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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.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var abs = require( '@stdlib/math/base/special/abs' );
var max = require( '@stdlib/math/base/special/max' );
var copysign = require( '@stdlib/math/base/special/copysign' );
var dlamch = require( '@stdlib/lapack/base/dlamch' );
// FUNCTIONS //
/**
* Divides `temp` by a diagonal element `ak`, scaling to avoid overflow and, optionally, perturbing very small diagonal elements, and writes the result to `Y`.
*
* @private
* @param {number} temp - dividend
* @param {number} ak - diagonal element
* @param {boolean} perturb - boolean indicating whether to perturb very small diagonal elements to avoid overflow
* @param {number} tol - tolerance controlling the magnitude of the perturbation
* @param {number} sfmin - safe minimum (i.e., smallest number for which `1/sfmin` does not overflow)
* @param {number} bignum - reciprocal of the safe minimum
* @param {Float64Array} Y - output array
* @param {integer} iy - index at which to write the result in `Y`
* @returns {boolean} boolean indicating whether the division could be performed without overflow
*/
function divide( temp, ak, perturb, tol, sfmin, bignum, Y, iy ) {
var absak;
var pert;
if ( perturb ) {
pert = copysign( tol, ak );
}
for ( ; ; ) {
absak = abs( ak );
if ( absak < 1.0 ) {
if ( absak < sfmin ) {
if ( absak === 0.0 || abs( temp )*sfmin > absak ) {
if ( perturb ) {
ak += pert;
pert *= 2.0;
continue;
}
return false;
}
temp *= bignum;
ak *= bignum;
} else if ( abs( temp ) > absak*bignum ) {
if ( perturb ) {
ak += pert;
pert *= 2.0;
continue;
}
return false;
}
}
break;
}
Y[ iy ] = temp / ak;
return true;
}
// MAIN //
/**
* Solves a system of equations with a tridiagonal matrix `T` following a precomputed factorization of `T - lambda*I`.
*
* @private
* @param {integer} job - specifies the job to be performed
* @param {NonNegativeInteger} N - order of the matrix `T`
* @param {Float64Array} A - diagonal elements of `U`
* @param {integer} strideA - stride length for `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Float64Array} B - first super-diagonal elements of `U`
* @param {integer} strideB - stride length for `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @param {Float64Array} C - sub-diagonal elements of `L`
* @param {integer} strideC - stride length for `C`
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @param {Float64Array} D - second super-diagonal elements of `U`
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index for `D`
* @param {Int32Array} IN - details of the matrix `P`
* @param {integer} strideIN - stride length for `IN`
* @param {NonNegativeInteger} offsetIN - starting index for `IN`
* @param {Float64Array} Y - right-hand side vector which is overwritten by the solution vector
* @param {integer} strideY - stride length for `Y`
* @param {NonNegativeInteger} offsetY - starting index for `Y`
* @param {Float64Array} TOL - tolerance used to perturb very small diagonal elements when `job` is negative
* @param {NonNegativeInteger} offsetTOL - index for `TOL`
* @returns {integer} status code
*/
function dlagts( job, N, A, strideA, offsetA, B, strideB, offsetB, C, strideC, offsetC, D, strideD, offsetD, IN, strideIN, offsetIN, Y, strideY, offsetY, TOL, offsetTOL ) {
var perturb;
var bignum;
var sfmin;
var temp;
var tol;
var eps;
var ak;
var iy;
var ii;
var ic;
var k;
if ( N === 0 ) {
return 0;
}
eps = dlamch( 'E' );
sfmin = dlamch( 'S' );
bignum = 1.0 / sfmin;
tol = TOL[ offsetTOL ];
if ( job < 0 && tol <= 0.0 ) {
tol = abs( A[ offsetA ] );
if ( N > 1 ) {
tol = max( max( tol, abs( A[ offsetA+strideA ] ) ), abs( B[ offsetB ] ) );
}
for ( k = 3; k <= N; k++ ) {
tol = max( max( max( tol, abs( A[ offsetA+((k-1)*strideA) ] ) ), abs( B[ offsetB+((k-2)*strideB) ] ) ), abs( D[ offsetD+((k-3)*strideD) ] ) );
}
tol *= eps;
if ( tol === 0.0 ) {
tol = eps;
}
TOL[ offsetTOL ] = tol;
}
if ( abs( job ) === 1 ) {
// Apply the permutation `P` and the unit lower bidiagonal matrix `L`...
for ( k = 2; k <= N; k++ ) {
iy = offsetY + ( (k-1)*strideY );
ii = offsetIN + ( (k-2)*strideIN );
ic = offsetC + ( (k-2)*strideC );
if ( IN[ ii ] === 0 ) {
Y[ iy ] = Y[ iy ] - ( C[ ic ]*Y[ iy-strideY ] );
} else {
temp = Y[ iy-strideY ];
Y[ iy-strideY ] = Y[ iy ];
Y[ iy ] = temp - ( C[ ic ]*Y[ iy ] );
}
}
// Solve the upper triangular system `U*x = y`...
perturb = ( job === -1 );
for ( k = N; k >= 1; k-- ) {
iy = offsetY + ( (k-1)*strideY );
if ( k <= N-2 ) {
temp = Y[ iy ] - ( B[ offsetB+((k-1)*strideB) ]*Y[ iy+strideY ] ) - ( D[ offsetD+((k-1)*strideD) ]*Y[ iy+(2*strideY) ] );
} else if ( k === N-1 ) {
temp = Y[ iy ] - ( B[ offsetB+((k-1)*strideB) ]*Y[ iy+strideY ] );
} else {
temp = Y[ iy ];
}
ak = A[ offsetA+((k-1)*strideA) ];
if ( !divide( temp, ak, perturb, tol, sfmin, bignum, Y, iy ) ) {
return k;
}
}
} else {
// Solve the transposed upper triangular system `U^T*x = y`...
perturb = ( job === -2 );
for ( k = 1; k <= N; k++ ) {
iy = offsetY + ( (k-1)*strideY );
if ( k >= 3 ) {
temp = Y[ iy ] - ( B[ offsetB+((k-2)*strideB) ]*Y[ iy-strideY ] ) - ( D[ offsetD+((k-3)*strideD) ]*Y[ iy-(2*strideY) ] );
} else if ( k === 2 ) {
temp = Y[ iy ] - ( B[ offsetB+((k-2)*strideB) ]*Y[ iy-strideY ] );
} else {
temp = Y[ iy ];
}
ak = A[ offsetA+((k-1)*strideA) ];
if ( !divide( temp, ak, perturb, tol, sfmin, bignum, Y, iy ) ) {
return k;
}
}
// Apply the transposed unit lower bidiagonal matrix `L^T` and the permutation `P`...
for ( k = N; k >= 2; k-- ) {
iy = offsetY + ( (k-1)*strideY );
ii = offsetIN + ( (k-2)*strideIN );
ic = offsetC + ( (k-2)*strideC );
if ( IN[ ii ] === 0 ) {
Y[ iy-strideY ] = Y[ iy-strideY ] - ( C[ ic ]*Y[ iy ] );
} else {
temp = Y[ iy-strideY ];
Y[ iy-strideY ] = Y[ iy ];
Y[ iy ] = temp - ( C[ ic ]*Y[ iy ] );
}
}
}
return 0;
}
// EXPORTS //
module.exports = dlagts;
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