A toy strain-analysis pipeline has this workflow graph: : load the raw strain time…

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Computational Physics · Research software practice, verification and validation

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Problem

A toy strain-analysis pipeline has this workflow graph:

N_1

: load the raw strain time series (8 minutes)

N_2

: apply a matched filter to

N_1

by FFT convolution with a template (4 minutes)

N_3

: compute the Welch PSD of the filtered output and its Parseval check, depending on

N_2

(10 seconds)

N_4

: a chi-squared fit of a three-parameter Gaussian peak to the filtered signal-to-noise time series, depending on

N_2

(8 seconds)

N_5

: a figure of the filtered series with the fitted peak marked, depending on

N_4

(1 second)

N_6

: a summary table of the peak SNR and fitted parameters, depending on

N_4

(1 second) Someone edits the template used in

N_2

. ((a)) List the nodes that must rerun, and the total time this costs, against the time a full rerun of the whole graph would cost. ((b)) The fit in

N_4

has a normal-matrix condition number

\kappa = 4.5\times10^6

. Two machines, running identical package versions pinned in one lockfile, report the fitted peak position differing in the fifth significant digit. Using

\kappa\epsilon_{\rm mach}

for binary64 (

\epsilon_{\rm mach}=2^{-52}

), say whether a fifth-digit difference is consistent with rounding alone through this fit, and state what this implies about the lockfile.

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