cublasZgemm

cublasZgemm is a routine in NVIDIA's cuBLAS library that performs general matrix-matrix multiplication on complex double-precision data. It is the complex counterpart to the real and single/double-precision GEMM routines and is used for multiplying matrices whose elements are in the cuDoubleComplex data type.

Operation and formula. The function computes C = alpha * op(A) * op(B) + beta * C, where op(X) denotes X, its transpose, or its conjugate transpose, depending on the transa and transb parameters. The effective dimensions are op(A) is m-by-k and op(B) is k-by-n, producing C of size m-by-n. The scalars alpha and beta are complex double-precision values, and A, B, and C are stored in device memory as cuDoubleComplex elements.

Parameters and data types. The typical API takes a cuBLAS handle, two operation selectors (transa and transb), the matrix dimensions m, n, and k, pointers to alpha and beta, and pointers to A, B, and C along with their leading dimensions (lda, ldb, ldc). A, B, and C are arrays of cuDoubleComplex elements, and alpha and beta are pointers to cuDoubleComplex. The leading dimensions must satisfy the cuBLAS storage conventions, taking into account whether matrices are transposed or conjugate-transposed.

Storage and usage notes. cuBLAS assumes column-major storage consistent with the BLAS standard; row-major data can be used by adjusting the transposition flags. The routine runs on the GPU and requires a properly initialized cuBLAS handle and a CUDA context. There are batched variants (e.g., ZgemmBatched, ZgemmStridedBatched) for processing multiple matrices efficiently.

See also. cuBLAS, BLAS, cuDoubleComplex.