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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 isRowMajor = require( '@stdlib/ndarray/base/assert/is-row-major' );
var dscal = require( '@stdlib/blas/base/dscal' ).ndarray;
var dtrmv = require( '@stdlib/blas/base/dtrmv' ).ndarray;
// MAIN //
/**
* Computes the inverse of a triangular matrix.
*
* @private
* @param {string} uplo - specifies whether to copy the upper or lower triangular/trapezoidal part of matrix `A`
* @param {string} diag - specifies whether or not `A` is unit triangular
* @param {NonNegativeInteger} N - order of matrix `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`
* @returns {Float64Array} output matrix
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 1.0, 2.0, 0.0, 4.0 ] );
* dtrti2( 'upper', 'non-unit', 2, A, 2, 1, 0 );
* // A => <Float64Array>[ 1.0, -0.5, 0.0, 0.25 ]
*/
function dtrti2( uplo, diag, N, A, strideA1, strideA2, offsetA ) {
var nounit;
var upper;
var ajj;
var tmp;
var j;
upper = ( uplo === 'upper' );
nounit = ( diag === 'non-unit' );
if ( isRowMajor( [ strideA1, strideA2 ] ) ) {
upper = !upper;
tmp = strideA1;
strideA1 = strideA2;
strideA2 = tmp;
}
if ( upper ) {
for ( j = 0; j < N; j++ ) {
if ( nounit ) {
A[ offsetA + ( j * strideA1 ) + ( j * strideA2 ) ] = 1.0 / A[ offsetA + ( j * strideA1 ) + ( j * strideA2 ) ];
ajj = -A[ offsetA + ( j * strideA1 ) + ( j * strideA2 ) ];
} else {
ajj = -1.0;
}
// Compute elements 1:j-1 of j-th column
dtrmv( 'upper', 'no-transpose', diag, j, A, strideA1, strideA2, offsetA, A, strideA1, offsetA + ( j * strideA2 ) );
dscal( j, ajj, A, strideA1, offsetA + ( j * strideA2 ) );
}
return A;
}
// Compute inverse of lower triangular matrix
for ( j = N - 1; j >= 0; j-- ) {
if ( nounit ) {
A[ offsetA + ( j * strideA1 ) + ( j * strideA2 ) ] = 1.0 / A[ offsetA + ( j * strideA1 ) + ( j * strideA2 ) ];
ajj = -A[ offsetA + ( j * strideA1 ) + ( j * strideA2 ) ];
} else {
ajj = -1.0;
}
if ( j < N - 1 ) {
// Compute elements j+1:N of j-th column
dtrmv( 'lower', 'no-transpose', diag, N - j - 1, A, strideA1, strideA2, offsetA + ( ( j + 1 ) * strideA1 ) + ( ( j + 1 ) * strideA2 ), A, strideA1, offsetA + ( j * strideA2 ) + ( ( j + 1 ) * strideA1 ) );
dscal( N - j - 1, ajj, A, strideA1, offsetA + ( j * strideA2 ) + ( ( j + 1 ) * strideA1 ) );
}
}
return A;
}
// EXPORTS //
module.exports = dtrti2;
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