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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 dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
var dlarf1f = require( './dlarf1f.js' );
var initUnitColumns = require( './init_unit_columns.js' );
// MAIN //
/**
* Generates an M-by-N real matrix Q with orthonormal columns. The matrix Q is defined as the first N columns of a product of K elementary reflectors of order M. `Q = H(1) H(2) . . . H(K)` as returned by `dgeqrf`.
*
* @private
* @param {PositiveInteger} M - number of rows in matrix `A`
* @param {PositiveInteger} N - number of columns in matrix `A`
* @param {NonNegativeInteger} K - number of elementary reflectors whose product defines the matrix Q
* @param {Float64Array} A - input matrix
* @param {integer} strideA1 - stride of the first dimension of `A`
* @param {integer} strideA2 - stride of the second dimension of `A`
* @param {NonNegativeInteger} offsetA - index offset for `A`
* @param {Float64Array} tau - vector of K scalar factors of the elementary reflectors
* @param {integer} strideTau - stride length for `tau`
* @param {NonNegativeInteger} offsetTau - index offset for `tau`
* @param {Float64Array} work - workspace array
* @param {integer} strideWork - stride length for `work`
* @param {NonNegativeInteger} offsetWork - index offset for `work`
* @returns {Float64Array} matrix `A` overwritten with the orthogonal matrix Q
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
* var tau = new Float64Array( [ 0.0, 0.0 ] );
* var work = new Float64Array( [ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ] );
*
* dorg2r( 3, 2, 2, A, 1, 3, 0, tau, 1, 0, work, 1, 0 );
* // A => <Float64Array>[ 1.0, 0.0, 0.0, 0.0, 1.0, 0.0 ]
*/
function dorg2r( M, N, K, A, strideA1, strideA2, offsetA, tau, strideTau, offsetTau, work, strideWork, offsetWork ) { // eslint-disable-line max-len, max-params
var ia1;
var ia3;
var del;
var ia2;
var it;
var i;
var j;
if ( N <= 0 ) {
return A;
}
// Initialize columns k+1:n to columns of the unit matrix
initUnitColumns( M, N, K, A, strideA1, strideA2, offsetA );
del = strideA1 + strideA2;
it = offsetTau + ((K-1)*strideTau);
ia1 = offsetA + ((K-1)*(strideA1+strideA2));
ia2 = offsetA + ((K-1)*strideA2);
// Apply H(i) to A(i:m,i:n) from the left
for ( i = K-1; i >= 0; i-- ) {
if ( i < N ) {
// Apply H(i) to A(i:m,i+1:n) from the left
dlarf1f( 'left', M-i, N-i-1, A, strideA1, ia1, tau[ it ], A, strideA1, strideA2, ia1 + strideA2, work, strideWork, offsetWork );
}
if ( i < M ) {
// Scale A(i+1:m,i) by -tau(i)
dscal( M-i-1, -tau[ it ], A, strideA1, ia1 + strideA1 );
}
// Set A(i,i) = 1 - tau(i)
A[ ia1 ] = 1.0 - tau[ it ];
ia3 = 0;
// Set A(0:i-1,i) to zero
for ( j = 0; j < i; j++ ) {
A[ ia2 + ia3 ] = 0.0;
ia3 += strideA1;
}
it -= strideTau;
ia1 -= del;
ia2 -= strideA2;
}
return A;
}
// EXPORTS //
module.exports = dorg2r;
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