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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 isMatrixTriangle = require( '@stdlib/blas/base/assert/is-matrix-triangle' );
var isTransposeOperation = require( '@stdlib/blas/base/assert/is-transpose-operation' );
var isDiagonal = require( '@stdlib/blas/base/assert/is-diagonal-type' );
var format = require( '@stdlib/string/format' );
var base = require( './base.js' );
// 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 band matrix, with ( `K` + 1 ) diagonals.
*
* @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 {NonNegativeInteger} K - number of super-diagonals or sub-diagonals of the 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`
* @param {Float64Array} x - input vector
* @param {integer} strideX - `x` stride length
* @param {NonNegativeInteger} offsetX - starting index for `x`
* @throws {TypeError} first argument must specify whether a lower or upper triangular matrix is supplied
* @throws {TypeError} second argument must be a valid transpose operation
* @throws {TypeError} third argument must be a valid diagonal type
* @throws {RangeError} fourth argument must be a nonnegative integer
* @throws {RangeError} fifth argument must be a nonnegative integer
* @throws {RangeError} seventh argument must be non-zero
* @throws {RangeError} eighth argument must be non-zero
* @throws {RangeError} eleventh argument must be non-zero
* @returns {Float64Array} `x`
*
* @example
* var Float64Array = require( '@stdlib/array/float64' );
*
* var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] ); // => [ [ 1.0, 4.0, 0.0 ], [ 0.0, 2.0, 5.0 ], [ 0.0, 0.0, 3.0 ] ]
* var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
*
* dtbsv( 'upper', 'no-transpose', 'unit', 3, 1, A, 2, 1, 0, x, 1, 0 );
* // x => <Float64Array>[ 8.0, -7.0, 3.0 ]
*/
function dtbsv( uplo, trans, diag, N, K, A, strideA1, strideA2, offsetA, x, strideX, offsetX ) { // eslint-disable-line max-params, max-len
if ( !isMatrixTriangle( uplo ) ) {
throw new TypeError( format( 'invalid argument. First argument must specify whether the lower or upper triangular matrix is supplied. Value: `%s`.', uplo ) );
}
if ( !isTransposeOperation( trans ) ) {
throw new TypeError( format( 'invalid argument. Second argument must be a valid transpose operation. Value: `%s`.', trans ) );
}
if ( !isDiagonal( diag ) ) {
throw new TypeError( format( 'invalid argument. Third argument must be a valid diagonal type. Value: `%s`.', diag ) );
}
if ( N < 0 ) {
throw new RangeError( format( 'invalid argument. Fourth argument must be a nonnegative integer. Value: `%d`.', N ) );
}
if ( K < 0 ) {
throw new RangeError( format( 'invalid argument. Fifth argument must be a nonnegative integer. Value: `%d`.', K ) );
}
if ( strideA1 === 0 ) {
throw new RangeError( format( 'invalid argument. Seventh argument must be non-zero. Value: `%d`.', strideX ) );
}
if ( strideA2 === 0 ) {
throw new RangeError( format( 'invalid argument. Eighth argument must be non-zero. Value: `%d`.', strideA1 ) );
}
if ( strideX === 0 ) {
throw new RangeError( format( 'invalid argument. Eleventh argument must be non-zero. Value: `%d`.', strideA2 ) );
}
if ( N === 0 ) {
return x;
}
return base( uplo, trans, diag, N, K, A, strideA1, strideA2, offsetA, x, strideX, offsetX ); // eslint-disable-line max-len
}
// EXPORTS //
module.exports = dtbsv;
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