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| <!-- | ||
| @license Apache-2.0 | ||
| Copyright (c) 2024 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. | ||
| --> | ||
|
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| # dspmv | ||
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| > Perform the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors and, `A` is an `N` by `N` symmetric matrix supplied in packed form. | ||
| <section class = "usage"> | ||
|
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| ## Usage | ||
|
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| ```javascript | ||
| var dspmv = require( '@stdlib/blas/base/dspmv' ); | ||
| ``` | ||
|
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| #### dspmv( order, uplo, N, α, AP, x, sx, β, y, sy ) | ||
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| Performs the matrix-vector operation `y = α*A*x + β*y` where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix supplied in packed form `AP`. | ||
|
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| ```javascript | ||
| var Float64Array = require( '@stdlib/array/float64' ); | ||
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| var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); | ||
| var x = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
| var y = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
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| dspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, 1 ); | ||
| // y => <Float64Array>[ 7.0, 12.0, 15.0 ] | ||
| ``` | ||
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| The function has the following parameters: | ||
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| - **order**: storage layout. | ||
| - **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` is supplied. | ||
| - **N**: specifies the order of the matrix `A`. | ||
| - **α**: scalar constant. | ||
| - **AP**: packed form of a symmetric matrix `A` stored in linear memory as a [`Float64Array`][mdn-float64array]. | ||
| - **x**: input [`Float64Array`][mdn-float64array]. | ||
| - **sx**: index increment for `x`. | ||
| - **β**: scalar constant. | ||
| - **y**: output [`Float64Array`][mdn-float64array]. | ||
| - **sy**: index increment for `y`. | ||
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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 `y` in reverse order, | ||
|
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| ```javascript | ||
| var Float64Array = require( '@stdlib/array/float64' ); | ||
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| var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); | ||
| var x = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
| var y = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
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| dspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, -1 ); | ||
| // y => <Float64Array>[ 15.0, 12.0, 7.0 ] | ||
| ``` | ||
|
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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 | ||
| var Float64Array = require( '@stdlib/array/float64' ); | ||
|
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| // Initial arrays... | ||
| var x0 = new Float64Array( [ 1.0, 1.0 ] ); | ||
| var y0 = new Float64Array( [ 1.0, 1.0 ] ); | ||
| var AP = new Float64Array( [ 1.0, 2.0, 3.0 ] ); | ||
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| // Create offset views... | ||
| var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*0 ); // start at 1st element | ||
| var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*0 ); // start at 1st element | ||
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| dspmv( 'row-major', 'upper', 2, 1.0, AP, x1, -1, 1.0, y1, -1 ); | ||
| // y0 => <Float64Array>[ 6.0, 4.0 ] | ||
| ``` | ||
|
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| #### dspmv.ndarray( order, uplo, N, α, AP, x, sx, ox, β, y, sy, oy ) | ||
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| Performs the matrix-vector operation `y = α*A*x + β*y` using alternative indexing semantics and where `α` and `β` are scalars, `x` and `y` are `N` element vectors, and `A` is an `N` by `N` symmetric matrix supplied in packed form `AP`. | ||
|
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| ```javascript | ||
| var Float64Array = require( '@stdlib/array/float64' ); | ||
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| var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); | ||
| var x = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
| var y = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
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| dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 ); | ||
| // y => <Float64Array>[ 7.0, 12.0, 15.0 ] | ||
| ``` | ||
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| The function has the following additional parameters: | ||
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| - **ox**: starting index for `x`. | ||
| - **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 | ||
| var Float64Array = require( '@stdlib/array/float64' ); | ||
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| var AP = new Float64Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] ); | ||
| var x = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
| var y = new Float64Array( [ 1.0, 1.0, 1.0 ] ); | ||
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| dspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, -1, 2 ); | ||
| // y => <Float64Array>[ 15.0, 12.0, 7.0 ] | ||
| ``` | ||
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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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| - `dspmv()` corresponds to the [BLAS][blas] level 2 function [`dspmv`][dspmv]. | ||
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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 | ||
| var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); | ||
| var dspmv = require( '@stdlib/blas/base/dspmv' ); | ||
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| var opts = { | ||
| 'dtype': 'float64' | ||
| }; | ||
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| var N = 3; | ||
| var AP = discreteUniform( N * ( N + 1 ) / 2, -10, 10, opts ); | ||
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| var x = discreteUniform( N, -10, 10, opts ); | ||
| var y = discreteUniform( N, -10, 10, opts ); | ||
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| dspmv.ndarray( 'row-major', 'upper', N, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 ); | ||
| console.log( y ); | ||
| ``` | ||
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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 | ||
| TODO | ||
| ``` | ||
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| #### TODO | ||
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| TODO. | ||
|
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| ```c | ||
| TODO | ||
| ``` | ||
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| TODO | ||
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| ```c | ||
| TODO | ||
| ``` | ||
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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 | ||
| TODO | ||
| ``` | ||
|
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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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| [dspmv]: https://www.netlib.org/lapack/explore-html/d0/d4b/group__hpmv_ga739f8dc2316523832bde2b237fcad8a6.html#ga739f8dc2316523832bde2b237fcad8a6 | ||
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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 --> |
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