potrs¶
Solves a system of linear equations with a Cholesky-factored symmetric (Hermitian) positive-definite coefficient matrix.
Description
potrs supports the following precisions.
T
float
double
std::complex<float>
std::complex<double>
The routine solves for \(X\) the system of linear equations \(AX = B\) with a symmetric positive-definite or, for complex data, Hermitian positive-definite matrix \(A\), given the Cholesky factorization of \(A\):
\(A = U^TU\) for real data, \(A = U^HU\) for complex data |
if |
|---|---|
\(A = LL^T\) for real data, \(A = LL^H\) for complex data |
if |
where \(L\) is a lower triangular matrix and \(U\) is upper triangular. The system is solved with multiple right-hand sides stored in the columns of the matrix \(B\).
Before calling this routine, you must call potrf to compute the Cholesky factorization of \(A\).
potrs (Buffer Version)¶
Syntax
namespace oneapi::mkl::lapack {
void potrs(cl::sycl::queue &queue, oneapi::mkl::uplo upper_lower, std::int64_t n, std::int64_t nrhs, cl::sycl::buffer<T,1> &a, std::int64_t lda, cl::sycl::buffer<T,1> &b, std::int64_t ldb, cl::sycl::buffer<T,1> &scratchpad, std::int64_t scratchpad_size)
}
Input Parameters
- queue
The queue where the routine should be executed.
- upper_lower
Indicates how the input matrix has been factored:
If
upper_lower = oneapi::mkl::uplo::upper, the upper triangle \(U\) of \(A\) is stored, where \(A\) = \(U^{T}\) for real data, \(A\) = \(U^{H}U\) for complex data.If
upper_lower = oneapi::mkl::uplo::lower, the lower triangle \(L\) of \(A\) is stored, where \(A\) = \(LL^{T}\) for real data, \(A\) = \(LL^{H}\) for complex data.- n
The order of matrix \(A\) (\(0 \le n\)).
- nrhs
The number of right-hand sides (\(0 \le \text{nrhs}\)).
- a
Buffer containing the factorization of the matrix A, as returned by potrf. The second dimension of
amust be at least \(\max(1, n)\).- lda
The leading dimension of
a.- 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 potrs_scratchpad_size function.
Output Parameters
- b
Overwritten by the solution matrix \(X\).
- scratchpad
Buffer holding scratchpad memory to be used by routine for storing intermediate results.
Throws
This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.
oneapi::mkl::unsupported_device
oneapi::mkl::lapack::invalid_argument
oneapi::mkl::lapack::computation_error
Exception is thrown in case of problems during calculations. The
infocode of the problem can be obtained by info() method of exception object:If \(\text{info}=-i\), the \(i\)-th parameter had an illegal value.
If \(\text{info}=i\), the \(i\)-th diagonal element of the Cholesky factor is zero, and the solve could not be completed.
If
infoequals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object.
potrs (USM Version)¶
Syntax
namespace oneapi::mkl::lapack {
cl::sycl::event potrs(cl::sycl::queue &queue, oneapi::mkl::uplo upper_lower, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, T *b, std::int64_t ldb, T *scratchpad, std::int64_t scratchpad_size, const std::vector<cl::sycl::event> &events = {})
}
Input Parameters
- queue
The queue where the routine should be executed.
- upper_lower
Indicates how the input matrix has been factored:
If
upper_lower = oneapi::mkl::uplo::upper, the upper triangle \(U\) of \(A\) is stored, where \(A\) = \(U^{T}U\) for real data, \(A\) = \(U^{H}U\) for complex data.If
upper_lower = oneapi::mkl::uplo::lower, the lower triangle \(L\) of \(A\) is stored, where \(A\) = \(LL^{T}\) for real data, \(A\) = \(LL^{H}\) for complex data.- n
The order of matrix \(A\) (\(0 \le n\)).
- 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 potrf. The second dimension of
amust be at least \(\max(1, n)\).- lda
The leading dimension of
a.- 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 potrs_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- b
Overwritten by the solution matrix \(X\).
- scratchpad
Pointer to scratchpad memory to be used by routine for storing intermediate results.
Throws
This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.
oneapi::mkl::unsupported_device
oneapi::mkl::lapack::invalid_argument
oneapi::mkl::lapack::computation_error
Exception is thrown in case of problems during calculations. The
infocode of the problem can be obtained by info() method of exception object:If \(\text{info}=-i\), the \(i\)-th parameter had an illegal value.
If \(\text{info}=i\), the \(i\)-th diagonal element of the Cholesky factor is zero, and the solve could not be completed.
If
infoequals to value passed as scratchpad size, and detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by detail() method of exception object.
Return Values
Output event to wait on to ensure computation is complete.
Parent topic: LAPACK Linear Equation Routines