mfem::BatchedLinAlg Class Reference

Class for performing batched linear algebra operations, potentially using accelerated algorithms (GPU BLAS or MAGMA). Accessed using static member functions. More...

#include <batched.hpp>

Public Types
enum	Backend { NATIVE , GPU_BLAS , MAGMA , NUM_BACKENDS }
	Available backends for implementations of batched algorithms. More...
enum	Op { N , T }
	Operation type (transposed or not transposed) More...

Static Public Member Functions
static void	AddMult (const DenseTensor &A, const Vector &x, Vector &y, real_t alpha=1.0, real_t beta=1.0, Op op=Op::N)
	Computes \(y = \alpha A^{op} x + \beta y\).
static void	Mult (const DenseTensor &A, const Vector &x, Vector &y)
	Computes \(y = A x\) (e.g. by calling AddMult(A,x,y,1,0,Op::N)).
static void	MultTranspose (const DenseTensor &A, const Vector &x, Vector &y)
	Computes \(y = A^T x\) (e.g. by calling AddMult(A,x,y,1,0,Op::T)).
static void	Invert (DenseTensor &A)
	Replaces the block diagonal matrix \(A\) with its inverse \(A^{-1}\).
static void	LUFactor (DenseTensor &A, Array< int > &P)
	Replaces the block diagonal matrix \(A\) with its LU factors. The pivots are stored in P.
static void	LUSolve (const DenseTensor &A, const Array< int > &P, Vector &x)
	Replaces \(x\) with \(A^{-1} x\), given the LU factors A and pivots P of the block-diagonal matrix \(A\).
static bool	IsAvailable (Backend backend)
	Returns true if the requested backend is available.
static void	SetActiveBackend (Backend backend)
	Set the default backend for batched linear algebra operations.
static Backend	GetActiveBackend ()
	Get the default backend for batched linear algebra operations.
static const BatchedLinAlgBase &	Get (Backend backend)
	Get the BatchedLinAlgBase object associated with a specific backend.

Detailed Description

Class for performing batched linear algebra operations, potentially using accelerated algorithms (GPU BLAS or MAGMA). Accessed using static member functions.

The static member functions will delegate to the active backend (which can be set using SetActiveBackend(), see BatchedLinAlg::Backend for all available backends and the order in which they will be chosen initially). Operations can be performed directly with a specific backend using Get().

Definition at line 31 of file batched.hpp.

Member Enumeration Documentation

Backend

enum mfem::BatchedLinAlg::Backend

Available backends for implementations of batched algorithms.

The initially active backend will be the first available backend in this order: MAGMA, GPU_BLAS, NATIVE.

Enumerator
NATIVE	The standard MFEM backend, implemented using mfem::forall kernels. Not as performant as the other kernels.
GPU_BLAS	Either cuBLAS or hipBLAS, depending on whether MFEM is using CUDA or HIP. Not available otherwise.
MAGMA	MAGMA backend, only available if MFEM is compiled with MAGMA support.
NUM_BACKENDS	Counter for the number of backends.

Definition at line 38 of file batched.hpp.

Op

enum mfem::BatchedLinAlg::Op

Operation type (transposed or not transposed)

Enumerator
N	Not transposed.
T	Transposed.

Definition at line 53 of file batched.hpp.

Member Function Documentation

AddMult()

void mfem::BatchedLinAlg::AddMult ( const DenseTensor & A, const Vector & x, Vector & y, real_t alpha = 1.0, real_t beta = 1.0, Op op = Op::N )

static

Computes \(y = \alpha A^{op} x + \beta y\).

\(A^{op}\) is either \(A\) or \(A^T\) depending on the value of op. \(A\) is a block diagonal matrix, represented by the DenseTensor A with shape (m, n, n_mat). \(x\) has shape (tr?m:n, k, n_mat), and \(y\) has shape (tr?n:m, k, n_mat), where 'tr' is true in the transposed case.

Definition at line 54 of file batched.cpp.

Get()

const BatchedLinAlgBase & mfem::BatchedLinAlg::Get ( BatchedLinAlg::Backend backend )

static

Get the BatchedLinAlgBase object associated with a specific backend.

This allows the user to perform specific operations with a backend different from the active backend.

Definition at line 103 of file batched.cpp.

GetActiveBackend()

BatchedLinAlg::Backend mfem::BatchedLinAlg::GetActiveBackend ( )

static

Get the default backend for batched linear algebra operations.

Definition at line 98 of file batched.cpp.

Invert()

void mfem::BatchedLinAlg::Invert ( DenseTensor & A )

static

Replaces the block diagonal matrix \(A\) with its inverse \(A^{-1}\).

\(A\) is represented by the DenseTensor A with shape (m, m, n_mat).

Definition at line 71 of file batched.cpp.

IsAvailable()

bool mfem::BatchedLinAlg::IsAvailable ( BatchedLinAlg::Backend backend )

static

Returns true if the requested backend is available.

The available backends depend on which third-party libraries MFEM is compiled with, and whether the CUDA/HIP device is enabled.

Definition at line 87 of file batched.cpp.

LUFactor()

void mfem::BatchedLinAlg::LUFactor ( DenseTensor & A, Array< int > & P )

static

Replaces the block diagonal matrix \(A\) with its LU factors. The pivots are stored in P.

\(A\) is represented by the DenseTensor A with shape (n, n, n_mat). On output, \(P\) has shape (n, n_mat).

Definition at line 76 of file batched.cpp.

LUSolve()

void mfem::BatchedLinAlg::LUSolve ( const DenseTensor & A, const Array< int > & P, Vector & x )

static

Replaces \(x\) with \(A^{-1} x\), given the LU factors A and pivots P of the block-diagonal matrix \(A\).

The LU factors and pivots of \(A\) should be obtained by first calling LUFactor(). \(A\) has shape (n, n, n_mat) and \(x\) has shape (n, n_rhs, n_mat).

Warning

LUSolve() and LUFactor() should be called using the same backend because of potential incompatibilities (e.g. 0-based or 1-based indexing).

Definition at line 81 of file batched.cpp.

Mult()

void mfem::BatchedLinAlg::Mult ( const DenseTensor & A, const Vector & x, Vector & y )

static

Computes \(y = A x\) (e.g. by calling AddMult(A,x,y,1,0,Op::N)).

Definition at line 60 of file batched.cpp.

MultTranspose()

void mfem::BatchedLinAlg::MultTranspose ( const DenseTensor & A, const Vector & x, Vector & y )

static

Computes \(y = A^T x\) (e.g. by calling AddMult(A,x,y,1,0,Op::T)).

Definition at line 65 of file batched.cpp.

SetActiveBackend()

void mfem::BatchedLinAlg::SetActiveBackend ( BatchedLinAlg::Backend backend )

static

Set the default backend for batched linear algebra operations.

Definition at line 92 of file batched.cpp.

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The documentation for this class was generated from the following files:

• linalg/batched/batched.hpp
• linalg/batched/batched.cpp