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Optimized GPU implementation of batched matrix multiply operation

Since R2020a


[D1,D2] = gpucoder.batchedMatrixMultiply(A1,B1,A2,B2) performs matrix-matrix multiplication of a batch of matrices A1,B1 and A2,B2. The gpucoder.batchedMatrixMultiply function performs matrix-matrix multiplication of the form:


where α is a scalar multiplication factor, A, B, and D are matrices with dimensions m-by-k, k-by-n, and m-by-n respectively. You can optionally transpose or hermitian-conjugate A and B. By default, α is set to one and the matrices are not transposed. To specify a different scalar multiplication factor and perform transpose operations on the input matrices, use the Name,Value pair arguments.

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

[D1,...,DN] = gpucoder.batchedMatrixMultiply(A1,B1,...,AN,BN) performs matrix-matrix multiplication of multiple A, B pairs of the form:



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


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Perform a simple batched matrix-matrix multiplication and use the gpucoder.batchedMatrixMultiply function to generate CUDA® code that calls corresponding cublas<t>gemmBatched APIs.

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

function [D1,D2] = myBatchMatMul(A1,B1,A2,B2,alpha)

[D1,D2] = gpucoder.batchedMatrixMultiply(A1,B1,A2,B2, ...


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

A1 = coder.newtype('double',[15,42],[0 0]);
A2 = coder.newtype('double',[15,42],[0 0]);
B1 = coder.newtype('double',[42,30],[0 0]);
B2 = coder.newtype('double',[42,30],[0 0]);
alpha = 0.3;
inputs = {A1,B1,A2,B2,alpha};

To generate a CUDA library, use the codegen function.

cfg = coder.gpuConfig('lib');
cfg.GpuConfig.EnableCUBLAS = true;
cfg.GpuConfig.EnableCUSOLVER = true;
cfg.GenerateReport = true;
codegen -config cfg-args inputs myBatchMatMul

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

// File:
void myBatchMatMul(const double A1[630], const double B1[1260], const double A2
                   [630], const double B2[1260], double alpha, double D1[450],
                   double D2[450])
  double alpha1;

  myBatchMatMul_kernel1<<<dim3(2U, 1U, 1U), dim3(512U, 1U, 1U)>>>(*gpu_A2,
    *gpu_A1, *gpu_input_cell_f2, *gpu_input_cell_f1);
  cudaMemcpy(gpu_B2, (void *)&B2[0], 10080UL, cudaMemcpyHostToDevice);
  cudaMemcpy(gpu_B1, (void *)&B1[0], 10080UL, cudaMemcpyHostToDevice);
  myBatchMatMul_kernel2<<<dim3(3U, 1U, 1U), dim3(512U, 1U, 1U)>>>(*gpu_B2,
    *gpu_B1, *gpu_input_cell_f4, *gpu_input_cell_f3);
  myBatchMatMul_kernel3<<<dim3(1U, 1U, 1U), dim3(480U, 1U, 1U)>>>(gpu_r3, gpu_r2);
  myBatchMatMul_kernel4<<<dim3(1U, 1U, 1U), dim3(32U, 1U, 1U)>>>(gpu_r2,
  myBatchMatMul_kernel5<<<dim3(1U, 1U, 1U), dim3(32U, 1U, 1U)>>>(gpu_r3,

  cublasDgemmBatched(getCublasGlobalHandle(), CUBLAS_OP_N, CUBLAS_OP_N, 15, 30,
                     42, (double *)gpu_alpha1, (double **)gpu_Aarray, 15,
                     (double **)gpu_Barray, 42, (double *)gpu_beta1, (double **)
                     gpu_Carray, 15, 2);
  myBatchMatMul_kernel6<<<dim3(1U, 1U, 1U), dim3(480U, 1U, 1U)>>>(*gpu_D2,
    *gpu_out_cell, *gpu_D1);

Input Arguments

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

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

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: [D1,D2] = gpucoder.batchedMatrixMultiply(A1,B1,A2,B2,'alpha',0.3,'transpose','CC');

Value of the scalar used for multiplication with A. 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.

Version History

Introduced in R2020a