A laboratory noise study has the following workflow graph

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

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Problem

A laboratory noise study has the following workflow graph, with each node's runtime and dependency stated:

N_1

: load the raw time series from disk (2 minutes)

N_2

: compute a one-sided Welch power spectral density with a chosen window and

K=8

segments, depending on

N_1

(3 minutes)

N_3

: the Parseval check

\sum_k S_k\Delta f = \overline{x^2}

, depending on

N_2

(1 second)

N_4

: a least-squares fit of a four-parameter Lorentzian noise model to the PSD by the normal equations, depending on

N_2

(5 seconds)

N_5

: a figure of the PSD with the fit overlaid, depending on

N_2

and

N_4

(1 second)

N_6

: a summary table of the fitted parameters, depending on

N_4

(1 second) Someone edits the choice of window function 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 normal-matrix condition number of the fit in

N_4

\kappa = 9.0\times10^8

. Two machines, each running the identical package versions pinned in one lockfile, report the fitted parameters differing in the seventh significant digit. Using

\kappa\epsilon_{\rm mach}

for binary64 (

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

), say whether this is expected from rounding alone, and name one thing about the two machines that the lockfile does not fix.

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