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* @license Apache-2.0
*
* Copyright (c) 2024 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 isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
// MAIN //
/**
* Performs the symmetric rank 2 operation `A = α*x*y^T + α*y*x^T + A` where `α` is a scalar, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix.
*
* @private
* @param {string} uplo - specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced
* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
* @param {number} alpha - scalar
* @param {Float64Array} x - first input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @param {Float64Array} y - second input vector
* @param {integer} strideY - `y` stride length
* @param {NonNegativeInteger} offsetY - starting index for `y`
* @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 - starting index for `A`
* @returns {Float64Array} `A`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] ); // => [ [ 1.0, 2.0, 3.0 ], [ 0.0, 1.0, 2.0 ], [ 0.0, 0.0, 1.0 ] ]
* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
* var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );
*
* dsyr2( 'upper', 3, 1.0, x, 1, 0, y, 1, 0, A, 3, 1, 0 );
* // A => <Float64Array>[ 3.0, 6.0, 9.0, 0.0, 9.0, 14.0, 0.0, 0.0, 19.0 ]
*/
function dsyr2( uplo, N, alpha, x, strideX, offsetX, y, strideY, offsetY, A, strideA1, strideA2, offsetA ) { // eslint-disable-line max-len, max-params
var tmp1;
var tmp2;
var isrm;
var ix0;
var ix1;
var iy0;
var iy1;
var sa0;
var sa1;
var i0;
var i1;
var oa;
var ox;
var oy;
isrm = isRowMajor( [ strideA1, strideA2 ] );
if ( isrm ) { // row-major
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2; // stride for innermost loop
sa1 = strideA1; // stride for outermost loop
} else { // column-major
// For column-major matrices, the first dimension has the fastest changing index...
sa0 = strideA1; // stride for innermost loop
sa1 = strideA2; // stride for outermost loop
}
ox = offsetX;
oy = offsetY;
ix1 = ox;
iy1 = oy;
if (
( isrm && uplo === 'lower' ) ||
( !isrm && uplo === 'upper' )
) {
for ( i1 = 0; i1 < N; i1++ ) {
if ( ( x[ ix1 ] !== 0.0 ) || ( y[ iy1 ] !== 0.0 ) ) {
tmp1 = alpha * y[ iy1 ];
tmp2 = alpha * x[ ix1 ];
oa = offsetA + (sa1*i1);
ix0 = ox;
iy0 = oy;
for ( i0 = 0; i0 <= i1; i0++ ) {
A[ oa+(sa0*i0) ] += ( x[ ix0 ] * tmp1 ) + ( y[ iy0 ] * tmp2 ); // eslint-disable-line max-len
ix0 += strideX;
iy0 += strideY;
}
}
ix1 += strideX;
iy1 += strideY;
}
return A;
}
// ( isrm && uplo === 'upper' ) || ( !isrm && uplo === 'lower' )
for ( i1 = 0; i1 < N; i1++ ) {
if ( ( x[ ix1 ] !== 0.0 ) || ( y[ iy1 ] !== 0.0 ) ) {
tmp1 = alpha * y[ iy1 ];
tmp2 = alpha * x[ ix1 ];
oa = offsetA + (sa1*i1);
ix0 = ix1;
iy0 = iy1;
for ( i0 = i1; i0 < N; i0++ ) {
A[ oa+(sa0*i0) ] += ( x[ ix0 ] * tmp1 ) + ( y[ iy0 ] * tmp2 );
ix0 += strideX;
iy0 += strideY;
}
}
ix1 += strideX;
iy1 += strideY;
}
return A;
}
// EXPORTS //
module.exports = dsyr2;
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