Press n or j to go to the next uncovered block, b, p or k for the previous block.
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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.
*/
/* eslint-disable max-len, max-params */
'use strict';
// MODULES //
var max = require( '@stdlib/math/base/special/max' );
var dormlq = require( './dormlq.js' );
var dormqr = require( './dormqr.js' );
// 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 //
/**
* Multiply a general matrix by the orthogonal matrix from a bi-diagonal reduction determined by `DGEBRD`.
*
* ## Notes
*
* - `Q` and `P^T` are the orthogonal matrices determined by `DGEBRD` when reducing a real matrix `A` to bi-diagonal form, `A = Q * B * P^T`.
*
* - If VECT = 'Q', `DORMBR` overwrites the general real `M` by `N` matrix `C` with,
*
* - `Q * C` if SIDE = 'left' and TRANS = 'no-transpose', or
* - `Q^T * C` if SIDE = 'left' and TRANS = 'transpose', or
* - `C * Q` if SIDE = 'right' and TRANS = 'no-transpose', or
* - `C * Q^T` if SIDE = 'right' and TRANS = 'transpose'.
*
* - If VECT = 'P', `DORMBR` overwrites the general real `M` by `N` matrix `C` with,
*
* - `P * C` if SIDE = 'left' and TRANS = 'no-transpose', or
* - `P^T * C` if SIDE = 'left' and TRANS = 'transpose', or
* - `C * P` if SIDE = 'right' and TRANS = 'no-transpose', or
* - `C * P^T` if SIDE = 'right' and TRANS = 'transpose'.
*
* - If SIDE = 'left', `LWORK >= max(1,N)`.
*
* - If SIDE = 'right', `LWORK >= max(1,M)`.
*
* - For optimum performance, `LWORK >= N*NB` if SIDE = 'left', and `LWORK >= M*NB` if SIDE = 'right', where `NB` is the optimal blocksize.
*
* - If `LWORK = -1`, then a workspace query is assumed; the routine only calculates the optimal size of the `WORK` array and returns this value as the first entry of the `WORK` array.
*
* @private
* @param {string} vect - specifies whether the matrix `Q` or the matrix `P` is applied
* @param {string} side - specifies the side of multiplication with `C`
* @param {string} trans - `'no-transpose'` for `Q`, `'transpose'` for `Q^T`
* @param {NonNegativeInteger} M - number of rows of `C`
* @param {NonNegativeInteger} N - number of columns of `C`
* @param {NonNegativeInteger} K - number of elementary reflectors
* @param {Float64Array} A - reflector vectors from `DGEBRD`
* @param {integer} strideA1 - stride of the first dimension of A
* @param {integer} strideA2 - stride of the second dimension of A
* @param {NonNegativeInteger} offsetA - starting index for A
* @param {Float64Array} TAU - scalar factors of reflectors
* @param {integer} strideTAU - stride for TAU
* @param {NonNegativeInteger} offsetTAU - starting index for TAU
* @param {Float64Array} C - input/output 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 for `WORK`
* @param {NonNegativeInteger} offsetWORK - starting index for `WORK`
* @param {NonNegativeInteger} LWORK - dimension of the array `WORK`
* @returns {integer} status code (0 if successful)
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1, 0, 0 ] );
* var TAU = new Float64Array( [ 2 ] );
* var C = new Float64Array( [ 1, 3, 5, 2, 4, 6 ] );
* var WORK = new Float64Array( 3 );
*
* var info = dormbr( 'Q', 'left', 'no-transpose', 2, 3, 1, A, 2, 1, 0, TAU, 1, 0, C, 3, 1, 0, WORK, 1, 0, 3 );
* // returns 0
* // C => <Float64Array>[ -1, -3, -5, 2, 4, 6 ]
* // WORK => <Float64Array>[ 96, 0, 0 ]
*/
function dormbr( vect, side, trans, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, C, strideC1, strideC2, offsetC, WORK, strideWORK, offsetWORK, LWORK ) {
var isTrans;
var applyq;
var isLeft;
var lquery;
var transt;
var lwkopt;
var mi;
var ni;
var i1;
var i2;
var nb;
var nq;
var nw;
applyq = ( vect === 'Q' );
isLeft = isLeftSide( side );
isTrans = ( trans === 'transpose' );
lquery = ( LWORK === -1 );
// NQ is the order of Q or P and NW is the minimum dimension of WORK...
if ( isLeft ) {
nq = M;
nw = max( 1, N );
} else {
nq = N;
nw = max( 1, M );
}
nb = 32;
lwkopt = nw*nb;
WORK[ offsetWORK ] = lwkopt;
if ( lquery ) {
return 0;
}
// Quick return:
WORK[ offsetWORK ] = 1;
if ( M === 0 || N === 0 ) {
return 0;
}
if ( applyq ) {
// Apply Q...
if ( nq >= K ) {
// Q was determined by a call to DGEBRD with NQ >= K
dormqr( side, trans, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, C, strideC1, strideC2, offsetC, WORK, strideWORK, offsetWORK, LWORK );
} else if ( nq > 1 ) {
// Q was determined by a call to DGEBRD with NQ < K
if ( isLeft ) {
mi = M - 1;
ni = N;
i1 = 1;
i2 = 0;
} else {
mi = M;
ni = N - 1;
i1 = 0;
i2 = 1;
}
dormqr( side, trans, mi, ni, nq - 1, A, strideA1, strideA2, offsetA + strideA1, TAU, strideTAU, offsetTAU, C, strideC1, strideC2, offsetC + ( i1 * strideC1 ) + ( i2 * strideC2 ), WORK, strideWORK, offsetWORK, LWORK );
}
} else {
// Apply P...
if ( isTrans ) {
transt = 'no-transpose';
} else {
transt = 'transpose';
}
if ( nq > K ) {
// P was determined by a call to DGEBRD with NQ > K
dormlq( side, transt, M, N, K, A, strideA1, strideA2, offsetA, TAU, strideTAU, offsetTAU, C, strideC1, strideC2, offsetC, WORK, strideWORK, offsetWORK, LWORK );
} else if ( nq > 1 ) {
// P was determined by a call to DGEBRD with NQ <= K
if ( isLeft ) {
mi = M - 1;
ni = N;
i1 = 1;
i2 = 0;
} else {
mi = M;
ni = N - 1;
i1 = 0;
i2 = 1;
}
dormlq( side, transt, mi, ni, nq - 1, A, strideA1, strideA2, offsetA + strideA2, TAU, strideTAU, offsetTAU, C, strideC1, strideC2, offsetC + ( i1 * strideC1 ) + ( i2 * strideC2 ), WORK, strideWORK, offsetWORK, LWORK );
}
}
WORK[ offsetWORK ] = lwkopt;
return 0;
}
// EXPORTS //
module.exports = dormbr;
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