potri¶
Computes the inverse of a symmetric (Hermitian) positive-definite matrix using the Cholesky factorization.
Description
potri supports the following precisions.
T
float
double
std::complex<float>
std::complex<double>
The routine computes the inverse \(A^{-1}\) of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix \(A\). Before calling this routine, call potrf to factorize \(A\).
potri (Buffer Version)¶
Syntax
namespace oneapi::mkl::lapack {
void potri(cl::sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, cl::sycl::buffer<T,1> &a, std::int64_t lda, 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 \(A\) has been factored:
If
upper_lower = onemkl::uplo::upper, the upper triangle of \(A\) is stored.If
upper_lower = onemkl::uplo::lower, the lower triangle of \(A\) is stored.- n
Specifies the order of the matrix \(A\) (\(0 \le n\)).
- a
Contains 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.- 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 potri_scratchpad_size function.
Output Parameters
- a
Overwritten by the upper or lower triangle of the inverse of \(A\). Specified by
upper_lower.- 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 (and therefore the factor itself) is zero, and the inversion 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.
potri (USM Version)¶
Syntax
namespace oneapi::mkl::lapack {
cl::sycl::event potri(cl::sycl::queue &queue, onemkl::uplo upper_lower, std::int64_t n, T *a, std::int64_t lda, T *scratchpad, std::int64_t scratchpad_size, const cl::sycl::vector_class<cl::sycl::event> &events = {})
}
Input Parameters
- queue
The queue where the routine should be executed.
- upper_lower
Indicates how the input matrix \(A\) has been factored:
If
upper_lower = onemkl::uplo::upper, the upper triangle of \(A\) is stored.If
upper_lower = onemkl::uplo::lower, the lower triangle of \(A\) is stored.- n
Specifies the order of the matrix \(A\) (\(0 \le n\)).
- a
Contains 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.- 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 potri_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- a
Overwritten by the upper or lower triangle of the inverse of \(A\). Specified by
upper_lower.- 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 (and therefore the factor itself) is zero, and the inversion 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