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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:
LaTex Math image.
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.