# strmv
> Perform one of the matrix-vector operations `x = A*x` or `x = A^T*x`.
## Usage
```javascript
var strmv = require( '@stdlib/blas/base/strmv' );
```
#### strmv( order, uplo, trans, diag, N, A, LDA, x, sx )
Performs one of the matrix-vector operations `x = A*x` or `x = A^T*x`, where `x` is an `N` element vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular matrix.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
strmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, 1 );
// x => [ 14.0, 8.0, 3.0 ]
```
The function has the following parameters:
- **order**: storage layout.
- **uplo**: specifies whether `A` is an upper or lower triangular matrix.
- **trans**: specifies whether `A` should be transposed, conjugate-transposed, or not transposed.
- **diag**: specifies whether `A` has a unit diagonal.
- **N**: number of elements along each dimension of `A`.
- **A**: input matrix stored in linear memory as a [`Float32Array`][mdn-float32array].
- **lda**: stride of the first dimension of `A` (a.k.a., leading dimension of the matrix `A`).
- **x**: input vector [`Float32Array`][mdn-float32array].
- **sx**: `x` stride length.
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 Float32Array = require( '@stdlib/array/float32' );
var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
strmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x, -1 );
// x => [ 1.0, 4.0, 10.0 ]
```
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( [ 1.0, 1.0, 1.0, 1.0 ] );
var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
// Create offset views...
var x1 = new Float32Array( x0.buffer, x0.BYTES_PER_ELEMENT*1 ); // start at 2nd element
strmv( 'row-major', 'upper', 'no-transpose', 'unit', 3, A, 3, x1, 1 );
// x0 => [ 1.0, 6.0, 3.0, 1.0 ]
```
#### strmv.ndarray( uplo, trans, diag, N, A, sa1, sa2, oa, x, sx, ox )
Performs one of the matrix-vector operations `x = A*x` or `x = A^T*x`, using alternative indexing semantics and where `x` is an `N` element vector and `A` is an `N` by `N` unit, or non-unit, upper or lower triangular matrix.
```javascript
var Float32Array = require( '@stdlib/array/float32' );
var A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
strmv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, 1, 0 );
// x => [ 14.0, 8.0, 3.0 ]
```
The function has the following additional parameters:
- **sa1**: stride of the first dimension of `A`.
- **sa2**: stride of the second dimension of `A`.
- **oa**: starting index for `A`.
- **ox**: starting index for `x`.
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 A = new Float32Array( [ 1.0, 2.0, 3.0, 0.0, 1.0, 2.0, 0.0, 0.0, 1.0 ] );
var x = new Float32Array( [ 1.0, 2.0, 3.0 ] );
strmv.ndarray( 'upper', 'no-transpose', 'unit', 3, A, 3, 1, 0, x, -1, 2 );
// x => [ 1.0, 4.0, 10.0 ]
```
## Notes
- `strmv()` corresponds to the [BLAS][blas] level 2 function [`strmv`][blas-strmv].
## Examples
```javascript
var discreteUniform = require( '@stdlib/random/array/discrete-uniform' );
var strmv = require( '@stdlib/blas/base/strmv' );
var opts = {
'dtype': 'float32'
};
var N = 5;
var A = discreteUniform( N*N, -10.0, 10.0, opts );
var x = discreteUniform( N, -10.0, 10.0, opts );
strmv( 'column-major', 'upper', 'no-transpose', 'unit', N, A, N, x, 1 );
console.log( x );
strmv.ndarray( 'upper', 'no-transpose', 'unit', N, A, 1, N, 0, x, 1, 0 );
console.log( x );
```
* * *
## C APIs
### Usage
```c
TODO
```
#### TODO
TODO.
```c
TODO
```
TODO
```c
TODO
```
### Examples
```c
TODO
```
[blas]: http://www.netlib.org/blas
[blas-strmv]: https://www.netlib.org/lapack/explore-html/d6/d1c/group__trmv_ga7b90369d2b2b19f78f168e10dd9eb8ad.html#ga7b90369d2b2b19f78f168e10dd9eb8ad
[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