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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 dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
var swaps = require( './swaps.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
*
* @private
* @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 {integer} strideScale - stride of `scale`
* @param {NonNegativeInteger} offsetScale - starting index for `scale`
* @param {Float64Array} V - input matrix
* @param {integer} strideV1 - stride of the first dimension of `V`
* @param {integer} strideV2 - stride of the second dimension of `V`
* @param {NonNegativeInteger} offsetV - starting index for `V`
* @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( 'scale', 'right', 3, 2, 0, 2, scale, 1, 0, V, 2, 1, 0 );
* // returns <Float64Array>[ 0.5, 2, 4, 10, 3, 6 ]
*/
function dgebak( job, side, N, M, ilo, ihi, scale, strideScale, offsetScale, V, strideV1, strideV2, offsetV ) { // eslint-disable-line max-len, max-params
var is;
var iv;
var i;
var s;
if ( N === 0 || M === 0 || job === 'none' ) {
return V;
}
if ( ilo === ihi ) {
if ( job === 'permute' || job === 'both' ) {
swaps( N, M, ilo, ihi, scale, strideScale, offsetScale, V, strideV1, strideV2, offsetV ); // eslint-disable-line max-len
}
return V;
}
if ( job === 'scale' || job === 'both' ) {
is = offsetScale + ( ilo * strideScale );
iv = offsetV + ( ilo * strideV1 );
for ( i = ilo; i <= ihi; i++ ) {
if ( side === 'right' ) {
s = scale[ is ];
} else {
s = 1.0 / scale[ is ];
}
dscal( M, s, V, strideV2, iv );
is += strideScale;
iv += strideV1;
}
}
if ( job === 'permute' || job === 'both' ) {
swaps( N, M, ilo, ihi, scale, strideScale, offsetScale, V, strideV1, strideV2, offsetV ); // eslint-disable-line max-len
}
return V;
}
// EXPORTS //
module.exports = dgebak;
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