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feat: add blas/base/dtbmv
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‎lib/node_modules/@stdlib/blas/base/dtbmv/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2025 The Stdlib Authors.
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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-->
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# dtbmv
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> Solve one of the systems of equations `A*x = b` or `A^T*x = b`.
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<section class="usage">
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## Usage
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```javascript
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var dtbmv = require( '@stdlib/blas/base/dtbmv' );
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```
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#### dtbmv( order, uplo, trans, diag, N, K, A, LDA, x, sx )
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Performs one of the matrix-vector operations `x = A*x` or `x = A^T*x` where `x` is an `N` element vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular band matrix, with ( `K` + 1 ) diagonals.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
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dtbmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, 1, A, 2, x, 1 );
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// x => <Float64Array>[ 3.0, 11.0, 3.0 ]
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```
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The function has the following parameters:
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- **order**: storage layout.
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- **uplo**: specifies whether `A` is an upper or lower triangular matrix.
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- **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
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- **diag**: specifies whether `A` has a unit diagonal.
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- **N**: number of elements along each dimension of `A`.
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- **K**: number of super-diagonals or sub-diagonals of the matrix `A`.
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- **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
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- **lda**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
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- **x**: input vector [`Float64Array`][mdn-float64array].
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- **sx**: `x` stride length.
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The stride parameters determine how elements in the input arrays are accessed at runtime. For example, to iterate over the elements of `x` in reverse order,
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var x = new Float64Array( [ 3.0, 2.0, 1.0 ] );
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dtbmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, 1, A, 2, x, -1 );
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// x => <Float64Array>[ 3.0, 11.0, 3.0 ]
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```
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Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
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<!-- eslint-disable stdlib/capitalized-comments -->
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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// Initial arrays...
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var x0 = new Float64Array( [ 0.0, 1.0, 2.0, 3.0 ] );
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var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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// Create offset views...
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var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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dtbmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, 1, A, 2, x1, 1 );
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// x1 => <Float64Array>[ 3.0, 11.0, 3.0 ]
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```
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#### dtbmv.ndarray( uplo, trans, diag, N, K, A, sa1, sa2, oa, x, sx, ox )
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Performs one of the matrix-vector operations `x = A*x` or `x = A^T*x`, using alternative indexing semantics and where `x` is an `N` element vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular band matrix, with ( `K` + 1 ) diagonals.
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
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dtbmv.ndarray( 'upper', 'no-transpose', 'unit', 3, 1, A, 2, 1, 0, x, 1, 0 );
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// x => <Float64Array>[ 3.0, 11.0, 3.0 ]
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```
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The function has the following additional parameters:
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- **sa1**: stride of the first dimension of `A`.
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- **sa2**: stride of the second dimension of `A`.
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- **oa**: starting index for `A`.
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- **ox**: starting index for `x`.
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While [`typed array`][mdn-typed-array] views mandate a view offset based on the underlying buffer, the offset parameters support indexing semantics based on starting indices. For example,
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```javascript
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var Float64Array = require( '@stdlib/array/float64' );
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var A = new Float64Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0 ] );
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var x = new Float64Array( [ 3.0, 2.0, 1.0 ] );
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dtbmv.ndarray( 'upper', 'no-transpose', 'unit', 3, 1, A, 2, 1, 0, x, -1, 2 );
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// x => <Float64Array>[ 3.0, 11.0, 3.0 ]
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```
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</section>
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<!-- /.usage -->
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<section class="notes">
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## Notes
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- `dtbmv()` corresponds to the [BLAS][blas] level 2 function [`dtbmv`][blas-dtbmv].
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- Neither routine tests for singularity or near-singularity. Such tests must be performed before calling the routines.
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</section>
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<!-- /.notes -->
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<section class="examples">
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## Examples
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<!-- eslint no-undef: "error" -->
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```javascript
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var dtbmv = require( '@stdlib/blas/base/dtbmv' );
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var opts = {
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'dtype': 'float64'
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};
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var N = 3;
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var A = [ 1.0, 2.0, 3.0, 4.0, 5.0, 0.0 ];
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var x = discreteUniform( N, -10, 10, opts );
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dtbmv( 'row-major', 'upper', 'no-transpose', 'unit', N, 1, A, N, x, 1 );
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console.log( x );
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dtbmv.ndarray( 'upper', 'no-transpose', 'unit', N, 1, A, N, 1, 0, x, 1, 0 );
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console.log( x );
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```
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</section>
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<!-- /.examples -->
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<!-- C interface documentation. -->
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* * *
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<section class="c">
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## C APIs
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<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. -->
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<section class="intro">
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</section>
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<!-- /.intro -->
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<!-- C usage documentation. -->
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<section class="usage">
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### Usage
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```c
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TODO
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```
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#### TODO
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TODO.
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```c
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TODO
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```
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TODO
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```c
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TODO
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```
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</section>
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<!-- /.usage -->
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<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="notes">
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</section>
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<!-- /.notes -->
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<!-- C API usage examples. -->
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<section class="examples">
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### Examples
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```c
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TODO
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```
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</section>
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<!-- /.examples -->
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</section>
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<!-- /.c -->
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<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->
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<section class="related">
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</section>
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<!-- /.related -->
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<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. -->
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<section class="links">
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[blas]: http://www.netlib.org/blas
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[blas-dtbmv]: https://www.netlib.org/lapack/explore-html-3.6.1/d7/d15/group__double__blas__level2_ga9f64da9e0125c712672fd89d166d3b9c.html
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[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array
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[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray
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</section>
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<!-- /.links -->

‎lib/node_modules/@stdlib/blas/base/dtbmv/benchmark/benchmark.js‎

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/**
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* @license Apache-2.0
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*
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* Copyright (c) 2024 The Stdlib Authors.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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'use strict';
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// MODULES //
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var bench = require( '@stdlib/bench' );
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var isnan = require( '@stdlib/math/base/assert/is-nan' );
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var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
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var zeros = require( '@stdlib/array/zeros' );
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var pow = require( '@stdlib/math/base/special/pow' );
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var floor = require( '@stdlib/math/base/special/floor' );
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var pkg = require( './../package.json' ).name;
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var dtbmv = require( './../lib/dtbmv.js' );
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// VARIABLES //
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var options = {
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'dtype': 'float64'
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};
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// FUNCTIONS //
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/**
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* Creates a benchmark function.
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*
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* @private
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* @param {PositiveInteger} N - number of elements along each dimension
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* @returns {Function} benchmark function
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*/
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function createBenchmark( N ) {
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var A = discreteUniform( N*N, -10.0, 10.0, options );
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var x = zeros( N, options.dtype );
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return benchmark;
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/**
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* Benchmark function.
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*
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* @private
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* @param {Benchmark} b - benchmark instance
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*/
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function benchmark( b ) {
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var z;
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var i;
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b.tic();
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for ( i = 0; i < b.iterations; i++ ) {
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z = dtbmv( 'row-major', 'upper', 'transpose', 'non-unit', N, 1, A, N, x, 1 );
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if ( isnan( z[ i%z.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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}
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b.toc();
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if ( isnan( z[ i%z.length ] ) ) {
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b.fail( 'should not return NaN' );
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}
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b.pass( 'benchmark finished' );
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b.end();
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}
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}
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// MAIN //
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/**
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* Main execution sequence.
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*
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* @private
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*/
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function main() {
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var min;
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var max;
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var N;
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var f;
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var i;
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min = 1; // 10^min
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max = 6; // 10^max
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for ( i = min; i <= max; i++ ) {
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N = floor( pow( pow( 10, i ), 1.0/2.0 ) );
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f = createBenchmark( N );
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bench( pkg+':size='+(N*N), f );
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}
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}
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main();

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