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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 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` using alternative indexing semantics, 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` to `scale`, the infinity-norm of `X` to `xnorm`, and a status code to `info`. The status code is `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} 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 {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `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 {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`
* @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 {integer} strideX1 - stride of the first dimension of `X`
* @param {integer} strideX2 - stride of the second dimension of `X`
* @param {NonNegativeInteger} offsetX - starting index for `X`
* @param {Float64Array} scale - array containing an element which is overwritten by the scaling factor
* @param {NonNegativeInteger} offsetScale - index of the element in `scale`
* @param {Float64Array} xnorm - array containing an element which is overwritten by the infinity-norm of `X`
* @param {NonNegativeInteger} offsetXnorm - index of the element in `xnorm`
* @param {Int32Array} info - array containing an element which is overwritten by the status code
* @param {NonNegativeInteger} offsetInfo - index of the element in `info`
* @throws {TypeError} first argument must be a valid transpose operation
* @throws {RangeError} second argument must be either `1` or `2`
* @throws {RangeError} third argument must be either `1` or `2`
* @returns {Float64Array} `X`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
* var Int32Array = require( '@stdlib/array/int32' );
*
* 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 scale = new Float64Array( 1 );
* var xnorm = new Float64Array( 1 );
* var info = new Int32Array( 1 );
*
* dlaln2( 'no-transpose', 2, 1, 1.0e-3, 1.0, A, 1, 2, 0, 1.0, 1.0, B, 1, 2, 0, 0.5, 0.0, X, 1, 2, 0, scale, 0, xnorm, 0, info, 0 );
* // X => <Float64Array>[ ~-0.087, ~1.391 ]
* // scale => <Float64Array>[ 1.0 ]
* // xnorm => <Float64Array>[ ~1.391 ]
* // info => <Int32Array>[ 0 ]
*/
function dlaln2( trans, NA, NW, smin, ca, A, strideA1, strideA2, offsetA, d1, d2, B, strideB1, strideB2, offsetB, wr, wi, X, strideX1, strideX2, offsetX, scale, offsetScale, xnorm, offsetXnorm, info, offsetInfo ) { // eslint-disable-line max-params
if ( !isTransposeOperation( trans ) ) {
throw new TypeError( format( 'invalid argument. First argument must be one of the following: "%s". Value: `%s`.', join( transposeOperations(), '", "' ), trans ) );
}
if ( NA !== 1 && NA !== 2 ) {
throw new RangeError( format( 'invalid argument. Second argument must be either 1 or 2. Value: `%d`.', NA ) );
}
if ( NW !== 1 && NW !== 2 ) {
throw new RangeError( format( 'invalid argument. Third argument must be either 1 or 2. Value: `%d`.', NW ) );
}
return base( trans, NA, NW, smin, ca, A, strideA1, strideA2, offsetA, d1, d2, B, strideB1, strideB2, offsetB, wr, wi, X, strideX1, strideX2, offsetX, scale, offsetScale, xnorm, offsetXnorm, info, offsetInfo );
}
// EXPORTS //
module.exports = dlaln2;
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