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Co-authored-by: Albert Steppi <[email protected]>
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mdhaber and steppi authored Jan 8, 2025
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# Summary

Numerical integration, series summation, differentiation, optimization, and root finding are fundamental problems with applications in essentially all domains of science and engineering. Frequently, such problems do not arise individually, but rather in batches; e.g., differentiation of a single curve at many points or minimization of a function for many values of a parameter. In array computing, operations on batches of values can be vectorized. With NumPy [@numpy], operations on arrays expressed in Python can be evaluated as (sequential) loops in efficient native code, or in some cases in parallel with SIMD [@nep38]. Other Python array libraries such as CuPy [@cupy], PyTorch [@pytorch], and JAX [@jax] are able to exploit GPUs to parallelize vectorized computations. However, SciPy [@scipy] – the de facto standard Python library for solving the above problems – did not offer features to vectorize the solution process with NumPy [@numpy] arrays, let alone array library agnostic implementations.
Numerical integration, series summation, differentiation, optimization, and root finding are fundamental problems with applications in essentially all domains of science and engineering. Frequently, such problems do not arise individually, but rather in batches; e.g., differentiation of a single curve at many points or minimization of a function for many values of a parameter. In array computing, operations on batches of values can be vectorized. With NumPy [@numpy], operations on arrays expressed in Python can be evaluated as (sequential) loops in efficient native code, or in some cases in parallel with SIMD [@nep38]. Other Python array libraries such as CuPy [@cupy], PyTorch [@pytorch], and JAX [@jax] are able to exploit GPUs to parallelize vectorized computations. However, SciPy [@scipy] – the de facto standard Python library for solving the above problems – offered few functions capable of vectorizing the solution of such problems with NumPy [@numpy], let alone with alternative array libraries.

This paper discusses several new features that fill this gap, included in SciPy 1.15.0:

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