# getrs#

Solves a system of linear equations with an LU-factored square coefficient matrix, with multiple right-hand sides.

Description

getrs supports the following precisions.

T

float

double

std::complex<float>

std::complex<double>

The routine solves for $$X$$ the following systems of linear equations:

$$AX = B$$

if trans=oneapi::mkl::transpose::nontrans

$$A^TX = B$$

if trans=oneapi::mkl::transpose::trans

$$A^HX = B$$

if trans=oneapi::mkl::transpose::conjtrans

Before calling this routine, you must call getrf to compute the LU factorization of $$A$$.

## getrs (Buffer Version)#

Syntax

namespace oneapi::mkl::lapack {
void getrs(cl::sycl::queue &queue, oneapi::mkl::transpose trans, std::int64_t n, std::int64_t nrhs, cl::sycl::buffer<T,1> &a, std::int64_t lda, cl::sycl::buffer<std::int64_t,1> &ipiv, 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.

trans

Indicates the form of the equations:

If trans=oneapi::mkl::transpose::nontrans, then $$AX = B$$ is solved for $$X$$.

If trans=oneapi::mkl::transpose::trans, then $$A^TX = B$$ is solved for $$X$$.

If trans=oneapi::mkl::transpose::conjtrans, then $$A^HX = B$$ is solved for $$X$$.

n

The order of the matrix $$A$$ and the number of rows in matrix $$B(0 \le n)$$.

nrhs

The number of right-hand sides ($$0 \le \text{nrhs}$$).

a

Buffer containing the factorization of the matrix $$A$$, as returned by getrf. The second dimension of a must be at least $$\max(1, n)$$.

lda

The leading dimension of a.

ipiv

Array, size at least $$\max(1, n)$$. The ipiv array, as returned by getrf.

b

The array b contains the matrix $$B$$ whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least $$\max(1,\text{nrhs})$$.

ldb

The leading dimension of b.

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by getrs_scratchpad_size function.

Output Parameters

b

The buffer b is overwritten by the solution matrix $$X$$.

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::unimplemented

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=i, the $$i$$-th diagonal element of $$U$$ is zero, and the solve could not be completed.

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.

## getrs (USM Version)#

Syntax

namespace oneapi::mkl::lapack {
cl::sycl::event getrs(cl::sycl::queue &queue, oneapi::mkl::transpose trans, std::int64_t n, std::int64_t nrhs, T *a, std::int64_t lda, std::int64_t *ipiv, 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.

trans

Indicates the form of the equations:

If trans=oneapi::mkl::transpose::nontrans, then $$AX = B$$ is solved for $$X$$.

If trans=oneapi::mkl::transpose::trans, then $$A^TX = B$$ is solved for $$X$$.

If trans=oneapi::mkl::transpose::conjtrans, then $$A^HX = B$$ is solved for $$X$$.

n

The order of the matrix $$A$$ and the number of rows in matrix $$B(0 \le n)$$.

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 getrf. The second dimension of a must be at least $$\max(1, n)$$.

lda

The leading dimension of a.

ipiv

Array, size at least $$\max(1, n)$$. The ipiv array, as returned by getrf.

b

The array b contains the matrix $$B$$ whose columns are the right-hand sides for the systems of equations. The second dimension of b must be at least $$\max(1,\text{nrhs})$$.

ldb

The leading dimension of b.

Size of scratchpad memory as a number of floating point elements of type T. Size should not be less than the value returned by getrs_scratchpad_size function.

events

List of events to wait for before starting computation. Defaults to empty list.

Output Parameters

b

The array b is overwritten by the solution matrix $$X$$.

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::unimplemented

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=i, the $$i$$-th diagonal element of $$U$$ is zero, and the solve could not be completed.

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 Linear Equation Routines