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* @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( [ 1.0, 5.0, 9.0, 2.0, 6.0, 10.0, 3.0, 7.0, 11.0, 4.0, 8.0, 12.0 ] );
* 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;
}
// i points to the last element in V
i = offsetV + ( ( lastv - 1 ) * strideV );
// Move i to the last non-zero element in V
while ( lastv > 0 && V[ i ] === 0.0 ) {
lastv -= 1;
i -= strideV;
}
if ( side === 'left' ) {
lastc = iladlc( lastv + 1, N, C, strideC1, strideC2, offsetC ) + 1; // to account for the difference between zero-based and one-based indexing
} else {
lastc = iladlr( M, lastv + 1, 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;
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