Optimized GPU implementation of batched matrix multiply with add operation

## Description

[D1,D2] = gpucoder.batchedMatrixMultiplyAdd(A1,B1,C1,A2,B2,C2) performs matrix-matrix multiplication and add of a batch of matrices A1,B1,C1 and A2,B2,C2. gpucoder.batchedMatrixMultiplyAdd performs matrix-matrix multiplication of the form:

$D=\alpha AB+\beta C$

where $\alpha$ and $\beta$ are scalar multiplication factors, A, B, C, and D are matrices with dimensions m-by-k, k-by-n, m-by-n, and m-by-n respectively. A, B, and C can optionally be transposed or hermitian-conjugated. By default, $\alpha$ and $\beta$ are set to one and the matrices are not transposed. Use the Name,Value pair arguments to specify a different scalar multiplication factor and to specify transpose operations on the input matrices.

All the batches passed to the gpucoder.batchedMatrixMultiplyAdd function must be uniform. That is, all instances must have the same dimensions m,n,k.

[D1,...,DN] = gpucoder.batchedMatrixMultiplyAdd(A1,B1,C1,...,AN,BN,CN) performs matrix-matrix multiplication and add of multiple A, B, C pairs of the form:

${D}_{i}=\alpha {A}_{i}{B}_{i}+\beta {C}_{i}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}i=1\dots N$

example

___ = gpucoder.batchedMatrixMultiplyAdd(___,Name,Value) performs batched matrix multiply and add operation using the options specified by one or more Name,Value pair arguments.

## Examples

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This example performs a simple batched matrix-matrix multiplication with add and uses the gpucoder.batchedMatrixMultiplyAdd function to generate CUDA® code that calls appropriate cublas<t>gemmBatched APIs.

In one file, write an entry-point function myBatchMatMulAdd that accepts matrix inputs A1, B1, C1, A2, B2, and C2. The input matrices are not transposed, therefore use the 'nn' option.

'alpha',alpha,,'beta',beta,'transpose','nn');

end

Use the coder.newtype function to create a type for a matrix of doubles for use in code generation.

A1 = coder.newtype('double',[12,14],[0 0]);
A2 = coder.newtype('double',[12,14],[0 0]);
B1 = coder.newtype('double',[14,16],[0 0]);
B2 = coder.newtype('double',[14,16],[0 0]);
C1 = coder.newtype('double',[12,16],[0 0]);
C2 = coder.newtype('double',[12,16],[0 0]);
alpha = 0.3;
beta = 0.6;
inputs = {A1,B1,C1,A2,B2,C2,alpha,beta};

Use the codegen function to generate a CUDA library.

cfg = coder.gpuConfig('lib');
cfg.GpuConfig.EnableCUBLAS = true;
cfg.GpuConfig.EnableCUSOLVER = true;
cfg.GenerateReport = true;

The generated CUDA code contains kernels: myBatchMatMulAdd_kernelNN for initializing the input and output matrices. It also contains the cublasDgemmBatched API calls to the cuBLAS library. The following is a snippet of the generated code.

//
//
...
void myBatchMatMulAdd(const double A1[168], const double B1[224], const double
C1[192], const double A2[168], const double B2[224], const
double C2[192], double alpha, double beta, double D1[192],
double D2[192])
{
double alpha1;
...

myBatchMatMulAdd_kernel2<<<dim3(1U, 1U, 1U), dim3(224U, 1U, 1U)>>>(*gpu_B2,
*gpu_B1, *gpu_input_cell_f4, *gpu_input_cell_f3);
cudaMemcpy(gpu_C2, (void *)&C2[0], 1536UL, cudaMemcpyHostToDevice);
cudaMemcpy(gpu_C1, (void *)&C1[0], 1536UL, cudaMemcpyHostToDevice);
myBatchMatMulAdd_kernel3<<<dim3(1U, 1U, 1U), dim3(192U, 1U, 1U)>>>(*gpu_C2,
*gpu_C1, gpu_r3, gpu_r2);
myBatchMatMulAdd_kernel4<<<dim3(1U, 1U, 1U), dim3(32U, 1U, 1U)>>>(gpu_r2,
*gpu_out_cell);
myBatchMatMulAdd_kernel5<<<dim3(1U, 1U, 1U), dim3(32U, 1U, 1U)>>>(gpu_r3,
*gpu_out_cell);
...

cublasDgemmBatched(getCublasGlobalHandle(), CUBLAS_OP_N, CUBLAS_OP_N, 12, 16,
14, (double *)gpu_alpha1, (double **)gpu_Aarray, 12,
(double **)gpu_Barray, 14, (double *)gpu_beta1, (double **)
gpu_Carray, 12, 2);
myBatchMatMulAdd_kernel6<<<dim3(1U, 1U, 1U), dim3(192U, 1U, 1U)>>>(*gpu_D2,
...

}

## Input Arguments

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Operands, specified as vectors or matrices. A, B, and C must be 2-D arrays. The number of columns in A must be equal to the number of rows in B. The number of rows in A must be equal to the number of rows in C. The number of columns in B must be equal to the number of columns in C.

Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64
Complex Number Support: Yes

### Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Value of the scalar used for multiplication with A. Default value is one.

Value of the scalar used for multiplication with C. Default value is one.

Character vector or string composed of two characters, indicating the operation performed on the matrices A and B prior to matrix multiplication. Possible values are normal ('N'), transposed ('T'), or complex conjugate transpose ('C').

## Output Arguments

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Product, returned as a scalar, vector, or matrix. Array D has the same number of rows as input A and the same number of columns as input B.