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I'm going to normalize the y-axis (Intensity) to values between 0 and 1 and draw a line based on the Lorentzian function of each individual data point.\n\n## Lorentzian function\n\nThe Lorentzian function gives the shape of certain types of spectral lines. It is the singly peaked function given by:","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":166,"value":"

\n \n L \n (\n x \n) \n \n = \n \frac{\n}{1} \n \n \frac{\n}{\n \frac{\n}{1} \n \n Γ \n} \n

","pinned":false,"hidden":false,"mode":"html","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":209,"value":"viewof gamma = Inputs.range([1, 1000], { label: \"gamma\", step: 1 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":196,"value":"single_distribution = {\n const points = 200;\n const step = 4000 / points;\n const half_gamma = gamma / 2;\n const x_0 = 0;\n\n function lorentz(x) {\n return (\n (1 / Math.PI) *\n (half_gamma / (Math.pow(x - x_0, 2) + Math.pow(half_gamma, 2)))\n );\n }\n\n const data = Array.from({ length: points }, (_, i) => {\n const x = -2000 + step * i;\n return {\n x,\n y: lorentz(x)\n };\n });\n\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":219,"value":"Plot.plot({\n marks: [\n Plot.ruleY([0]),\n Plot.lineY(single_distribution, { x: \"x\", y: \"y\", stroke: \"red\" }),\n Plot.ruleX([0], { strokeWidth: 4, stroke: \"#ccc\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":236,"value":"lines = {\n return data.map((d) => {\n const points = 200;\n const step = 4000 / points;\n return Array.from({ length: points }, (_, i) => {\n const x = step * i;\n const y = lorentz(x, d.x) * d.y;\n return {\n x,\n y\n };\n });\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":248,"value":"{\n const maxValues = lines.map((line) => Math.max(...line.map((d) => d.y)));\n return Plot.plot({\n x: { label: \"Frequency\", reverse: true, domain: [0, 4000] },\n y: { label: \"Intensity\" },\n marks: [\n Plot.ruleY([0]),\n Plot.rectY(data, {\n x1: (d) => d.x - 10,\n x2: (d) => d.x + 10,\n y: \"y\",\n fill: \"#ccc\"\n }),\n ...lines.map((line, i) =>\n Plot.lineY(line, {\n x: \"x\",\n y: (d) => (d.y * data[i].y) / maxValues[i],\n stroke: \"red\"\n })\n )\n ]\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":280,"value":"sum_lines = {\n const data = new Array(200);\n for (let i = 0; i < 200; ++i) {\n let yAcc = 0;\n for (const line of lines) {\n yAcc += line[i].y;\n }\n data[i] = { x: lines[0][i].x, y: yAcc };\n }\n return data;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":284,"value":"Plot.plot({\n x: { label: \"Frequency\", reverse: true, domain: [0, 4000] },\n y: { label: \"Intensity\" },\n marks: [\n Plot.ruleY([0]),\n Plot.rectY(data, {\n x1: (d) => d.x - 10,\n x2: (d) => d.x + 10,\n y: \"y\",\n fill: \"#ccc\"\n }),\n Plot.lineY(sum_lines, { x: \"x\", y: \"y\", stroke: \"red\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":290,"value":"normalized_sum_line = {\n const max = Math.max(...sum_lines.map((d) => d.y));\n\n return sum_lines.map((d) => {\n d.y = d.y / max;\n return d;\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":294,"value":"Plot.plot({\n x: { label: \"Frequency\", reverse: true, domain: [0, 4000] },\n y: { label: \"Intensity\", reverse: true },\n marks: [\n Plot.ruleY([1, 0]),\n Plot.rectY(data, {\n x1: (d) => d.x - 10,\n x2: (d) => d.x + 10,\n y: \"y\",\n fill: \"#ccc\"\n }),\n Plot.lineY(normalized_sum_line, { x: \"x\", y: \"y\", stroke: \"red\" })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"---\n\n### Constants","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":12,"value":"$43","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":263,"value":"data = {\n const raw = Array.from({ length: data_raw.length });\n const max = Math.max(...data_raw.map(({ y }) => y));\n\n return data_raw.map((d) => {\n d.y = d.y / max;\n return d;\n });\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":238,"value":"lorentz = function lorentz(x, x_0) {\n const half_gamma = gamma / 2;\n\n return (\n (1 / Math.PI) *\n (half_gamma / (Math.pow(x - x_0, 2) + Math.pow(half_gamma, 2)))\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W44","stdlib":"1"}} 42:"$41:body"