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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 reinterpret = require( '@stdlib/strided/base/reinterpret-complex64' );
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
// MAIN //
/**
* Performs the hermitian rank 1 operation `A = alpha*x*x**H + A`, where `alpha` is a real scalar, `X` is an `N` element vector and `A` is an `N` by `N` hermitian matrix.
*
* @private
* @param {string} uplo - specifies whether `A` is an upper or lower triangular part of matrix is supplied.
* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
* @param {number} alpha - scalar
* @param {Complex64Array} x - input array
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting `x` index
* @param {Complex64Array} 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 {Complex64Array} `A`
*
* @example
* var Complex64Array = require( '@stdlib/array/complex64' );
*
* var x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0 ] );
* var A = new Complex64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 3.0, 4.0, 0.0 ] );
*
* cher( 'lower', x.length, 2.0, x, 1, 0, A, 2, 1, 0 );
* // A => <Complex64Array>[ 11.0, 0.0, 0.0, 0.0, 24.0, -1.0, 54.0, 0.0 ]
*/
function cher( uplo, N, alpha, x, strideX, offsetX, A, strideA1, strideA2, offsetA ) {
var viewX;
var viewA;
var isrm;
var ix1;
var ix0;
var re0;
var re1;
var im0;
var im1;
var idx;
var sa0;
var sa1;
var i1;
var i0;
var ix;
var ia;
var re;
var im;
var sx;
viewX = reinterpret( x, 0 );
viewA = reinterpret( A, 0 );
isrm = isRowMajor( [ strideA1, strideA2 ] );
if ( isrm ) {
sa0 = strideA2 * 2; // Stride for columns (inner dimension)
sa1 = strideA1 * 2; // Stride for rows (outer dimension)
} else {
sa0 = strideA1 * 2; // Stride for rows (inner dimension)
sa1 = strideA2 * 2; // Stride for columns (outer dimension)
}
ix = offsetX * 2;
ia = offsetA * 2;
sx = strideX * 2;
if ( ( isrm && uplo === 'upper' ) || ( !isrm && uplo === 'lower' ) ) {
for ( i1 = 0; i1 < N; i1++ ) {
ix1 = ix + ( i1 * sx );
re0 = viewX[ ix1 ];
im0 = viewX[ ix1 + 1 ];
for ( i0 = i1; i0 < N; i0++ ) {
ix0 = ix + ( i0 * sx );
re1 = viewX[ ix0 ];
im1 = viewX[ ix0 + 1 ];
re = alpha * ( ( re0 * re1 ) + ( im0 * im1 ) );
im = alpha * ( ( im0 * re1 ) - ( re0 * im1 ) );
idx = ia + ( i0 * sa0 ) + ( i1 * sa1 );
viewA[ idx ] += re;
viewA[ idx + 1 ] += im;
if ( i0 === i1 ) {
viewA[ idx + 1 ] = 0.0;
}
}
}
return A;
}
// ( isrm && uplo === 'lower' ) || ( !isrm && uplo === 'upper' )
for ( i1 = 0; i1 < N; i1++ ) {
ix1 = ix + ( i1 * sx );
re0 = viewX[ ix1 ];
im0 = viewX[ ix1 + 1 ];
for ( i0 = 0; i0 <= i1; i0++ ) {
ix0 = ix + ( i0 * sx );
re1 = viewX[ ix0 ];
im1 = viewX[ ix0 + 1 ];
re = alpha * ( ( re0 * re1 ) + ( im0 * im1 ) );
im = alpha * ( ( im0 * re1 ) - ( re0 * im1 ) );
idx = ia + ( i0 * sa0 ) + ( i1 * sa1 );
viewA[ idx ] += re;
viewA[ idx + 1 ] += im;
if ( i0 === i1 ) {
viewA[ idx + 1 ] = 0.0;
}
}
}
return A;
}
// EXPORTS //
module.exports = cher;
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