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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.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var isLayout = require( '@stdlib/blas/base/assert/is-layout' );
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major-string' );
var format = require( '@stdlib/string/format' );
var base = require( './base.js' );
// MAIN //
/**
* Performs a single, small shift multiline QR sweep.
*
* @param {string} order - storage layout
* @param {boolean} wantT - boolean value indicating whether the quasi triangular Schur factor is being computed
* @param {boolean} wantZ - boolean value indicating whether the orthogonal Schur factor is being computed
* @param {integer} kacc22 - integer value ranging from 0 to 2 (inclusive), specifies the computation mode for far-from-diagonal updates
* @param {integer} N - number of rows/columns in `H`
* @param {integer} KTOP - first row and column of the submatrix of `H` where the QR sweep will be applied
* @param {integer} KBOT - last row and column of the submatrix of `H` where the QR sweep will be applied
* @param {integer} nshifts - number of simultaneous shifts, must be even and positive
* @param {Float64Array} SR - real parts of the shifts of origin that define the QR sweep
* @param {Float64Array} SI - imaginary parts of the shifts of origin that define the QR sweep
* @param {Float64Array} H - input upper hessenberg matrix
* @param {PositiveInteger} LDH - stride of the first dimension of `H` (a.k.a., leading dimension of the matrix `H`)
* @param {integer} iloZ - starting row from where the transformation must be applied if `wantZ` is true
* @param {integer} ihiZ - ending row from where the transformation must be applied if `wantZ` is true
* @param {Float64Array} Z - the QR sweep orthogonal similarity transformation is accumulated into `Z` between the rows and columns `iloZ` and `ihiZ` if `wantZ` is true, otherwise `Z` is not referenced
* @param {PositiveInteger} LDZ - stride of the first dimension of `Z` (a.k.a., leading dimension of the matrix `Z`)
* @param {Float64Array} V - householder vectors are stored column-wise, used in forming bulges for the multi shift QR algorithm
* @param {PositiveInteger} LDV - stride of the first dimension of `V` (a.k.a., leading dimension of the matrix `V`)
* @param {Float64Array} U - used to hold the product of householder reflector that represent accumulated orthogonal transformations from the bulge-chasing process
* @param {PositiveInteger} LDU - stride of the first dimension of `U` (a.k.a., leading dimension of the matrix `U`)
* @param {integer} NH - number of columns in `WH` available for workspace
* @param {Float64Array} WH - workspace array
* @param {PositiveInteger} LDWH - stride of the first dimension of `WH` (a.k.a., leading dimension of the matrix `WH`)
* @param {integer} NV - number of rows in `WV` available for workspace
* @param {Float64Array} WV - workspace array
* @param {PositiveInteger} LDWV - stride of the first dimension of `WV` (a.k.a., leading dimension of the matrix `WV`)
* @throws {TypeError} first argument must be a valid order
* @throws {RangeError} fourth argument must be greater than or equal to max(1,N)
* @returns {void} permuted matrix `A`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var H = new Float64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 2.0, 1.5, 0.0, 0.0, 0.0, 3, 2.0, 0.0, 0.0, 0.0, 4.0 ] );
* var Z = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0 ] );
* var V = new Float64Array( 6 );
* var U = new Float64Array( 10 );
* var WH = new Float64Array( 16 );
* var WV = new Float64Array( 16 );
* var SR = new Float64Array( [ 1.1, 2.2 ] );
* var SI = new Float64Array( [ 0.0, 0.0 ] );
*
* dlaqr5( 'row-major', true, true, 0, 4, 1, 4, 2, SR, SI, H, 4, 1, 4, Z, 4, V, 2, U, 2, 4, WH, 4, 4, WV, 4 );
* // H => <Float64Array>[ 1.0, 1.0, 0.0, 0.0, 0.0, 2.0, 1.5, 0.0, 0.0, 0.0, 3, 2.0, 0.0, 0.0, 0.0, 4.0 ]
* // Z => <Float64Array>[ 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0 ]
*/
function dlaqr5( order, wantT, wantZ, kacc22, N, KTOP, KBOT, nshifts, SR, SI, H, LDH, iloZ, ihiZ, Z, LDZ, V, LDV, U, LDU, NH, WH, LDWH, NV, WV, LDWV ) {
var swh1;
var swh2;
var swv1;
var swv2;
var sh1;
var sh2;
var sz1;
var sz2;
var sv1;
var sv2;
var su1;
var su2;
if ( !isLayout( order ) ) {
throw new TypeError( format( 'invalid argument. First argument must be a valid order. Value: `%s`.', order ) );
}
if ( isRowMajor( order ) ) {
sh1 = LDH;
sh2 = 1;
sz1 = LDZ;
sz2 = 1;
sv1 = LDV;
sv2 = 1;
su1 = LDU;
su2 = 1;
swh1 = LDWH;
swh2 = 1;
swv1 = LDWV;
swv2 = 1;
} else { // order === 'col-major'
sh1 = 1;
sh2 = LDH;
sz1 = 1;
sz2 = LDZ;
sv1 = 1;
sv2 = LDV;
su1 = 1;
su2 = LDU;
swh1 = 1;
swh2 = LDWH;
swv1 = 1;
swv2 = LDWV;
}
base( wantT, wantZ, kacc22, N, KTOP, KBOT, nshifts, SR, 1, 0, SI, 1, 0, H, sh1, sh2, 0, iloZ, ihiZ, Z, sz1, sz2, 0, V, sv1, sv2, 0, U, su1, su2, 0, NH, WH, swh1, swh2, 0, NV, WV, swv1, swv2, 0 );
}
// EXPORTS //
module.exports = dlaqr5;
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