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Many programs for scientic computing in Python are based on NumPy and therefore make heavy use of numerical linear algebra (NLA) functions, vectorized operations, slicing and broadcasting. AlgoPy provides the means to compute derivatives of arbitrary order and Taylor approximations of such programs. The approach is based on a combination of univariate… (More)

We derive algorithms for higher order derivative computation of the rectangular QR and eigenvalue decomposition of symmetric matrices with distinct eigenvalues in the forward and reverse mode of al-gorithmic differentiation (AD) using univariate Taylor propagation of matrices (UTPM). Linear algebra functions are regarded as elementary functions and not as… (More)

This paper is concerned with the efficient evaluation of higher-order derivatives of functions $f$ that are composed of matrix operations. I.e., we want to compute the $D$-th derivative tensor $\nabla^D f(X) \in \mathbb R^{N^D}$, where $f:\mathbb R^{N} \to \mathbb R$ is given as an algorithm that consists of many matrix operations. We propose a method that… (More)

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