-
-
Notifications
You must be signed in to change notification settings - Fork 0
Commit
This commit does not belong to any branch on this repository, and may belong to a fork outside of the repository.
- Loading branch information
1 parent
2c665ca
commit de68156
Showing
40 changed files
with
2,948 additions
and
94 deletions.
There are no files selected for viewing
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
Original file line number | Diff line number | Diff line change |
---|---|---|
@@ -0,0 +1,255 @@ | ||
<!-- | ||
@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. | ||
--> | ||
|
||
# dspr | ||
|
||
> Perform the symmetric rank 1 operation `A = α*x*x^T + A`. | ||
<section class = "usage"> | ||
|
||
## Usage | ||
|
||
```javascript | ||
var dspr = require( '@stdlib/blas/base/dspr' ); | ||
``` | ||
|
||
#### dspr( order, uplo, N, α, x, sx, AP ) | ||
|
||
Performs the symmetric rank 1 operation `A = α*x*x^T + A` where `α` is a scalar, `x` is an `N` element vector, and `A` is an `N` by `N` symmetric matrix supplied in packed form. | ||
|
||
```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
|
||
var AP = new Float64Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] ); | ||
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] ); | ||
|
||
dspr( 'row-major', 'upper', 3, 1.0, x, 1, AP ); | ||
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ] | ||
``` | ||
|
||
The function has the following parameters: | ||
|
||
- **order**: storage layout. | ||
- **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` is supplied. | ||
- **N**: number of elements along each dimension of `A`. | ||
- **α**: scalar constant. | ||
- **x**: input [`Float64Array`][mdn-float64array]. | ||
- **sx**: index increment for `x`. | ||
- **AP**: packed form of a symmetric matrix `A` stored as a [`Float64Array`][mdn-float64array]. | ||
|
||
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, | ||
|
||
```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
|
||
var AP = new Float64Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] ); | ||
var x = new Float64Array( [ 3.0, 2.0, 1.0 ] ); | ||
|
||
dspr( 'row-major', 'upper', 3, 1.0, x, -1, AP ); | ||
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ] | ||
``` | ||
|
||
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views. | ||
|
||
<!-- eslint-disable stdlib/capitalized-comments --> | ||
|
||
```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
|
||
// Initial arrays... | ||
var x0 = new Float64Array( [ 0.0, 3.0, 2.0, 1.0 ] ); | ||
var AP = new Float64Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] ); | ||
|
||
// Create offset views... | ||
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element | ||
|
||
dspr( 'row-major', 'upper', 3, 1.0, x1, -1, AP ); | ||
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ] | ||
``` | ||
|
||
#### dspr.ndarray( uplo, N, α, x, sx, ox, AP, sap, oap ) | ||
|
||
Performs the symmetric rank 1 operation `A = α*x*x^T + A`, using alternative indexing semantics and where `α` is a scalar, `x` is an `N` element vector, and `A` is an `N` by `N` symmetric matrix supplied in packed form. | ||
|
||
```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
|
||
var AP = new Float64Array( [ 1.0, 1.0, 2.0, 1.0, 2.0, 3.0 ] ); | ||
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] ); | ||
|
||
dspr.ndarray( 'row-major', 'lower', 3, 1.0, x, 1, 0, AP, 1, 0 ); | ||
// AP => <Float64Array>[ 2.0, 3.0, 6.0, 4.0, 8.0, 12.0 ] | ||
``` | ||
|
||
The function has the following additional parameters: | ||
|
||
- **ox**: starting index for `x`. | ||
- **sap**: `AP` stride length. | ||
- **oap**: starting index for `AP`. | ||
|
||
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, | ||
|
||
```javascript | ||
var Float64Array = require( '@stdlib/array/float64' ); | ||
|
||
var AP = new Float64Array( [ 1.0, 2.0, 3.0, 1.0, 2.0, 1.0 ] ); | ||
var x = new Float64Array( [ 3.0, 2.0, 1.0 ] ); | ||
|
||
dspr.ndarray( 'row-major', 'upper', 3, 1.0, x, -1, 2, AP, 1, 0 ); | ||
// AP => <Float64Array>[ 2.0, 4.0, 6.0, 5.0, 8.0, 10.0 ] | ||
``` | ||
|
||
</section> | ||
|
||
<!-- /.usage --> | ||
|
||
<section class="notes"> | ||
|
||
## Notes | ||
|
||
- `dspr()` corresponds to the [BLAS][blas] level 2 function [`dspr`][blas-dspr]. | ||
|
||
</section> | ||
|
||
<!-- /.notes --> | ||
|
||
<section class="examples"> | ||
|
||
## Examples | ||
|
||
<!-- eslint no-undef: "error" --> | ||
|
||
```javascript | ||
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' ); | ||
var dspr = require( '@stdlib/blas/base/dspr' ); | ||
|
||
var opts = { | ||
'dtype': 'float64' | ||
}; | ||
|
||
var N = 5; | ||
|
||
var AP = discreteUniform( N * ( N + 1 ) / 2, -10.0, 10.0, opts ); | ||
var x = discreteUniform( N, -10.0, 10.0, opts ); | ||
|
||
dspr( 'column-major', 'upper', N, 1.0, x, 1, AP ); | ||
console.log( AP ); | ||
|
||
dspr.ndarray( 'column-major', 'upper', N, 1.0, x, 1, 0, AP, 1, 0 ); | ||
console.log( AP ); | ||
``` | ||
|
||
</section> | ||
|
||
<!-- /.examples --> | ||
|
||
<!-- C interface documentation. --> | ||
|
||
* * * | ||
|
||
<section class="c"> | ||
|
||
## C APIs | ||
|
||
<!-- Section to include introductory text. Make sure to keep an empty line after the intro `section` element and another before the `/section` close. --> | ||
|
||
<section class="intro"> | ||
|
||
</section> | ||
|
||
<!-- /.intro --> | ||
|
||
<!-- C usage documentation. --> | ||
|
||
<section class="usage"> | ||
|
||
### Usage | ||
|
||
```c | ||
TODO | ||
``` | ||
|
||
#### TODO | ||
|
||
TODO. | ||
|
||
```c | ||
TODO | ||
``` | ||
|
||
TODO | ||
|
||
```c | ||
TODO | ||
``` | ||
|
||
</section> | ||
|
||
<!-- /.usage --> | ||
|
||
<!-- C API usage notes. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> | ||
|
||
<section class="notes"> | ||
|
||
</section> | ||
|
||
<!-- /.notes --> | ||
|
||
<!-- C API usage examples. --> | ||
|
||
<section class="examples"> | ||
|
||
### Examples | ||
|
||
```c | ||
TODO | ||
``` | ||
|
||
</section> | ||
|
||
<!-- /.examples --> | ||
|
||
</section> | ||
|
||
<!-- /.c --> | ||
|
||
<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. --> | ||
|
||
<section class="related"> | ||
|
||
</section> | ||
|
||
<!-- /.related --> | ||
|
||
<!-- Section for all links. Make sure to keep an empty line after the `section` element and another before the `/section` close. --> | ||
|
||
<section class="links"> | ||
|
||
[blas]: http://www.netlib.org/blas | ||
|
||
[blas-dspr]: https://www.netlib.org/lapack/explore-html/d5/df9/group__hpr_gaa5d4297738fb1391709c645a7c2bee5e.html#gaa5d4297738fb1391709c645a7c2bee5e | ||
|
||
[mdn-float64array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float64Array | ||
|
||
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray | ||
|
||
</section> | ||
|
||
<!-- /.links --> |
Oops, something went wrong.