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lapack/base/dlarfg/base.js.html

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// MAIN //
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&nbsp;
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/**
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* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X`.
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* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; X]` zeros out `X`.
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*
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* ## Notes
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*
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* - `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.
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* - the input vector is `[alpha; x]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
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* - the result of applying `H` to `[alpha; x]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
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* - `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.
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* - the input vector is `[alpha; X]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
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* - the result of applying `H` to `[alpha; X]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
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* - if all elements of `X` are zero, then `tau = 0` and `H` is the identity matrix.
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* - otherwise, `1 &lt;= tau &lt;= 2`
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*
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* @param {Float64Array} out - array to store `alpha` and `tau`, first indexed element stores `alpha` and the second indexed element stores `tau`
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* @param {integer} strideOut - stride length for `out`
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* @param {NonNegativeInteger} offsetOut - starting index of `out`
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* @returns {void} overwrites the array `X` and `out` in place
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* @returns {void}
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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var i;
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if ( N &lt;= 1 ) {
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tau = 0.0; // tau = 0.0
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out[ offsetOut + strideOut ] = tau;
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out[ offsetOut + strideOut ] = 0.0;
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return;
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}
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xnorm = dnrm2( N - 1, X, strideX, offsetX );
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alpha = out[ offsetOut ];
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if ( xnorm === 0.0 ) {
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tau = 0.0; // tau = 0.0
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out[ strideOut + offsetOut ] = tau;
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out[ strideOut + offsetOut ] = 0.0;
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} else {
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beta = -1.0 * sign( dlapy2( alpha, xnorm ), alpha );
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safemin = dlamch( 'S' ) / dlamch( 'E' );
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safemin = dlamch( 'safemin' ) / dlamch( 'epsilon' );
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knt = 0;
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if ( abs( beta ) &lt; safemin ) {
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rsafmin = 1.0 / safemin;
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while ( abs( beta ) &lt; safemin &amp;&amp; knt &lt; 20 ) {
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knt += 1;
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dscal( N-1, rsafmin, X, strideX, offsetX );
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beta *= rsafmin;
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alpha *= rsafmin; // alpha *= rsafmin
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alpha *= rsafmin;
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}
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xnorm = dnrm2( N - 1, X, strideX, offsetX );
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beta = -1.0 * sign( dlapy2( alpha, xnorm ), alpha );
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}
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tau = ( beta - alpha ) / beta; // tau = (beta - alpha) / beta
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tau = ( beta - alpha ) / beta;
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dscal( N-1, 1.0 / ( alpha - beta ), X, strideX, offsetX );
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for ( i = 0; i &lt; knt; i++ ) {
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beta *= safemin;
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}
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alpha = beta;
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out[ offsetOut ] = alpha;
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out[ offsetOut ] = beta;
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out[ strideOut + offsetOut ] = tau;
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}
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}
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<div class='footer quiet pad2 space-top1 center small'>
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lapack/base/dlarfg/coverage.ndjson

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[357,357,100,16,16,100,3,3,100,357,357,100,"f7e00903b9ba8f89fdd21c7790c09f3e56f2a369","2025-06-04 09:00:14 +0530"]
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[354,354,100,16,16,100,3,3,100,354,354,100,"0f4398806745d808d58539ed169bdaf990f9d9ff","2025-06-05 04:48:53 +0000"]

lapack/base/dlarfg/dlarfg.js.html

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// MAIN //
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/**
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* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X`.
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* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; X]` zeros out `X`.
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*
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* - `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.
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* - `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.
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* - the input vector is `[alpha; X]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
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* - the result of applying `H` to `[alpha; X]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
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* @param {Float64Array} X - overwritten by the vector `V` on exit, expects `N - 1` indexed elements
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* @returns {void}
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* @example
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lapack/base/dlarfg/index.html

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lapack/base/dlarfg/index.js.html

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'use strict';
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&nbsp;
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/**
245-
* LAPACK routine to generate a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X`.
245+
* LAPACK routine to generate a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; X]` zeros out `X`.
246246
*
247247
* ## Notes
248248
*
249-
* - `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.
250-
* - the input vector is `[alpha; x]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
251-
* - the result of applying `H` to `[alpha; x]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
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* - `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.
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* - the input vector is `[alpha; X]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
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* - the result of applying `H` to `[alpha; X]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
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* - otherwise, `1 &lt;= tau &lt;= 2`
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*
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lapack/base/dlarfg/main.js.html

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lapack/base/dlarfg/ndarray.js.html

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&nbsp;
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/**
224-
* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; x]` zeros out `X` using alternative indexing semantics.
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* Generates a real elementary reflector `H` of order `N` such that applying `H` to a vector `[alpha; X]` zeros out `X` using alternative indexing semantics.
225225
*
226226
* ## Notes
227227
*
228-
* - `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.
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* - the input vector is `[alpha; x]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
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* - the result of applying `H` to `[alpha; x]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
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* - `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.
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* - the input vector is `[alpha; X]`, where `alpha` is a scalar and `X` is a real `(n-1)`-element vector.
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* - the result of applying `H` to `[alpha; X]` is `[beta; 0]`, with `beta` being a scalar and the rest of the vector zeroed.
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*
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* @param {Float64Array} out - array to store `alpha` and `tau`, first indexed element stores `alpha` and the second indexed element stores `tau`
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* @param {integer} strideOut - stride length for `out`
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* @returns {void}
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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<div class='footer quiet pad2 space-top1 center small'>
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Code coverage generated by
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at 2025-06-04T03:31:12.657Z
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