unmtr¶
Multiplies a complex matrix by the complex unitary matrix Q determined by hetrd.
Description
unmtr
supports the following precisions.
T
std::complex<float>
std::complex<double>
The routine multiplies a complex matrix \(C\) by \(Q\) or \(Q^{H}\), where \(Q\) is the unitary matrix \(Q\) formed by hetrd when reducing a complex Hermitian matrix \(A\) to tridiagonal form: \(A = QTQ^H\). Use this routine after a call to hetrd.
Depending on the parameters side
and trans
, the routine can
form one of the matrix products \(QC\), \(Q^{H}C\),
\(CQ\), or \(CQ^{H}\) (overwriting the result on \(C\)).
unmtr (Buffer Version)¶
Syntax
namespace oneapi::mkl::lapack {
void unmtr(cl::sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::uplo upper_lower, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, cl::sycl::buffer<T,1> &a, std::int64_t lda, cl::sycl::buffer<T,1> &tau, cl::sycl::buffer<T,1> &c, std::int64_t ldc, cl::sycl::buffer<T,1> &scratchpad, std::int64_t scratchpad_size)
}
Input Parameters
In the descriptions below, r
denotes the order of \(Q\):
\(r\)=\(m\) |
if |
---|---|
\(r\)=\(n\) |
if |
- queue
The queue where the routine should be executed.
- side
Must be either
side::left
orside::right
.If
side=side::left
, \(Q\) or \(Q^{H}\) is applied to \(C\) from the left.If
side=side::right
, \(Q\) or \(Q^{H}\) is applied to \(C\) from the right.- upper_lower
Must be either
uplo::upper
oruplo::lower
. Uses the sameupper_lower
as supplied to hetrd.- trans
Must be either
transpose::nontrans
ortranspose::conjtrans
.If
trans=transpose::nontrans
, the routine multiplies \(C\) by \(Q\).If
trans=transpose::conjtrans
, the routine multiplies \(C\) by \(Q^{H}\).- m
The number of rows in the matrix \(C\) (\(m \ge 0\)).
- n
The number of columns the matrix \(C\) (\(n \ge 0\)).
- k
The number of elementary reflectors whose product defines the matrix \(Q\) (\(0 \le k \le n\)).
- a
The buffer
a
as returned by hetrd.- lda
The leading dimension of
a
\((\max(1,r) \le \text{lda})\).- tau
The buffer
tau
as returned by hetrd. The dimension oftau
must be at least \(\max(1,r-1)\).- c
The buffer
c
contains the matrix \(C\). The second dimension ofc
must be at least \(\max(1,n)\).- ldc
The leading dimension of
c
\((\max(1,n) \le \text{ldc})\).- 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 unmtr_scratchpad_size function.
Output Parameters
- c
Overwritten by the product \(QC\), \(Q^{H}C\), \(CQ\), or \(CQ^{H}\) (as specified by
side
andtrans
).- 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
info
code of the problem can be obtained by info() method of exception object:If \(info=-i\), the \(i\)-th parameter had an illegal value.
If
info
equals 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.
unmtr (USM Version)¶
Syntax
namespace oneapi::mkl::lapack {
cl::sycl::event unmtr(cl::sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::uplo upper_lower, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, T *a, std::int64_t lda, T *tau, T *c, std::int64_t ldc, T *scratchpad, std::int64_t scratchpad_size, const std::vector<cl::sycl::event> &events = {})
}
Input Parameters
In the descriptions below, r
denotes the order of \(Q\):
\(r\)=\(m\) |
if |
---|---|
\(r\)=\(n\) |
if |
- queue
The queue where the routine should be executed.
- side
Must be either
side::left
orside::right
.If
side=side::left
, \(Q\) or \(Q^{H}\) is applied to \(C\) from the left.If
side=side::right
, \(Q\) or \(Q^{H}\) is applied to \(C\) from the right.- upper_lower
Must be either
uplo::upper
oruplo::lower
. Uses the sameupper_lower
as supplied to hetrd.- trans
Must be either
transpose::nontrans
ortranspose::conjtrans
.If
trans=transpose::nontrans
, the routine multiplies \(C\) by \(Q\).If
trans=transpose::conjtrans
, the routine multiplies \(C\) by \(Q^{H}\).- m
The number of rows in the matrix \(C\) (\(m \ge 0\)).
- n
The number of columns the matrix \(C\) (\(n \ge 0\)).
- k
The number of elementary reflectors whose product defines the matrix \(Q\) (\(0 \le k \le n\)).
- a
The pointer to
a
as returned by hetrd.- lda
The leading dimension of
a
\((\max(1,r) \le \text{lda})\).- tau
The pointer to
tau
as returned by hetrd. The dimension oftau
must be at least \(\max(1,r-1)\).- c
The array
c
contains the matrix \(C\). The second dimension ofc
must be at least \(\max(1,n)\).- ldc
The leading dimension of
c
\((\max(1,n) \le \text{ldc})\).- 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 unmtr_scratchpad_size function.- events
List of events to wait for before starting computation. Defaults to empty list.
Output Parameters
- c
Overwritten by the product \(QC\), \(Q^{H}C\), \(CQ\), or \(CQ^{H}\) (as specified by
side
and trans).- 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
info
code of the problem can be obtained by info() method of exception object:If \(info=-i\), the \(i\)-th parameter had an illegal value.
If
info
equals 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 Singular Value and Eigenvalue Problem Routines