unmtr¶

Multiplies a complex matrix by the complex unitary matrix Q determined by hetrd.

unmtr supports the following precisions.

T

std::complex<float>

std::complex<double>

Description

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 = Q*T*QH. Use this routine after a call to hetrd.

Depending on the parameters left_right and trans, the routine can form one of the matrix products Q*C, Q^H*C, C*Q, or C*Q^H (overwriting the result on C).

unmtr (BUFFER Version)¶

Syntax

void onemkl::lapack::unmtr(cl::sycl::queue &queue, onemkl::side left_right, onemkl::uplo upper_lower, onemkl::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 `left_right = side::left`
`r`=`n`	if `left_right = side::right`

queue

The queue where the routine should be executed.

left_right

Must be either side::left or side::right.

If left_right=side::left, Q or Q^H is applied to C from the left.

If left_right=side::right, Q or Q^H is applied to C from the right.

upper_lower

Must be either uplo::upper or uplo::lower. Uses the same upper_lower as supplied to hetrd.

trans

Must be either transpose::nontrans or transpose::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≥0).

n

The number of columns the matrix C (n≥0).

k

The number of elementary reflectors whose product defines the matrix Q (0≤k≤n).

a

The buffer a as returned by hetrd.

lda

The leading dimension of a(max(1,r)≤lda).

tau

The buffer tau as returned by hetrd. The dimension of tau must be at least max(1,r-1).

c

The buffer c contains the matrix C. The second dimension of c must be at least max(1,n).

ldc

The leading dimension of c(max(1,n)≤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 Q*C, Q^H*C, C*Q, or C*Q^H (as specified by left_right and trans).
scratchpad: Buffer holding scratchpad memory to be used by routine for storing intermediate results.

Throws

onemkl::lapack::exception

Exception is thrown in case of problems happened during calculations. The info code of the problem can be obtained by get_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 get_detail() returns non zero, then passed scratchpad is of insufficient size, and required size should not be less than value return by get_detail() method of exception object.

unmtr (USM Version)¶