feat: add base implementation

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Author: aayush0325

lib/node_modules/@stdlib/lapack/base/dlarfg/lib/base.js

@@ -0,0 +1,116 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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` and `H` is orthogonal, i.e., `H^T * H = I`.
+*
+* @private
+* @param {NonNegativeInteger} N - order of matrix `A`
+* @param {Float64Array} X - overwritten by the vector `V` on exit
+* @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;

lib/node_modules/@stdlib/lapack/base/dlarfg/lib/dlapy2.js

@@ -0,0 +1,67 @@
+/**
+* @license Apache-2.0
+*
+* Copyright (c) 2024 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/abs' );
+var min = require( '@stdlib/math/base/special/min' );
+var max = require( '@stdlib/math/base/special/max' );
+var sqrt = require( '@stdlib/math/base/special/sqrt' );
+var pow = require( '@stdlib/math/base/special/pow' );
+
+
+// MAIN //
+
+/**
+* Returns sqrt( x^2 + y^2 ) in a manner which doesn't cause unnecessary overflow.
+*
+* @private
+* @param {number} x - order of matrix `A`
+* @param {number} y - order of matrix `A`
+* @returns {integer} status code
+*
+* @example
+* var out = dlapy2( 3.0, 4.0, );
+* // returns 5
+*/
+function dlapy2( x, y ) {
+	// TODO - make a separate package for this
+	var xabs;
+	var yabs;
+	var w;
+	var z;
+
+	xabs = abs( x );
+	yabs = abs( y );
+
+	w = max( xabs, yabs );
+	z = min( xabs, yabs );
+
+	if ( z === 0.0 ) {
+		return w;
+	}
+
+	return w * ( sqrt( 1.0 + pow( z / w, 2.0 ) ) );
+}
+
+
+// EXPORTS //
+
+module.exports = dlapy2;