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* @license Apache-2.0
*
* Copyright (c) 2026 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 */
// cspell:ignore lastv lastc
// 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;
// FUNCTIONS //
/**
* Tests whether an operation should be applied to the left side.
*
* @private
* @param {string} side - operation side
* @returns {boolean} boolean indicating if an operation should be applied to the left side
*/
function isLeftSide( side ) {
return side === 'left';
}
// MAIN //
/**
* Applies a real elementary reflector `H = I - tau * v * v^T` to a real M by N matrix `C`.
*
* ## Notes
*
* - If `side = 'left'`,
*
* - `work` should have `N` indexed elements.
* - `V` should have `1 + (M-1) * abs(strideV)` indexed elements.
* - `C` is overwritten by `H * C`.
*
* - If `side = 'right'`,
*
* - `work` should have `M` indexed elements.
* - `V` should have `1 + (N-1) * abs(strideV)` indexed elements.
* - `C` is overwritten by `C * H`.
*
* @private
* @param {string} side - specifies the side of multiplication with `C`
* @param {NonNegativeInteger} M - number of rows in `C`
* @param {NonNegativeInteger} N - number of columns in `C`
* @param {Float64Array} V - the vector `v`
* @param {integer} strideV - stride length for `V`
* @param {NonNegativeInteger} offsetV - starting index for `V`
* @param {number} tau - scalar constant
* @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 = dlarf( 'left', 4, 3, V, 1, 0, 1.0, C, 3, 1, 0, work, 1, 0 );
* // returns <Float64Array>[ -1.5, -1.5, -1.5, -0.5, -0.5, -0.5, 0.5, 0.5, 0.5, 1.5, 1.5, 1.5 ]
*/
function dlarf( 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;
if ( tau === 0.0 ) {
return C;
}
if ( isLeftSide( side ) ) {
lastv = M;
} else {
lastv = N;
}
// Initialize `i` to point to the last element in `V`:
i = offsetV + ( ( lastv - 1 ) * strideV );
// Look for the last non-zero row in V:
while ( lastv > 0 && V[ i ] === 0.0 ) {
lastv -= 1;
i -= strideV;
}
if ( isLeftSide( side ) ) {
// Scan for the last non-zero column in C(0:lastv-1,:):
lastc = iladlc( lastv, N, C, strideC1, strideC2, offsetC ) + 1; // adjust by +1 to account for the difference between zero-based and one-based indexing
} else {
// Scan for the last non-zero row in C(:,0:lastv-1):
lastc = iladlr( M, lastv, C, strideC1, strideC2, offsetC ) + 1; // adjust by +1 to account for the difference between zero-based and one-based indexing
}
// Note that lastc === 0 renders the BLAS operations null; no special case is needed at this level...
if ( isLeftSide( side ) ) {
// Form: H * C
if ( lastv > 0 ) {
// w(0:lastc-1) := C(0:lastv-1, 0:lastc-1)^T * v(0:lastv-1)
dgemv( 'transpose', lastv, lastc, 1.0, C, strideC1, strideC2, offsetC, V, strideV, offsetV, 0.0, work, strideWork, offsetWork );
// C(0:lastv-1, 0:lastc-1) := C(...) - tau * v(0:lastv-1) * w(0:lastc-1)^T
dger( lastv, lastc, -tau, V, strideV, offsetV, work, strideWork, offsetWork, C, strideC1, strideC2, offsetC );
}
return C;
}
// Form: C * H
if ( lastv > 0 ) {
// w(0:lastc-1) := C(0:lastc-1, 0:lastv-1) * v(0:lastv-1)
dgemv( 'no-transpose', lastc, lastv, 1.0, C, strideC1, strideC2, offsetC, V, strideV, offsetV, 0.0, work, strideWork, offsetWork );
// C(0:lastc-1, 0:lastv-1) := C(...) - tau * w(0:lastc-1) * v(0:lastv-1)^T
dger( lastc, lastv, -tau, work, strideWork, offsetWork, V, strideV, offsetV, C, strideC1, strideC2, offsetC );
}
return C;
}
// EXPORTS //
module.exports = dlarf;
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