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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 abs = require( '@stdlib/math/base/special/abs' );
var max = require( '@stdlib/math/base/special/max' );
var dlamch = require( '@stdlib/lapack/base/dlamch' );
// MAIN //
/**
* Computes an `LU` factorization of a matrix `T - lambda*I`, where `T` is a general real tridiagonal matrix, and `lambda` a scalar, using partial pivoting with row interchanges.
*
* @private
* @param {NonNegativeInteger} N - order of the matrix T
* @param {Float64Array} A - diagonal elements of T
* @param {integer} strideA - stride length for A
* @param {NonNegativeInteger} offsetA - starting index of A
* @param {number} lambda - scalar constant
* @param {Float64Array} B - super-diagonal elements of T
* @param {integer} strideB - stride length for B
* @param {NonNegativeInteger} offsetB - starting index of B
* @param {Float64Array} C - sub-diagonal elements of T
* @param {integer} strideC - stride length for C
* @param {NonNegativeInteger} offsetC - starting index of C
* @param {number} tol - tolerance constant
* @param {Float64Array} D - second super-diagonal elements of U
* @param {integer} strideD - stride length for D
* @param {NonNegativeInteger} offsetD - starting index of D
* @param {Int32Array} IN - pivot and singularity indices
* @param {integer} strideIN - stride length for IN
* @param {NonNegativeInteger} offsetIN - starting index of IN
* @returns {integer} status code
*/
function dlagtf( N, A, strideA, offsetA, lambda, B, strideB, offsetB, C, strideC, offsetC, tol, D, strideD, offsetD, IN, strideIN, offsetIN ) { // eslint-disable-line max-len, max-params
var scale1;
var scale2;
var mult;
var temp;
var piv1;
var piv2;
var iinN;
var eps;
var iin;
var ia;
var ib;
var ic;
var id;
var tl;
var k;
if ( N === 0 ) {
return 0;
}
ia = offsetA;
ib = offsetB;
ic = offsetC;
id = offsetD;
iin = offsetIN;
iinN = offsetIN + ( ( N - 1 ) * strideIN );
A[ ia ] -= lambda;
IN[ iinN ] = 0;
if ( N === 1 ) {
if ( A[ ia ] === 0.0 ) {
IN[ offsetIN ] = 1;
}
return 0;
}
eps = dlamch( 'e' );
tl = max( tol, eps );
scale1 = abs( A[ ia ] ) + abs( B[ ib ] );
for ( k = 0; k < N - 1; k++ ) {
A[ ia + strideA ] -= lambda;
scale2 = abs( C[ ic ] ) + abs( A[ ia + strideA ] );
if ( k < N - 2 ) {
scale2 += abs( B[ ib + strideB ] );
}
if ( A[ ia ] === 0.0 ) {
piv1 = 0.0;
} else {
piv1 = abs( A[ ia ] ) / scale1;
}
if ( C[ ic ] === 0.0 ) {
IN[ iin ] = 0;
piv2 = 0.0;
scale1 = scale2;
if ( k < N - 2 ) {
D[ id ] = 0.0;
}
} else {
piv2 = abs( C[ ic ] ) / scale2;
if ( piv2 <= piv1 ) {
IN[ iin ] = 0;
scale1 = scale2;
C[ ic ] /= A[ ia ];
A[ ia + strideA ] -= C[ ic ] * B[ ib ];
if ( k < N - 2 ) {
D[ id ] = 0.0;
}
} else {
IN[ iin ] = 1;
mult = A[ ia ] / C[ ic ];
A[ ia ] = C[ ic ];
temp = A[ ia + strideA ];
A[ ia + strideA ] = B[ ib ] - ( mult * temp );
if ( k < N - 2 ) {
D[ id ] = B[ ib + strideB ];
B[ ib + strideB ] = -mult * D[ id ];
}
B[ ib ] = temp;
C[ ic ] = mult;
}
}
if ( max( piv1, piv2 ) <= tl && IN[ iinN ] === 0 ) {
IN[ iinN ] = k + 1;
}
ia += strideA;
ib += strideB;
ic += strideC;
if ( k < N - 2 ) {
id += strideD;
}
iin += strideIN;
}
if ( abs( A[ ia ] ) <= scale1 * tl && IN[ iinN ] === 0 ) {
IN[ iinN ] = N;
}
return 0;
}
// EXPORTS //
module.exports = dlagtf;
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