3e:null 3f:["$","title",null,{"children":"Preconditioner Benchmark | David Gleich | Observable"}] 45:T2956,viewof filter_options = { // Assume these variables exist from elsewhere in the notebook const data_min_size = data_stats.min_size; const data_max_size = data_stats.max_size; const data_min_nnz = data_stats.min_nnz; const data_max_nnz = data_stats.max_nnz; const data_min_density = 0; const data_max_density = data_stats.max_density; // Residual tolerance settings const min_residual_exp = -10; // 10^-10 const max_residual_exp = -2; // 10^-2 const default_residual_exp = -8; // 10^-8 const log10 = Math.log10; const pow10 = x => Math.pow(10, x); // Format residual in scientific notation const formatResidual = (exp) => { // Convert from exponent to full value const value = Math.pow(10, exp); // Format in scientific notation return value.toExponential(1); }; const form = html`

Matrix Size

Min: ${data_min_size}

Max: ${data_max_size}

Non-zeros (NNZ)

Min: ${data_min_nnz}

Max: ${data_max_nnz}

Density

Min: ${data_min_density}

Max: ${data_max_density}

Performance Calculation Options

Include per-iteration work within the solver

Include preconditioner generation time

Plot best configurations only for a preconditioner

Compare to direct solver

Residual Tolerance

Value: ${formatResidual(default_residual_exp)}

`; // Residual slider connection form.residual_slider.oninput = () => { const exp = +form.residual_slider.value; const formattedValue = formatResidual(exp); form.querySelector("#residual_display").textContent = formattedValue; updateFormValue(); }; // Size slider connections form.min_size_slider.oninput = () => { const value = Math.floor(pow10(+form.min_size_slider.value)); form.min_size.value = value; form.querySelector("#min_size_display").textContent = value.toLocaleString(); updateFormValue(); }; form.max_size_slider.oninput = () => { const value = Math.floor(pow10(+form.max_size_slider.value)); form.max_size.value = value; form.querySelector("#max_size_display").textContent = value.toLocaleString(); updateFormValue(); }; form.min_size.oninput = () => { const value = +form.min_size.value; if (value > 0) { form.min_size_slider.value = log10(value); form.querySelector("#min_size_display").textContent = value.toLocaleString(); } updateFormValue(); }; form.max_size.oninput = () => { const value = +form.max_size.value; if (value > 0) { form.max_size_slider.value = log10(value); form.querySelector("#max_size_display").textContent = value.toLocaleString(); } updateFormValue(); }; // NNZ slider connections form.min_nnz_slider.oninput = () => { const value = Math.floor(pow10(+form.min_nnz_slider.value)); form.min_nnz.value = value; form.querySelector("#min_nnz_display").textContent = value.toLocaleString(); updateFormValue(); }; form.max_nnz_slider.oninput = () => { const value = Math.floor(pow10(+form.max_nnz_slider.value)); form.max_nnz.value = value; form.querySelector("#max_nnz_display").textContent = value.toLocaleString(); updateFormValue(); }; form.min_nnz.oninput = () => { const value = +form.min_nnz.value; if (value > 0) { form.min_nnz_slider.value = log10(value); form.querySelector("#min_nnz_display").textContent = value.toLocaleString(); } updateFormValue(); }; form.max_nnz.oninput = () => { const value = +form.max_nnz.value; if (value > 0) { form.max_nnz_slider.value = log10(value); form.querySelector("#max_nnz_display").textContent = value.toLocaleString(); } updateFormValue(); }; // Density slider connections (linear scale) form.min_density_slider.oninput = () => { const value = +form.min_density_slider.value; form.min_density.value = value; form.querySelector("#min_density_display").textContent = value.toFixed(4); updateFormValue(); }; form.max_density_slider.oninput = () => { const value = +form.max_density_slider.value; form.max_density.value = value; form.querySelector("#max_density_display").textContent = value.toFixed(4); updateFormValue(); }; form.min_density.oninput = () => { form.min_density_slider.value = +form.min_density.value; form.querySelector("#min_density_display").textContent = (+form.min_density.value).toFixed(4); updateFormValue(); }; form.max_density.oninput = () => { form.max_density_slider.value = +form.max_density.value; form.querySelector("#max_density_display").textContent = (+form.max_density.value).toFixed(4); updateFormValue(); }; // Handle checkboxes const checkboxes = form.querySelectorAll('input[type="checkbox"]'); checkboxes.forEach(checkbox => { checkbox.onclick = () => updateFormValue(); }); function updateFormValue() { form.value = { // Residual value residual: Math.pow(10, +form.residual_slider.value), residual_exp: +form.residual_slider.value, // Size filters min_size: +form.min_size.value, max_size: +form.max_size.value, // NNZ filters min_nnz: +form.min_nnz.value, max_nnz: +form.max_nnz.value, // Density filters min_density: +form.min_density.value, max_density: +form.max_density.value, // Checkboxes include_method_time: form.include_method_time.checked, include_generation_time: form.include_generation_time.checked, plot_best_only: form.plot_best_only.checked, compare_to_direct: form.compare_to_direct.checked }; form.dispatchEvent(new Event("input")); } // Initialize form value updateFormValue(); return form; }46:T8e5,Plot.plot({ width: 600, height: 400, marginTop: 30, marginBottom: 40, marginLeft: 80, marginRight: 40, style: { fontSize: "16px" }, clip: true, // Hide data outside the axis y: { label: "Fraction of problems solved", domain: [0, 1], ticks: 10, grid: true }, x: { label: filter_options.compare_to_direct ? "Performance ratio (vs Direct)" : "Performance ratio (vs Control)", type: "log", grid: true, domain: [1/128, 4], base: 2, ticks: [1/128, 1/64, 1/32, 1/16, 1/8, 1/4, 1/2, 1, 2, 4], tickFormat: x => { if (x<1) { return `${Math.round(1/x)}x`; } else { return `${(1/x)}x`; } } }, color: { type: "categorical", domain: [...new Set(data_filtered.map(d => d.preconditioner))], legend: true }, marks: [ Plot.line(profile_lines_to_plot.filter( d => filter_options.compare_to_direct ? true : d.preconditioner !== "Control"), { x: "ratio", y: "fraction", stroke: "preconditioner", strokeWidth: 2, curve: "step-after", z: "config" }), // Add tooltips/tips for the lines // Add invisible points for tooltips using Voronoi Plot.dot(profile_lines_to_plot.filter(d => d.preconditioner !== "Control"), Plot.pointer({ x: "ratio", y: "fraction", z: "config", fill: "preconditioner", r: 0, // Make the dots invisible title: d => { const ratioDisplay = d.ratio < 1 ? `${(1/d.ratio).toFixed(2)}x faster than Control` : `${(1/d.ratio).toFixed(2)}x slower than Control`; return `${d.ordering} - ${d.preconditioner} (${d.preconditioner_args}) Ratio: ${ratioDisplay} Fraction: ${(d.fraction * 100).toFixed(1)}%`; }, tip: true })), // Add a reference line at y=1 (Control performance) Plot.ruleX([1], {stroke: "black", strokeDasharray: "4 4"}), Plot.text([{x: 1, y: 0}], { x: "x", y: "y", text: [filter_options.compare_to_direct? "Direct reference" : "Control reference"], dy: -10 }) ] });47:T422,viewof filteredPreconditioners = { // Assume uniquePreconditioners exists from elsewhere in the notebook const preconditioner_list = uniquePreconditioners; const box_list = preconditioner_list.map((d) => d == "Control" ? "" : `

${d}

` ); const form = html``; // Handle checkboxes const checkboxes = form.querySelectorAll('input[type="checkbox"]'); checkboxes.forEach(checkbox => { checkbox.onclick = () => updateFormValue(); }); function updateFormValue() { const checkedBoxes = form.querySelectorAll('input[type="checkbox"]:checked'); form.value = new Set(Array.from(checkedBoxes).map(cb => cb.value)); form.value.add("Control"); form.dispatchEvent(new Event("input")); } // Initialize form value updateFormValue(); return form; }48:T417,data_filtered = data.filter( d=> { const density = d.matrix_nnz / (d.matrix_size * d.matrix_size); return Math.abs(d.convergence - filter_options.residual) / filter_options.residual <= 0.5 && d.solver == "cg" && d.preconditioner !== "CombinatorialMG" && d.preconditioner !== "LaplaceStripped" && d.preconditioner !== "SteepestDescent" && filteredPreconditioners.has(d.preconditioner) && //((d.preconditioner == "IncompleteCholesky" && d.ordering == "AMD")|| d.preconditioner == "Control") && //((d.preconditioner == "IncompleteCholesky" && ((d.preconditioner_args == "1.0e-5,1" && d.ordering == "AMD") || (d.preconditioner_args == "0.0001,1" && d.ordering == "AMD")))|| d.preconditioner == "Control") && d.matrix_size >= filter_options.min_size && d.matrix_size <= filter_options.max_size && d.matrix_nnz >= filter_options.min_nnz && d.matrix_nnz <= filter_options.max_nnz && density >= filter_options.min_density && density <= filter_options.max_density; } )49:Ta5b,performanceProfiles = { // compute the control cost for each matrix. const control_results = d3.group( data_filtered.filter(d=>d.preconditioner == "Control"), d=>d.ordering, d=>d.matrix_name) // Now, let's process this grouped data to create performance profiles const performanceProfiles = []; // For each group, we need to: // 1. Get all the solve times for that combination // 2. Calculate ratios compared to the best (smallest) solve time // 3. Sort by ratio to create the performance profile curve grouped.forEach((orderingGroup, ordering) => { orderingGroup.forEach((preconditionerGroup, preconditioner) => { preconditionerGroup.forEach((items, preconditioner_args) => { items.forEach(item => { const matrixName = item.matrix_name; // Alternative with more error handling const controlCost = (() => { const orderingMap = control_results.get(ordering); if (!orderingMap) { throw new Error(`No Control data found for ordering: ${ordering}`); } const matrixMap = orderingMap.get(matrixName); if (!matrixMap || matrixMap.length === 0) { throw new Error(`No Control data found for matrix: ${matrixName} with ordering: ${ordering}`); } return parseFloat(matrixMap[0].solver_cost); })(); // Access the control data using .get() for Maps if (controlCost !== null) { var control_work = parseFloat(item.control_cost) + (filter_options.include_method_time ? parseFloat(item.additional_control_work) : 0); if (filter_options.compare_to_direct) { control_work = parseFloat(item.direct_cost) + parseFloat(item.direct_generation_cost); } const preconditioned_work = parseFloat(item.solver_cost) + parseFloat(item.preconditioner_cost) + (filter_options.include_method_time ? parseFloat(item.additional_solver_work) : 0) + (filter_options.include_generation_time ? parseFloat(item.generate_cost) : 0) ; const ratio = preconditioned_work / control_work; performanceProfiles.push({ matrix_name: matrixName, ordering, preconditioner, preconditioner_args, ratio, config: `${ordering}-${preconditioner}-${preconditioner_args}` }); } else { } }); }); }); }); return performanceProfiles; }4a:T919,profile_lines_to_plot = { const profileLines = d3.groups(performanceProfiles, d => d.config).map(([config, items]) => { const sortedRatios = items.map(d => d.ratio).sort((a, b) => a - b); return { config, ordering: items[0].ordering, preconditioner: items[0].preconditioner, preconditioner_args: items[0].preconditioner_args, // Create points for the performance profile points: sortedRatios.map((ratio, i) => ({ fraction: (i + 1) / filtered_problem_list.length, ratio })), // Calculate area under curve (lower is better) // Use trapezoidal rule for integration // area: sortedRatios.reduce((sum, ratio, i) => { // if (i === 0) return sum; // if (ratio > 1) return sum; // const prevRatio = sortedRatios[i-1]; // const prevFraction = i / filtered_problem_list.length // const fraction = (i + 1) / filtered_problem_list.length // // Area of trapezoid // return sum + (1/ratio + 1/prevRatio) * (fraction - prevFraction) / 2 // }, 0) area: _compute_auc(sortedRatios) }; }); if (filter_options.plot_best_only) { // Group by preconditioner and find the one with biggest area (best performance) const bestConfigs = d3.groups(profileLines, d => d.preconditioner) .map(([precond, items]) => { // Find the configuration with the smallest area return items.reduce((best, current) => current.area > best.area ? current : best, items[0]); }); // Flatten each best config's points into the format needed for plotting return bestConfigs.flatMap(config => config.points.map(point => ({ config: config.config, ordering: config.ordering, preconditioner: config.preconditioner, preconditioner_args: config.preconditioner_args, fraction: point.fraction, ratio: point.ratio })) ); } else { // Return all profile lines return profileLines.flatMap(config => config.points.map(point => ({ config: config.config, ordering: config.ordering, preconditioner: config.preconditioner, preconditioner_args: config.preconditioner_args, fraction: point.fraction, ratio: point.ratio })) ); } }4b:T572,function _compute_auc(sortedRatios) { // integrate the ratios const left_reference = 128; // this is the value we'll use to integrate to one. const right_reference = 0.25; const xy = sortedRatios.map((d,i)=>({x: Math.log(1/d), y: (i+1)/filtered_problem_list.length })); const reference_area = Math.log(left_reference) - Math.log(right_reference); var area = 0.0; var can_add_extra = true; // I'm being lazy with the termination. for (var i=0; i 0 && i-1 < sortedRatios.length && xy[i-1].x > Math.log(right_reference) ) { console.log(xy[i-1].x, xy[i-1].y, xy[i-1].x- Math.log(right_reference) ) // adjust the final area. area += (xy[i-1].y)*(xy[i-1].x-Math.log(right_reference)); } console.log("final area ", area, area/reference_area) return area/reference_area; }4c:[{"id":"c6d02badd3641dc73b2749a71dd6aea30609516e191bdd7199ba3251a06d17998aa9a48b628bddd44ef4827823bf74dc19823389302285f54a9372718d38f742","href":"https://static.observableusercontent.com/files/c6d02badd3641dc73b2749a71dd6aea30609516e191bdd7199ba3251a06d17998aa9a48b628bddd44ef4827823bf74dc19823389302285f54a9372718d38f742","name":"cappa-logo.png","type":"image/png","lastModified":1747962566124.973,"size":51124},{"id":"3b7b2bc37f4d585965c227548a70f233dd10bd1b7a5804ca2c65ffaec741ff56c8578a0f85c973ba31a416cc4b7ade64a8becc3c9919dee73f81eb376d506188","href":"https://static.observableusercontent.com/files/3b7b2bc37f4d585965c227548a70f233dd10bd1b7a5804ca2c65ffaec741ff56c8578a0f85c973ba31a416cc4b7ade64a8becc3c9919dee73f81eb376d506188","name":"results.zip","type":"application/zip","lastModified":1745800819739.302,"size":10906691}] 43:{"id":"d3b7fa92cee9eb4b","slug":"preconditioner-benchmark","title":"Preconditioner Benchmark","thumbnail":"d967c94964276bcebb1bcd82b9fbcfc0efea45a25a39ef6b3bb59b5c76799f85","access_level":"unlisted","create_time":"$D2025-04-28T00:38:39.345Z","update_time":"$D2025-06-10T19:30:21.105Z","view_time":null,"first_public_time":null,"has_unpublished_edits":null,"fork":false,"stars":0,"starred":false,"owner":{"type":"team","id":"6eb20c1ddb15eb50","login":"dgleich","name":"David Gleich","avatar_url":"https://avatars-next.observableusercontent.com/a3c08599106298c961b8f1ab3e63728e19fe017254cf5241bac6f38e6a90cb79","tier":"starter_2024","bio":""},"version":515,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"0d9ae5abee7b5420","login":"dgleich","name":"David Gleich","avatar_url":"https://avatars-next.observableusercontent.com/a3c08599106298c961b8f1ab3e63728e19fe017254cf5241bac6f38e6a90cb79","tier":null,"bio":""}],"members":[{"type":"individual","id":"0d9ae5abee7b5420","login":"dgleich","name":"David Gleich","avatar_url":"https://avatars-next.observableusercontent.com/a3c08599106298c961b8f1ab3e63728e19fe017254cf5241bac6f38e6a90cb79","tier":null,"role":"editor"},{"type":"team","id":"6eb20c1ddb15eb50","login":"dgleich","name":"David Gleich","avatar_url":"https://avatars-next.observableusercontent.com/a3c08599106298c961b8f1ab3e63728e19fe017254cf5241bac6f38e6a90cb79","tier":"starter_2024","role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"lapsed":null,"subscribed":null,"forks":3,"collection":null,"type":"notebook","body":{"titling":"auto","title":"Preconditioner Benchmark","cells":[{"id":364,"value":"$${html`

`}\n# Preconditioner Benchmark\nby [Marc Tunnell](https://tunnellm.github.io) and [David Gleich](https://dgleich.com). See our [CAPPA repository for more information.](https://tunnellm.github.io/CAPPA-repository) along with our [arXiv paper](https://arxiv.org/abs/2505.20696) and [github code to generate these results](https://github.com/tunnellm/CAPPABenchmarkTools.jl).\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":170,"value":"$45","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":69,"value":"$46","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":348,"value":"Above, we show the performance profile plot for ${uniqueMatrices.length} matrices. For each preconditioner, we look at the fraction of problems where its work is some multiple less than ${filter_options.compare_to_direct? \"a sparse direct method\" : \"unpreconditioned CG\"}.","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":330,"value":"Plot.plot({\n marginTop: 20, // More space at top\n marginBottom: 40, // More space at bottom for x-axis label\n marginLeft: 75, // More space at left for y-axis label\n marginRight: 40, // More space at right\n width: 400,\n height: 484,\n style: {\n fontSize: \"16px\", // Overall font size\n },\n x: {\n type: \"log\",\n label: \"Matrix size\",\n domain: [5000, 10000000],\n grid: true\n },\n y: {\n type: \"log\", \n label: \"Matrix NNZ\",\n domain: [50000, 500000000],\n grid: true\n },\n marks: [\n Plot.dot(uniqueMatrices, {x: \"matrix_size\", y: \"matrix_nnz\", stroke: \"#ff7f0e\"}),\n Plot.dot(uniqueMatrices, Plot.pointer({\n x: \"matrix_size\", y: \"matrix_nnz\",\n r: 0, // Make the dots invisible\n title: d => {\n return `${d.matrix_name}`;\n },\n tip: true\n })),\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":212,"value":"{ \n \n // Create a table\n const matrixTable = Inputs.table(uniqueMatrices, {\n columns: [\n \"matrix_name\", \n \"matrix_size\", \n \"matrix_nnz\", \n \"matrix_density\"\n ],\n header: {\n matrix_name: \"Matrix Name\",\n matrix_size: \"Size (n)\",\n matrix_nnz: \"Non-zeros\",\n matrix_density: \"Density\"\n },\n format: {\n matrix_size: d => d.toLocaleString(),\n matrix_nnz: d => d.toLocaleString()\n },\n width: {\n matrix_name: 200,\n matrix_size: 120,\n matrix_nnz: 120,\n matrix_density: 120\n },\n sort: \"matrix_name\"\n });\n \n // Display the table\n return matrixTable;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":483,"value":"$47","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"results_zip = FileAttachment(\"results.zip\").zip();","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":10,"value":"data = results_zip.file(\"preconditioner_data.csv\").csv()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":160,"value":"$48","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":42,"value":"grouped = d3.group(data_filtered, \n d => d.ordering,\n d => d.preconditioner,\n d => d.preconditioner_args\n);\n","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":45,"value":"$49","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":66,"value":"profileLines = d3.groups(performanceProfiles, d => d.config).map(([config, items]) => {\n const sortedRatios = items.map(d => d.ratio).sort();\n return sortedRatios.map((ratio, i) => ({\n config,\n ordering: items[0].ordering,\n preconditioner: items[0].preconditioner,\n preconditioner_args: items[0].preconditioner_args,\n fraction: (i + 1) / sortedRatios.length,\n ratio\n }));\n }).flat();","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":104,"value":"$4a","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":417,"value":"_compute_auc([1/120,1/64,1/63])","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":450,"value":"ic_amd_1em5 = data_filtered.filter(d=>d.preconditioner == \"IncompleteCholesky\" && d.ordering==\"AMD\" )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":454,"value":"ic_rcm_1em4 = data_filtered.filter(d=>d.preconditioner == \"IncompleteCholesky\" && d.ordering==\"AMD\" )","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":362,"value":"$4b","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":457,"value":"test_grouped = d3.groups(performanceProfiles, d => d.config)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":241,"value":"test_lines = {\n const profileLines = d3.groups(performanceProfiles, d => d.config).map(([config, items]) => {\n const sortedRatios = items.map(d => d.ratio).sort((a, b) => a - b);\n \n return {\n config,\n ordering: items[0].ordering,\n preconditioner: items[0].preconditioner,\n preconditioner_args: items[0].preconditioner_args,\n // Create points for the performance profile\n points: sortedRatios.map((ratio, i) => ({\n fraction: (i + 1) / filtered_problem_list.length,\n ratio\n })),\n // Calculate area under curve (lower is better)\n // Use trapezoidal rule for integration\n area: _compute_auc(sortedRatios)\n };\n });\n return profileLines.filter(d => d.preconditioner == \"IncompleteCholesky\");\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":49,"value":"getUniqueValues = (data, column) => {\n return [...new Set(data.map(d => d[column]))].sort();\n};\n","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"uniquePreconditioners = getUniqueValues(data, 'preconditioner');","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":140,"value":"full_problem_list = getUniqueValues(data, 'matrix_name')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"filtered_problem_list = getUniqueValues(data_filtered, 'matrix_name')","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":95,"value":"dataParsed = data_filtered.map(d=>({ solver_cost: +(d.solver_cost), control_cost: +(d.control_cost), direct_cost: +(d.direct_cost) + +(d.direct_generation_cost), nnz: +(d.matrix_nnz) }))","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":186,"value":"### Compute data extrema\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"},{"id":188,"value":"data_stats = {\n return { \n min_size: d3.min(data, d => +d.matrix_size),\n max_size: d3.max(data, d => +d.matrix_size),\n min_nnz: d3.min(data, d => +d.matrix_nnz),\n max_nnz: d3.max(data, d => +d.matrix_nnz),\n min_density: d3.min(data, d => +d.matrix_nnz / (+d.matrix_size * +d.matrix_size)),\n max_density: d3.max(data, d => +d.matrix_nnz / (+d.matrix_size * +d.matrix_size))\n }; \n};","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":190,"value":"data_stats","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":222,"value":"data_filtered","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":269,"value":"uniqueMatrices = { // Get unique matrix metadata entries\n const uniqueMatrices = Array.from(new Map(\n data_filtered.map(d => {\n const size = +d.matrix_size;\n const nnz = +d.matrix_nnz;\n const density = nnz / (size * size);\n \n return [\n d.matrix_name, // Use matrix name as the key for uniqueness\n {\n matrix_name: d.matrix_name,\n matrix_size: size,\n matrix_nnz: nnz,\n matrix_density: density.toExponential(4)\n }\n ];\n })\n ).values());\n \n // Sort by name\n uniqueMatrices.sort((a, b) => a.matrix_name.localeCompare(b.matrix_name));\n\n return uniqueMatrices;\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"$undefined","database":"$undefined"},{"id":497,"value":"Plot.plot({\n x: {\n type: \"log\"\n },\n y: {\n type: \"log\"\n },\n marks: [\n Plot.auto(dataParsed, {x: \"nnz\", y: \"direct_cost\"})\n ]\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","tool":"$undefined","providerMetadata":"$undefined","attachments":"$undefined","output":"","database":"$undefined"}],"files":"$W4c","stdlib":"1"}} 44:"$43:body"

Matrix Size

Non-zeros (NNZ)

Density

Performance Calculation Options

Residual Tolerance

Preconditioner Choices