feat: add lapack/base/dlarf1f

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Author: aayush0325

lib/node_modules/@stdlib/lapack/base/dlarf1f/lib/base.js

@@ -0,0 +1,128 @@
+/**
+* @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';
+
+/* eslint-disable max-len */
+
+// MODULES //
+
+var iladlc = require( '@stdlib/lapack/base/iladlc' ).ndarray;
+var iladlr = require( '@stdlib/lapack/base/iladlr' ).ndarray;
+var dgemv = require( '@stdlib/blas/base/dgemv' ).ndarray;
+var dger = require( '@stdlib/blas/base/dger' ).ndarray;
+var daxpy = require( '@stdlib/blas/base/daxpy' ).ndarray;
+var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
+
+
+// MAIN //
+
+/**
+* Applies a real elementary reflector `H = I - tau * v * v ^ T` to a real M by N matrix `C`.
+*
+* ## Notes
+*
+* -   `work` should have `N` indexed elements if side = `left` and `M` indexed elements if side = `right`.
+* -   `V` should have `1 + (M-1) * abs(strideV)` indexed elements if side = `left` and `1 + (N-1) * abs(strideV)` indexed elements if side = `right`.
+* -   `C` is overwritten by `H * C` if side = `left` and `C * H` if side = `right`.
+*
+* @private
+* @param {string} side - use `left` to form `H * C` and `right` to from `C * H`
+* @param {NonNegativeInteger} M - number of rows in `C`
+* @param {NonNegativeInteger} N - number of columns in `C`
+* @param {Float64Array} V - the vector `v` in the representation of `H`
+* @param {integer} strideV - stride length for `V`
+* @param {NonNegativeInteger} offsetV - starting index for `V`
+* @param {number} tau - the value of `tau` in representation of `H`
+* @param {Float64Array} C - input matrix
+* @param {integer} strideC1 - stride of the first dimension of `C`
+* @param {integer} strideC2 - stride of the second dimension of `C`
+* @param {NonNegativeInteger} offsetC - starting index for `C`
+* @param {Float64Array} work - workspace array
+* @param {integer} strideWork - stride length for `work`
+* @param {NonNegativeInteger} offsetWork - starting index for `work`
+* @returns {Float64Array} `C * H` or `H * C`
+*
+* @example
+* var Float64Array = require( '@stdlib/array/float64' );
+*
+* var C = new Float64Array( [ 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 ] );
+* var V = new Float64Array( [ 0.5, 0.5, 0.5, 0.5 ] );
+* var work = new Float64Array( 3 );
+*
+* var out = dlarf1f( 'left', 4, 3, V, 1, 0, 1.0, C, 3, 1, 0, work, 1, 0 );
+* // returns <Float64Array>[ -4.5, -10.5, -16.5, -0.75, -1.75, -2.75, 0.25, -0.75, -1.75, 1.25,  0.25, -0.75 ]
+*/
+function dlarf1f( side, M, N, V, strideV, offsetV, tau, C, strideC1, strideC2, offsetC, work, strideWork, offsetWork ) { // eslint-disable-line max-params
+	var lastv;
+	var lastc;
+	var i;
+
+	lastv = 1;
+	lastc = 0;
+	if ( tau !== 0.0 ) {
+		if ( side === 'left' ) {
+			lastv = M;
+		} else {
+			lastv = N;
+		}
+		if ( strideV > 0 ) {
+			i = offsetV + ( ( lastv - 1 ) * strideV );
+		} else {
+			i = offsetV;
+		}
+		while ( lastv > 0 && V[ i ] === 0.0 ) {
+			lastv -= 1;
+			i -= strideV;
+		}
+		if ( side === 'left' ) {
+			lastc = iladlc( lastv, N, C, strideC1, strideC2, offsetC ) + 1; // to account for the difference between zero-based and one-based indexing
+		} else {
+			lastc = iladlr( M, lastv, C, strideC1, strideC2, offsetC ) + 1; // to account for the difference between zero-based and one-based indexing
+		}
+		// lastc is zero if a matrix is filled with zeros
+	}
+	if ( lastc === 0 ) {
+		// Returns C unchanged if tau is zero or all elements in C are zero
+		return C;
+	}
+	if ( side === 'left' ) {
+		if ( lastv === 0 ) {
+			dscal( lastc, 1.0 - tau, C, strideC2, offsetC ); // scale the first row
+		} else {
+			dgemv( 'transpose', lastv-1, lastc, 1.0, C, strideC1, strideC2, offsetC + strideC1, V, strideV, offsetV + strideV, 0.0, work, strideWork, offsetWork ); // C( 1, 0 ) is accessed here
+			daxpy( lastc, 1.0, C, strideC2, offsetC, work, strideWork, offsetWork ); // operates on the first row of C
+			daxpy( lastc, -tau, work, strideWork, offsetWork, C, strideC2, offsetC ); // operates on the first row of C
+			dger( lastv-1, lastc, -tau, V, strideV, offsetV + strideV, work, strideWork, offsetWork, C, strideC1, strideC2, offsetC + strideC1 ); // C( 1, 0 ) is accessed here
+		}
+	} else if ( lastv === 0 ) {
+		dscal( lastc, 1.0 - tau, C, strideC1, offsetC ); // scale the first column
+	} else {
+		dgemv( 'no-transpose', lastc, lastv-1, 1.0, C, strideC1, strideC2, offsetC + strideC2, V, strideV, offsetV + strideV, 0.0, work, strideWork, offsetWork ); // C( 0, 1 ) is accessed here
+		daxpy( lastc, 1.0, C, strideC1, offsetC, work, strideWork, offsetWork ); // operates on the first column of C
+		daxpy( lastc, -tau, work, strideWork, offsetWork, C, strideC1, offsetC ); // operates on the first column of C
+		dger( lastc, lastv-1, -tau, work, strideWork, offsetWork, V, strideV, offsetV + strideV, C, strideC1, strideC2, offsetC + strideC2 ); // C( 0, 1 ) is accessed here
+	}
+
+	return C;
+}
+
+
+// EXPORTS //
+
+module.exports = dlarf1f;