Skip to content

Commit

Permalink
Updated 07_01
Browse files Browse the repository at this point in the history
Added some more words about interpolation, and little more explanation to provide some context.
  • Loading branch information
charlesblakemore committed May 16, 2024
1 parent 4958e16 commit ad69fa0
Showing 1 changed file with 11 additions and 1 deletion.
12 changes: 11 additions & 1 deletion nb/07_01_Cuts_Acceptance_Leakage.ipynb
Original file line number Diff line number Diff line change
Expand Up @@ -317,7 +317,17 @@
"id": "55114f8d",
"metadata": {},
"source": [
"You could also *interpolate* the `signalAcceptance` and `backgroundLeakage` data arrays to evaluate them numerically given a specific cut value"
"You could also *interpolate* the `signalAcceptance` and `backgroundLeakage` data arrays that we just created in order to evaluate these quantities numerically given any specific cut value, rather than just doing our best to read it off a plot for some choice of cut value.\n",
"\n",
"There are many different ways to interpolate data, the most trivial method being accomplished by just \"connecting the dots\", i.e. building up a piecewise function comprised of linear segments between each data point. If we have data points $(x_i, \\, y_i)$, then the linear interpolating function that describes their relation over the domain $\\{x_i\\}$ is given by,\n",
"$$\n",
"f_{\\rm interp}(x) = \n",
" \\begin{dcases}\n",
" \\dots, & \\dots \\\\\n",
" \\left(\\frac{y_{i+1} - y_i}{x_{i+1} - x_i}\\right) (x - x_i) + y_i, & x_{i+1} > x \\geq x_i \\\\\n",
" \\dots, & \\dots \\\\\n",
" \\end{dcases}\n",
"$$"
]
},
{
Expand Down

0 comments on commit ad69fa0

Please sign in to comment.