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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 | 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x 2x | /** * @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 abs = require( '@stdlib/math/base/special/fast/abs' ); // MAIN // /** * Given a 2-by-2 or a 3-by-3 matrix `H`, this function sets `V` to a scalar multiple of the first column of `K` where `K = (H - (sr1 + i*si1)*I)*(H - (sr2 + i*si2)*I)`. * * ## Notes * * - It is expected that either `sr1 = sr2` and `si1 + si2 = 0` or `si1 = si2 = 0` (i.e., they represent complex conjugate values). * - This is useful for starting double implicit shift bulges in the QR algorithm. * - `V` should have at least `N` indexed elements. * * @private * @param {PositiveInteger} N - number of row/columns in `H` * @param {Float64Array} H - input matrix * @param {integer} strideH1 - stride of the first dimension of `H` * @param {integer} strideH2 - stride of the second dimension of `H` * @param {NonNegativeInteger} offsetH - index offset for `H` * @param {number} sr1 - real part of the first conjugate complex shift * @param {number} si1 - imaginary part of the first conjugate complex shift * @param {number} sr2 - real part of the second conjugate complex shift * @param {number} si2 - imaginary part of the second conjugate complex shift * @param {Float64Array} V - output array * @param {integer} strideV - stride length for `V` * @param {NonNegativeInteger} offsetV - index offset for `V` * @returns {Float64Array} `V` * * @example * var Float64Array = require( '@stdlib/array/float64' ); * * var H = new Float64Array( [ 1.0, 3.0, 2.0, 2.0, 4.0, 6.0, 0.0, 5.0, 7.0 ] ); // => [ [ 1.0, 3.0, 2.0 ], [ 2.0, 4.0, 6.0 ], [ 0.0, 5.0, 7.0 ] ] * var V = new Float64Array( 3 ); * * var out = dlaqr1( 3, H, 3, 1, 0, 1.5, 0.0, 2.5, 0.0, V, 1, 0 ); * // returns <Float64Array>[ ~1.93, ~0.57, ~2.86 ] */ function dlaqr1( N, H, strideH1, strideH2, offsetH, sr1, si1, sr2, si2, V, strideV, offsetV ) { // eslint-disable-line max-params, max-len var h21s; var h31s; var h11; var h12; var h13; var h21; var h22; var h23; var h31; var h32; var h33; var iv; var s; var i; h11 = offsetH; h12 = offsetH + strideH2; h21 = offsetH + strideH1; h22 = h21 + strideH2; if ( N === 2 ) { s = abs( H[ h11 ] - sr2 ) + abs( si2 ) + abs( H[ h21 ] ); if ( s === 0.0 ) { V[ offsetV ] = 0.0; V[ strideV + offsetV ] = 0.0; return V; } h21s = H[ h21 ] / s; V[ offsetV ] = ( h21s * H[ h12 ] ) + ( ( H[ h11 ]-sr1 ) * ( ( H[ h11 ]-sr2 ) / s ) ) - ( si1*( si2 / s ) ); // eslint-disable-line max-len V[ offsetV + strideV ] = h21s*( H[ h11 ]+H[ h22 ]-sr1-sr2 ); return V; } h13 = h12 + strideH2; h31 = h21 + strideH1; h33 = h22 + strideH1 + strideH2; h23 = h22 + strideH2; h32 = h22 + strideH1; s = abs( H[ h11 ]-sr2 ) + abs( si2 ) + abs( H[ h21 ] ) + abs( H[ h31 ] ); if ( s === 0.0 ) { iv = offsetV; for ( i = 0; i < 3; i++ ) { V[ iv ] = 0.0; iv += strideV; } return V; } h21s = H[ h21 ] / s; h31s = H[ h31 ] / s; iv = offsetV; V[ iv ] = (( H[ h11 ]-sr1 )*( ( H[ h11 ]-sr2 ) / s )) - (si1*( si2 / s )) + ((H[ h12 ]*h21s) + (H[ h13 ]*h31s)); // eslint-disable-line max-len iv += strideV; V[ iv ] = (h21s*( H[ h11 ]+H[ h22 ]-sr1-sr2 )) + (H[ h23 ]*h31s); iv += strideV; V[ iv ] = (h31s*( H[ h11 ]+H[ h33 ]-sr1-sr2 )) + (h21s*H[ h32 ]); return V; } // EXPORTS // module.exports = dlaqr1; |