2b:null 2c:["$","title",null,{"children":"Histogram Vis Mk. III | IOP Systems | Observable"}] 31:T51a,# Histogram Vis Mk. III Our histogram is made up of base-${base} logarithmic segments. The parameters a and b together determine a cutoff value which is ${base}^{a + b + 1}. - The parameter a bounds absolute error on the low end by controlling the bin width below the cutoff. - The parameter b bounds relative error on the high end by controlling the bin width above the cutoff. In the example below, a = ${a} and b = ${b} and the cutoff is ${base}^{a + b + 1} = ${comma(C)}. The power of the cutoff value, _a + b + 1_, is referred to as c = ${c}. - Logarithmic segments below the cutoff are covered by linear bins ${base}^a = ${A} unit${plural(A)} wide each, which gives an absolute error of ${comma( A )} unit${plural(A)}. - Logarithmic segments above the cutoff are each divided into (${base} - 1) * ${base}^b = ${numLinearStepsPerLogBin} linear bins, which gives a relative error of ${base}^-b = ${percent( base ** -b ).replace(/\.0+%$/,'%')}. The original (_m_, _r_) parameters can be rephrased as _m_ = _a_ = ${a} and _r_ = _a + b + 1_ = _c_ = ${a + b + 1}.32:[] 2f:{"id":"35f0b601ed888da9","slug":null,"title":"Histogram Vis Mk. 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III","cells":[{"id":0,"value":"$31","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":563,"value":"viewof base = Inputs.radio([2, 3, 10], { label: \"Base\", value: 2 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1001,"value":"viewof a = Inputs.range([-2, 64], {\n label: html`a`,\n step: 1,\n value: this?.value ?? 0\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":998,"value":"viewof b = Inputs.range([0, 64], {\n label: html`b`,\n step: 1,\n value: this?.value ?? 0\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1047,"value":"viewof n = Inputs.range([0, 64], { label: \"n\", step: 1, value: 6 })","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1873,"value":"viewof data = Inputs.radio(\n new Map([\n [\"groups\", groups],\n [\"bins\", bins]\n ]),\n {\n label: \"visualize\",\n value: groups // groups //groups // note: resets when the other sliders change...\n }\n)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1056,"value":"viewof xScale = Inputs.radio([\"linear\", \"log\"], {\n label: \"x scale\",\n value: \"log\"\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":71,"value":"Plot.plot({\n marks: [\n Plot.rectX(data, {\n x1: \"lo\",\n x2: \"hi\",\n stroke: (d) => (d.logbin === null ? \"#999\" : \"#000\"),\n fill: \"logbin\",\n title: JSON.stringify,\n tip: true\n })\n ],\n width,\n height: 75,\n y: { axis: null },\n x: {\n transform: xScale == \"log\" ? (d) => Math.max(d, 1) : (d) => d, // hack to have 0 show up on a log axis\n type: xScale,\n tickFormat: \"s\",\n base,\n ticks: [0, ...d3.range(n + 1).map((n) => base ** n)]\n },\n color: {\n zero: true,\n label: \"Log bin\",\n legend: logbins.length > 0,\n scheme: \"cubehelix\",\n range: [0.075, 0.5],\n reverse: true,\n unknown: \"#fff\",\n // ticks: logbins,\n tickFormat: Math.round\n },\n caption: `(${b}, ${a}) histogram with absolute error = ${comma(\n A\n )} unit${plural(A)} and relative error = ${percent(\n base ** -b\n )}. Linear bins are colored white. There are ${comma(\n d3.sum(groups, (d) => d.num_bins)\n )} bins and values range up to ${comma(2 ** n)}.`\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2068,"value":"d3.sum(groups, (d) => d.num_bins)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2070,"value":"groups","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1501,"value":"Inputs.table(data, {\n header: {\n lo: \"low value\",\n hi: \"high value\",\n type: \"bin type\",\n logbin: \"log bin\",\n num_bins: \"num bins\"\n }\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2117,"value":"data","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1915,"value":"bins","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1932,"value":"Imagine we want to aggregate a histogram into a coarser histogram.\n\nEach histogram is made up of a linear section and a log section, which can be independently coarsened or refined. Since aggregation makes sense only when both segments are no finer than the original, we can only aggregate from (_a_, _b_) to (_a′_, _b′_) if _a′_ ≥ _a_ and _b′_ ≤ _b_.\n\n```rs\nfor (index, count) in histogram_1.enumerate() {\n let value = histogram_1.low(index);\n histogram_2.increment(value, count);\n}\n\n// todo: make the a and b red and blue\n```\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":2052,"value":"1 << (b + 1)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":2054,"value":"1 << ( c - a)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1864,"value":"groups = {\n console.clear();\n // linear bins: there are linear bins of width A up to base^c.\n const ret = [\n { lo: 0, hi: base ** c, type: \"linear\", logbin: null, num_bins: C / A }\n ];\n for (let i = c; i < n; i++) {\n ret.push({\n lo: base ** i,\n hi: base ** (i + 1),\n type: \"log\",\n logbin: i,\n num_bins: numLinearStepsPerLogBin\n });\n }\n return ret;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1918,"value":"// suggestion: (10, 5, n) histogram for 1024 unit absolute error and 3.13% relative error","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":275,"value":"// bins = [] \nbins = {\n console.clear();\n const ret = [];\n // linear bins: there are linear bins of width A up to base^c.\n const cutoff = Math.min(C, N);\n for (let i = 0; i < cutoff; i += A) {\n ret.push({ lo: i, hi: i + A, type: \"linear\", logbin: null });\n }\n for (let i = c; i < n; i++) {\n const lo = base ** i;\n const hi = base ** (i + 1);\n const step = base ** (i - b);\n for (let j = 0; j < numLinearStepsPerLogBin; j++) {\n ret.push({\n lo: lo + j * step,\n hi: lo + (j + 1) * step,\n type: \"log\",\n logbin: i\n });\n }\n }\n return ret;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1847,"value":"// m is a\n// r is a + b + 1 (which is our c)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":1625,"value":"