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‎lib/node_modules/@stdlib/blas/base/sgbmv/README.md‎

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<!--
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@license Apache-2.0
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Copyright (c) 2024 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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# sgbmv
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> Perform one of the matrix-vector operations `y = α*A*x + β*y` or `y = α*A^T*x + β*y`.
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<section class="usage">
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## Usage
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```javascript
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var sgbmv = require( '@stdlib/blas/base/sgbmv' );
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```
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#### sgbmv( ord, trans, M, N, KL, KU, α, A, LDA, x, sx, β, y, sy )
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Performs one of the matrix-vector operations `y := α*A*x + β*y, or y := α*A**T*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors and `A` is an `M` by `N` band matrix, with `KL` sub-diagonals and `KU` super-diagonals.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 0.0 ] );
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var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
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sgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, 1.0, A, 3, x, 1, 1.0, y, 1 );
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// y => <Float32Array>[ 3.0, 12.0, 13.0 ]
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```
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The function has the following parameters:
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- **ord**: storage layout.
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- **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
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- **M**: number of rows in the matrix `A`.
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- **N**: number of columns in the matrix `A`.
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- **α**: scalar constant.
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- **A**: input matrix stored in linear memory as a [`Float32Array`][mdn-float32array].
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- **lda**: stride of the first dimension of `A` (leading dimension of `A`).
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- **x**: input [`Float32Array`][mdn-float32array].
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- **sx**: index increment for `x`.
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- **β**: scalar constant.
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- **y**: output [`Float32Array`][mdn-float32array].
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- **sy**: index increment for `y`.
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The stride parameters determine how operations are performed. For example, to iterate over every other element in `x` and `y`,
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 0.0 ] );
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var x = new Float32Array( [ 1.0, 1.0, 1.0, 1.0, 1.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0, 0.0, 0.0 ] );
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sgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, 1.0, A, 3, x, 2, 1.0, y, 2 );
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// y => <Float32Array>[ 3.0, 0.0, 12.0, 0.0, 13.0 ]
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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 Float32Array = require( '@stdlib/array/float32' );
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// Initial arrays...
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var x0 = new Float32Array( [ 1.0, 1.0, 1.0, 1.0 ] );
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var y0 = new Float32Array( [ 0.0, 0.0, 0.0, 0.0 ] );
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var A = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 0.0 ] );
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// Create offset views...
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var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
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sgbmv( 'row-major', 'no-transpose', 3, 3, 1, 1, 1.0, A, 3, x1, 1, 1.0, y1, 1 );
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// y0 => <Float32Array>[ 0.0, 3.0, 12.0, 13.0 ]
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```
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#### sgbmv.ndarray( trans, M, N, KL, KU, α, A, sa1, sa2, oa, x, sx, ox, β, y, sy, oy )
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Performs one of the matrix-vector operations `y := α*A*x + β*y, or y := α*A**T*x + β*y`, where `α` and `β` are scalars, `x` and `y` are vectors and `A` is an `M` by `N` band matrix, with `KL` sub-diagonals and `KU` super-diagonals.
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```javascript
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var Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 0.0 ] );
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var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
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sgbmv.ndarray( 'no-transpose', 3, 3, 1, 1, 1.0, A, 3, 1, 0, x, 1, 0, 1.0, y, 1, 0 );
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// y => <Float32Array>[ 3.0, 12.0, 13.0 ]
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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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- **oy**: starting index for `y`.
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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 Float32Array = require( '@stdlib/array/float32' );
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var A = new Float32Array( [ 0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 0.0 ] );
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var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
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var y = new Float32Array( [ 0.0, 0.0, 0.0 ] );
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sgbmv.ndarray( 'no-transpose', 3, 3, 1, 1, 1.0, A, 3, 1, 0, x, 1, 1, 1.0, y, -2, 2 );
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// y => <Float32Array>[ 12.0, 0.0, 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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- `sgbmv()` corresponds to the [BLAS][blas] level 2 function [`sgbmv`][blas-sgbmv].
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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 sgbmv = require( '@stdlib/blas/base/sgbmv' );
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var opts = {
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'dtype': 'float32'
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};
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var M = 3;
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var N = 3;
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var A = [ 0, 9, 10, 11, 12, 5, 1, 2, 0 ];
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var x = discreteUniform( N, 0, 255, opts );
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var y = discreteUniform( M, 0, 255, opts );
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sgbmv( 'row-major', 'no-transpose', M, N, 1, 1, 1.0, A, N, x, 1, 1.0, y, 1 );
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console.log( y );
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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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#include "stdlib/blas/base/sgbmv.h"
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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-sgbmv]: https://www.netlib.org/lapack/explore-html/d7/dda/group__gemv_ga0d35d880b663ad18204bb23bd186e380.html#ga0d35d880b663ad18204bb23bd186e380
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[mdn-float32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float32Array
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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 -->

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