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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';
// MODULES //
var dlarf1f = require( './dlarf1f.js' );
// MAIN //
/**
* Multiplies a matrix `C` by an orthogonal matrix `Q` from a QR factorization.
*
* ## Notes
*
* `dorm2r` overwrites the general real M by N matrix C with
*
* - `Q * C` if side = 'left' and trans = 'no-transpose'
* - `Q^T * C` if side = 'left' and trans = 'transpose'
* - `C * Q` if side = 'right' and trans = 'no-transpose'
* - `C * Q^T` if side = 'right' and trans = 'transpose'
*
* where Q is a real orthogonal matrix defined as the product of K elementary reflectors `Q = H(1) H(2) ... H(K)` as returned by `dgeqrf`. Q is of order M if side = 'left' and of order N if side = 'right'.
*
* @private
* @param {string} side - specifies the side of multiplication with `C`
* @param {string} trans - specifies the operation to be performed
* @param {NonNegativeInteger} M - number of rows in matrix `C`
* @param {NonNegativeInteger} N - number of columns in matrix `C`
* @param {NonNegativeInteger} K - number of elementary reflectors whose product defines the matrix `Q`
* @param {Float64Array} A - input matrix containing the elementary reflectors
* @param {integer} strideA1 - stride length for the first dimension of `A`
* @param {integer} strideA2 - stride length for the second dimension of `A`
* @param {NonNegativeInteger} offsetA - starting index for `A`
* @param {Float64Array} tau - array containing the scalar factors of the elementary reflectors
* @param {integer} strideTau - stride length for `tau`
* @param {NonNegativeInteger} offsetTau - starting index for `tau`
* @param {Float64Array} C - input/output matrix to be multiplied
* @param {integer} strideC1 - stride length for the first dimension of `C`
* @param {integer} strideC2 - stride length for the second dimension of `C`
* @param {NonNegativeInteger} offsetC - starting index for `C`
* @param {Float64Array} work - workspace array for intermediate calculations
* @param {integer} strideWork - stride length for `work`
* @param {NonNegativeInteger} offsetWork - starting index for `work`
* @returns {Float64Array} the modified matrix `C`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 0.0, 0.0, 2.0, 4.0, 0.0, 3.0, 5.0, 6.0 ] );
* var tau = new Float64Array( [ 7.0, 8.0, 9.0 ] );
* var C = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
* var work = new Float64Array( 3 );
*
* dorm2r( 'left', 'no-transpose', 3, 3, 3, A, 3, 1, 0, tau, 1, 0, C, 3, 1, 0, work, 1, 0 );
* // C => <Float64Array>[ -261638.0, -298618.0, -335598.0, -521066.0, -594715.0, -668364.0, -773933.0, -883324.0, -992715.0 ]
*/
function dorm2r( side, trans, M, N, K, A, strideA1, strideA2, offsetA, tau, strideTau, offsetTau, C, strideC1, strideC2, offsetC, work, strideWork, offsetWork ) { // eslint-disable-line max-params, max-len
var aOffset;
var cOffset;
var tauVal;
var notran;
var left;
var i1;
var i2;
var i3;
var mi;
var ni;
var ic;
var jc;
var i;
// Quick return if possible
if ( M === 0 || N === 0 || K === 0 ) {
return C;
}
left = ( side === 'left' );
notran = ( trans === 'no-transpose' );
// Determine loop indices based on side and trans
if ( ( left && !notran ) || ( !left && notran ) ) {
i1 = 1;
i2 = K;
i3 = 1;
} else {
i1 = K;
i2 = 1;
i3 = -1;
}
// Initialize dimensions
if ( left ) {
ni = N;
jc = 0; // 0-based indexing
} else {
mi = M;
ic = 0; // 0-based indexing
}
// Main loop
for ( i = i1; ( i3 > 0 ) ? ( i <= i2 ) : ( i >= i2 ); i += i3 ) {
if ( left ) {
// H(i) is applied to C(i:m,1:n)
mi = M - i + 1;
ic = i - 1; // Convert to 0-based indexing
} else {
// H(i) is applied to C(1:m,i:n)
ni = N - i + 1;
jc = i - 1; // Convert to 0-based indexing
}
// Apply H(i) using `dlarf1f`
tauVal = tau[ offsetTau + ( ( i - 1 ) * strideTau ) ];
aOffset = offsetA + ( ( i - 1 ) * strideA1 ) + ( ( i - 1 ) * strideA2 );
cOffset = offsetC + ( ic * strideC1 ) + ( jc * strideC2 );
dlarf1f( side, mi, ni, A, strideA1, aOffset, tauVal, C, strideC1, strideC2, cOffset, work, strideWork, offsetWork ); // eslint-disable-line max-len
}
return C;
}
// EXPORTS //
module.exports = dorm2r;
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