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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' );
// MAIN //
/**
* Solves one of the systems of equations `A*x = b` or `A^T*x = b` or `A^H*x = b` where `b` and `x` are `N` element complex vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular complex matrix.
*
* @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 {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`
* @param {Complex64Array} x - input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @returns {Complex64Array} `x`
*
* @example
* var Complex64Array = require( '@stdlib/array/complex64' );
*
* var A = new Complex64Array( [ 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 2.0, 2.0, 4.0, 4.0, 0.0, 0.0, 3.0, 3.0, 5.0, 5.0, 6.0, 6.0 ] );
* var x = new Complex64Array( [ 1.0, 1.0, 2.0, 2.0, 3.0, 3.0 ] );
*
* ctrsv( 'lower', 'no-transpose', 'non-unit', 3, A, 3, 1, 0, x, 1, 0 );
* // x => <Complex64Array>[ 1.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
*/
function ctrsv( uplo, trans, diag, N, 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 magsq;
var remul;
var immul;
var ixend;
var isrm;
var sign;
var doa2;
var rex;
var imx;
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 ] );
// Diagonal
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;
doa2 = sa1 + sa0;
if (
( !isrm && uplo === 'upper' && trans === 'no-transpose' ) ||
( isrm && uplo === 'lower' && trans !== 'no-transpose' )
) {
ix1 = ox + ( ( N - 1 ) * sx );
oa2 = oa + ( doa2 * ( N - 1 ) );
for ( i1 = N - 1; i1 >= 0; i1-- ) {
rex = viewX[ ix1 ];
imx = viewX[ ix1 + 1 ];
if ( rex !== 0.0 || imx !== 0.0 ) {
if ( nonunit ) {
ia = oa2;
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
magsq = f32( ( rea * rea ) + ( ima * ima ) );
retmp = f32( f32( ( rex * rea ) + ( imx * ima ) ) / magsq );
imtmp = f32( f32( ( imx * rea ) - ( rex * ima ) ) / magsq );
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
} else {
retmp = rex;
imtmp = imx;
}
ia = oa2 - sa0;
ix0 = ix1 - sx;
for ( i0 = i1 - 1; i0 >= 0; i0-- ) {
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex = viewX[ ix0 ];
imx = viewX[ ix0 + 1 ];
remul = f32( ( retmp * rea ) - ( imtmp * ima ) );
immul = f32( ( retmp * ima ) + ( imtmp * rea ) );
viewX[ ix0 ] = f32( rex - remul );
viewX[ ix0 + 1 ] = f32( imx - immul );
ix0 -= sx;
ia -= sa0;
}
}
oa2 -= doa2;
ix1 -= sx;
}
return x;
}
if (
( !isrm && uplo === 'lower' && trans === 'no-transpose' ) ||
( isrm && uplo === 'upper' && trans !== 'no-transpose' )
) {
ix1 = ox;
oa2 = oa;
for ( i1 = 0; i1 < N; i1++ ) {
rex = viewX[ ix1 ];
imx = viewX[ ix1 + 1 ];
if ( rex !== 0.0 || imx !== 0.0 ) {
if ( nonunit ) {
ia = oa2;
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
magsq = f32( ( rea * rea ) + ( ima * ima ) );
retmp = f32( f32( ( rex * rea ) + ( imx * ima ) ) / magsq );
imtmp = f32( f32( ( imx * rea ) - ( rex * ima ) ) / magsq );
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
} else {
retmp = rex;
imtmp = imx;
}
ia = oa2 + sa0;
ix0 = ix1 + sx;
for ( i0 = i1 + 1; i0 < N; i0++ ) {
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex = viewX[ ix0 ];
imx = viewX[ ix0 + 1 ];
remul = f32( ( retmp * rea ) - ( imtmp * ima ) );
immul = f32( ( retmp * ima ) + ( imtmp * rea ) );
viewX[ ix0 ] = f32( rex - remul );
viewX[ ix0 + 1 ] = f32( imx - immul );
ia += sa0;
ix0 += sx;
}
}
oa2 += doa2;
ix1 += sx;
}
return x;
}
if (
( !isrm && uplo === 'upper' && trans !== 'no-transpose' ) ||
( isrm && uplo === 'lower' && trans === 'no-transpose' )
) {
ix1 = ox;
oa2 = oa;
for ( i1 = 0; i1 < N; i1++ ) {
rex = viewX[ ix1 ];
imx = viewX[ ix1 + 1 ];
retmp = rex;
imtmp = imx;
ix0 = ox;
ia = oa2;
for ( i0 = 0; i0 < i1; i0++ ) {
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex = viewX[ ix0 ];
imx = viewX[ ix0 + 1 ];
retmp = f32( retmp - f32( ( rex * rea ) - ( imx * ima ) ) );
imtmp = f32( imtmp - f32( ( rex * ima ) + ( imx * rea ) ) );
ix0 += sx;
ia += sa0;
}
if ( nonunit ) {
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
magsq = f32( ( rea * rea ) + ( ima * ima ) );
remul = f32( ( retmp * rea ) + ( imtmp * ima ) );
immul = f32( ( imtmp * rea ) - ( retmp * ima ) );
retmp = f32( remul / magsq );
imtmp = f32( immul / magsq );
}
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
ix1 += sx;
oa2 += sa1;
}
return x;
}
// ( !isrm && uplo === 'lower' && trans !== 'no-transpose' ) || ( isrm && uplo === 'upper' && trans === 'no-transpose' )
ix1 = ox + ( ( N - 1 ) * sx );
ixend = ix1;
oa2 = oa + ( doa2 * ( N - 1 ) );
for ( i1 = N - 1; i1 >= 0; i1-- ) {
rex = viewX[ ix1 ];
imx = viewX[ ix1 + 1 ];
retmp = rex;
imtmp = imx;
ix0 = ixend;
ia = oa2;
for ( i0 = N - 1; i0 > i1; i0-- ) {
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
rex = viewX[ ix0 ];
imx = viewX[ ix0 + 1 ];
retmp = f32( retmp - f32( ( rex * rea ) - ( imx * ima ) ) );
imtmp = f32( imtmp - f32( ( rex * ima ) + ( imx * rea ) ) );
ia -= sa0;
ix0 -= sx;
}
if ( nonunit ) {
rea = viewA[ ia ];
ima = sign * viewA[ ia + 1 ];
magsq = f32( ( rea * rea ) + ( ima * ima ) );
remul = f32( ( retmp * rea ) + ( imtmp * ima ) );
immul = f32( ( imtmp * rea ) - ( retmp * ima ) );
retmp = f32( remul / magsq );
imtmp = f32( immul / magsq );
}
viewX[ ix1 ] = retmp;
viewX[ ix1 + 1 ] = imtmp;
ix1 -= sx;
oa2 -= sa1;
}
return x;
}
// EXPORTS //
module.exports = ctrsv;
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