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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 isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var binomcoef = require( '@stdlib/math/base/special/binomcoef' );
var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
var dfill = require( '@stdlib/blas/ext/base/dfill' ).ndarray;
// FUNCTIONS //
/**
* Initializes a workspace with the indices of the first combination of a specified length.
*
* @private
* @param {NonNegativeInteger} k - combination length
* @param {boolean} replacement - boolean indicating whether to allow duplication in combination
* @param {Int32Array} workspace - workspace array
* @param {integer} strideW - stride length for `workspace`
* @param {NonNegativeInteger} offsetW - starting index for `workspace`
*/
function firstCombination( k, replacement, workspace, strideW, offsetW ) {
var iw;
var p;
iw = offsetW;
if ( replacement ) {
for ( p = 0; p < k; p++ ) {
workspace[ iw ] = 0;
iw += strideW;
}
} else {
for ( p = 0; p < k; p++ ) {
workspace[ iw ] = p;
iw += strideW;
}
}
}
/**
* Advances a workspace to the indices of the next combination of a specified length.
*
* ## Notes
*
* - If a workspace contains the last combination, the workspace is left unchanged.
*
* @private
* @param {NonNegativeInteger} k - combination length
* @param {NonNegativeInteger} N - number of indexed elements
* @param {boolean} replacement - boolean indicating whether to allow duplication in combination
* @param {Int32Array} workspace - workspace array
* @param {integer} strideW - stride length for `workspace`
* @param {NonNegativeInteger} offsetW - starting index for `workspace`
*/
function nextCombination( k, N, replacement, workspace, strideW, offsetW ) {
var val;
var iw;
var i;
var p;
// Starting from the rightmost index, find the rightmost index which can be incremented...
iw = offsetW + ( ( k-1 ) * strideW );
i = k - 1;
if ( replacement ) {
while ( i >= 0 && workspace[ iw ] === N - 1 ) {
i -= 1;
iw -= strideW;
}
if ( i >= 0 ) {
val = workspace[ iw ] + 1;
for ( p = i; p < k; p++ ) {
workspace[ iw ] = val;
iw += strideW;
}
}
} else {
while ( i >= 0 && workspace[ iw ] === N - k + i ) {
i -= 1;
iw -= strideW;
}
if ( i >= 0 ) {
workspace[ iw ] += 1;
val = workspace[ iw ];
for ( p = i + 1; p < k; p++ ) {
iw += strideW;
val += 1;
workspace[ iw ] = val;
}
}
}
}
// MAIN //
/**
* Computes combinations of a specified length from double-precision floating-point strided array elements using alternative indexing semantics.
*
* @param {NonNegativeInteger} N - number of indexed elements
* @param {NonNegativeInteger} k - number of elements to combine
* @param {boolean} replacement - boolean indicating whether to allow duplication in combination
* @param {Float64Array} x - input array
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} out - output array
* @param {integer} strideOut1 - stride length for the first dimension of `out`
* @param {integer} strideOut2 - stride length for the second dimension of `out`
* @param {NonNegativeInteger} offsetOut - starting index for `out`
* @param {Int32Array} workspace - workspace array
* @param {integer} strideW - stride length for `workspace`
* @param {NonNegativeInteger} offsetW - starting index for `workspace`
* @returns {Float64Array} output array
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var Int32Array = require( '@stdlib/array/int32' );
*
* var x = new Float64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
* var out = new Float64Array( 12 );
* var workspace = new Int32Array( 2 );
*
* dcombinations( 4, 2, false, x, 1, 0, out, 2, 1, 0, workspace, 1, 0 );
* // out => <Float64Array>[ 1.0, 2.0, 1.0, 3.0, 1.0, 4.0, 2.0, 3.0, 2.0, 4.0, 3.0, 4.0 ]
*/
function dcombinations( N, k, replacement, x, strideX, offsetX, out, strideOut1, strideOut2, offsetOut, workspace, strideW, offsetW ) { // eslint-disable-line max-len, max-params
var runLen;
var rem;
var io;
var iw;
var oj;
var np;
var C;
var L;
var c;
var j;
var v;
if ( N <= 0 || k <= 0 ) {
return out;
}
if ( !replacement && k > N ) {
return out;
}
// For `k` equal to one, each combination consists of a single element, and, thus, we can directly copy the input array elements to the output array (i.e., no need for a workspace)...
if ( k === 1 ) {
dcopy( N, x, strideX, offsetX, out, strideOut1, offsetOut );
return out;
}
if ( isRowMajor( [ strideOut1, strideOut2 ] ) ) {
// For row-major order, combinations are stored as contiguous rows, and, thus, we resolve one combination at a time, writing each combination's elements consecutively...
// Compute the total number of combinations:
if ( replacement ) {
C = binomcoef( N + k - 1, k );
} else {
C = binomcoef( N, k );
}
firstCombination( k, replacement, workspace, strideW, offsetW );
io = offsetOut;
for ( c = 0; c < C; c++ ) {
// Resolve the current combination's indices to input array values and write them to the output array:
iw = offsetW;
oj = io;
for ( j = 0; j < k; j++ ) {
out[ oj ] = x[ offsetX + ( workspace[ iw ] * strideX ) ];
oj += strideOut2;
iw += strideW;
}
io += strideOut1;
nextCombination( k, N, replacement, workspace, strideW, offsetW );
}
} else {
// For column-major order, the elements at a given combination position are stored contiguously within a column. As consecutive combinations share long prefixes, each column consists of runs of repeated elements (with run lengths equal to binomial coefficients), and, thus, we can fill each column as a sequence of contiguous runs...
for ( j = 0; j < k; j++ ) {
// The `j`-th column is determined by the `(j+1)`-element prefixes of each combination, enumerated in lexicographic order:
L = j + 1;
rem = k - 1 - j;
// Enumerate only those prefixes which can be completed to a full combination. Without replacement, a prefix is extendable only if its last index leaves room for the remaining `rem` elements, and, thus, we restrict enumeration to a reduced universe of `N-rem` indices in order to avoid generating zero-length runs:
if ( replacement ) {
np = N;
C = binomcoef( N + L - 1, L );
} else {
np = N - rem;
C = binomcoef( np, L );
}
firstCombination( L, replacement, workspace, strideW, offsetW );
io = offsetOut + ( j * strideOut2 );
// Resolve the workspace index of each prefix's last element (i.e., the column's index value), which is invariant across prefixes:
iw = offsetW + ( ( L-1 ) * strideW );
for ( c = 0; c < C; c++ ) {
v = workspace[ iw ];
// Resolve the run length (i.e., the number of ways to complete the remaining `rem` positions with indices not less than `v`):
if ( rem === 0 ) {
runLen = 1;
} else if ( replacement ) {
runLen = binomcoef( N - v + rem - 1, rem );
} else {
runLen = binomcoef( N - 1 - v, rem );
}
// Write a run of the resolved input array value down the column:
dfill( runLen, x[ offsetX + ( v * strideX ) ], out, strideOut1, io ); // eslint-disable-line max-len
io += runLen * strideOut1;
nextCombination( L, np, replacement, workspace, strideW, offsetW ); // eslint-disable-line max-len
}
}
}
return out;
}
// EXPORTS //
module.exports = dcombinations;
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