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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 //
/**
* Solves one of the systems of equations `A*x = b` or `A^T*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 {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`
* @param {Float64Array} x - input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @returns {Float64Array} `x`
*
* @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 ] );
* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
*
* dtrsv( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
* // x => <Float64Array>[ 0.0, -4.0, 3.0 ]
*/
function dtrsv( uplo, trans, diag, N, A, strideA1, strideA2, offsetA, x, strideX, offsetX ) { // eslint-disable-line max-params, max-len
var nonunit;
var isrm;
var tmp;
var sa0;
var sa1;
var ix0;
var ix1;
var i0;
var i1;
var oa;
var ox;
// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
isrm = isRowMajor( [ strideA1, strideA2 ] );
nonunit = ( diag === 'non-unit' );
if ( isrm ) {
// 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 { // isColMajor
// 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;
if (
( !isrm && trans === 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'lower' )
) {
ix1 = ox + ( ( N - 1 ) * strideX );
for ( i1 = N-1; i1 >= 0; i1-- ) {
if ( x[ ix1 ] !== 0.0 ) {
oa = offsetA + (sa1*i1);
if ( nonunit ) {
x[ ix1 ] /= A[ oa+(sa0*i1) ];
}
tmp = x[ ix1 ];
ix0 = ix1;
for ( i0 = i1-1; i0 >= 0; i0-- ) {
ix0 -= strideX;
x[ ix0 ] -= tmp * A[ oa+(sa0*i0) ];
}
}
ix1 -= strideX;
}
return x;
}
if (
( !isrm && trans === 'no-transpose' && uplo === 'lower' ) ||
( isrm && trans !== 'no-transpose' && uplo === 'upper' )
) {
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
if ( x[ ix1 ] !== 0.0 ) {
oa = offsetA + (sa1*i1);
if ( nonunit ) {
x[ ix1 ] /= A[ oa+(sa0*i1) ];
}
tmp = x[ ix1 ];
ix0 = ix1;
for ( i0 = i1+1; i0 < N; i0++ ) {
ix0 += strideX;
x[ ix0 ] -= tmp * A[ oa+(sa0*i0) ];
}
}
ix1 += strideX;
}
return x;
}
if (
( !isrm && trans !== 'no-transpose' && uplo === 'upper' ) ||
( isrm && trans === 'no-transpose' && uplo === 'lower' )
) {
ix1 = ox;
for ( i1 = 0; i1 < N; i1++ ) {
tmp = x[ ix1 ];
oa = offsetA + (sa1*i1);
ix0 = ox;
for ( i0 = 0; i0 <= i1-1; i0++ ) {
tmp -= x[ ix0 ] * A[ oa+(sa0*i0) ];
ix0 += strideX;
}
if ( nonunit ) {
tmp /= A[ oa+(sa0*i1) ];
}
x[ ix1 ] = tmp;
ix1 += strideX;
}
return x;
}
// ( !isrm && trans !== 'no-transpose' && uplo === 'lower' ) || ( isrm && trans === 'no-transpose' && uplo === 'upper' )
ox += ( N - 1 ) * strideX;
ix1 = ox;
for ( i1 = N-1; i1 >= 0; i1-- ) {
tmp = x[ ix1 ];
oa = offsetA + (sa1*i1);
ix0 = ox;
for ( i0 = N-1; i0 > i1; i0-- ) {
tmp -= x[ ix0 ] * A[ oa+(sa0*i0) ];
ix0 -= strideX;
}
if ( nonunit ) {
tmp /= A[ oa+(sa0*i1) ];
}
x[ ix1 ] = tmp;
ix1 -= strideX;
}
return x;
}
// EXPORTS //
module.exports = dtrsv;
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