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The implementation of the computation, analysis, and visualization step is a combination of interactive computing (Goldin et al. 2010), knowledge discovery (Fayyad and Stolorz 1997), information visualization (Card et al. 1999), and visual analytics (Wright 1997; Heer and Shneiderman 2012).
Par-allelization with respect to frequencies and an efficient implementation of the computation of Green's tensors further accelerate the calculations.
Indeed, estimated background variations can be adjusted by incrementation/decrementation steps, whereas time constant values of recursive averages are limited by the physical implementation of the computation.
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In particular, a straight-forward implementation of the computations of the determinants in steps (3)–(4), via e.g. the LU factorization (with partial pivoting), renders a total cost of 2m p 4 / 3 flops, which results from having to compute mp factorizations of p × p matrices, with a cost of 2p 3 / 3 flops per LU factorization.
The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH.
To our knowledge, there exists neither an overview of the various computational methods for PH nor a comprehensive benchmarking of the state-of-the-art implementations for the computation of persistent homology.
Furthermore, as we summarize in Table 2 (in Section 7), most of the implementations for the computation of PH work with (mathbb{F}_{2}).
There are several publicly-available implementations for the computation of PH.
Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients.
We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH.
Figure 13 describes the hardware implementation of the Zernike computation block.
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