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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 format = require( '@stdlib/string/format' );
var base = require( './base.js' );
// MAIN //
/**
* Computes an `LU` factorization of a real tri diagonal matrix `A` using elimination with partial pivoting and row interchanges.
*
* ## Notes
*
* - On exit, `DL` is overwritten by the multipliers that define the matrix `L` from the `LU` factorization of `A`.
* - On exit, `D` is overwritten by the diagonal elements of the upper triangular matrix `U` from the `LU` factorization of `A`.
* - On exit, `DU` is overwritten by the elements of the first super-diagonal of `U`.
* - On exit, `DU2` is overwritten by the elements of the second super-diagonal of `U`.
* - On exit, for 0 <= i < n, row i of the matrix was interchanged with row IPIV(i). IPIV(i) will always be either i or i+1; IPIV(i) = i indicates a row interchange was not required.
*
* @param {NonNegativeInteger} N - order of matrix A
* @param {Float64Array} DL - sub diagonal elements of A.
* @param {Float64Array} D - diagonal elements of A.
* @param {Float64Array} DU - super diagonal elements of A.
* @param {Float64Array} DU2 - vector to store the second super diagonal of `U`
* @param {Int32Array} IPIV - vector of pivot indices
* @throws {RangeError} first argument must be a nonnegative integer
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var Int32Array = require( '@stdlib/array/int32' );
*
* var DL = new Float64Array( [ 1.0, 1.0 ] );
* var D = new Float64Array( [ 2.0, 3.0, 1.0 ] );
* var DU = new Float64Array( [ 1.0, 1.0 ] );
* var DU2 = new Float64Array( 1 );
* var IPIV = new Int32Array( 3 );
*
* dgttrf( 3, DL, D, DU, DU2, IPIV );
* // DL => <Float64Array>[ 0.5, 0.4 ]
* // D => <Float64Array>[ 2, 2.5, 0.6 ]
* // DU => <Float64Array>[ 1, 1 ]
* // DU2 => <Float64Array>[ 0 ]
* // IPIV => <Int32Array>[ 0, 1, 2 ]
*/
function dgttrf( N, DL, D, DU, DU2, IPIV ) {
if ( N < 0 ) {
throw new RangeError( format( 'invalid argument. First argument must be a nonnegative integer. Value: `%d`.', N ) );
}
return base( N, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0 );
}
// EXPORTS //
module.exports = dgttrf;
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