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* @license Apache-2.0
*
* Copyright (c) 2025 The Stdlib Authors.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
'use strict';
// MODULES //
var max = require( '@stdlib/math/base/special/fast/max' );
var min = require( '@stdlib/math/base/special/fast/min' );
var zeros2d = require( '@stdlib/array/base/zeros2d' );
// MAIN //
/**
* Converts a two-dimensional symmetric banded nested array to compact banded storage.
*
* @param {string} uplo - specifies whether to reference the upper or lower triangular part of the input array
* @param {Array<Array>} arr - input two-dimensional array
* @param {NonNegativeInteger} k - number of super-/sub-diagonals
* @param {boolean} colexicographic - specifies whether to store diagonals in colexicographic access order
* @returns {Array<Array>} output array
*
* @example
* var M = [
* [ 11, 2, 0 ],
* [ 2, 12, 4 ],
* [ 0, 4, 13 ]
* ];
*
* var out = toCompact( 'upper', M, 1, false );
* // returns [ [ 0, 2, 4 ], [ 11, 12, 13 ] ]
*
* @example
* var M = [
* [ 11, 2, 0 ],
* [ 2, 12, 4 ],
* [ 0, 4, 13 ]
* ];
*
* var out = toCompact( 'lower', M, 1, false );
* // returns [ [ 11, 12, 13 ], [ 2, 4, 0 ] ]
*
* @example
* var M = [
* [ 11, 2, 0 ],
* [ 2, 12, 4 ],
* [ 0, 4, 13 ]
* ];
*
* var out = toCompact( 'upper', M, 1, true );
* // returns [ [ 11, 2 ], [ 12, 4 ], [ 13, 0 ] ]
*
* @example
* var M = [
* [ 11, 2, 0 ],
* [ 2, 12, 4 ],
* [ 0, 4, 13 ]
* ];
*
* var out = toCompact( 'lower', M, 1, true );
* // returns [ [ 0, 11 ], [ 2, 12 ], [ 4, 13 ] ]
*/
function toCompact( uplo, arr, k, colexicographic ) {
var out;
var to;
var ta;
var m;
var i;
var j;
var o;
m = arr.length;
// Check whether to store diagonals along the columns...
if ( colexicographic ) {
out = zeros2d( [ m, k+1 ] );
if ( uplo === 'upper' ) {
for ( i = 0; i < m; i++ ) {
to = out[ i ];
ta = arr[ i ];
for ( j = i; j < min( m, i+k+1 ); j++ ) {
to[ j-i ] = ta[ j ];
}
}
return out;
}
// uplo === 'lower'
for ( i = 0; i < m; i++ ) {
to = out[ i ];
ta = arr[ i ];
o = max( 0, k-i );
for ( j = max( 0, i-k ); j <= i; j++ ) {
to[ o ] = ta[ j ];
o += 1;
}
}
return out;
}
// Store diagonals along the rows...
out = zeros2d( [ k+1, m ] );
if ( uplo === 'upper' ) {
for ( j = 0; j < m; j++ ) {
o = k - j;
for ( i = max( 0, j-k ); i <= j; i++ ) {
out[ o+i ][ j ] = arr[ i ][ j ];
}
}
return out;
}
// uplo === 'lower'
for ( j = 0; j < m; j++ ) {
o = -j;
for ( i = j; i < min( m, j+k+1 ); i++ ) {
out[ o+i ][ j ] = arr[ i ][ j ];
}
}
return out;
}
// EXPORTS //
module.exports = toCompact;
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