ArrayFire: matmul (original) (raw)

Matrix multiplication. More...

Matrix multiplication.

Performs a matrix multiplication on the two input arrays after performing the operations specified in the options. The operations are done while reading the data from memory. This results in no additional memory being used for temporary buffers.

Batched matrix multiplications are supported. The supported types of batch operations for any given set of two matrices A and B are given below,

where M, K, N are dimensions of the matrix and b2, b3 indicate batch size along the respective dimension.

For the last two entries in the above table, the 2D matrix is broadcasted to match the dimensions of 3D/4D array. This broadcast doesn't involve any additional memory allocations either on host or device.

Note

Sparse support was added to ArrayFire in v3.4.0. This function can be used for Sparse-Dense matrix multiplication. See the notes of the function for usage and restrictions.

Note

Limited support for s8 was added to the CUDA backend in ArrayFire v3.10.0. See s8 Support notes for details.

◆ af_gemm()

C Interface to multiply two matrices.

This provides an interface to the BLAS level 3 general matrix multiply (GEMM) of two af_array objects, which is generally defined as:

\[ C = \alpha * opA(A)opB(B) + \beta * C \]

where \(\alpha\) (alpha) and \(\beta\) (beta) are both scalars; \(A\) and \(B\) are the matrix multiply operands; and \(opA\) and \(opB\) are noop (if AF_MAT_NONE) or transpose (if AF_MAT_TRANS) operations on \(A\) or \(B\) before the actual GEMM operation. Batched GEMM is supported if at least either \(A\) or \(B\) have more than two dimensions (see af::matmul for more details on broadcasting). However, only one alpha and one beta can be used for all of the batched matrix operands.

The af_array that out points to can be used both as an input and output. An allocation will be performed if you pass a null af_array handle (i.e. af_array c = 0;). If a valid af_array is passed as \(C\), the operation will be performed on that af_array itself. The C af_array must be the correct type and shape; otherwise, an error will be thrown.

Note

Passing an af_array that has not been initialized to the C array is will cause undefined behavior.

This example demonstrates the usage of the af_gemm function on two matrices. The \(C\) af_array handle is initialized to zero here, so af_gemm will perform an allocation.

dim_t adims[] = {5, 3, 2};

dim_t bdims[] = {3, 5, 2};

float alpha = 1.f;

float beta = 0.f;

@ f32

32-bit floating point values

AFAPI af_err af_gemm(af_array *C, const af_mat_prop opA, const af_mat_prop opB, const void *alpha, const af_array A, const af_array B, const void *beta)

C Interface to multiply two matrices.

AFAPI af_err af_constant(af_array *arr, const double val, const unsigned ndims, const dim_t *const dims, const af_dtype type)

C Interface to generate an array with elements set to a specified value.

The following example shows how you can write to a previously allocated af_array using the af_gemm call. Here we are going to use the af_array s from the previous example and index into the first slice. Only the first slice of the original \(C\) af_array will be modified by this operation.

alpha = 1.f;

beta = 1.f;

af_index(&Asub, A, 3, first_slice);

af_index(&Bsub, B, 3, first_slice);

af_index(&Csub, C, 3, first_slice);

AFAPI af_err af_index(af_array *out, const af_array in, const unsigned ndims, const af_seq *const index)

Lookup the values of input array based on sequences.

static const af_seq af_span

C-style struct to creating sequences for indexing.

Note

s8 Support

Starting with ArrayFire version v3.10.0, the CUDA backend supports A, B input arrays of type s8.

Scalars alpha, beta must be of type f32.

Output array C will be of type f32.

Requires

CUDA version >= 10 on devices with compute capability >= 5.0

Parameters

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

◆ af_matmul()

C Interface to multiply two matrices.

Performs matrix multiplication on two arrays.

Note

The following applies for Sparse-Dense matrix multiplication.

This function can be used with one sparse input. The sparse input must always be the lhs and the dense matrix must be rhs.

The sparse array can only be of AF_STORAGE_CSR format.

The returned array is always dense.

optLhs an only be one of AF_MAT_NONE, AF_MAT_TRANS, AF_MAT_CTRANS.

optRhs can only be AF_MAT_NONE.

Parameters

Returns

AF_SUCCESS, if function returns successfully, else an af_err code is given

◆ matmul() [1/3]

C++ Interface to chain multiply three matrices.

The matrix multiplications are done in a way to reduce temporary memory.

This function is not supported in GFOR.

Parameters

Returns

a x b x c

◆ matmul() [2/3]

C++ Interface to chain multiply three matrices.

The matrix multiplications are done in a way to reduce temporary memory.

This function is not supported in GFOR.

Parameters

Returns

a x b x c x d

◆ matmul() [3/3]

C++ Interface to multiply two matrices.

Performs a matrix multiplication on the two input arrays after performing the operations specified in the options. The operations are done while reading the data from memory. This results in no additional memory being used for temporary buffers.

Batched matrix multiplications are supported. The supported types of batch operations for any given set of two matrices A and B are given below,

where M, K, N are dimensions of the matrix and b2, b3 indicate batch size along the respective dimension.

For the last two entries in the above table, the 2D matrix is broadcasted to match the dimensions of 3D/4D array. This broadcast doesn't involve any additional memory allocations either on host or device.

Note

Sparse support was added to ArrayFire in v3.4.0. This function can be used for Sparse-Dense matrix multiplication. See the notes of the function for usage and restrictions.

Note

Limited support for s8 was added to the CUDA backend in ArrayFire v3.10.0. See s8 Support notes for details.

optLhs and optRhs can only be one of AF_MAT_NONE, AF_MAT_TRANS, AF_MAT_CTRANS.

This function is not supported in GFOR.

Note

The following applies for Sparse-Dense matrix multiplication.

This function can be used with one sparse input. The sparse input must always be the lhs and the dense matrix must be rhs.

The sparse array can only be of AF_STORAGE_CSR format.

The returned array is always dense.

optLhs an only be one of AF_MAT_NONE, AF_MAT_TRANS, AF_MAT_CTRANS.

optRhs can only be AF_MAT_NONE.

Parameters

Returns

lhs * rhs

Examples

pde/bhrt.cpp.

◆ matmulNT()

C++ Interface to multiply two matrices.

The second matrix will be transposed.

Performs a matrix multiplication on the two input arrays after performing the operations specified in the options. The operations are done while reading the data from memory. This results in no additional memory being used for temporary buffers.

Batched matrix multiplications are supported. The supported types of batch operations for any given set of two matrices A and B are given below,

where M, K, N are dimensions of the matrix and b2, b3 indicate batch size along the respective dimension.

For the last two entries in the above table, the 2D matrix is broadcasted to match the dimensions of 3D/4D array. This broadcast doesn't involve any additional memory allocations either on host or device.

Note

Sparse support was added to ArrayFire in v3.4.0. This function can be used for Sparse-Dense matrix multiplication. See the notes of the function for usage and restrictions.

Note

Limited support for s8 was added to the CUDA backend in ArrayFire v3.10.0. See s8 Support notes for details.

This function is not supported in GFOR.

Parameters

Returns

lhs * transpose(rhs)

◆ matmulTN()

C++ Interface to multiply two matrices.

The first matrix will be transposed.

Performs a matrix multiplication on the two input arrays after performing the operations specified in the options. The operations are done while reading the data from memory. This results in no additional memory being used for temporary buffers.

Batched matrix multiplications are supported. The supported types of batch operations for any given set of two matrices A and B are given below,

where M, K, N are dimensions of the matrix and b2, b3 indicate batch size along the respective dimension.

For the last two entries in the above table, the 2D matrix is broadcasted to match the dimensions of 3D/4D array. This broadcast doesn't involve any additional memory allocations either on host or device.

Note

Sparse support was added to ArrayFire in v3.4.0. This function can be used for Sparse-Dense matrix multiplication. See the notes of the function for usage and restrictions.

Note

Limited support for s8 was added to the CUDA backend in ArrayFire v3.10.0. See s8 Support notes for details.

This function is not supported in GFOR.

Parameters

Returns

transpose(lhs) * rhs

◆ matmulTT()

C++ Interface to multiply two matrices.

Both matrices will be transposed.

Performs a matrix multiplication on the two input arrays after performing the operations specified in the options. The operations are done while reading the data from memory. This results in no additional memory being used for temporary buffers.

Batched matrix multiplications are supported. The supported types of batch operations for any given set of two matrices A and B are given below,

where M, K, N are dimensions of the matrix and b2, b3 indicate batch size along the respective dimension.

For the last two entries in the above table, the 2D matrix is broadcasted to match the dimensions of 3D/4D array. This broadcast doesn't involve any additional memory allocations either on host or device.

Note

Sparse support was added to ArrayFire in v3.4.0. This function can be used for Sparse-Dense matrix multiplication. See the notes of the function for usage and restrictions.

Note

Limited support for s8 was added to the CUDA backend in ArrayFire v3.10.0. See s8 Support notes for details.

This function is not supported in GFOR.

Parameters

Returns

transpose(lhs) * transpose(rhs)