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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 dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
var dtrmm = require( './dtrmm.js' );
// MAIN //
/**
* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the right, with forward direction and column storage.
*
* @private
* @param {NonNegativeInteger} M - number of rows of the matrix C
* @param {NonNegativeInteger} N - number of columns of the matrix C
* @param {NonNegativeInteger} K - order of the matrix T
* @param {Float64Array} V - input matrix
* @param {integer} strideV1 - stride of the first dimension of V
* @param {integer} strideV2 - stride of the second dimension of V
* @param {integer} offsetV - index offset for V
* @param {Float64Array} T - input matrix
* @param {integer} strideT1 - stride of the first dimension of T
* @param {integer} strideT2 - stride of the second dimension of T
* @param {integer} offsetT - index offset for T
* @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 {integer} offsetC - index offset for C
* @param {Float64Array} work - work array
* @param {integer} strideWork1 - stride of the first dimension of work
* @param {integer} strideWork2 - stride of the second dimension of work
* @param {integer} offsetWork - index offset for work
* @param {string} trans - specifies whether to apply H or H^T
* @returns {Float64Array} updated matrix C
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
* var work = new Float64Array( 9 );
*
* var result = rightForwardColumns( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
* // returns <Float64Array>[ -630.0, -14392.0, -114296.0, -1130.0, -25802.0, -202816.0, -1630.0, -37212.0, -291336.0 ]
*/
function rightForwardColumns( M, N, K, V, strideV1, strideV2, offsetV, T, strideT1, strideT2, offsetT, C, strideC1, strideC2, offsetC, work, strideWork1, strideWork2, offsetWork, trans ) { // eslint-disable-line max-params, max-len
var da0;
var da1;
var db0;
var db1;
var i0;
var i1;
var sh;
var sa;
var sb;
var S0;
var S1;
var ia;
var ib;
var ic;
var iv;
var iw;
var j;
var o;
/* Let V = ( V1 ) (first K rows)
* ( V2 )
* Where V1 is unit lower triangular.
*/
/* Form C * H or C * H^T where C = ( C1 C2 )
* W := C * V = (C1*V1 + C2*V2) (stored in WORK)
* W := C1
*/
ic = offsetC;
iw = offsetWork;
for ( j = 0; j < K; j++ ) {
dcopy( M, C, strideC1, ic, work, strideWork1, iw );
ic += strideC2;
iw += strideWork2;
}
// W := W * V1
dtrmm( 'right', 'lower', 'no-transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
if ( N > K ) {
// W := W + C2 * V2
ic = offsetC + ( K * strideC2 );
iv = offsetV + ( K * strideV1 );
dgemm( 'no-transpose', 'no-transpose', M, K, N-K, 1.0, C, strideC1, strideC2, ic, V, strideV1, strideV2, iv, 1.0, work, strideWork1, strideWork2, offsetWork );
}
// W := W * T or W * T**T
dtrmm( 'right', 'upper', trans, 'non-unit', M, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
// C := C - W * V**T
if ( N > K ) {
// C2 := C2 - W * V2**T
ic = offsetC + ( K * strideC2 );
iv = offsetV + ( K * strideV1 );
dgemm( 'no-transpose', 'transpose', M, N-K, K, -1.0, work, strideWork1, strideWork2, offsetWork, V, strideV1, strideV2, iv, 1.0, C, strideC1, strideC2, ic );
}
// W := W * V1**T
dtrmm( 'right', 'lower', 'transpose', 'unit', M, K, 1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork );
// C1 := C1 - W
o = loopOrder( [ K, M ], [ strideC2, strideC1 ], [ strideWork2, strideWork1 ] ); // eslint-disable-line max-len
sh = o.sh;
sa = o.sx;
sb = o.sy;
// Extract loop variables for loop interchange
S0 = sh[ 0 ];
S1 = sh[ 1 ];
da0 = sa[ 0 ];
da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
db0 = sb[ 0 ];
db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
// Set pointers to first indexed elements
ia = offsetC;
ib = offsetWork;
// Iterate over matrix dimensions with optimized loop order
for ( i1 = 0; i1 < S1; i1++ ) {
for ( i0 = 0; i0 < S0; i0++ ) {
C[ ia ] -= work[ ib ];
ia += da0;
ib += db0;
}
ia += da1;
ib += db1;
}
return C;
}
// EXPORTS //
module.exports = rightForwardColumns;
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