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* @license Apache-2.0
*
* Copyright (c) 2025 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 isLayout = require( '@stdlib/blas/base/assert/is-layout' );
var isColumnMajor = require( '@stdlib/ndarray/base/assert/is-column-major-string' );
var max = require( '@stdlib/math/base/special/max' );
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major-string' );
var format = require( '@stdlib/string/format' );
var isOperationSide = require( '@stdlib/blas/base/assert/is-operation-side' );
var isJob = require( './isjob.js' );
var base = require( './base.js' );
// MAIN //
/**
* Forms the right or left eigenvectors of a real general matrix by backward transformation on the computed eigenvectors of the balanced matrix output by `dgebal`.
*
* ## Notes
*
* The job parameter can be one of the following:
*
* - `none`: none, return immediately
* - `permute`: permute only
* - `scale`: scale only
* - `both`: both permute and scale
*
* @param {string} order - storage layout
* @param {string} job - type of transformation.
* @param {string} side - specifies the side of the eigenvectors in `V` (`right` or `left`)
* @param {NonNegativeInteger} N - number of rows in matrix `V`
* @param {NonNegativeInteger} M - number of columns in matrix `V`
* @param {NonNegativeInteger} ilo - index of leftmost column of the submatrix computed by `dgebal` (zero-based)
* @param {NonNegativeInteger} ihi - index of rightmost column of the submatrix computed by `dgebal` (zero-based)
* @param {Float64Array} scale - contains the details of the permutations and scaling factors applied when balancing `V`, computed by `dgebal`
* @param {Float64Array} V - input matrix
* @param {integer} LDV - leading dimension of `V`
* @throws {TypeError} first argument must be a valid order
* @throws {TypeError} second argument must be a valid job
* @throws {TypeError} third argument must be a valid side
* @throws {RangeError} fourth argument must be greater than or equal to max(1,M)
* @returns {Float64Array} `V`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var scale = new Float64Array( [ 0.5, 2.0, 1.0 ] );
* var V = new Float64Array( [ 1.0, 4.0, 2.0, 5.0, 3.0, 6.0 ] );
*
* var out = dgebak( 'row-major', 'scale', 'right', 3, 2, 0, 2, scale, V, 2 );
* // returns <Float64Array>[ 0.5, 2, 4, 10, 3, 6 ]
*/
function dgebak( order, job, side, N, M, ilo, ihi, scale, V, LDV ) {
var sa1;
var sa2;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( !isJob( job ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a valid job. Value: `%s`.', job ) );
}
if ( !isOperationSide( side ) ) {
throw new TypeError( format( 'invalid argument. Third argument must be a valid side. Value: `%s`.', side ) );
}
if ( isRowMajor( order ) && LDV < max( 1, M ) ) {
throw new RangeError( format( 'invalid argument. Tenth argument must be greater than or equal to max(1,%d). Value: `%d`.', M, LDV ) );
}
if ( isColumnMajor( order ) ) {
sa1 = 1;
sa2 = LDV;
} else { // order === 'row-major'
sa1 = LDV;
sa2 = 1;
}
return base( job, side, N, M, ilo, ihi, scale, 1, 0, V, sa1, sa2, 0 );
}
// EXPORTS //
module.exports = dgebak;
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