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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 isLayout = require( '@stdlib/blas/base/assert/is-layout' );
var format = require( '@stdlib/string/format' );
var base = require( './base.js' );
// MAIN //
/**
* Solves a system of linear equations with a tri diagonal matrix using the LU factorization computed by `dgttrf`.
*
* ## Notes
*
* - To solve A * X = B (no transpose), use itrans = 0.
* - To solve AT * X = B (transpose), use itrans = 1.
* - To solve AT * X = B (conjugate transpose = transpose), use itrans = 2.
*
* @param {string} order - storage layout of B
* @param {integer} itrans - specifies the form of the system of equations
* @param {NonNegativeInteger} N - order of the matrix A
* @param {NonNegativeInteger} nrhs - number of right-hand sides, i.e., the number of columns of the matrix B
* @param {Float64Array} DL - multipliers that define the matrix L
* @param {Float64Array} D - diagonal elements of the upper triangular matrix U
* @param {Float64Array} DU - elements of the first super-diagonal of U
* @param {Float64Array} DU2 - elements of the second super-diagonal of U
* @param {Int32Array} IPIV - vector of pivot indices
* @param {Float64Array} B - right-hand side matrix B, overwritten by the solution matrix X
* @param {NonNegativeInteger} LDB - leading dimension of array B
* @throws {TypeError} first argument must be a valid order
* @throws {RangeError} eleventh argument must be greater than or equal to N
* @returns {Float64Array} The solution matrix X
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var Int32Array = require( '@stdlib/array/int32' );
*
* var DL = new Float64Array( [ 0.25, 0.26666667 ] );
* var D = new Float64Array( [ 4.0, 3.75, 3.73333333 ] );
* var DU = new Float64Array( [ 1.0, 0.73333333 ] );
* var DU2 = new Float64Array( [ 0.0 ] );
* var IPIV = new Int32Array( [ 0, 1, 2 ] );
* var B = new Float64Array( [ 7.0, 8.0, 7.0 ] );
*
* var out = dgtts2( 'column-major', 1, 3, 1, DL, D, DU, DU2, IPIV, B, 3 );
* // out => <Float64Array>[ ~1.44, ~1.25, ~1.55 ]
*/
function dgtts2( order, itrans, N, nrhs, DL, D, DU, DU2, IPIV, B, LDB ) { // eslint-disable-line max-params
var sb1;
var sb2;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( order === 'column-major' ) {
sb1 = 1;
sb2 = LDB;
} else { // order === 'row-major'
if ( LDB < nrhs ) {
throw new RangeError( format( 'invalid argument. Eighth argument must be greater than or equal to %d. Value: `%d`.', N, LDB ) );
}
sb1 = LDB;
sb2 = 1;
}
return base( itrans, N, nrhs, DL, 1, 0, D, 1, 0, DU, 1, 0, DU2, 1, 0, IPIV, 1, 0, B, sb1, sb2, 0 ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = dgtts2;
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