Public
Edited
May 15, 2023
midpoint = (rate1 * time1 - rate2 * time2 + Math.log(rate1) - Math.log(-rate2)) / (rate1 - rate2)
double_logistic_derivative = (t, asymptote, time1, time2, rate1, rate2, level1, level2) => {
return -asymptote * (-Math.exp(-rate1 * (t - time1)) * rate1 - Math.exp(-rate2 * (t - time2)) * rate2) / Math.pow(1 + Math.exp(-rate1 * (t - time1)) + Math.exp(-rate2 * (t - time2)), 2);
}
double_logistic_derivative2 = (t, asymptote, time1, time2, rate1, rate2, level1, level2) => {
const denom = 1 + Math.exp(-rate1 * (t - time1)) + Math.exp(-rate2 * (t - time2));
return asymptote * (
2 * Math.pow((-Math.exp(-rate1 * (t - time1)) * rate1 - Math.exp(-rate2 * (t - time2)) * rate2), 2) / Math.pow(denom, 3)
- (Math.exp(-rate1 * (t - time1)) * Math.pow(rate1, 2) + Math.exp(-rate2 * (t - time2)) * Math.pow(rate2, 2)) / Math.pow(denom, 2)
);
}
viewof asymptote2 = Inputs.range([0, 1], {label: "Asymptote 2"})
Plot.plot({
marks: [
Plot.ruleY([0]),
Plot.lineY(data2, {x: "t", y: "y"})
]
})
ts = [...Array(n)].map((x, i) => xlim[0] + (xlim[1] - xlim[0]) * i / (n - 1))
ys = ts.map((t) => double_logistic(t, asymptote, time1, time2, rate1, rate2, level1, level2))
dys = ts.map((t) => double_logistic_derivative(t, asymptote, time1, time2, rate1, rate2, level1, level2))
dys2 = ts.map((t) => double_logistic_derivative2(t, asymptote, time1, time2, rate1, rate2, level1, level2))
data = ts.map((t, i) => ({ t: t, y: ys[i], dy: dys[i], dy2: dys2[i] }))
ys2 = ts.map((t) => double_logistic2(t, asymptote, asymptote2, time1, time2, time3, time4, rate1, rate2, rate3, rate4, level1, level2))
data2 = ts.map((t, i) => ({ t: t, y: ys2[i] }))
xlim = [-10, 10]
n = 1000
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