getrs#
Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.
Description
getrs supports the following precisions.
T
float
double
std::complex<float>
std::complex<double>
The routine solves for \(X\) the following systems of linear equations:
\(AX = B\)
if
trans=oneapi::mkl::transpose::nontrans\(A^TX = B\)
if
trans=oneapi::mkl::transpose::trans\(A^HX = B\)
if
trans=oneapi::mkl::transpose::conjtrans
Before calling this routine, you must call getrf to compute the LU factorization of \(A\).
getrs (Buffer Version)#
Syntax
namespace oneapi::mkl::lapack {
void getrs(sycl::queue &queue, oneapi::mkl::transpose trans, std::int64_t n, std::int64_t nrhs, sycl::buffer<T,1> &a, std::int64_t lda, sycl::buffer<std::int64_t,1> &ipiv, sycl::buffer<T,1> &b, std::int64_t ldb, sycl::buffer<T,1> &scratchpad, std::int64_t scratchpad_size)
}
Input Parameters
- queue
The queue where the routine should be executed.
- trans
Indicates the form of the equations:
If
trans=oneapi::mkl::transpose::nontrans, then \(AX = B\) is solved for \(X\).If
trans=oneapi::mkl::transpose::trans, then \(A^TX = B\) is solved for \(X\).If
trans=oneapi::mkl::transpose::conjtrans, then \(A^HX = B\) is solved for \(X\).- n
The order of the matrix \(A\) and the number of rows in matrix \(B(0 \le n)\).
- nrhs
The number of right-hand sides (\(0 \le \text{nrhs}\)).
- a
Buffer containing the factorization of the matrix \(A\), as returned by getrf. The second dimension of
amust be at least \(\max(1, n)\).- lda
The leading dimension of
a.- ipiv
Array, size at least \(\max(1, n)\). The
ipivarray, as returned by getrf.- b
The array
bcontains the matrix \(B\) whose columns are the right-hand sides for the systems of equations. The second dimension ofbmust be at least \(\max(1,\text{nrhs})\).- ldb
The leading dimension of
b.- scratchpad_size
Size of scratchpad memory as a number of floating point elements of type
T. Size should not be less than the value returned by getrs_scratchpad_size function.
Output Parameters
- b
The buffer
bis overwritten by the solution matrix \(X\).- scratchpad
Buffer holding scratchpad memory to be used by routine for storing intermediate results.
getrs (USM Version)#
Syntax
namespace oneapi::mkl::lapack {
sycl::event getrs(sycl::queue &queue, oneapi::mkl::transpose trans, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, std::int64_t *ipiv, T *b, std::int64_t ldb, T *scratchpad, std::int64_t scratchpad_size, const std::vector<sycl::event> &events = {})
}
Input Parameters
- queue
The queue where the routine should be executed.
- trans
Indicates the form of the equations:
If
trans=oneapi::mkl::transpose::nontrans, then \(AX = B\) is solved for \(X\).If
trans=oneapi::mkl::transpose::trans, then \(A^TX = B\) is solved for \(X\).If
trans=oneapi::mkl::transpose::conjtrans, then \(A^HX = B\) is solved for \(X\).- n
The order of the matrix \(A\) and the number of rows in matrix \(B(0 \le n)\).
- nrhs
The number of right-hand sides (\(0 \le \text{nrhs}\)).
- a
Pointer to array containing the factorization of the matrix \(A\), as returned by getrf. The second dimension of
amust be at least \(\max(1, n)\).- lda
The leading dimension of
a.- ipiv
Array, size at least \(\max(1, n)\). The
ipivarray, as returned by getrf.- b
The array
bcontains the matrix \(B\) whose columns are the right-hand sides for the systems of equations. The second dimension ofbmust be at least \(\max(1,\text{nrhs})\).- ldb
The leading dimension of
b.- scratchpad_size
Size of scratchpad memory as a number of floating point elements of type
T. Size should not be less than the value returned by getrs_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- b
The array
bis overwritten by the solution matrix \(X\).- scratchpad
Pointer to scratchpad memory to be used by routine for storing intermediate results.
Return Values
Output event to wait on to ensure computation is complete.
Parent topic: LAPACK Linear Equation Routines