_modules/@stdlib/stats/covarmtk/test/test.main.js b/lib/node_modules/@stdlib/stats/covarmtk/test/test.main.js
new file mode 100644
index 000000000000..1cc91927d932
--- /dev/null
+++ b/lib/node_modules/@stdlib/stats/covarmtk/test/test.main.js
@@ -0,0 +1,368 @@
+/**
+* @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 isndarrayLike = require( '@stdlib/assert/is-ndarray-like' );
+var Float64Array = require( '@stdlib/array/float64' );
+var ndarray = require( '@stdlib/ndarray/ctor' );
+var zeros = require( '@stdlib/ndarray/zeros' );
+var empty = require( '@stdlib/ndarray/empty' );
+var scalar2ndarray = require( '@stdlib/ndarray/from-scalar' );
+var ndarray2array = require( '@stdlib/ndarray/to-array' );
+var getDType = require( '@stdlib/ndarray/dtype' );
+var getShape = require( '@stdlib/ndarray/shape' );
+var isAlmostSameValue = require( '@stdlib/assert/is-almost-same-value' );
+var covarmtk = require( './../lib' );
+
+
+// TESTS //
+
+tape( 'main export is a function', function test( t ) {
+ t.ok( true, __filename );
+ t.strictEqual( typeof covarmtk, 'function', 'main export is a function' );
+ t.end();
+});
+
+tape( 'the function throws an error if provided a first argument which is not an ndarray-like object', function test( t ) {
+ var correction;
+ var values;
+ var meanx;
+ var meany;
+ var x;
+ var i;
+
+ x = zeros( [ 3 ], {
+ 'dtype': 'float64'
+ });
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+
+ values = [
+ '5',
+ 5,
+ NaN,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+ 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() {
+ covarmtk( value, x, correction, meanx, meany );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a second argument which is not an ndarray-like object', function test( t ) {
+ var correction;
+ var values;
+ var meanx;
+ var meany;
+ var x;
+ var i;
+
+ x = zeros( [ 3 ], {
+ 'dtype': 'float64'
+ });
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+
+ values = [
+ '5',
+ 5,
+ NaN,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ {},
+ function noop() {}
+ ];
+ 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() {
+ covarmtk( x, value, correction, meanx, meany );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a first argument which is not an ndarray-like object having a supported data type', function test( t ) {
+ var correction;
+ var values;
+ var meanx;
+ var meany;
+ var x;
+ var i;
+
+ x = zeros( [ 3 ], {
+ 'dtype': 'float64'
+ });
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+
+ values = [
+ empty( [ 3 ], {
+ 'dtype': 'bool'
+ })
+ ];
+ 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() {
+ covarmtk( value, x, correction, meanx, meany );
+ };
+ }
+});
+
+tape( 'the function throws an error if provided a sixth argument which is not an object', function test( t ) {
+ var correction;
+ var values;
+ var meanx;
+ var meany;
+ var x;
+ var i;
+
+ x = zeros( [ 3 ], {
+ 'dtype': 'float64'
+ });
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 0.0, {
+ 'dtype': 'float64'
+ });
+
+ values = [
+ '5',
+ 5,
+ NaN,
+ true,
+ false,
+ null,
+ void 0,
+ [],
+ function noop() {}
+ ];
+ 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() {
+ covarmtk( x, x, correction, meanx, meany, value );
+ };
+ }
+});
+
+tape( 'the function computes the covariance of two ndarrays provided known means', function test( t ) {
+ var correction;
+ var expected;
+ var meanx;
+ var meany;
+ var xbuf;
+ var ybuf;
+ var out;
+ var x;
+ var y;
+
+ xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+
+ x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+
+ out = covarmtk( x, y, correction, meanx, meany );
+
+ expected = 3.8333333333333335;
+ t.strictEqual( isndarrayLike( out ), true, 'returns an ndarray' );
+ t.deepEqual( getShape( out ), [], 'returns zero-dim array' );
+ t.strictEqual( isAlmostSameValue( out.get(), expected, 5 ), true, 'returns expected value');
+ t.end();
+});
+
+tape( 'the function computes the covariance of two ndarrays along a specific dimension', function test( t ) {
+ var correction;
+ var expected;
+ var actual;
+ var meanx;
+ var meany;
+ var xbuf;
+ var ybuf;
+ var out;
+ var x;
+ var y;
+ var i;
+ var j;
+
+ xbuf = new Float64Array( [ 1.0, 2.0, 2.0, -7.0, -2.0, 3.0, 4.0, 2.0 ] );
+ ybuf = new Float64Array( [ 2.0, 1.0, 2.0, 1.0, -2.0, 2.0, 3.0, 4.0 ] );
+
+ x = new ndarray( 'float64', xbuf, [ 2, 2, 2 ], [ 4, 2, 1 ], 0, 'row-major' );
+ y = new ndarray( 'float64', ybuf, [ 2, 2, 2 ], [ 4, 2, 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 1.25, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 1.25, {
+ 'dtype': 'float64'
+ });
+
+ out = covarmtk( x, y, correction, meanx, meany, {
+ 'dims': [ 2 ]
+ });
+
+ expected = [
+ [ -0.375, 2.625 ],
+ [ 11.875, 6.875 ]
+ ];
+ actual = ndarray2array( out );
+ for ( i = 0; i < 2; i++ ) {
+ for ( j = 0; j < 2; j++ ) {
+ t.strictEqual( actual[ i ][ j ], expected[ i ][ j ], 'returns expected value' );
+ }
+ }
+ t.end();
+});
+
+tape( 'the function supports the `keepdims` option', function test( t ) {
+ var correction;
+ var meanx;
+ var meany;
+ var xbuf;
+ var ybuf;
+ var out;
+ var x;
+ var y;
+
+ xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+
+ x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+
+ out = covarmtk( x, y, correction, meanx, meany, {
+ 'keepdims': true
+ });
+
+ t.deepEqual( getShape( out ), [ 1 ], 'returns singleton dimension' );
+ t.strictEqual( isAlmostSameValue( out.get( 0 ), 3.8333333333333335, 5 ), true, 'returns expected value' );
+ t.end();
+});
+
+tape( 'the function supports specifying the output array data type', function test( t ) {
+ var correction;
+ var meanx;
+ var meany;
+ var xbuf;
+ var ybuf;
+ var out;
+ var x;
+ var y;
+
+ xbuf = new Float64Array( [ 1.0, -2.0, 2.0 ] );
+ ybuf = new Float64Array( [ 2.0, -2.0, 1.0 ] );
+
+ x = new ndarray( 'float64', xbuf, [ 3 ], [ 1 ], 0, 'row-major' );
+ y = new ndarray( 'float64', ybuf, [ 3 ], [ 1 ], 0, 'row-major' );
+
+ correction = scalar2ndarray( 1.0, {
+ 'dtype': 'float64'
+ });
+ meanx = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+ meany = scalar2ndarray( 1.0/3.0, {
+ 'dtype': 'float64'
+ });
+
+ out = covarmtk( x, y, correction, meanx, meany, {
+ 'dtype': 'generic'
+ });
+
+ t.strictEqual( getDType( out ), 'generic', 'returns expected data type' );
+ t.strictEqual( isAlmostSameValue( out.get(), 3.8333333333333335, 5 ), true, 'returns expected value' );
+ t.end();
+});