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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.
*/
'use strict';
// MODULES //
var isLayout = require( '@stdlib/blas/base/assert/is-layout' );
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major-string' );
var isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' );
var max = require( '@stdlib/math/base/special/fast/max' );
var format = require( '@stdlib/string/format' );
var ndarray = require( './ndarray.js' );
// MAIN //
/**
* Initializes centroids by performing the k-means++ initialization procedure on double-precision floating-point data points.
*
* ## Method
*
* The k-means++ algorithm for choosing initial centroids is as follows:
*
* 1. Select a data point uniformly at random from a data set \\( X \\). This data point is first centroid and denoted \\( c_0 \\).
*
* 2. Compute the distance from each data point to \\( c_0 \\). Denote the distance between \\( c_j \\) and data point \\( m \\) as \\( d(x_m, c_j) \\).
*
* 3. Select the next centroid, \\( c_1 \\), at random from \\( X \\) with probability
*
* ```tex
* \frac{d^2(x_m, c_0)}{\sum_{j=0}^{n-1} d^2(x_j, c_0)}
* ```
*
* where \\( n \\) is the number of data points.
*
* 4. To choose centroid \\( j \\),
*
* a. Compute the distances from each data point to each centroid and assign each data point to its closest centroid.
*
* b. For \\( i = 0,\ldots,n-1 \\) and \\( p = 0,\ldots,j-2 \\), select centroid \\( j \\) at random from \\( X \\) with probability
*
* ```tex
* \frac{d^2(x_i, c_p)}{\sum_{\{h; x_h \exits C_p\}} d^2(x_h, c_p)}
* ```
*
* where \\( C_p \\) is the set of all data points closest to centroid \\( c_p \\) and \\( x_i \\) belongs to \\( c_p \\).
*
* Stated more plainly, select each subsequent centroid with a probability proportional to the distance from the centroid to the closest centroid already chosen.
*
* 5. Repeat step `4` until \\( k \\) centroids have been chosen.
*
* ## 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>.
*
* @param {string} order - storage layout
* @param {PositiveInteger} k - number of clusters
* @param {PositiveInteger} M - number of data points
* @param {PositiveInteger} N - number of features
* @param {Float64Array} out - input array
* @param {integer} LDO - stride of the first dimension of `out` (a.k.a., leading dimension of the matrix `out`)
* @param {Float64Array} X - input array
* @param {integer} LDX - stride of the first dimension of `x` (a.k.a., leading dimension of the matrix `x`)
* @param {string} metric - distance metric
* @param {PositiveInteger} trials - number of potential centroids per iteration (>= 1)
* @param {*} seed - PRNG seed
* @throws {TypeError} first argument must be a valid order
* @throws {TypeError} tenth argument must be a valid trials (>=1)
* @throws {RangeError} sixth argument must be greater than or equal to max(1,N)
* @throws {RangeError} eighth argument must be greater than or equal to max(1,N)
* @returns {Float64Array} centroids
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var k = 3;
* var M = 5;
* var N = 2;
*
* var out = new Float64Array( k*N );
*
* // Specify data points:
* var xbuf = new Float64Array([
* 0.0, 0.0,
* 1.0, 1.0,
* 1.0, -1.0,
* -1.0, -1.0,
* -1.0, 1.0
* ]);
*
* var v = dkmeansInitPlusPlus( 'row-major', k, M, N, out, 2, xbuf, 2, 'sqeuclidean', 3, 44 );
* // returns <Float64Array>[0,0,1,-1,1,1]
*/
function dkmeansInitPlusPlus( order, k, M, N, out, LDO, X, LDX, metric, trials, seed ) { // eslint-disable-line max-len, max-params
var so1;
var so2;
var sx1;
var sx2;
var so;
var sx;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( trials < 1 ) {
throw new TypeError( format( 'invalid argument. Tenth argument must be a valid trials (>=1). Value: `%s`.', trials ) );
}
if ( isRowMajor( order ) ) {
so = N;
sx = N;
} else {
so = k;
sx = M;
}
if ( LDO < max( 1, so ) ) {
throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to max(1,%d). Value: `%d`.', so, LDO ) );
}
if ( LDX < max( 1, sx ) ) {
throw new RangeError( format( 'invalid argument. Fifth argument must be greater than or equal to max(1,%d). Value: `%d`.', sx, LDO ) );
}
if ( isColumnMajor( order ) ) {
so1 = 1;
so2 = LDO;
sx1 = 1;
sx2 = LDX;
} else { // order === 'row-major'
so1 = LDO;
so2 = 1;
sx1 = LDX;
sx2 = 1;
}
return ndarray( k, M, N, out, so1, so2, 0, X, sx1, sx2, 0, metric, trials, seed ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = dkmeansInitPlusPlus;
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