# 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(sycl::queue &queue, oneapi::mkl::side side, oneapi::mkl::uplo upper_lower, oneapi::mkl::transpose trans, std::int64_t m, std::int64_t n, sycl::buffer<T,1> &a, std::int64_t lda, sycl::buffer<T,1> &tau, sycl::buffer<T,1> &c, std::int64_t ldc, 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 side = side::left

$$r$$=$$n$$

if side = side::right

queue

The queue where the routine should be executed.

side

Must be either side::left or side::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 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 $$C$$ ($$m \ge 0$$).

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 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 $$(\max(1,n) \le \text{ldc})$$.

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 and trans).

Buffer holding scratchpad memory to be used by routine for storing intermediate results.

## unmtr (USM Version)¶

Syntax

namespace oneapi::mkl::lapack {
sycl::event unmtr(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<sycl::event> &events = {})
}


Input Parameters

In the descriptions below, r denotes the order of $$Q$$:

$$r$$=$$m$$

if side = side::left

$$r$$=$$n$$

if side = side::right

queue

The queue where the routine should be executed.

side

Must be either side::left or side::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 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 $$C$$ ($$m \ge 0$$).

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 of tau must be at least $$\max(1,r-1)$$.

c

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

ldc

The leading dimension of c $$(\max(1,n) \le \text{ldc})$$.

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).