Contents

# tbsv

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

## Description

The
tbsv
routines solve a system of linear equations whose coefficients are in a triangular band matrix. The operation is defined as:
where:
• op(
A
) is one of op(
A
) =
A
, or op(
A
) =
A
T
, or op(
A
) =
A
H
• A
is
n
x
n
unit or non-unit, upper or lower triangular band matrix, with (
k
+ 1) diagonals
• b
and
x
are vectors of length
n
tbsv
supports the following precisions:
T
float
double
std::complex<float>
std::complex<double>

## tbsv (Buffer Version)

Syntax
``````namespace oneapi::mkl::blas::column_major {
void tbsv(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t n,
std::int64_t k,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &x,
std::int64_t incx)
}``````
``````namespace oneapi::mkl::blas::row_major {
void tbsv(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t n,
std::int64_t k,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &x,
std::int64_t incx)
}``````
Input Parameters
queue
The queue where the routine should be executed.
upper_lower
Specifies whether matrix
A
is upper or lower triangular. See Data Types for more details.
trans
Specifies op(
A
), the transposition operation applied to matrix
A
. See Data Types for more details.
unit_diag
Specifies whether matrix
A
is unit triangular or not. See Data Types for more details.
n
Number of rows and columns of matrix
A
. Must be at least zero.
k
Number of sub/super-diagonals of matrix
A
. Must be at least zero.
a
Buffer holding input matrix
A
. Size of the buffer must be at least
lda
*
n
. See Matrix Storage for more details.
lda
Leading dimension of matrix
A
. Must be at least (
k
+ 1) and positive.
x
Buffer holding input vector
x
. Size of the buffer must be at least (1 + (
n
- 1)*abs(
incx
)). See Matrix Storage for more details.
incx
Stride of vector
x
.
Output Parameters
x
Buffer holding solution vector
x
.

## tbsv (USM Version)

Syntax
``````namespace oneapi::mkl::blas::column_major {
sycl::event tbsv(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t n,
std::int64_t k,
const T *a,
std::int64_t lda,
T *x,
std::int64_t incx,
const std::vector<sycl::event> &dependencies = {})
}``````
``````namespace oneapi::mkl::blas::row_major {
sycl::event tbsv(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
oneapi::mkl::diag unit_diag,
std::int64_t n,
std::int64_t k,
const T *a,
std::int64_t lda,
T *x,
std::int64_t incx,
const std::vector<sycl::event> &dependencies = {})
}``````
Input Parameters
queue
The queue where the routine should be executed.
upper_lower
Specifies whether matrix
A
is upper or lower triangular. See Data Types for more details.
trans
Specifies op(
A
), the transposition operation applied to matrix
A
. See Data Types for more details.
unit_diag
Specifies whether matrix
A
is unit triangular or not. See Data Types for more details.
n
Number of rows and columns of matrix
A
. Must be at least zero.
k
Number of sub/super-diagonals of matrix
A
. Must be at least zero.
a
Pointer to input matrix
A
. Size of the array holding input matrix
A
must be at least
lda
*
n
. See Matrix Storage for more details.
lda
Leading dimension of matrix
A
. Must be at least (
k
+ 1) and positive.
x
Pointer to input vector
x
. Size of the array holding input vector
x
must be at least (1 + (
n
- 1)*abs(
incx
)). See Matrix Storage for more details.
incx
Stride of vector
x
.
dependencies
List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.
Output Parameters
x
Pointer to solution vector
x
.
Return Values
Output event to wait on to ensure computation is complete.

#### Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.