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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.
*/
'use strict';
// MODULES //
var reinterpret = require( '@stdlib/strided/base/reinterpret-complex64' );
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
var max = require( '@stdlib/math/base/special/max' );
var min = require( '@stdlib/math/base/special/min' );
// MAIN //
/**
* Performs one of the matrix-vector operations `x = A*x` or `x = A^T*x` or `x = A^H*x` where `x` is an `N` element complex vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular band matrix, with (`K` + 1) diagonals.
*
* @private
* @param {string} uplo - specifies whether `A` is an upper or lower triangular matrix
* @param {string} trans - specifies whether `A` should be transposed, conjugate-transposed, or not transposed
* @param {string} diag - specifies whether `A` has a unit diagonal
* @param {NonNegativeInteger} N - number of elements along each dimension of `A`
* @param {NonNegativeInteger} K - number of super-diagonals or sub-diagonals of the matrix `A`
* @param {Complex64Array} A - input complex 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`
* @param {Complex64Array} x - input complex vector
* @param {integer} strideX - stride length for `x`
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @returns {Complex64Array} `x`
*
* @example
* var Complex64Array = require( '@stdlib/array/complex64' );
* var Complex64 = require( '@stdlib/complex/float32/ctor' );
*
* var A = new Complex64Array( [ 0.0, 0.0, 1.0, 1.0, 2.0, 2.0, 3.0, 3.0, 4.0, 4.0, 5.0, 5.0 ] );
* var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
*
* ctbmv( 'lower', 'no-transpose', 'non-unit', 3, 1, A, 2, 1, 0, x, 1, 0 );
* // x => <Complex64Array>[ 0.0, 2.0, 0.0, 16.0, 0.0, 46.0 ]
*/
function ctbmv( uplo, trans, diag, N, K, A, strideA1, strideA2, offsetA, x, strideX, offsetX ) { // eslint-disable-line max-params, max-len
var nonunit;
var viewA;
var viewX;
var retmp;
var imtmp;
var isrm;
var sign;
var rex0;
var imx0;
var rex1;
var imx1;
var rea;
var ima;
var ix0;
var ix1;
var sa0;
var sa1;
var oa2;
var ox;
var sx;
var oa;
var i0;
var i1;
var ia;
// Layout
isrm = isRowMajor( [ strideA1, strideA2 ] );
nonunit = ( diag === 'non-unit' );
// Reinterpret arrays to raw numeric views
viewA = reinterpret( A, 0 );
viewX = reinterpret( x, 0 );
// Set sign to handle conjugation: flip the imaginary part for conjugate-transpose
if ( trans === 'conjugate-transpose' ) {
sign = -1;
} else {
sign = 1;
}
if ( isrm ) {
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2 * 2; // offset increment for innermost loop
sa1 = strideA1 * 2; // offset increment for outermost loop
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
sa0 = strideA1 * 2; // offset increment for innermost loop
sa1 = strideA2 * 2; // offset increment for outermost loop
}
// Vector indexing base
oa = offsetA * 2;
ox = offsetX * 2;
// Vector strides
sx = strideX * 2;
if (
( !isrm && trans === 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'lower' )
) {
for ( i1 = 0; i1 < N; i1++ ) {
oa2 = oa + ( i1 * sa1 ) + ( K * sa0 );
ix1 = ox + ( i1 * sx );
rex1 = viewX[ ix1 ];
imx1 = viewX[ ix1 + 1 ];
if ( nonunit ) {
rea = viewA[ oa2 ];
ima = sign * viewA[ oa2 + 1 ];
retmp = f32( ( rea * rex1 ) - ( ima * imx1 ) );
imtmp = f32( ( rea * imx1 ) + ( ima * rex1 ) );
} else {
retmp = rex1;
imtmp = imx1;
}
for ( i0 = i1 + 1; i0 <= min( N - 1, i1 + K ); i0++ ) {
ix0 = ox + ( i0 * sx );
ia = oa2 + ( (i0 - i1) * ( sa1 - sa0 ) );
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex0 = viewX[ ix0 ];
imx0 = viewX[ ix0 + 1 ];
retmp += f32( ( rea * rex0 ) - ( ima * imx0 ) );
imtmp += f32( ( rea * imx0 ) + ( ima * rex0 ) );
}
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
}
return x;
}
if (
( !isrm && trans === 'no-transpose' && uplo === 'lower' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'upper' )
) {
for ( i1 = N - 1; i1 >= 0; i1-- ) {
oa2 = oa + ( i1 * sa1 );
ix1 = ox + ( i1 * sx );
rex1 = viewX[ ix1 ];
imx1 = viewX[ ix1 + 1 ];
if ( nonunit ) {
rea = viewA[ oa2 ];
ima = sign * viewA[ oa2 + 1 ];
retmp = f32( ( rea * rex1 ) - ( ima * imx1 ) );
imtmp = f32( ( rea * imx1 ) + ( ima * rex1 ) );
} else {
retmp = rex1;
imtmp = imx1;
}
for ( i0 = max( 0, i1 - K ); i0 < i1; i0++ ) {
ix0 = ox + ( i0 * sx );
ia = oa2 + ( ( i0 - i1 ) * ( sa1 - sa0 ) );
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex0 = viewX[ ix0 ];
imx0 = viewX[ ix0 + 1 ];
retmp += f32( ( rea * rex0 ) - ( ima * imx0 ) );
imtmp += f32( ( rea * imx0 ) + ( ima * rex0 ) );
}
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
}
return x;
}
if (
( !isrm && trans !== 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans === 'no-transpose' && uplo === 'lower' )
) {
for ( i1 = N - 1; i1 >= 0; i1-- ) {
oa2 = oa + ( i1 * sa1 ) + ( K * sa0 );
ix1 = ox + ( i1 * sx );
rex1 = viewX[ ix1 ];
imx1 = viewX[ ix1 + 1 ];
if ( nonunit ) {
rea = viewA[ oa2 ];
ima = sign * viewA[ oa2 + 1 ];
retmp = f32( ( rea * rex1 ) - ( ima * imx1 ) );
imtmp = f32( ( rea * imx1 ) + ( ima * rex1 ) );
} else {
retmp = rex1;
imtmp = imx1;
}
for ( i0 = max( 0, i1 - K ); i0 < i1; i0++ ) {
ix0 = ox + ( i0 * sx );
ia = oa2 + ( ( i0 - i1 ) * sa0 );
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex0 = viewX[ ix0 ];
imx0 = viewX[ ix0 + 1 ];
retmp += f32( ( rea * rex0 ) - ( ima * imx0 ) );
imtmp += f32( ( rea * imx0 ) + ( ima * rex0 ) );
}
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
}
return x;
}
// ( !isrm && trans !== 'no-transpose' && uplo === 'lower' ) || ( isrm && trans === 'no-transpose' && uplo === 'upper' )
for ( i1 = 0; i1 < N; i1++ ) {
oa2 = oa + ( i1 * sa1 );
ix1 = ox + ( i1 * sx );
rex1 = viewX[ ix1 ];
imx1 = viewX[ ix1 + 1 ];
if ( nonunit ) {
rea = viewA[ oa2 ];
ima = sign * viewA[ oa2 + 1 ];
retmp = f32( ( rea * rex1 ) - ( ima * imx1 ) );
imtmp = f32( ( rea * imx1 ) + ( ima * rex1 ) );
} else {
retmp = rex1;
imtmp = imx1;
}
for ( i0 = i1 + 1; i0 <= min( N - 1, i1 + K ); i0++ ) {
ix0 = ox + ( i0 * sx );
ia = oa2 + ( ( i0 - i1 ) * sa0 );
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex0 = viewX[ ix0 ];
imx0 = viewX[ ix0 + 1 ];
retmp += f32( ( rea * rex0 ) - ( ima * imx0 ) );
imtmp += f32( ( rea * imx0 ) + ( ima * rex0 ) );
}
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
}
return x;
}
// EXPORTS //
module.exports = ctbmv;
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