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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.
*/
/* eslint-disable max-len, max-statements, max-lines-per-function */
'use strict';
// MODULES //
var isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
// FUNCTIONS //
/**
* Fills a matrix with zeros.
*
* @private
* @param {NonNegativeInteger} M - number of rows
* @param {NonNegativeInteger} N - number of columns
* @param {Float64Array} X - matrix to fill
* @param {integer} strideX1 - stride of the first dimension of `X`
* @param {integer} strideX2 - stride of the second dimension of `X`
* @param {NonNegativeInteger} offsetX - starting index for `X`
* @returns {Float64Array} input matrix
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
*
* zeros( 2, 3, X, 3, 1, 0 );
* // X => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var X = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
*
* zeros( 2, 3, X, 1, 2, 0 );
* // X => <Float64Array>[ 0.0, 0.0, 0.0, 0.0, 0.0, 0.0 ]
*/
function zeros( M, N, X, strideX1, strideX2, offsetX ) { // TODO: consider moving to a separate package
var dx0;
var dx1;
var S0;
var S1;
var i0;
var i1;
var ix;
if ( isRowMajor( [ strideX1, strideX2 ] ) ) {
// For row-major matrices, the last dimension has the fastest changing index...
S0 = N;
S1 = M;
dx0 = strideX2; // offset increment for innermost loop
dx1 = strideX1 - ( S0*strideX2 ); // offset increment for outermost loop
} else { // column-major
// For column-major matrices, the first dimension has the fastest changing index...
S0 = M;
S1 = N;
dx0 = strideX1; // offset increment for innermost loop
dx1 = strideX2 - ( S0*strideX1 ); // offset increment for outermost loop
}
ix = offsetX;
for ( i1 = 0; i1 < S1; i1++ ) {
for ( i0 = 0; i0 < S0; i0++ ) {
X[ ix ] = 0.0;
ix += dx0;
}
ix += dx1;
}
return X;
}
// MAIN //
/**
* Solves matrix equation `op(A) * X = α * B` or `X * op(A) = α * B` where `α` is a scalar, `X` and `B` are `M` by `N` matrices, `A` is a unit, or non-unit, upper or lower triangular matrix and `op(A)` is one of `op(A) = A` or `op(A) = A^T`. The matrix `X` is overwritten on `B`.
*
* @private
* @param {string} side - specifies whether `op( A )` appears on the left or right of `X`
* @param {string} uplo - specifies whether the upper or lower triangular part of the matrix `A` is supplied
* @param {string} transa - specifies whether `op( A )` should be transposed, conjugate-transposed, or not transposed
* @param {string} diag - specifies whether or not `A` is unit triangular
* @param {NonNegativeInteger} M - number of rows in `B`
* @param {NonNegativeInteger} N - number of columns in `B`
* @param {number} alpha - scalar constant
* @param {Float64Array} A - input matrix `A`
* @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} B - input matrix `B`
* @param {integer} strideB1 - stride of the first dimension of `B`
* @param {integer} strideB2 - stride of the second dimension of `B`
* @param {NonNegativeInteger} offsetB - starting index for `B`
* @returns {Float64Array} `B`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 0.0, 0.0, 2.0, 3.0, 0.0, 4.0, 5.0, 6.0 ] );
* var B = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0 ] );
*
* dtrsm( 'left', 'lower', 'no-transpose', 'unit', 3, 3, 1.0, A, 3, 1, 0, B, 3, 1, 0 );
* // B => <Float64Array>[ 1.0, 2.0, 3.0, 2.0, 1.0, 0.0, -7.0, -5.0, -3.0 ]
*/
function dtrsm( side, uplo, transa, diag, M, N, alpha, A, strideA1, strideA2, offsetA, B, strideB1, strideB2, offsetB ) { // eslint-disable-line max-params
var nonunit;
var isrma;
var tmp;
var oa2;
var ob2;
var sa0;
var sa1;
var sb0;
var sb1;
var oa;
var ob;
var i;
var j;
var k;
// Note on variable naming convention: sa#, ix#, i# where # corresponds to the loop number, with `0` being the innermost loop...
isrma = isRowMajor( [ strideA1, strideA2 ] );
nonunit = ( diag === 'non-unit' );
if ( M === 0 || N === 0 ) {
return B;
}
if ( isrma ) {
// For row-major matrices, the last dimension has the fastest changing index...
sa0 = strideA2; // stride for innermost loop
sa1 = strideA1; // stride for outermost loop
sb0 = strideB2;
sb1 = strideB1;
} 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
sb0 = strideB1;
sb1 = strideB2;
}
if ( alpha === 0.0 ) {
zeros( M, N, B, sb0, sb1, offsetB );
return B;
}
if (
( isrma && side === 'left' && uplo === 'upper' && transa === 'no-transpose' ) ||
( !isrma && side === 'right' && uplo === 'lower' && transa === 'no-transpose' )
) {
for ( k = N - 1; k >= 0; k-- ) {
if ( nonunit ) {
oa2 = offsetA + ( k * sa1 ) + ( k * sa0 );
tmp = 1.0 / A[ oa2 ];
for ( i = 0; i < M; i++ ) {
ob2 = offsetB + ( i * sb0 ) + ( k * sb1 );
B[ ob2 ] *= tmp;
}
}
for ( j = 0; j < k; j++ ) {
oa2 = offsetA + ( j * sa1 ) + ( k * sa0 );
if ( A[ oa2 ] !== 0.0 ) {
for ( i = 0; i < M; i++ ) {
ob = offsetB + ( i * sb0 );
B[ ob + ( j * sb1 ) ] -= A[ oa2 ] * B[ ob + ( k * sb1 ) ];
}
}
}
if ( alpha !== 1.0 ) {
for ( i = 0; i < M; i++ ) {
ob2 = offsetB + ( i * sb0 ) + ( k * sb1 );
B[ ob2 ] *= alpha;
}
}
}
return B;
}
if (
( isrma && side === 'left' && uplo === 'lower' && transa === 'no-transpose' ) ||
( !isrma && side === 'right' && uplo === 'upper' && transa === 'no-transpose' )
) {
for ( j = 0; j < N; j++ ) {
ob = offsetB + ( j * sb0 );
if ( alpha !== 1.0 ) {
for ( i = 0; i < M; i++ ) {
B[ ob + ( i * sb1 ) ] *= alpha;
}
}
for ( k = 0; k < M; k++ ) {
oa2 = offsetA + ( k * sa1 ) + ( k * sa0 );
ob2 = ob + ( k * sb1 );
if ( B[ ob2 ] !== 0.0 ) {
if ( nonunit ) {
B[ ob2 ] /= A[ oa2 ];
}
for ( i = k + 1; i < M; i++ ) {
oa2 = offsetA + ( i * sa1 ) + ( k * sa0 );
B[ ob + ( i * sb1 ) ] -= B[ ob2 ] * A[ oa2 ];
}
}
}
}
return B;
}
if (
( isrma && side === 'left' && uplo === 'upper' && transa !== 'no-transpose' ) ||
( !isrma && side === 'right' && uplo === 'lower' && transa !== 'no-transpose' )
) {
for ( j = 0; j < N; j++ ) {
for ( i = 0; i < M; i++ ) {
ob2 = offsetB + ( i * sb0 ) + ( j * sb1 );
if ( alpha !== 1.0 ) {
B[ ob2 ] *= alpha;
}
}
for ( k = 0; k < j; k++ ) {
for ( i = 0; i < M; i++ ) {
ob = offsetB + ( i * sb0 );
oa2 = offsetA + ( k * sa1 ) + ( j * sa0 );
if ( A[ oa2 ] !== 0.0 ) {
B[ ob + ( j * sb1 ) ] -= A[ oa2 ] * B[ ob + ( k * sb1 ) ];
}
}
}
if ( nonunit ) {
oa2 = offsetA + ( j * sa1 ) + (j * sa0 );
tmp = 1.0 / A[ oa2 ];
for ( i = 0; i < M; i++ ) {
ob2 = offsetB + ( i * sb0 ) + ( j * sb1 );
B[ ob2 ] *= tmp;
}
}
}
return B;
}
if (
( isrma && side === 'left' && uplo === 'lower' && transa !== 'no-transpose' ) ||
( !isrma && side === 'right' && uplo === 'upper' && transa === 'transpose' )
) {
for ( j = 0; j < N; j++ ) {
ob = offsetB + ( j * sb0 );
if ( alpha !== 1.0 ) {
for ( i = 0; i < M; i++ ) {
B[ ob + ( i * sb1 ) ] *= alpha;
}
}
for ( i = M - 1; i >= 0; i-- ) {
ob2 = ob + ( i * sb1 );
for ( k = i + 1; k < M; k++ ) {
oa2 = offsetA + ( i * sa0 ) + ( k * sa1 );
B[ ob2 ] -= A[ oa2 ] * B[ ob + ( k * sb1 ) ];
}
if ( nonunit ) {
oa2 = offsetA + ( i * sa0 ) + ( i * sa1 );
B[ ob2 ] /= A[ oa2 ];
}
B[ ob + ( i * sb1 ) ] = B[ ob2 ];
}
}
return B;
}
if (
( isrma && side === 'right' && uplo === 'upper' && transa === 'no-transpose' ) ||
( !isrma && side === 'left' && uplo === 'lower' && transa === 'no-transpose' )
) {
for ( j = 0; j < N; j++ ) {
ob = offsetB + ( j * sb1 );
for ( i = 0; i < M; i++ ) {
oa2 = offsetA + ( i * sa1 ) + ( i * sa0 );
tmp = B[ ob + ( i * sb0 ) ] * alpha;
for ( k = 0; k < i; k++ ) {
oa = offsetA + ( k * sa1 );
tmp -= A[ oa + ( i * sa0 ) ] * B[ ob + ( k * sb0 ) ];
}
if ( nonunit ) {
tmp /= A[ oa2 ];
}
B[ ob + ( i * sb0 ) ] = tmp;
}
}
return B;
}
if (
( isrma && side === 'right' && uplo === 'lower' && transa === 'no-transpose' ) ||
( !isrma && side === 'left' && uplo === 'upper' && transa === 'no-transpose' )
) {
for ( j = N - 1; j >= 0; j-- ) {
for ( i = 0; i < M; i++ ) {
ob2 = offsetB + ( i * sb1 ) + ( j * sb0 );
if ( alpha !== 1.0 ) {
B[ ob2 ] *= alpha;
}
}
for ( k = j + 1; k < N; k++ ) {
for ( i = 0; i < M; i++ ) {
ob2 = offsetB + ( i * sb1 );
oa2 = offsetA + ( k * sa1 );
if ( A[ oa2 + ( j * sa0 ) ] !== 0.0 ) {
B[ ob2 + ( j * sb0 ) ] -= A[ oa2 + ( j * sa0 ) ] * B[ ob2 + ( k * sb0 ) ];
}
}
}
if ( nonunit ) {
oa2 = offsetA + ( j * sa1 ) + ( j * sa0 );
tmp = 1.0 / A[ oa2 ];
for ( i = 0; i < M; i++ ) {
ob2 = offsetB + ( i * sb1 ) + ( j * sb0 );
B[ ob2 ] *= tmp;
}
}
}
return B;
}
if (
( isrma && side === 'right' && uplo === 'upper' && transa !== 'no-transpose' ) ||
( !isrma && side === 'left' && uplo === 'lower' && transa !== 'no-transpose' )
) {
for ( j = 0; j < N; j++ ) {
ob = offsetB + ( j * sb1 );
if ( alpha !== 1.0 ) {
for ( i = 0; i < M; i++ ) {
B[ ob + ( i * sb0 ) ] = B[ ob + ( i * sb0 ) ] * alpha;
}
}
for ( k = M - 1; k >= 0; k-- ) {
oa2 = offsetA + ( k * sa1 ) + ( k * sa0 );
ob2 = ob + ( k * sb0 );
if ( B[ ob2 ] !== 0.0 ) {
if ( nonunit ) {
B[ ob2 ] /= A[ oa2 ];
}
for ( i= 0; i < k; i++ ) {
oa = offsetA + ( i * sa1 ) + ( k * sa0 );
B[ ob + ( i * sb0 ) ] -= B[ ob2 ] * A[ oa ];
}
}
}
}
return B;
}
// ( isrma && side === 'right' && uplo === 'lower' && transa !== 'no-transpose' ) || ( !isrma && side === 'left' && uplo === 'upper' && transa !== 'no-transpose' )
for ( k = 0; k < N; k++ ) {
ob = offsetB + ( k * sb0 );
oa = offsetA + ( k * sa1 );
oa2 = oa + ( k * sa0 );
if ( nonunit ) {
tmp = 1.0 / A[ oa2 ];
for ( i = 0; i < M; i++ ) {
B[ ob + ( i * sb1 ) ] *= tmp;
}
}
for ( j = k + 1; j < N; j++ ) {
ob2 = offsetB + ( j * sb0 );
oa2 = offsetA + ( j * sa1 ) + ( k * sa0 );
if ( A[ oa2 ] !== 0.0 ) {
for ( i = 0; i < M; i++ ) {
B[ ob2 + ( i * sb1 ) ] -= A[ oa2 ] * B[ ob + ( i * sb1 ) ];
}
}
}
if ( alpha !== 1.0 ) {
for ( i = 0; i < M; i++ ) {
B[ ob + ( i * sb1 ) ] *= alpha;
}
}
}
return B;
}
// EXPORTS //
module.exports = dtrsm;
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