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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' );
var f32 = require( '@stdlib/number/float64/base/to-float32' );
// MAIN //
/**
* Solves one of the systems of equations `A*x = b`, `A^T*x = b`, or `A^H*x = b` where `b` and `x` are `N` element vectors and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular 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, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0 ] );
* var x = new Complex64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
*
* ctrsv( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
* // x => <Complex64Array>
*/
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 denom;
var isrm;
var sign;
var tmp;
var ima;
var imx;
var im0;
var im1;
var imd;
var ix0;
var ix1;
var oa2;
var rea;
var rex;
var re0;
var re1;
var red;
var sa0;
var sa1;
var i0;
var i1;
var ox;
var sx;
// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
viewA = reinterpret( A, 0 );
viewX = reinterpret( x, 0 );
isrm = isRowMajor( [ strideA1, strideA2 ] );
nonunit = ( diag === 'non-unit' );
if ( isrm ) {
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2 * 2; // stride for innermost loop
sa1 = strideA1 * 2; // stride for outermost loop
} else { // isColMajor
// For column-major matrices, the first dimension has the fastest changing index...
sa0 = strideA1 * 2; // stride for innermost loop
sa1 = strideA2 * 2; // stride for outermost loop
}
ox = offsetX * 2;
sx = strideX * 2;
if ( trans === 'conjugate-transpose' ) {
sign = -1;
} else {
sign = 1;
}
if (
( !isrm && trans === 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'lower' )
) {
ix1 = ox + ( ( N - 1 ) * sx );
for ( i1 = N - 1; i1 >= 0; i1-- ) {
re1 = viewX[ ix1 ];
im1 = viewX[ ix1 + 1 ];
if ( re1 !== 0.0 || im1 !== 0.0 ) {
oa2 = ( offsetA * 2 ) + ( sa1 * i1 );
if ( nonunit ) {
red = viewA[ oa2 + ( sa0 * i1 ) ];
imd = sign * viewA[ oa2 + ( sa0 * i1 ) + 1 ];
denom = f32( f32( red * red ) + f32( imd * imd ) );
tmp = re1;
re1 = f32( f32( f32( tmp * red ) + f32( im1 * imd ) ) / denom ); // eslint-disable-line max-len
im1 = f32( f32( f32( im1 * red ) - f32( tmp * imd ) ) / denom ); // eslint-disable-line max-len
viewX[ ix1 ] = re1;
viewX[ ix1 + 1 ] = im1;
}
ix0 = ix1;
for ( i0 = i1 - 1; i0 >= 0; i0-- ) {
ix0 -= sx;
rea = viewA[ oa2 + ( sa0 * i0 ) ];
ima = sign * viewA[ oa2 + ( sa0 * i0 ) + 1 ];
viewX[ ix0 ] = f32( viewX[ ix0 ] - f32( f32( re1 * rea ) - f32( im1 * ima ) ) ); // eslint-disable-line max-len
viewX[ ix0 + 1 ] = f32( viewX[ ix0 + 1 ] - f32( f32( re1 * ima ) + f32( im1 * rea ) ) ); // eslint-disable-line max-len
}
}
ix1 -= sx;
}
return x;
}
if (
( !isrm && trans === 'no-transpose' && uplo === 'lower' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'upper' )
) {
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
re1 = viewX[ ix1 ];
im1 = viewX[ ix1 + 1 ];
if ( re1 !== 0.0 || im1 !== 0.0 ) {
oa2 = ( offsetA * 2 ) + ( sa1 * i1 );
if ( nonunit ) {
red = viewA[ oa2 + ( sa0 * i1 ) ];
imd = sign * viewA[ oa2 + ( sa0 * i1 ) + 1 ];
denom = f32( f32( red * red ) + f32( imd * imd ) );
tmp = re1;
re1 = f32( f32( f32( tmp * red ) + f32( im1 * imd ) ) / denom ); // eslint-disable-line max-len
im1 = f32( f32( f32( im1 * red ) - f32( tmp * imd ) ) / denom ); // eslint-disable-line max-len
viewX[ ix1 ] = re1;
viewX[ ix1 + 1 ] = im1;
}
ix0 = ix1;
for ( i0 = i1 + 1; i0 < N; i0++ ) {
ix0 += sx;
rea = viewA[ oa2 + ( sa0 * i0 ) ];
ima = sign * viewA[ oa2 + ( sa0 * i0 ) + 1 ];
viewX[ ix0 ] = f32( viewX[ ix0 ] - f32( f32( re1 * rea ) - f32( im1 * ima ) ) ); // eslint-disable-line max-len
viewX[ ix0 + 1 ] = f32( viewX[ ix0 + 1 ] - f32( f32( re1 * ima ) + f32( im1 * rea ) ) ); // eslint-disable-line max-len
}
}
ix1 += sx;
}
return x;
}
if (
( !isrm && trans !== 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans === 'no-transpose' && uplo === 'lower' )
) {
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
re0 = viewX[ ix1 ];
im0 = viewX[ ix1 + 1 ];
oa2 = ( offsetA * 2 ) + ( sa1 * i1 );
ix0 = ox;
for ( i0 = 0; i0 <= i1 - 1; i0++ ) {
rea = viewA[ oa2 + ( sa0 * i0 ) ];
ima = sign * viewA[ oa2 + ( sa0 * i0 ) + 1 ];
rex = viewX[ ix0 ];
imx = viewX[ ix0 + 1 ];
re0 = f32( re0 - f32( f32( rea * rex ) - f32( ima * imx ) ) ); // eslint-disable-line max-len
im0 = f32( im0 - f32( f32( rea * imx ) + f32( ima * rex ) ) ); // eslint-disable-line max-len
ix0 += sx;
}
if ( nonunit ) {
red = viewA[ oa2 + ( sa0 * i1 ) ];
imd = sign * viewA[ oa2 + ( sa0 * i1 ) + 1 ];
denom = f32( f32( red * red ) + f32( imd * imd ) );
tmp = re0;
re0 = f32( f32( f32( tmp * red ) + f32( im0 * imd ) ) / denom ); // eslint-disable-line max-len
im0 = f32( f32( f32( im0 * red ) - f32( tmp * imd ) ) / denom ); // eslint-disable-line max-len
}
viewX[ ix1 ] = re0;
viewX[ ix1 + 1 ] = im0;
ix1 += sx;
}
return x;
}
// ( !isrm && trans !== 'no-transpose' && uplo === 'lower' ) || ( isrm && trans === 'no-transpose' && uplo === 'upper' )
ox += ( N - 1 ) * sx;
ix1 = ox;
for ( i1 = N - 1; i1 >= 0; i1-- ) {
re0 = viewX[ ix1 ];
im0 = viewX[ ix1 + 1 ];
oa2 = ( offsetA * 2 ) + ( sa1 * i1 );
ix0 = ox;
for ( i0 = N - 1; i0 > i1; i0-- ) {
rea = viewA[ oa2 + ( sa0 * i0 ) ];
ima = sign * viewA[ oa2 + ( sa0 * i0 ) + 1 ];
rex = viewX[ ix0 ];
imx = viewX[ ix0 + 1 ];
re0 = f32( re0 - f32( f32( rea * rex ) - f32( ima * imx ) ) );
im0 = f32( im0 - f32( f32( rea * imx ) + f32( ima * rex ) ) );
ix0 -= sx;
}
if ( nonunit ) {
red = viewA[ oa2 + ( sa0 * i1 ) ];
imd = sign * viewA[ oa2 + ( sa0 * i1 ) + 1 ];
denom = f32( f32( red * red ) + f32( imd * imd ) );
tmp = re0;
re0 = f32( f32( f32( tmp * red ) + f32( im0 * imd ) ) / denom ); // eslint-disable-line max-len
im0 = f32( f32( f32( im0 * red ) - f32( tmp * imd ) ) / denom ); // eslint-disable-line max-len
}
viewX[ ix1 ] = re0;
viewX[ ix1 + 1 ] = im0;
ix1 -= sx;
}
return x;
}
// EXPORTS //
module.exports = ctrsv;
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