Press n or j to go to the next uncovered block, b, p or k for the previous block.
| 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 | 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 24x 24x 24x 24x 24x 24x 24x 24x 24x 24x 24x 6x 6x 6x 6x 18x 18x 18x 18x 24x 6x 6x 24x 12x 12x 12x 12x 6x 6x 6x 6x 6x 6x 6x 6x 6x 6x 12x 12x 12x 6x 6x 12x 12x 12x 12x 12x 24x 3x 3x 3x 3x 3x | /**
* @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 dnrm2 = require( '@stdlib/blas/base/dnrm2' ).ndarray;
var sign = require( '@stdlib/math/base/special/copysign' );
var dlamch = require( '@stdlib/lapack/base/dlamch' );
var abs = require( '@stdlib/math/base/special/abs' );
var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
var dlapy2 = require( './dlapy2.js' );
// MAIN //
/**
* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X`.
*
* ## Notes
*
* - `H` is a Householder matrix with the form `H = I - tau * [1; v] * [1, v^T]`, where `tau` is a scalar and `v` is a vector.
* - the input vector is `[alpha; x]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
* - the result of applying `H` to `[alpha; x]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
* - if all elements of `X` are zero, then `tau = 0` and `H` is the identity matrix.
* - otherwise, `1 <= tau <= 2`
*
* @private
* @param {NonNegativeInteger} N - number of rows/columns of the elementary reflector `H`
* @param {Float64Array} X - overwritten by the vector `V` on exit, expects `N - 1` indexed elements
* @param {integer} strideX - stride length for `X`
* @param {NonNegativeInteger} offsetX - starting index of `X`
* @param {Float64Array} out - array to store `alpha` and `tau`, first indexed element stores `alpha` and the second indexed element stores `tau`
* @param {integer} strideOut - stride length for `out`
* @param {NonNegativeInteger} offsetOut - starting index of `out`
* @returns {void} overwrites the array `X` and `out` in place
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 2.0, 3.0, 4.0 ] );
* var out = new Float64Array( [ 4.0, 0.0 ] );
*
* dlarfg( 4, X, 1, 0, out, 1, 0 );
* // X => <Float64Array>[ ~0.19, ~0.28, ~0.37 ]
* // out => <Float64Array>[ ~-6.7, ~1.6 ]
*/
function dlarfg( N, X, strideX, offsetX, out, strideOut, offsetOut ) {
var safemin;
var rsafmin;
var xnorm;
var alpha;
var beta;
var tau;
var knt;
var i;
if ( N <= 1 ) {
tau = 0.0; // tau = 0.0
out[ offsetOut + strideOut ] = tau;
return;
}
xnorm = dnrm2( N - 1, X, strideX, offsetX );
alpha = out[ offsetOut ];
if ( xnorm === 0.0 ) {
tau = 0.0; // tau = 0.0
out[ strideOut + offsetOut ] = tau;
} else {
beta = -1.0 * sign( dlapy2( alpha, xnorm ), alpha );
safemin = dlamch( 'S' ) / dlamch( 'E' );
knt = 0;
if ( abs( beta ) < safemin ) {
rsafmin = 1.0 / safemin;
while ( abs( beta ) < safemin && knt < 20 ) {
knt += 1;
dscal( N-1, rsafmin, X, strideX, offsetX );
beta *= rsafmin;
alpha *= rsafmin; // alpha *= rsafmin
}
xnorm = dnrm2( N - 1, X, strideX, offsetX );
beta = -1.0 * sign( dlapy2( alpha, xnorm ), alpha );
}
tau = ( beta - alpha ) / beta; // tau = (beta - alpha) / beta
dscal( N-1, 1.0 / ( alpha - beta ), X, strideX, offsetX );
for ( i = 0; i < knt; i++ ) {
beta *= safemin;
}
alpha = beta;
out[ offsetOut ] = alpha;
out[ strideOut + offsetOut ] = tau;
}
}
// EXPORTS //
module.exports = dlarfg;
|