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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 */
'use strict';
// MODULES //
var isTransposeOperation = require( '@stdlib/blas/base/assert/is-transpose-operation' );
var isLayout = require( '@stdlib/blas/base/assert/is-layout' );
var isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' );
var transposeOperations = require( '@stdlib/blas/base/transpose-operations' );
var join = require( '@stdlib/array/base/join' );
var format = require( '@stdlib/string/format' );
var base = require( './base.js' );
// MAIN //
/**
* Solves a system of the form `(ca*A - w*D) X = s*B` or `(ca*A^T - w*D) X = s*B` with possible scaling and perturbation of `A`, where `A` is an `NA` by `NA` real matrix (`NA` is 1 or 2), `ca` is a real scalar, `D` is an `NA` by `NA` real diagonal matrix, and `w` is a real or complex scalar.
*
* ## Notes
*
* - If `w` is complex (`NW = 2`), `X` and `B` are `NA` by `2` matrices whose first column contains the real part and whose second column contains the imaginary part.
* - `s` is a scaling factor (`<= 1`) chosen so that `X` can be computed without overflow. `X` is further scaled if necessary to assure that `norm(ca*A - w*D) * norm(X)` is less than overflow.
* - The function writes the scaling factor `s` and the infinity-norm of `X` to the first and second elements of `out`, respectively.
* - The function returns `1` if `ca*A - w*D` had to be perturbed to make its smallest (or only) singular value greater than `smin` and `0` otherwise.
*
* @param {string} order - storage layout
* @param {string} trans - specifies whether `A` should be transposed
* @param {PositiveInteger} NA - size of the matrix `A` (either `1` or `2`)
* @param {PositiveInteger} NW - `1` if `w` is real and `2` if `w` is complex
* @param {number} smin - desired lower bound on the singular values of `A`
* @param {number} ca - coefficient by which `A` is multiplied
* @param {Float64Array} A - input matrix
* @param {PositiveInteger} LDA - stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`)
* @param {number} d1 - first diagonal element of `D`
* @param {number} d2 - second diagonal element of `D` (not used if `NA = 1`)
* @param {Float64Array} B - right-hand side matrix
* @param {PositiveInteger} LDB - stride of the first dimension of `B` (a.k.a., leading dimension of the matrix `B`)
* @param {number} wr - real part of `w`
* @param {number} wi - imaginary part of `w` (not used if `NW = 1`)
* @param {Float64Array} X - output matrix
* @param {PositiveInteger} LDX - stride of the first dimension of `X` (a.k.a., leading dimension of the matrix `X`)
* @param {Float64Array} out - output array containing the scaling factor and the infinity-norm of `X`
* @throws {TypeError} first argument must be a valid order
* @throws {TypeError} second argument must be a valid transpose operation
* @throws {RangeError} third argument must be either `1` or `2`
* @throws {RangeError} fourth argument must be either `1` or `2`
* @throws {RangeError} eighth argument must be a valid stride
* @throws {RangeError} twelfth argument must be a valid stride
* @throws {RangeError} sixteenth argument must be a valid stride
* @returns {integer} status code
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 5.0, 1.0, 1.0, 2.0 ] );
* var B = new Float64Array( [ 1.0, 2.0 ] );
* var X = new Float64Array( 2 );
* var out = new Float64Array( 2 );
*
* var info = dlaln2( 'row-major', 'no-transpose', 2, 1, 1.0e-3, 1.0, A, 2, 1.0, 1.0, B, 1, 0.5, 0.0, X, 1, out );
* // returns 0
*
* // X => <Float64Array>[ ~-0.087, ~1.391 ]
* // out => <Float64Array>[ 1.0, ~1.391 ]
*/
function dlaln2( order, trans, NA, NW, smin, ca, A, LDA, d1, d2, B, LDB, wr, wi, X, LDX, out ) { // eslint-disable-line max-params
var sa1;
var sa2;
var sb1;
var sb2;
var sx1;
var sx2;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( !isTransposeOperation( trans ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be one of the following: "%s". Value: `%s`.', join( transposeOperations(), '", "' ), trans ) );
}
if ( NA !== 1 && NA !== 2 ) {
throw new RangeError( format( 'invalid argument. Third argument must be either 1 or 2. Value: `%d`.', NA ) );
}
if ( NW !== 1 && NW !== 2 ) {
throw new RangeError( format( 'invalid argument. Fourth argument must be either 1 or 2. Value: `%d`.', NW ) );
}
if ( LDA < NA ) {
throw new RangeError( format( 'invalid argument. Eighth argument must be greater than or equal to %d. Value: `%d`.', NA, LDA ) );
}
if ( isColumnMajor( order ) ) {
if ( LDB < NA ) {
throw new RangeError( format( 'invalid argument. Twelfth argument must be greater than or equal to %d. Value: `%d`.', NA, LDB ) );
}
if ( LDX < NA ) {
throw new RangeError( format( 'invalid argument. Sixteenth argument must be greater than or equal to %d. Value: `%d`.', NA, LDX ) );
}
sa1 = 1;
sa2 = LDA;
sb1 = 1;
sb2 = LDB;
sx1 = 1;
sx2 = LDX;
} else { // order === 'row-major'
if ( LDB < NW ) {
throw new RangeError( format( 'invalid argument. Twelfth argument must be greater than or equal to %d. Value: `%d`.', NW, LDB ) );
}
if ( LDX < NW ) {
throw new RangeError( format( 'invalid argument. Sixteenth argument must be greater than or equal to %d. Value: `%d`.', NW, LDX ) );
}
sa1 = LDA;
sa2 = 1;
sb1 = LDB;
sb2 = 1;
sx1 = LDX;
sx2 = 1;
}
return base( trans, NA, NW, smin, ca, A, sa1, sa2, 0, d1, d2, B, sb1, sb2, 0, wr, wi, X, sx1, sx2, 0, out, 1, 0 );
}
// EXPORTS //
module.exports = dlaln2;
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