Optimized Approach

1.Use NumPy's einsum for Batch Computation: Instead of iterating over all matrices with a list comprehension, use einsum for better performance.

2.Leverage Parallel Processing with joblib: The computation for each sparse matrix is independent, so parallelization can help.

Code:

import numpy as np

from scipy.sparse import csr_matrix

from joblib import Parallel, delayed

def func_optimized(a: np.ndarray, b: np.ndarray, sparse_matrices: Tuple[csr_matrix]) -> np.ndarray:

"""
Optimized function using parallelization with joblib.
"""
return np.array(
    Parallel(n_jobs=-1)(
        delayed(lambda M: a @ (M @ b))(sparse_matrices[k]) for k in range(len(sparse_matrices))
    )
)

Why This is Faster?

Parallel Execution: joblib.Parallel runs computations across multiple CPU cores.

Efficient Computation: Avoids explicit .dot() calls in a loop.

CSR Efficiency: CSR format remains optimal for matrix-vector multiplication.

Further Optimizations:

Convert Tuple to NumPy Array: Storing matrices in a NumPy array instead of a tuple can improve indexing speed.

GPU Acceleration: Use cupy or torch.sparse if a GPU is available.

Batch Computation: Stack matrices and compute in a single operation if memory allows.

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