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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';
// MAIN //
/**
* Solves a tridiagonal system of the form `A * X = B` using the `L * D * L^T` factorization of `A` computed by `dpttrf`.
*
* @private
* @param {NonNegativeInteger} N - order of the tridiagonal matrix `A`
* @param {NonNegativeInteger} nrhs - number of right-hand sides (i.e., the number of columns of the matrix `B`)
* @param {Float64Array} D - the `N` diagonal elements of the diagonal matrix `D` from the factorization of `A`
* @param {integer} strideD - stride length for `D`
* @param {NonNegativeInteger} offsetD - starting index for `D`
* @param {Float64Array} E - the `N-1` subdiagonal elements of the unit bidiagonal factor `L` from the factorization of `A`
* @param {integer} strideE - stride length for `E`
* @param {NonNegativeInteger} offsetE - starting index for `E`
* @param {Float64Array} B - input matrix (overwritten by the solution matrix `X`)
* @param {integer} strideB1 - stride of the first dimension of `B`
* @param {integer} strideB2 - stride of the second dimension of `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @returns {Float64Array} solution matrix `X` (stored in `B`)
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var D = new Float64Array( [ 4.0, 4.75, 5.157894736842105 ] );
* var E = new Float64Array( [ 0.25, 0.42105263157894735 ] );
* var B = new Float64Array( [ 1.0, 2.0, 3.0 ] );
*
* dptts2( 3, 1, D, 1, 0, E, 1, 0, B, 1, 3, 0 );
* // B => <Float64Array>[ ~0.2041, ~0.1837, ~0.4388 ]
*/
function dptts2( N, nrhs, D, strideD, offsetD, E, strideE, offsetE, B, strideB1, strideB2, offsetB ) {
var da;
var ib;
var id;
var ie;
var oj;
var i;
var j;
if ( N <= 1 ) {
if ( N === 1 ) {
// Scale each right-hand side by `1 / D[0]` (multiplying by the reciprocal, matching `DSCAL`)...
da = 1.0 / D[ offsetD ];
ib = offsetB;
for ( j = 0; j < nrhs; j++ ) {
B[ ib ] *= da;
ib += strideB2;
}
}
return B;
}
// Solve `A * X = B` using the factorization `A = L * D * L^T`, overwriting each right-hand side vector with its solution...
for ( j = 0; j < nrhs; j++ ) {
oj = offsetB + ( j * strideB2 );
// Solve `L * x = b`...
ib = oj;
ie = offsetE;
for ( i = 1; i < N; i++ ) {
// B[i,j] = B[i,j] - ( B[i-1,j] * E[i-1] )
B[ ib+strideB1 ] -= B[ ib ] * E[ ie ];
ib += strideB1;
ie += strideE;
}
// Solve `D * L^T * x = b`. On entry, `ib` points to `B[N-1,j]`...
id = offsetD + ( (N-1)*strideD );
B[ ib ] /= D[ id ];
ie = offsetE + ( (N-2)*strideE );
for ( i = N-2; i >= 0; i-- ) {
id -= strideD;
// B[i,j] = ( B[i,j] / D[i] ) - ( B[i+1,j] * E[i] )
B[ ib-strideB1 ] = ( B[ ib-strideB1 ] / D[ id ] ) - ( B[ ib ] * E[ ie ] );
ib -= strideB1;
ie -= strideE;
}
}
return B;
}
// EXPORTS //
module.exports = dptts2;
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