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 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 12x 12x 12x 12x 12x 12x 12x 12x 12x 12x 12x 12x 3x 3x 3x 12x 3x 3x 3x 9x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 3x 12x 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 dlamch = require( '@stdlib/lapack/base/dlamch' );
var sqrt = require( '@stdlib/math/base/special/sqrt' );
var abs = require( '@stdlib/math/base/special/fast/abs' );
var sign = require( '@stdlib/math/base/special/copysign' );
var min = require( '@stdlib/math/base/special/fast/min' );
var max = require( '@stdlib/math/base/special/maxn' );
// VARIABLES //
var safmin = dlamch( 'safe minimum' );
var safmax = 1.0 / safmin;
var rtmin = sqrt( safmin );
var rtmax = sqrt( safmax / 2.0 );
// MAIN //
/**
* Constructs a Givens rotation of a two-dimensional vector that zeros out the second component.
*
* For a two-dimensional vector ( f, g ) it computes the sine `S`, cosine `C` and the resultant `R` such that the following equation is satisfied:
*
* ```tex
* \(\begin{bmatrix} C & S \\ -S & C \end{bmatrix} \begin{bmatrix} F \\ G \end{bmatrix} = \begin{bmatrix} R \\ 0 \end{bmatrix}\)
* ```
*
* @private
* @param {Float64Array} F - single element array representing the first component of the vector to be rotated
* @param {NonNegativeInteger} offsetF - starting index for `F`
* @param {Float64Array} G - single element array representing the second component of the vector to be rotated
* @param {NonNegativeInteger} offsetG - starting index for `G`
* @param {Float64Array} C - single element array overwritten by the cosine of the rotation
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @param {Float64Array} S - single element array overwritten by the sine of the rotation
* @param {NonNegativeInteger} offsetS - starting index for `S`
* @param {Float64Array} R - single element array overwritten by the length of the rotated vector
* @param {NonNegativeInteger} offsetR - starting index for `R`
* @returns {void}
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var F = new Float64Array( [ 3.0 ] );
* var G = new Float64Array( [ 4.0 ] );
* var C = new Float64Array( 1 );
* var S = new Float64Array( 1 );
* var R = new Float64Array( 1 );
*
* dlartg( F, 0, G, 0, C, 0, S, 0, R, 0 );
* // R => <Float64Array>[ 5.0 ]
* // C => <Float64Array>[ 0.6 ]
* // S => <Float64Array>[ 0.8 ]
*/
function dlartg( F, offsetF, G, offsetG, C, offsetC, S, offsetS, R, offsetR ) {
var f1;
var g1;
var fs;
var gs;
var u;
var d;
f1 = abs( F[ offsetF ] );
g1 = abs( G[ offsetG ] );
if ( G[ offsetG ] === 0.0 ) {
C[ offsetC ] = 1.0;
S[ offsetS ] = 0.0;
R[ offsetR ] = F[ offsetF ];
} else if ( F[ offsetF ] === 0.0 ) {
C[ offsetC ] = 0.0;
S[ offsetS ] = sign( 1.0, G[ offsetG ] );
R[ offsetR ] = g1;
} else if ( f1 > rtmin && f1 < rtmax && g1 > rtmin && g1 < rtmax ) {
d = sqrt( (F[ offsetF ]*F[ offsetF ]) + (G[ offsetG ]*G[ offsetG ]) );
C[ offsetC ] = f1 / d;
R[ offsetR ] = sign( d, F[ offsetF ] );
S[ offsetS ] = G[ offsetG ] / R[ offsetR ];
} else {
u = min( safmax, max( safmin, f1, g1 ) );
fs = F[ offsetF ] / u;
gs = G[ offsetG ] / u;
d = sqrt( (fs*fs) + (gs*gs) );
C[ offsetC ] = abs( fs ) / d;
R[ offsetR ] = sign( d, F[ offsetF ] );
S[ offsetS ] = gs / R[ offsetR ];
R[ offsetR ] *= u;
}
}
// EXPORTS //
module.exports = dlartg;
|