# trsv¶

Solves a system of linear equations whose coefficients are in a triangular matrix.

Syntax

void `trsv`(queue &exec_queue, uplo upper_lower, transpose trans, diag unit_nonunit, std::int64_t n, std::int64_t k, buffer<T, 1> &a, std::int64_t lda, buffer<T, 1> &x, std::int64_t incx)

`trsv` supports the following precisions and devices.

T

Devices Supported

`float`

Host, CPU, and GPU

`double`

Host, CPU, and GPU

`std::complex<float>`

Host, CPU, and GPU

`std::complex<double>`

Host, CPU, and GPU

Description

The trsv routines compute a matrix-vector product with a triangular band matrix. The operation is defined as

```op(A)*x = b
```

where:

op(`A`) is one of op(`A`) = `A`, or op(`A`) = `A`T, or op(`A`) = `A`H,

`A` is an `n`-by-`n` unit or non-unit, upper or lower triangular matrix,

`b` and `x` are vectors of length `n`.

Input Parameters

exec_queue

The queue where the routine should be executed.

upper_lower

Specifies whether `A` is upper or lower triangular. See Data Types for more details.

trans

Specifies op(`A`), the transposition operation applied to `A`. See Data Types for more details.

unit_nonunit

Specifies whether the matrix `A` is unit triangular or not. See Data Types for more details.

n

Numbers of rows and columns of `A`. Must be at least zero.

a

Buffer holding input matrix `A`. Must have size at least `lda`*`n`. See Matrix and Vector Storage for more details.

lda

Leading dimension of matrix `A`. Must be at least `n`, and positive.

x

Buffer holding the `n`-element right-hand side vector `b`. The buffer must be of size at least (1 + (`n` - 1)*abs(`incx`)). See Matrix and Vector Storage for more details.

incx

Stride of vector `x`.

Output Parameters

x

Buffer holding the solution vector `x`.