Figure 9.20:

Uncertainty in activation energy E and rate constant \ln k_m versus number of replicated experiments.

Code for Figure 9.20

Text of the GNU GPL.

main.py

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# Converted from replicate.m - confidence ellipses for replicated experiments
import numpy as np
from scipy.stats import chi2
from misc import save_ascii, ellipse

alpha   = 0.95
p       = 2
chisq   = chi2.ppf(alpha, p)
Tmin    = 300.0; Tmax = 500.0
nTvals  = 10
Tmeas   = np.linspace(Tmin, Tmax, nTvals)
S       = np.eye(2)
meanT   = np.mean(Tmeas)
sets    = np.array([1, 2, 5, 100])
nsets_v = len(sets)
measvar = 1e-3
table   = None

for i, nrep in enumerate(sets):
    Tmeasset = np.tile(Tmeas, nrep)
    ndata    = len(Tmeasset)
    Tcenter  = -1.0/Tmeasset + 1.0/meanT
    X        = np.column_stack([np.ones(ndata), Tcenter])
    amat     = S @ X.T @ X @ S / measvar
    level    = chisq
    x, y     = ellipse(amat, level, 150)[:2]
    block    = np.column_stack([x, y])
    table    = block if table is None else np.column_stack([table, block])

save_ascii('replicate.dat', table)