# sspmv
> 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.
## Usage
```javascript
var sspmv = require( '@stdlib/blas/base/sspmv' );
```
#### sspmv( order, uplo, N, α, AP, x, sx, β, y, sy )
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`.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var AP = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0 ] );
sspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, 1 );
// y => [ 7.0, 12.0, 15.0 ]
```
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**: specifies the order of the matrix `A`.
- **α**: scalar constant.
- **AP**: packed form of a symmetric matrix `A` stored in linear memory as a [`Float32Array`][mdn-float32array].
- **x**: input [`Float32Array`][mdn-float32array].
- **sx**: index increment for `x`.
- **β**: scalar constant.
- **y**: output [`Float32Array`][mdn-float32array].
- **sy**: index increment for `y`.
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,
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var AP = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0 ] );
sspmv( 'column-major', 'lower', 3, 1.0, AP, x, 1, 1.0, y, -1 );
// y => [ 15.0, 12.0, 7.0 ]
```
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
// Initial arrays...
var x0 = new Float32Array( [ 0.0, 1.0, 1.0 ] );
var y0 = new Float32Array( [ 0.0, 1.0, 1.0 ] );
var AP = new Float32Array( [ 1.0, 2.0, 3.0 ] );
// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float32Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
sspmv( 'row-major', 'upper', 2, 1.0, AP, x1, -1, 1.0, y1, -1 );
// y0 => [ 0.0, 6.0, 4.0 ]
```
#### sspmv.ndarray( order, uplo, N, α, AP, x, sx, ox, β, y, sy, oy )
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`.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var AP = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0 ] );
sspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 );
// y => [ 7.0, 12.0, 15.0 ]
```
The function has the following additional parameters:
- **ox**: starting index for `x`.
- **oy**: starting index for `y`.
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 Float32Array = require( '@stdlib/array/float32' );
var AP = new Float32Array( [ 1.0, 2.0, 3.0, 4.0, 5.0, 6.0 ] );
var x = new Float32Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float32Array( [ 1.0, 1.0, 1.0 ] );
sspmv.ndarray( 'column-major', 'lower', 3, 1.0, AP, x, 1, 0, 1.0, y, -1, 2 );
// y => [ 15.0, 12.0, 7.0 ]
```
## Notes
- `sspmv()` corresponds to the [BLAS][blas] level 2 function [`sspmv`][sspmv].
## Examples
```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var sspmv = require( '@stdlib/blas/base/sspmv' );
var opts = {
'dtype': 'float32'
};
var N = 3;
var AP = discreteUniform( N * ( N + 1 ) / 2, -10, 10, opts );
var x = discreteUniform( N, -10, 10, opts );
var y = discreteUniform( N, -10, 10, opts );
sspmv.ndarray( 'row-major', 'upper', N, 1.0, AP, x, 1, 0, 1.0, y, 1, 0 );
console.log( y );
```
* * *
## C APIs
### Usage
```c
TODO
```
#### TODO
TODO.
```c
TODO
```
TODO
```c
TODO
```
### Examples
```c
TODO
```
[blas]: http://www.netlib.org/blas
[sspmv]: https://www.netlib.org/lapack/explore-html/d0/d4b/group__hpmv_gacdad62873d30076fb56e99100e8a8a6c.html#gacdad62873d30076fb56e99100e8a8a6c
[mdn-float32array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Float32Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/TypedArray