feat: add ml/strided/dkmeans-init-plus-plus

lib/node_modules/@stdlib/ml/strided/dkmeans-init-plus-plus/README.md

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+<!--
+
+@license Apache-2.0
+
+Copyright (c) 2026 The Stdlib Authors.
+
+Licensed under the Apache License, Version 2.0 (the "License");
+you may not use this file except in compliance with the License.
+You may obtain a copy of the License at
+
+   http://www.apache.org/licenses/LICENSE-2.0
+
+Unless required by applicable law or agreed to in writing, software
+distributed under the License is distributed on an "AS IS" BASIS,
+WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+See the License for the specific language governing permissions and
+limitations under the License.
+
+-->
+
+# dkmeansInitPlusPlus
+
+> Initializes centroids by performing the [k-means++][kmeans-plus-plus] initialization procedure on double-precision floating-point data points.
+
+<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
+
+<section class="intro">
+
+</section>
+
+<!-- /.intro -->
+
+<!-- Package usage documentation. -->
+
+<section class="usage">
+
+## Usage
+
+```javascript
+var dkmeansInitPlusPlus = require( '@stdlib/ml/strided/dkmeans-init-plus-plus' );
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dkmeansInitPlusPlus( order, M, N, k, trials, metric, X, LDX, out, LDO, W1, sw1, W2, sw2\[, options] )
+
+<!-- lint enable maximum-heading-length -->
+
+Initializes centroids by performing the [k-means++][kmeans-plus-plus] initialization procedure on double-precision floating-point data points.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var k = 3;
+var M = 5;
+var N = 2;
+
+// Allocate an output matrix for the centroids:
+var out = new Float64Array( k*N );
+var W1 = new Float64Array( 2*M );
+var W2 = new Int32Array( k );
+
+/*
+    X = [
+        [  0.0,  0.0 ],
+        [  1.0,  1.0 ],
+        [  1.0, -1.0 ],
+        [ -1.0, -1.0 ],
+        [ -1.0,  1.0 ]
+    ]
+*/
+var X = new Float64Array( [ 0.0, 0.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0 ] );
+
+var centroids = dkmeansInitPlusPlus( 'row-major', M, N, k, 3, 'sqeuclidean', X, N, out, N, W1, 1, W2, 1 );
+```
+
+The function has the following parameters:
+
+-   **order**: storage layout.
+-   **M**: number of data points.
+-   **N**: number of features.
+-   **k**: number of clusters (i.e., the number of centroids to initialize).
+-   **trials**: number of candidate centroids to sample per iteration (must be `>= 1`).
+-   **metric**: distance metric. Must be one of the following: `'sqeuclidean'`, `'cosine'`, `'cityblock'`, or `'correlation'`.
+-   **X**: input matrix stored as a [`Float64Array`][@stdlib/array/float64].
+-   **LDX**: stride of the first dimension of `X` (a.k.a., leading dimension of the matrix `X`).
+-   **out**: output matrix stored as a [`Float64Array`][@stdlib/array/float64].
+-   **LDO**: stride of the first dimension of `out` (a.k.a., leading dimension of the matrix `out`).
+-   **W1**: first workspace array of size `2*M` for tracking squared distances and probabilities.
+-   **sw1**: stride length of `W1`.
+-   **W2**: second workspace array for tracking centroid candidates.
+-   **sw2**: stride length of `W2`.
+
+The output matrix `out` has shape `(k, N)`, with one initialized centroid per row, and the input matrix `X` has shape `(M, N)`, with one data point per row.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var k = 2;
+var M = 3;
+var N = 2;
+
+// Allocate an output matrix for the centroids:
+var out = new Float64Array( k*N );
+var W1 = new Float64Array( 2*M );
+var W2 = new Int32Array( k );
+
+/*
+    X = [
+        [  0.0,  0.0 ],
+        [  1.0,  3.0 ],
+        [  2.0,  4.0 ],
+    ]
+*/
+var X = new Float64Array( [ 0.0, 0.0, 1.0, 3.0, 2.0, 4.0 ] );
+
+var centroids = dkmeansInitPlusPlus( 'column-major', M, N, k, 3, 'sqeuclidean', X, M, out, k, W1, 1, W2, 1 );
+```
+
+Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var k = 3;
+var M = 5;
+var N = 2;
+
+// Allocate an output matrix for the centroids:
+var out = new Float64Array( k*N );
+var W1 = new Float64Array( 2*M );
+var W2 = new Int32Array( k );
+
+/*
+    X = [
+        [  0.0,  0.0 ],
+        [  1.0,  1.0 ],
+        [  1.0, -1.0 ],
+        [ -1.0, -1.0 ],
+        [ -1.0,  1.0 ]
+    ]
+*/
+var X = new Float64Array( [ 0.0, 0.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 2.0 ] );
+
+var X1 = new Float64Array( X.buffer, X.BYTES_PER_ELEMENT*1 ); // start at 2nd element
+
+var centroids = dkmeansInitPlusPlus( 'row-major', M, N, k, 3, 'sqeuclidean', X1, N, out, N, W1, 1, W2, 1 );
+```
+
+The function accepts the following `options`:
+
+-   **prng**: pseudorandom number generator for generating uniformly distributed pseudorandom numbers. If provided, the function **ignores** both the `state` and `seed` options. In order to seed the underlying pseudorandom number generator, one must seed the provided `prng` (assuming the provided `prng` is seedable).
+-   **seed**: pseudorandom number generator seed.
+-   **state**: a [`Uint32Array`][@stdlib/array/uint32] containing pseudorandom number generator state. If provided, the function ignores the `seed` option.
+-   **copy**: `boolean` indicating whether to copy a provided pseudorandom number generator state. Setting this option to `false` allows sharing state between two or more pseudorandom number generators. Setting this option to `true` ensures that an underlying generator has exclusive control over its internal state. Default: `true`.
+
+To use a custom PRNG as the underlying source of uniformly distributed pseudorandom numbers, set the `prng` option.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var minstd = require( '@stdlib/random/base/minstd' );
+
+var k = 3;
+var M = 5;
+var N = 2;
+
+// Allocate an output matrix for the centroids:
+var out = new Float64Array( k*N );
+var W1 = new Float64Array( 2*M );
+var W2 = new Int32Array( k );
+
+/*
+    X = [
+        [  0.0,  0.0 ],
+        [  1.0,  1.0 ],
+        [  1.0, -1.0 ],
+        [ -1.0, -1.0 ],
+        [ -1.0,  1.0 ]
+    ]
+*/
+var X = new Float64Array( [ 0.0, 0.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0 ] );
+
+var opts = {
+    'prng': minstd
+};
+
+var centroids = dkmeansInitPlusPlus( 'row-major', M, N, k, 3, 'sqeuclidean', X, N, out, N, W1, 1, W2, 1, opts );
+```
+
+To seed the underlying pseudorandom number generator, set the `seed` option.
+
+<!-- eslint-disable max-len -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var k = 3;
+var M = 5;
+var N = 2;
+
+// Allocate an output matrix for the centroids:
+var out = new Float64Array( k*N );
+var W1 = new Float64Array( 2*M );
+var W2 = new Int32Array( k );
+
+/*
+    X = [
+        [  0.0,  0.0 ],
+        [  1.0,  1.0 ],
+        [  1.0, -1.0 ],
+        [ -1.0, -1.0 ],
+        [ -1.0,  1.0 ]
+    ]
+*/
+var X = new Float64Array( [ 0.0, 0.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0 ] );
+
+var opts = {
+    'seed': 12345
+};
+
+var centroids = dkmeansInitPlusPlus( 'row-major', M, N, k, 3, 'sqeuclidean', X, N, out, N, W1, 1, W2, 1, opts );
+```
+
+<!-- lint disable maximum-heading-length -->
+
+#### dkmeansInitPlusPlus.ndarray( M, N, k, trials, metric, X, sx1, sx2, ox, out, so1, so2, oo, W1, sw1, ow1, W2, sw2, ow2\[, options] )
+
+<!-- lint disable maximum-heading-length -->
+
+Initializes centroids by performing the [k-means++][kmeans-plus-plus] initialization procedure on double-precision floating-point data points using alternative indexing semantics.
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+
+var k = 3;
+var M = 5;
+var N = 2;
+
+// Allocate an output matrix for the centroids:
+var out = new Float64Array( k*N );
+var W1 = new Float64Array( 2*M );
+var W2 = new Int32Array( k );
+
+/*
+    X = [
+        [  0.0,  0.0 ],
+        [  1.0,  1.0 ],
+        [  1.0, -1.0 ],
+        [ -1.0, -1.0 ],
+        [ -1.0,  1.0 ]
+    ]
+*/
+var X = new Float64Array( [ 0.0, 0.0, 1.0, 1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0 ] );
+
+var centroids = dkmeansInitPlusPlus.ndarray( M, N, k, 3, 'sqeuclidean', X, N, 1, 0, out, N, 1, 0, W1, 1, 0, W2, 1, 0 );
+```
+
+The function has the following parameters:
+
+-   **M**: number of data points.
+-   **N**: number of features.
+-   **k**: number of clusters (i.e., the number of centroids to initialize).
+-   **trials**: number of candidate centroids to sample per iteration (must be `>= 1`).
+-   **metric**: distance metric. Must be one of the following: `'sqeuclidean'`, `'cosine'`, `'cityblock'`, or `'correlation'`.
+-   **X**: input matrix stored as a [`Float64Array`][@stdlib/array/float64].
+-   **sx1**: stride of the first dimension of `X`.
+-   **sx2**: stride of the second dimension of `X`.
+-   **ox**: starting index for `X`.
+-   **out**: output matrix stored as a [`Float64Array`][@stdlib/array/float64].
+-   **so1**: stride of the first dimension of `out`.
+-   **so2**: stride of the second dimension of `out`.
+-   **oo**: starting index for `out`.
+-   **W1**: first workspace array of size `2*M` for tracking squared distances and probabilities.
+-   **sw1**: stride length of `W1`.
+-   **ow1**: starting index for `W1`.
+-   **W2**: second workspace array for tracking centroid candidates.
+-   **sw2**: stride length of `W2`.
+-   **ow2**: starting index for `W2`.
+
+</section>
+
+<!-- /.usage -->
+
+<!-- Package usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="notes">
+
+## Notes
+
+-   The k-means++ procedure is stochastic; providing the same `seed` yields reproducible centroids.
+-   Increasing the number of `trials` (the "greedy" k-means++ variant) samples multiple candidate centroids per iteration and keeps the candidate which minimizes the total squared distance, generally improving centroid quality at the cost of additional computation.
+
+</section>
+
+<!-- /.notes -->
+
+<!-- Package usage examples. -->
+
+<section class="examples">
+
+## Examples
+
+<!-- eslint no-undef: "error" -->
+
+```javascript
+var Float64Array = require( '@stdlib/array/float64' );
+var Int32Array = require( '@stdlib/array/int32' );
+var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
+var dkmeansInitPlusPlus = require( '@stdlib/ml/strided/dkmeans-init-plus-plus' );
+
+var k = 3;
+var M = 10;
+var N = 2;
+
+// Generate a random set of data points:
+var X = discreteUniform( M*N, -50, 50, {
+    'dtype': 'float64'
+});
+console.log( X );
+
+// Allocate an output matrix for the centroids:
+var out = new Float64Array( k*N );
+
+// Allocate workspace arrays:
+var W1 = new Float64Array( 2*M );
+var W2 = new Int32Array( k );
+
+// Set PRNG options
+var options = {
+    'seed': 1234
+};
+
+// Initialize centroids using the k-means++ procedure:
+var centroids = dkmeansInitPlusPlus( 'row-major', M, N, k, 3, 'sqeuclidean', X, N, out, N, W1, 1, W2, 1, options );
+
+console.log( centroids );
+// => <Float64Array>
+
+// Initialize centroids using the k-means++ procedure using alternative indexing semantics:
+centroids = dkmeansInitPlusPlus.ndarray( M, N, k, 3, 'sqeuclidean', X, N, 1, 0, out, N, 1, 0, W1, 1, 0, W2, 1, 0, options );
+
+console.log( centroids );
+// => <Float64Array>
+```
+
+</section>
+
+<!-- /.examples -->
+
+<section class="references">
+
+## References
+
+-   Arthur, David, and Sergei Vassilvitskii. 2007. "K-means++: The Advantages of Careful Seeding." In _Proceedings of the Eighteenth Annual Acm-Siam Symposium on Discrete Algorithms_, 1027–35. SODA '07. Philadelphia, PA, USA: Society for Industrial and Applied Mathematics. <http://dl.acm.org/citation.cfm?id=1283383.1283494>.
+
+</section>
+
+<!-- /.references -->
+
+<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
+
+<section class="related">
+
+</section>
+
+<!-- /.related -->
+
+<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
+
+<section class="links">
+
+[kmeans-plus-plus]: https://en.wikipedia.org/wiki/K-means%2B%2B
+
+[@stdlib/array/float64]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/float64
+
+[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
+
+[@stdlib/array/uint32]: https://github.com/stdlib-js/stdlib/tree/develop/lib/node_modules/%40stdlib/array/uint32
+
+</section>
+
+<!-- /.links -->