How can the multiplication process between a sparse matrix and a dense ndarray vector in SciPy be made faster?

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Here are a few ways to make the multiplication process between a sparse matrix and a dense ndarray vector in SciPy faster:

Use the

`dot`

method instead of the`*`

operator:The

`dot`

method is usually faster than the`*`

operator when multiplying a sparse matrix and a dense vector in SciPy. For example:`import numpy as np from scipy.sparse import csr_matrix # Create a random sparse matrix in CSR format shape = (10000, 10000) density = 0.01 sparse_mat = csr_matrix(np.random.rand(*shape) < density) # Create a random dense vector dense_vec = np.random.rand(shape[1]) # Multiply the sparse matrix and dense vector using dot method result = sparse_mat.dot(dense_vec)`

This method uses more efficient algorithms for matrix multiplication and can be significantly faster than the

`*`

operator.Use a more efficient sparse format:

Some sparse formats are more efficient than others for certain operations. For example, the Compressed Sparse Row (CSR) format is usually faster than the Compressed Sparse Column (CSC) format when multiplying a sparse matrix and a dense vector. You can convert a sparse matrix to a different format using the

`tocsr`

,`tocoo`

,`tocsc`

, or`todok`

methods. For example:`# Convert the sparse matrix to CSR format sparse_mat_csr = sparse_mat.tocsr() # Multiply the sparse matrix in CSR format and dense vector result = sparse_mat_csr.dot(dense_vec)`

This can be faster because the CSR format optimizes for accessing the row indices of the sparse matrix, which is the bottleneck for matrix-vector multiplication.

Use Cython or Numba:

Cython and Numba are tools that can be used to accelerate Python code by generating C or LLVM code, respectively. They can be used to speed up the matrix-vector multiplication operation in SciPy. For example:

`import numpy as np from scipy.sparse import csr_matrix from numba import njit # Create a random sparse matrix in CSR format shape = (10000, 10000) density = 0.01 sparse_mat = csr_matrix(np.random.rand(*shape) < density) # Create a random dense vector dense_vec = np.random.rand(shape[1]) # Multiply the sparse matrix and dense vector using a Numba JIT function @njit def matvec(sparse_mat, dense_vec): result = np.zeros(shape[0]) indptr = sparse_mat.indptr indices = sparse_mat.indices data = sparse_mat.data for i in range(shape[0]): for j in range(indptr[i], indptr[i+1]): result[i] += data[j] * dense_vec[indices[j]] return result result = matvec(sparse_mat, dense_vec)`

This method can be significantly faster because it directly translates the Python code to low-level machine code, bypassing the Python interpreter.

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Asked: ** 2021-05-12 11:00:00 +0000 **

Seen: **23 times**

Last updated: **Apr 11 '23**

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