# dsymv
> 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.
## Usage
```javascript
var dsymv = require( '@stdlib/blas/base/dsymv' );
```
#### dsymv( order, uplo, N, α, A, LDA, 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.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 0.0, 0.0, 0.0 ] );
dsymv( 'row-major', 'lower', 3, 1.0, A, 3, x, 1, 0.0, y, 1 );
// y => [ 1.0, 2.0, 3.0 ]
```
The function has the following parameters:
- **order**: storage layout.
- **uplo**: specifies whether the upper or lower triangular part of the symmetric matrix `A` should be referenced.
- **N**: number of elements along each dimension of `A`.
- **α**: scalar constant.
- **A**: input matrix stored in linear memory as a [`Float64Array`][mdn-float64array].
- **lda**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
- **x**: input [`Float64Array`][mdn-float64array].
- **sx**: index increment for `x`.
- **β**: scalar constant.
- **y**: output [`Float64Array`][mdn-float64array].
- **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 `x` in reverse order,
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );
dsymv( 'row-major', 'upper', 3, 2.0, A, 3, x, -1, 1.0, y, 1 );
// y => [ 7.0, 10.0, 9.0 ]
```
Note that indexing is relative to the first index. To introduce an offset, use [`typed array`][mdn-typed-array] views.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
// Initial arrays...
var x0 = new Float64Array( [ 1.0, 1.0, 1.0, 1.0 ] );
var y0 = new Float64Array( [ 1.0, 1.0, 1.0, 1.0 ] );
var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
// Create offset views...
var x1 = new Float64Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
var y1 = new Float64Array( y0.buffer, y0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
dsymv( 'row-major', 'upper', 3, 1.0, A, 3, x1, -1, 1.0, y1, -1 );
// y0 => [ 1.0, 4.0, 3.0, 2.0 ]
```
#### dsymv.ndarray( order, uplo, N, α, A, LDA, 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.
```javascript
var Float64Array = require( '@stdlib/array/float64' );
var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 2.0, 3.0 ] );
var y = new Float64Array( [ 1.0, 2.0, 3.0 ] );
dsymv.ndarray( 'row-major', 'upper', 3, 2.0, A, 3, x, -1, 2, 1.0, y, 1, 0 );
// y => [ 7.0, 10.0, 9.0 ]
```
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 Float64Array = require( '@stdlib/array/float64' );
var A = new Float64Array( [ 1.0, 0.0, 0.0, 0.0, 2.0, 0.0, 0.0, 0.0, 3.0 ] );
var x = new Float64Array( [ 1.0, 1.0, 1.0 ] );
var y = new Float64Array( [ 1.0, 1.0, 1.0 ] );
dsymv.ndarray( 'row-major', 'lower', 3, 1.0, A, 3, x, -1, 2, 1.0, y, -1, 2 );
// y => [ 4.0, 3.0, 2.0 ]
```
## Notes
- `dsymv()` corresponds to the [BLAS][blas] level 2 function [`dsymv`][dsymv].
## Examples
```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var ones = require( '@stdlib/array/ones' );
var dsymv = require( '@stdlib/blas/base/dsymv' );
var opts = {
'dtype': 'float64'
};
var N = 3;
var A = ones( N*N, opts.dtype );
var x = discreteUniform( N, 0, 255, opts );
var y = discreteUniform( N, 0, 255, opts );
dsymv.ndarray( 'row-major', 'upper', N, 1.0, A, N, 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
[dsymv]: https://www.netlib.org/lapack/explore-html/db/d17/group__hemv_ga0b20bcf6e94079dce2f3d035798e9738.html#ga0b20bcf6e94079dce2f3d035798e9738
[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