stridedbatched

Strided batched is a data layout and interface for performing a batch of identical linear algebra operations where the matrices for each batch item are stored in memory with a fixed stride between consecutive items. This pattern is commonly used for batched matrix-matrix multiplications (GEMMs) and other batched BLAS operations on accelerators, notably GPUs. In a strided batched GEMM, for i from 0 to batchCount-1, the operation is C_i = alpha * op(A_i) * op(B_i) + beta * C_i, where A_i, B_i, and C_i are matrices of fixed shapes, and op denotes optional transposition or conjugate transposition.

Typical parameterization (as in cuBLAS GEMM Strided Batched) includes: m, n, k defining the matrix dimensions; alpha and beta scalars; pointers to the first A, B, and C matrices; leading dimensions lda, ldb, ldc; and strides strideA, strideB, strideC that specify the distance in elements between the starts of A_i, B_i, and C_i for consecutive batch indices. The batchCount indicates how many batch items to process. For example, A_i is stored starting at baseA + i * strideA, B_i at baseB + i * strideB, and C_i at baseC + i * strideC. When matrices are stored contiguously, strideA = lda * k, strideB = ldb * n, and strideC = ldc * n.

Strided batched contrasts with pointer-based batched methods (arrays of pointers to A_i, B_i, C_i). Strided storage enables better memory coalescing and lower pointer overhead, but requires uniform shapes and regular strides. It is widely supported in high-performance libraries and is commonly used in GPU-accelerated workloads, such as deep learning and scientific computing, where many independent GEMMs of identical sizes must be computed efficiently.