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refactor: split base
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‎lib/node_modules/@stdlib/lapack/base/dlarfb/lib/base.js

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‎lib/node_modules/@stdlib/lapack/base/dlarfb/lib/index.js

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*
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* dlarfb( 'row-major', 'left', 'transpose', 'forward', 'columns', 3, 3, 3, V, 3, T, 3, C, 3, work, 3 );
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*
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* // C => <Float64Array>[ -1350.00, -1400.00, -1450.00, -30961.00, -32102.00, -33243.00, -266612.00, -275464.00, -284316.00 ]
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* // C => <Float64Array>[ -1350.0, -1400.0, -1450.0, -30961.0, -32102.0, -33243.0, -266612.0, -275464.0, -284316.0 ]
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*/
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// MODULES //

‎lib/node_modules/@stdlib/lapack/base/dlarfb/lib/left-backward-columns.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
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var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
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var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
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var dtrmm = require( './dtrmm.js' );
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// MAIN //
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/**
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* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the left, with backward direction and column storage.
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*
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* @private
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* @param {NonNegativeInteger} M - number of rows of the matrix C
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* @param {NonNegativeInteger} N - number of columns of the matrix C
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* @param {NonNegativeInteger} K - order of the matrix T
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* @param {Float64Array} V - input matrix
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* @param {integer} strideV1 - stride of the first dimension of V
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* @param {integer} strideV2 - stride of the second dimension of V
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* @param {integer} offsetV - index offset for V
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* @param {Float64Array} T - input matrix
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* @param {integer} strideT1 - stride of the first dimension of T
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* @param {integer} strideT2 - stride of the second dimension of T
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* @param {integer} offsetT - index offset for T
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* @param {Float64Array} C - input matrix
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* @param {integer} strideC1 - stride of the first dimension of C
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* @param {integer} strideC2 - stride of the second dimension of C
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* @param {integer} offsetC - index offset for C
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* @param {Float64Array} work - work array
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* @param {integer} strideWork1 - stride of the first dimension of work
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* @param {integer} strideWork2 - stride of the second dimension of work
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* @param {integer} offsetWork - index offset for work
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* @param {string} trans - specifies whether to apply H or H^T
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* @returns {Float64Array} updated matrix C
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
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* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
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* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
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* var work = new Float64Array( 9 );
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*
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* var result = leftBackwardColumns( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
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* // returns <Float64Array>[ -557890.0, -592880.0, -627870.0, -596341.0, -632662.0, -668983.0, -7412.0, -7864.0, -8316.0 ]
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*/
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function leftBackwardColumns( 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
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var transt;
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var da0;
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var da1;
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var db0;
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var db1;
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var sh;
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var sa;
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var sb;
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var S0;
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var S1;
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var ia;
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var ib;
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var ic;
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var iv;
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var iw;
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var i;
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var j;
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var o;
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// Quick return if possible
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if ( M <= 0 || N <= 0 ) {
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return C;
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}
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if ( trans === 'no-transpose' ) {
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transt = 'transpose';
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} else {
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transt = 'no-transpose';
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}
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/* Let V = ( V1 )
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* ( V2 ) (last K rows)
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* Where V2 is unit upper triangular.
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*/
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/* Form H * C or H^T * C where C = ( C1 )
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* ( C2 )
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* W := C**T * V = (C1**T * V1 + C2**T * V2) (stored in WORK)
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* W := C2**T
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*/
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ic = offsetC + ( (M-K) * strideC1 );
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iw = offsetWork;
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for ( j = 0; j < K; j++ ) {
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iw = offsetWork + ( j * strideWork2 );
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dcopy( N, C, strideC2, ic, work, strideWork1, iw );
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ic += strideC1;
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iw += strideWork2;
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}
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// W := W * V2
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iv = offsetV + ( (M-K) * strideV1 );
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dtrmm( 'right', 'upper', 'no-transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
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if ( M > K ) {
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// W := W + C1**T * V1
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dgemm( 'transpose', 'no-transpose', N, K, M-K, 1.0, C, strideC1, strideC2, offsetC, V, strideV1, strideV2, offsetV, 1.0, work, strideWork1, strideWork2, offsetWork );
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}
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// W := W * T**T or W * T
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dtrmm( 'right', 'lower', transt, 'non-unit', N, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
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// C := C - V * W**T
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if ( M > K ) {
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// C1 := C1 - V1 * W**T
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dgemm( 'no-transpose', 'transpose', M-K, N, K, -1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork, 1.0, C, strideC1, strideC2, offsetC );
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}
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// W := W * V2**T
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iv = offsetV + ( (M-K) * strideV1 );
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dtrmm( 'right', 'upper', 'transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
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// C2 := C2 - W**T
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o = loopOrder( [ K, N ], [ strideC2, strideC1 ], [ strideWork1, strideWork2 ] ); // eslint-disable-line max-len
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sh = o.sh;
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sa = o.sx;
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sb = o.sy;
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S0 = sh[ 0 ];
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S1 = sh[ 1 ];
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da0 = sa[ 0 ];
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da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
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db0 = sb[ 0 ];
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db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
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ia = offsetC + ( (M-K) * strideC1 );
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ib = offsetWork;
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for ( j = 0; j < S1; j++ ) {
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for ( i = 0; i < S0; i++ ) {
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C[ ia ] -= work[ ib ];
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ia += da0;
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ib += db0;
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}
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ia += da1;
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ib += db1;
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}
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return C;
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}
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// EXPORTS //
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module.exports = leftBackwardColumns;

‎lib/node_modules/@stdlib/lapack/base/dlarfb/lib/left-backward-rows.js

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2025 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var dgemm = require( '@stdlib/blas/base/dgemm' ).ndarray;
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var dcopy = require( '@stdlib/blas/base/dcopy' ).ndarray;
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var loopOrder = require( '@stdlib/ndarray/base/unary-loop-interchange-order' );
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var dtrmm = require( './dtrmm.js' );
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// MAIN //
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/**
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* Applies a real block reflector H or its transpose H^T to a real M by N matrix C from the left, with backward direction and row storage.
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*
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* @private
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* @param {NonNegativeInteger} M - number of rows of the matrix C
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* @param {NonNegativeInteger} N - number of columns of the matrix C
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* @param {NonNegativeInteger} K - order of the matrix T
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* @param {Float64Array} V - input matrix
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* @param {integer} strideV1 - stride of the first dimension of V
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* @param {integer} strideV2 - stride of the second dimension of V
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* @param {integer} offsetV - index offset for V
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* @param {Float64Array} T - input matrix
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* @param {integer} strideT1 - stride of the first dimension of T
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* @param {integer} strideT2 - stride of the second dimension of T
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* @param {integer} offsetT - index offset for T
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* @param {Float64Array} C - input matrix
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* @param {integer} strideC1 - stride of the first dimension of C
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* @param {integer} strideC2 - stride of the second dimension of C
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* @param {integer} offsetC - index offset for C
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* @param {Float64Array} work - work array
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* @param {integer} strideWork1 - stride of the first dimension of work
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* @param {integer} strideWork2 - stride of the second dimension of work
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* @param {integer} offsetWork - index offset for work
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* @param {string} trans - specifies whether to apply H or H^T
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* @returns {Float64Array} updated matrix C
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*
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* @example
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* var Float64Array = require( '@stdlib/array/float64' );
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*
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* var V = new Float64Array( [ 10.0, 40.0, 70.0, 20.0, 50.0, 80.0, 30.0, 60.0, 90.0 ] );
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* var T = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
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* var C = new Float64Array( [ 11.0, 12.0, 13.0, 21.0, 22.0, 23.0, 31.0, 32.0, 33.0 ] );
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* var work = new Float64Array( 9 );
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*
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* var result = leftBackwardRows( 3, 3, 3, V, 3, 1, 0, T, 3, 1, 0, C, 3, 1, 0, work, 3, 1, 0, 'no-transpose' );
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* // returns <Float64Array>[ -155530.0, -164560.0, -173590.0, -292241.0, -308662.0, -325083.0, -4832.0, -5104.0, -5376.0 ]
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*/
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function leftBackwardRows( 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
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var transt;
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var da0;
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var da1;
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var db0;
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var db1;
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var i0;
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var i1;
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var sh;
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var sa;
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var sb;
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var S0;
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var S1;
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var ia;
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var ib;
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var ic;
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var iv;
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var iw;
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var j;
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var o;
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// Quick return if possible
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if ( M <= 0 || N <= 0 ) {
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return C;
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}
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if ( trans === 'no-transpose' ) {
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transt = 'transpose';
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} else {
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transt = 'no-transpose';
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}
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/* Let V = ( V1 V2 ) (V2: last K columns)
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* Where V2 is unit lower triangular.
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*/
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/* Form H * C or H^T * C where C = ( C1 )
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* ( C2 )
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* W := C**T * V**T = (C1**T * V1**T + C2**T * V2**T) (stored in WORK)
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* W := C2**T
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*/
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ic = offsetC;
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iw = offsetWork;
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for ( j = 0; j < K; j++ ) {
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dcopy( N, C, strideC2, ic, work, strideWork1, iw );
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ic += strideC1;
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iw += strideWork2;
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}
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// W := W * V2**T
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iv = offsetV + ( (M-K) * strideV2 );
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dtrmm( 'right', 'lower', 'transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
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if ( M > K ) {
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// W := W + C1**T * V1**T
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dgemm( 'transpose', 'transpose', N, K, M-K, 1.0, C, strideC1, strideC2, offsetC, V, strideV1, strideV2, offsetV, 1.0, work, strideWork1, strideWork2, offsetWork );
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}
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// W := W * T**T or W * T
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dtrmm( 'right', 'lower', transt, 'non-unit', N, K, 1.0, T, strideT1, strideT2, offsetT, work, strideWork1, strideWork2, offsetWork );
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// C := C - V**T * W**T
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if ( M > K ) {
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// C1 := C1 - V1**T * W**T
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dgemm( 'transpose', 'transpose', M-K, N, K, -1.0, V, strideV1, strideV2, offsetV, work, strideWork1, strideWork2, offsetWork, 1.0, C, strideC1, strideC2, offsetC );
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}
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// W := W * V2
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iv = offsetV + ( (M-K) * strideV2 );
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dtrmm( 'right', 'lower', 'no-transpose', 'unit', N, K, 1.0, V, strideV1, strideV2, iv, work, strideWork1, strideWork2, offsetWork );
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// C2 := C2 - W**T
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o = loopOrder( [ K, N ], [ strideC1, strideC2 ], [ strideWork2, strideWork1 ] ); // eslint-disable-line max-len
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sh = o.sh;
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sa = o.sx;
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sb = o.sy;
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// Extract loop variables for loop interchange
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S0 = sh[ 0 ];
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S1 = sh[ 1 ];
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da0 = sa[ 0 ];
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da1 = sa[ 1 ] - ( S0 * sa[ 0 ] );
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db0 = sb[ 0 ];
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db1 = sb[ 1 ] - ( S0 * sb[ 0 ] );
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// Set pointers to first indexed elements
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ia = offsetC + ( (M-K) * strideC1 );
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ib = offsetWork;
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// Iterate over matrix dimensions with optimized loop order
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for ( i1 = 0; i1 < S1; i1++ ) {
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for ( i0 = 0; i0 < S0; i0++ ) {
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C[ ia ] -= work[ ib ];
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ia += da0;
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ib += db0;
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}
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ia += da1;
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ib += db1;
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}
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return C;
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}
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// EXPORTS //
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module.exports = leftBackwardRows;

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