Init

package.json

@@ -55,7 +55,10 @@
     "react-dom": "16.12.0",
     "reason-react": ">=0.7.0",
     "reschema": "1.3.0",
-    "tailwindcss": "1.2.0"
+    "tailwindcss": "1.2.0",
+    "binary-search-tree": "0.2.6",
+    "jstat": "1.9.2",
+    "mathjs": "6.6.0"
   },
   "alias": {
     "react": "./node_modules/react",

src/components/editor/distribution.js

@@ -0,0 +1,181 @@
+// This module defines an abstract BinnedDistribution class, which
+// should be implemented for each distribution. You need to decide
+// how to bin the distribution (use _adabin unless there's a nicer
+// way for your distr) and how to choose the distribution's support.
+const _math = require("mathjs");
+const math = _math.create(_math.all);
+const jStat = require("jstat");
+
+math.import({
+  normal: jStat.normal,
+  beta: jStat.beta,
+  lognormal: jStat.lognormal,
+  uniform: jStat.uniform
+});
+
+class BaseDistributionBinned {
+  constructor(args) {
+    this._set_props();
+    this.max_bin_size = 0.5;
+    this.min_bin_size = 0;
+    this.increment = 0.001;
+    this.desired_delta = 0.01;
+    this.start_bin_size = 0.01;
+
+    [this.params, this.pdf_func, this.sample] = this.get_params_and_pdf_func(
+      args
+    );
+
+    [this.start_point, this.end_point] = this.get_bounds();
+    [this.pdf_vals, this.divider_pts] = this.bin();
+  }
+
+  _set_props() {
+    // this is hacky but class properties aren't always supported
+    throw new Error("NotImplementedError");
+  }
+
+  _adabin() {
+    let point = this.start_point;
+    let vals = [this.pdf_func(point)];
+    let divider_pts = [point];
+    let support = this.end_point - this.start_point;
+    let bin_size = this.start_bin_size * support;
+
+    while (point < this.end_point) {
+      let val = this.pdf_func(point + bin_size);
+      if (Math.abs(val - vals[vals.length - 1]) > this.desired_delta) {
+        while (
+          (Math.abs(val - vals[vals.length - 1]) > this.desired_delta) &
+          (bin_size - this.increment * support > this.min_bin_size)
+          ) {
+          bin_size -= this.increment;
+          val = this.pdf_func(point + bin_size);
+        }
+      } else if (Math.abs(val - vals[vals.length - 1]) < this.desired_delta) {
+        while (
+          (Math.abs(val - vals[vals.length - 1]) < this.desired_delta) &
+          (bin_size < this.max_bin_size)
+          ) {
+          bin_size += this.increment;
+          val = this.pdf_func(point + bin_size);
+        }
+      }
+      point += bin_size;
+      vals.push(val);
+      divider_pts.push(point);
+    }
+    vals = vals.map((_, idx) => vals[idx] / 2 + vals[idx + 1] / 2);
+    vals = vals.slice(0, -1);
+    return [vals, divider_pts];
+  }
+
+  bin() {
+    throw new Error("NotImplementedError");
+  }
+
+  get_bounds() {
+    throw new Error("NotImplementedError");
+  }
+
+  get_params_and_pdf_func(args) {
+    let args_str = args.toString() + ")";
+    let substr = this.name + ".pdf(x, " + args_str;
+    let compiled = math.compile(substr);
+    function pdf_func(x) {
+      return compiled.evaluate({ x: x });
+    }
+    let mc_compiled = math.compile(this.name + ".sample(" + args_str);
+    let kv_pairs = this.param_names.map((val, idx) => [val, args[idx]]);
+    let params = Object.fromEntries(new Map(kv_pairs));
+    return [params, pdf_func, mc_compiled.evaluate];
+  }
+}
+
+class NormalDistributionBinned extends BaseDistributionBinned {
+  _set_props() {
+    this.name = "normal";
+    this.param_names = ["mean", "std"];
+  }
+  get_bounds() {
+    return [
+      this.params.mean - 4 * this.params.std,
+      this.params.mean + 4 * this.params.std
+    ];
+  }
+  bin() {
+    return this._adabin(this.params.std);
+  }
+}
+
+class UniformDistributionBinned extends BaseDistributionBinned {
+  _set_props() {
+    this.name = "uniform";
+    this.param_names = ["start_point", "end_point"];
+    this.num_bins = 200;
+  }
+  get_bounds() {
+    return [this.params.start_point, this.params.end_point];
+  }
+  bin() {
+    let divider_pts = evenly_spaced_grid(
+      this.params.start_point,
+      this.params.end_point,
+      this.num_bins
+    );
+    let vals = divider_pts.map(x =>
+      this.pdf_func(this.params.start_point / 2 + this.params.end_point / 2)
+    );
+    vals = vals.slice(0, -1);
+    return [vals, divider_pts];
+  }
+}
+
+class LogNormalDistributionBinned extends BaseDistributionBinned {
+  _set_props() {
+    this.name = "lognormal";
+    this.param_names = ["normal_mean", "normal_std"];
+    this.n_bounds_samples = 1000;
+    this.n_largest_bound_sample = 10;
+  }
+
+  _nth_largest(samples, n) {
+    var largest_buffer = Array(n).fill(-Infinity);
+    for (const sample of samples) {
+      if (sample > largest_buffer[n - 1]) {
+        var i = n;
+        while ((i > 0) & (sample > largest_buffer[i - 1])) {
+          i -= 1;
+        }
+        largest_buffer[i] = sample;
+      }
+    }
+    return largest_buffer[n - 1];
+  }
+  get_bounds() {
+    let samples = Array(this.n_bounds_samples)
+      .fill(0)
+      .map(() => this.sample());
+    return [
+      math.min(samples),
+      this._nth_largest(samples, this.n_largest_bound_sample)
+    ];
+  }
+  bin() {
+    return this._adabin();
+  }
+}
+
+function evenly_spaced_grid(start, stop, numel) {
+  return Array(numel)
+    .fill(0)
+    .map((_, idx) => start + (idx / numel) * (stop - start));
+}
+
+const distrs = {
+  normal: NormalDistributionBinned,
+  lognormal: LogNormalDistributionBinned,
+  uniform: UniformDistributionBinned
+};
+
+exports.distrs = distrs;

src/components/editor/index.js

@@ -0,0 +1,31 @@
+import "./styles.css";
+const embed = require("vega-embed").embed;
+const get_pdf_from_user_input = require("./main.js").get_pdf_from_user_input;
+
+let [y, x] = get_pdf_from_user_input("normal(1, 1)  / normal(10, 1)");
+
+let pdf = x.map((val, idx) => ({ x: val, pdf: y[idx] }));
+
+let spec = {
+  data: {
+    values: pdf
+  },
+  mark: { type: "area", line: true },
+  encoding: {
+    x: { field: "x", type: "quantitative" },
+    y: {
+      field: "pdf",
+      type: "quantitative",
+      scale: { domain: [0, 3 * Math.max(...y)] }
+    }
+  },
+  width: 500
+};
+
+embed("#viz", spec);
+
+console.log(y.reduce((a, b) => a + b));
+
+document.getElementById("app").innerHTML = `
+<div id="viz"></div>
+`;

src/components/editor/main.js

@@ -0,0 +1,278 @@
+// The main algorithmic work is done by functions in this module.
+// It also contains the main function, taking the user's string
+// and returning pdf values and x's.
+
+const distrs = require("./distribution.js").distrs;
+const parse = require("./parse.js");
+const _math = require("mathjs");
+const math = _math.create(_math.all);
+const bst = require("binary-search-tree");
+
+const NUM_MC_SAMPLES = 300;
+const OUTPUT_GRID_NUMEL = 300;
+
+function evenly_spaced_grid(start, stop, numel) {
+  return Array(numel)
+    .fill(0)
+    .map((_, idx) => start + (idx / numel) * (stop - start));
+}
+
+function get_distributions(substrings) {
+  // Takes an array of strings like "normal(0, 1)" and
+  // returns the corresponding distribution objects
+  let names_and_args = substrings.map(parse.get_distr_name_and_args);
+  let pdfs = names_and_args.map(x => new distrs[x[0]](x[1]));
+  return pdfs;
+}
+
+function update_transformed_divider_points_bst(
+  transform_func,
+  deterministic_pdf,
+  mc_distrs,
+  track_idx,
+  num_mc_samples,
+  bst_pts_and_idxs
+) {
+  // update the binary search tree with bin points of
+  // deterministic_pdf transformed by tansform func
+  // (transfrom func can be a stocahstic func with parameters
+  // sampled from mc_distrs)
+  var transformed_pts = [];
+  var pdf_inner_idxs = [];
+  var factors = [];
+  var start_pt = Infinity;
+  var end_pt = -Infinity;
+  let use_mc = mc_distrs.length > 0;
+  var num_outer_iters = use_mc ? num_mc_samples : 1;
+
+  for (let sample_idx = 0; sample_idx < num_outer_iters; ++sample_idx) {
+    var this_transformed_pts = deterministic_pdf.divider_pts;
+    if (use_mc) {
+      let samples = mc_distrs.map(x => x.sample());
+      this_transformed_pts = this_transformed_pts.map(x =>
+        transform_func([x].concat(samples))
+      );
+    } else {
+      this_transformed_pts = this_transformed_pts.map(x => transform_func([x]));
+    }
+    var this_transformed_pts_paired = [];
+    for (let tp_idx = 0; tp_idx < this_transformed_pts.length - 1; tp_idx++) {
+      let sorted = [
+        this_transformed_pts[tp_idx],
+        this_transformed_pts[tp_idx + 1]
+      ].sort((a, b) => a - b);
+      if (sorted[0] < start_pt) {
+        start_pt = sorted[0];
+      }
+      if (sorted[1] > end_pt) {
+        end_pt = sorted[1];
+      }
+      this_transformed_pts_paired.push(sorted);
+    }
+
+    transformed_pts = transformed_pts.concat(this_transformed_pts_paired);
+
+    pdf_inner_idxs = pdf_inner_idxs.concat([
+      ...Array(this_transformed_pts_paired.length).keys()
+    ]);
+    var this_factors = [];
+    for (let idx = 0; idx < this_transformed_pts_paired.length; idx++) {
+      this_factors.push(
+        (deterministic_pdf.divider_pts[idx + 1] -
+          deterministic_pdf.divider_pts[idx]) /
+        (this_transformed_pts_paired[idx][1] -
+          this_transformed_pts_paired[idx][0])
+      );
+    }
+    factors = factors.concat(this_factors);
+  }
+  for (let i = 0; i < transformed_pts.length; ++i) {
+    bst_pts_and_idxs.insert(transformed_pts[i][0], {
+      start: transformed_pts[i][0],
+      end: transformed_pts[i][1],
+      idx: [track_idx, pdf_inner_idxs[i]],
+      factor: factors[i] / num_outer_iters
+    });
+  }
+  return [start_pt, end_pt];
+}
+
+function get_final_pdf(pdf_vals, bst_pts_and_idxs, output_grid) {
+  // Take the binary search tree with transformed bin points,
+  // and an array of pdf values associated with the bins,
+  // and return a pdf over an evenly spaced grid
+  var offset = output_grid[1] / 2 - output_grid[0] / 2;
+  var active_intervals = new Map();
+  var active_endpoints = new bst.AVLTree();
+  var final_pdf_vals = [];
+  for (
+    let out_grid_idx = 0;
+    out_grid_idx < output_grid.length;
+    ++out_grid_idx
+  ) {
+    let startpoints_within_bin = bst_pts_and_idxs.betweenBounds({
+      $gte: output_grid[out_grid_idx] - offset,
+      $lt: output_grid[out_grid_idx] + offset
+    });
+    for (let interval of startpoints_within_bin) {
+      active_intervals.set(interval.idx, [
+        interval.start,
+        interval.end,
+        interval.factor
+      ]);
+      active_endpoints.insert(interval.end, interval.idx);
+    }
+    var contrib = 0;
+    for (let [pdf_idx, bounds_and_ratio] of active_intervals.entries()) {
+      let overlap_start = Math.max(
+        output_grid[out_grid_idx] - offset,
+        bounds_and_ratio[0]
+      );
+      let overlap_end = Math.min(
+        output_grid[out_grid_idx] + offset,
+        bounds_and_ratio[1]
+      );
+      let interval_size = bounds_and_ratio[1] - bounds_and_ratio[0];
+      let contrib_frac =
+        interval_size === 0
+          ? 0
+          : (overlap_end - overlap_start) * bounds_and_ratio[2];
+      let t = contrib_frac * pdf_vals[pdf_idx[0]][pdf_idx[1]];
+      contrib += t;
+    }
+    final_pdf_vals.push(contrib);
+    let endpoints_within_bin = active_endpoints.betweenBounds({
+      $gte: output_grid[out_grid_idx] - offset,
+      $lt: output_grid[out_grid_idx] + offset
+    });
+    for (let interval_idx of endpoints_within_bin) {
+      active_intervals.delete(interval_idx);
+    }
+  }
+  return final_pdf_vals;
+}
+
+function get_pdf_from_user_input(user_input_string) {
+  // Entrypoint. Pass user input strings to this function,
+  // get the corresponding pdf values and input points back.
+  // If the pdf requires monte carlo (it contains a between-distr function)
+  // we first determing which distr to have deterministic
+  // and whih to sample from. This is decided based on which
+  // choice gives the least variance.
+  let parsed = parse.parse_initial_string(user_input_string);
+  let mm_args = parse.separate_mm_args(parsed.mm_args_string);
+  const is_mm = mm_args.distrs.length > 0;
+  let tree = new bst.AVLTree();
+  let possible_start_pts = [];
+  let possible_end_pts = [];
+  let all_vals = [];
+  let weights = is_mm ? math.compile(mm_args.weights).evaluate()._data : [1];
+  let weights_sum = weights.reduce((a, b) => a + b);
+  weights = weights.map(x => x / weights_sum);
+  let n_iters = is_mm ? mm_args.distrs.length : 1;
+  for (let i = 0; i < n_iters; ++i) {
+    let distr_string = is_mm ? mm_args.distrs[i] : parsed.outer_string;
+    var [deterministic_pdf, mc_distrs] = choose_pdf_func(distr_string);
+    var grid_transform = get_grid_transform(distr_string);
+    var [start_pt, end_pt] = update_transformed_divider_points_bst(
+      grid_transform,
+      deterministic_pdf,
+      mc_distrs,
+      i,
+      NUM_MC_SAMPLES,
+      tree
+    );
+    possible_start_pts.push(start_pt);
+    possible_end_pts.push(end_pt);
+    all_vals.push(deterministic_pdf.pdf_vals.map(x => x * weights[i]));
+  }
+  start_pt = Math.min(...possible_start_pts);
+  end_pt = Math.max(...possible_end_pts);
+  let output_grid = evenly_spaced_grid(start_pt, end_pt, OUTPUT_GRID_NUMEL);
+  let final_pdf_vals = get_final_pdf(all_vals, tree, output_grid);
+  return [final_pdf_vals, output_grid];
+}
+
+function variance(vals) {
+  var vari = 0;
+  for (let i = 0; i < vals[0].length; ++i) {
+    let mean = 0;
+    let this_vari = 0;
+    for (let val of vals) {
+      mean += val[i] / vals.length;
+    }
+    for (let val of vals) {
+      this_vari += (val[i] - mean) ** 2;
+    }
+    vari += this_vari;
+  }
+  return vari;
+}
+
+function pluck_from_array(array, idx) {
+  return [array[idx], array.slice(0, idx).concat(array.slice(idx + 1))];
+}
+
+function choose_pdf_func(distr_string) {
+  // If distr_string requires MC, try all possible
+  // choices for the deterministic distribution,
+  // and pick the one with the least variance.
+  var variances = [];
+  let transform_func = get_grid_transform(distr_string);
+  let substrings = parse.get_distr_substrings(distr_string);
+  var pdfs = get_distributions(substrings);
+  if (pdfs.length === 1) {
+    return [pdfs[0], []];
+  }
+  var start_pt = 0;
+  var end_pt = 0;
+  for (let i = 0; i < pdfs.length; ++i) {
+    var outputs = [];
+    for (let j = 0; j < 20; ++j) {
+      let tree = new bst.AVLTree();
+      let [deterministic_pdf, mc_distrs] = pluck_from_array(pdfs, i);
+      let [this_start_pt, this_end_pt] = update_transformed_divider_points_bst(
+        transform_func,
+        deterministic_pdf,
+        mc_distrs,
+        0,
+        10,
+        tree
+      );
+      [start_pt, end_pt] =
+        j === 0 ? [this_start_pt, this_end_pt] : [start_pt, end_pt];
+      var output_grid = evenly_spaced_grid(start_pt, end_pt, 100);
+      let final_pdf_vals = get_final_pdf(
+        [deterministic_pdf.pdf_vals],
+        tree,
+        output_grid
+      );
+      outputs.push(final_pdf_vals);
+    }
+    variances.push(variance(outputs));
+  }
+  let best_variance = Math.min(...variances);
+  let best_idx = variances
+    .map((val, idx) => [val, idx])
+    .filter(x => x[0] === best_variance)[0][1];
+  let mc_distrs = pdfs.slice(0, best_idx).concat(pdfs.slice(best_idx + 1));
+  return [pdfs[best_idx], mc_distrs];
+}
+
+function get_grid_transform(distr_string) {
+  let substrings = parse.get_distr_substrings(distr_string);
+  let arg_strings = [];
+  for (let i = 0; i < substrings.length; ++i) {
+    distr_string = distr_string.replace(substrings[i], "x_" + i.toString());
+    arg_strings.push("x_" + i.toString());
+  }
+  let compiled = math.compile(distr_string);
+  function grid_transform(x) {
+    let kv_pairs = arg_strings.map((val, idx) => [val, x[idx]]);
+    let args_obj = Object.fromEntries(new Map(kv_pairs));
+    return compiled.evaluate(args_obj);
+  }
+  return grid_transform;
+}
+
+exports.get_pdf_from_user_input = get_pdf_from_user_input;

src/components/editor/parse.js

@@ -0,0 +1,119 @@
+// Functions for parsing/processing user input strings are here
+const _math = require("mathjs");
+const math = _math.create(_math.all);
+
+const DISTR_REGEXS = [
+  /beta\(/g,
+  /(log)?normal\(/g,
+  /multimodal\(/g,
+  /mm\(/g,
+  /uniform\(/g
+];
+
+function parse_initial_string(user_input_string) {
+  let outer_output_string = "";
+  let mm_args_string = "";
+  let idx = 0;
+  while (idx < user_input_string.length) {
+    if (
+      user_input_string.substring(idx - 11, idx) === "multimodal(" ||
+      user_input_string.substring(idx - 3, idx) === "mm("
+    ) {
+      let num_open_brackets = 1;
+      while (num_open_brackets > 0 && idx < user_input_string.length) {
+        mm_args_string += user_input_string[idx];
+        idx += 1;
+        if (user_input_string[idx] === ")") {
+          num_open_brackets -= 1;
+        } else if (user_input_string[idx] === "(") {
+          num_open_brackets += 1;
+        }
+      }
+      outer_output_string += ")";
+      idx += 1;
+    } else {
+      outer_output_string += user_input_string[idx];
+      idx += 1;
+    }
+  }
+  return {
+    outer_string: outer_output_string,
+    mm_args_string: mm_args_string
+  };
+}
+
+function separate_mm_args(mm_args_string) {
+  if (mm_args_string.endsWith(",")) {
+    mm_args_string = mm_args_string.slice(0, -1);
+  }
+  let args_array = [];
+  let num_open_brackets = 0;
+  let arg_substring = "";
+  for (let char of mm_args_string) {
+    if (num_open_brackets === 0 && char === ",") {
+      args_array.push(arg_substring.trim());
+      arg_substring = "";
+    } else {
+      if (char === ")" || char === "]") {
+        num_open_brackets -= 1;
+      } else if (char === "(" || char === "[") {
+        num_open_brackets += 1;
+      }
+      arg_substring += char;
+    }
+  }
+  return {
+    distrs: args_array,
+    weights: arg_substring.trim()
+  };
+}
+
+function get_distr_substrings(distr_string) {
+  let substrings = [];
+  for (let regex of DISTR_REGEXS) {
+    let matches = distr_string.matchAll(regex);
+    for (let match of matches) {
+      let idx = match.index + match[0].length;
+      let num_open_brackets = 1;
+      let distr_substring = "";
+      while (num_open_brackets !== 0 && idx < distr_string.length) {
+        distr_substring += distr_string[idx];
+        if (distr_string[idx] === "(") {
+          num_open_brackets += 1;
+        } else if (distr_string[idx] === ")") {
+          num_open_brackets -= 1;
+        }
+        idx += 1;
+      }
+      substrings.push((match[0] + distr_substring).trim());
+    }
+  }
+
+  return substrings;
+}
+
+function get_distr_name_and_args(substr) {
+  let distr_name = "";
+  let args_str = "";
+  let args_flag = false;
+  for (let char of substr) {
+    if (!args_flag && char !== "(") {
+      distr_name += char;
+    }
+    if (args_flag && char !== ")") {
+      args_str += char;
+    }
+    if (char === "(") {
+      args_str += "[";
+      args_flag = true;
+    }
+  }
+  args_str += "]";
+  let args = math.compile(args_str).evaluate()._data;
+  return [distr_name, args];
+}
+
+exports.get_distr_name_and_args = get_distr_name_and_args;
+exports.get_distr_substrings = get_distr_substrings;
+exports.separate_mm_args = separate_mm_args;
+exports.parse_initial_string = parse_initial_string;

yarn.lock

@@ -2333,6 +2333,13 @@ binary-extensions@^2.0.0:
   resolved "https://registry.yarnpkg.com/binary-extensions/-/binary-extensions-2.0.0.tgz#23c0df14f6a88077f5f986c0d167ec03c3d5537c"
   integrity sha512-Phlt0plgpIIBOGTT/ehfFnbNlfsDEiqmzE2KRXoX1bLIlir4X/MR+zSyBEkL05ffWgnRSf/DXv+WrUAVr93/ow==
 
+binary-search-tree@0.2.6:
+  version "0.2.6"
+  resolved "https://registry.yarnpkg.com/binary-search-tree/-/binary-search-tree-0.2.6.tgz#c6d29194e286827fcffe079010e6bf77def10ce3"
+  integrity sha1-xtKRlOKGgn/P/geQEOa/d97xDOM=
+  dependencies:
+    underscore "~1.4.4"
+
 bindings@^1.5.0:
   version "1.5.0"
   resolved "https://registry.yarnpkg.com/bindings/-/bindings-1.5.0.tgz#10353c9e945334bc0511a6d90b38fbc7c9c504df"
@@ -2889,7 +2896,7 @@ commander@2, commander@^2.11.0, commander@^2.18.0, commander@^2.19.0, commander@
   resolved "https://registry.yarnpkg.com/commander/-/commander-2.20.3.tgz#fd485e84c03eb4881c20722ba48035e8531aeb33"
   integrity sha512-GpVkmM8vF2vQUkj2LvZmD35JxeJOLCwJ9cUkugyk2nuhbv3+mJvpLYYt+0+USMxE+oj+ey/lJEnhZw75x/OMcQ==
 
-complex.js@2.0.11:
+complex.js@2.0.11, complex.js@^2.0.11:
   version "2.0.11"
   resolved "https://registry.yarnpkg.com/complex.js/-/complex.js-2.0.11.tgz#09a873fbf15ffd8c18c9c2201ccef425c32b8bf1"
   integrity sha512-6IArJLApNtdg1P1dFtn3dnyzoZBEF0MwMnrfF1exSBRpZYoy4yieMkpZhQDC0uwctw48vii0CFVyHfpgZ/DfGw==
@@ -3632,7 +3639,7 @@ decamelize@^1.2.0:
   resolved "https://registry.yarnpkg.com/decamelize/-/decamelize-1.2.0.tgz#f6534d15148269b20352e7bee26f501f9a191290"
   integrity sha1-9lNNFRSCabIDUue+4m9QH5oZEpA=
 
-decimal.js@10.2.0:
+decimal.js@10.2.0, decimal.js@^10.2.0:
   version "10.2.0"
   resolved "https://registry.yarnpkg.com/decimal.js/-/decimal.js-10.2.0.tgz#39466113a9e036111d02f82489b5fd6b0b5ed231"
   integrity sha512-vDPw+rDgn3bZe1+F/pyEwb1oMG2XTlRVgAa6B4KccTEpYgF8w6eQllVbQcfIJnZyvzFtFpxnpGtx8dd7DJp/Rw==
@@ -4043,7 +4050,7 @@ escape-html@~1.0.3:
   resolved "https://registry.yarnpkg.com/escape-html/-/escape-html-1.0.3.tgz#0258eae4d3d0c0974de1c169188ef0051d1d1988"
   integrity sha1-Aljq5NPQwJdN4cFpGI7wBR0dGYg=
 
-escape-latex@1.2.0:
+escape-latex@1.2.0, escape-latex@^1.2.0:
   version "1.2.0"
   resolved "https://registry.yarnpkg.com/escape-latex/-/escape-latex-1.2.0.tgz#07c03818cf7dac250cce517f4fda1b001ef2bca1"
   integrity sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw==
@@ -4438,7 +4445,7 @@ form-data@~2.3.2:
     combined-stream "^1.0.6"
     mime-types "^2.1.12"
 
-fraction.js@4.0.12:
+fraction.js@4.0.12, fraction.js@^4.0.12:
   version "4.0.12"
   resolved "https://registry.yarnpkg.com/fraction.js/-/fraction.js-4.0.12.tgz#0526d47c65a5fb4854df78bc77f7bec708d7b8c3"
   integrity sha512-8Z1K0VTG4hzYY7kA/1sj4/r1/RWLBD3xwReT/RCrUCbzPszjNQCCsy3ktkU/eaEqX3MYa4pY37a52eiBlPMlhA==
@@ -5410,7 +5417,7 @@ iterall@^1.2.1, iterall@^1.2.2:
   resolved "https://registry.yarnpkg.com/iterall/-/iterall-1.3.0.tgz#afcb08492e2915cbd8a0884eb93a8c94d0d72fea"
   integrity sha512-QZ9qOMdF+QLHxy1QIpUHUU1D5pS2CG2P69LF6L6CPjPYA/XMOmKV3PZpawHoAjHNyB0swdVTRxdYT4tbBbxqwg==
 
-javascript-natural-sort@0.7.1:
+javascript-natural-sort@0.7.1, javascript-natural-sort@^0.7.1:
   version "0.7.1"
   resolved "https://registry.yarnpkg.com/javascript-natural-sort/-/javascript-natural-sort-0.7.1.tgz#f9e2303d4507f6d74355a73664d1440fb5a0ef59"
   integrity sha1-+eIwPUUH9tdDVac2ZNFED7Wg71k=
@@ -6320,6 +6327,11 @@ jstat@1.9.0:
   resolved "https://registry.yarnpkg.com/jstat/-/jstat-1.9.0.tgz#96a625f5697566f6ba3b15832fb371f9451b8614"
   integrity sha512-xSsSJ3qY4rS+u8+dAwRcJ0LQGxNdibdW6rSalNPZDbLYkW1C7b0/j79IxXtQjrweqMNI3asN7FCIPceNSIJr2g==
 
+jstat@1.9.2:
+  version "1.9.2"
+  resolved "https://registry.yarnpkg.com/jstat/-/jstat-1.9.2.tgz#cd2d24df200fd3488861dc7868be01ff65a238cc"
+  integrity sha512-nc3uAadgrWWvJz6RyXUFN0lvTWEXYxMVIrm6ZVoOh4YPLvukLKYpqMofKIE2ReWkL7gFw6hEo6VWZjotYW2Bsw==
+
 kind-of@^3.0.2, kind-of@^3.0.3, kind-of@^3.2.0:
   version "3.2.2"
   resolved "https://registry.yarnpkg.com/kind-of/-/kind-of-3.2.2.tgz#31ea21a734bab9bbb0f32466d893aea51e4a3c64"
@@ -6559,6 +6571,20 @@ mathjs@5.10.3:
     tiny-emitter "2.1.0"
     typed-function "1.1.0"
 
+mathjs@6.6.0:
+  version "6.6.0"
+  resolved "https://registry.yarnpkg.com/mathjs/-/mathjs-6.6.0.tgz#0d71c7cc6b50bd112e160b55703a395caf4db4b1"
+  integrity sha512-gYYc1+irFbwuwYUx6O8G2YauvbD1+tPBbq829PaxAiRWpPzPEE8pvwGgvdMuk6c3pqhm6Do/mN26vLiQP46H5A==
+  dependencies:
+    complex.js "^2.0.11"
+    decimal.js "^10.2.0"
+    escape-latex "^1.2.0"
+    fraction.js "^4.0.12"
+    javascript-natural-sort "^0.7.1"
+    seed-random "^2.2.0"
+    tiny-emitter "^2.1.0"
+    typed-function "^1.1.1"
+
 md5.js@^1.3.4:
   version "1.3.5"
   resolved "https://registry.yarnpkg.com/md5.js/-/md5.js-1.3.5.tgz#b5d07b8e3216e3e27cd728d72f70d1e6a342005f"
@@ -9235,7 +9261,7 @@ screenfull@^5.0.0:
   resolved "https://registry.yarnpkg.com/screenfull/-/screenfull-5.0.2.tgz#b9acdcf1ec676a948674df5cd0ff66b902b0bed7"
   integrity sha512-cCF2b+L/mnEiORLN5xSAz6H3t18i2oHh9BA8+CQlAh5DRw2+NFAGQJOSYbcGw8B2k04g/lVvFcfZ83b3ysH5UQ==
 
-seed-random@2.2.0:
+seed-random@2.2.0, seed-random@^2.2.0:
   version "2.2.0"
   resolved "https://registry.yarnpkg.com/seed-random/-/seed-random-2.2.0.tgz#2a9b19e250a817099231a5b99a4daf80b7fbed54"
   integrity sha1-KpsZ4lCoFwmSMaW5mk2vgLf77VQ=
@@ -9989,7 +10015,7 @@ timsort@^0.3.0:
   resolved "https://registry.yarnpkg.com/timsort/-/timsort-0.3.0.tgz#405411a8e7e6339fe64db9a234de11dc31e02bd4"
   integrity sha1-QFQRqOfmM5/mTbmiNN4R3DHgK9Q=
 
-tiny-emitter@2.1.0:
+tiny-emitter@2.1.0, tiny-emitter@^2.1.0:
   version "2.1.0"
   resolved "https://registry.yarnpkg.com/tiny-emitter/-/tiny-emitter-2.1.0.tgz#1d1a56edfc51c43e863cbb5382a72330e3555423"
   integrity sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q==
@@ -10176,6 +10202,11 @@ typed-function@1.1.0:
   resolved "https://registry.yarnpkg.com/typed-function/-/typed-function-1.1.0.tgz#ea149706e0fb42aca1791c053a6d94ccd6c4fdcb"
   integrity sha512-TuQzwiT4DDg19beHam3E66oRXhyqlyfgjHB/5fcvsRXbfmWPJfto9B4a0TBdTrQAPGlGmXh/k7iUI+WsObgORA==
 
+typed-function@^1.1.1:
+  version "1.1.1"
+  resolved "https://registry.yarnpkg.com/typed-function/-/typed-function-1.1.1.tgz#a1316187ec3628c9e219b91ca96918660a10138e"
+  integrity sha512-RbN7MaTQBZLJYzDENHPA0nUmWT0Ex80KHItprrgbTPufYhIlTePvCXZxyQK7wgn19FW5bnuaBIKcBb5mRWjB1Q==
+
 typedarray-to-buffer@^3.1.5:
   version "3.1.5"
   resolved "https://registry.yarnpkg.com/typedarray-to-buffer/-/typedarray-to-buffer-3.1.5.tgz#a97ee7a9ff42691b9f783ff1bc5112fe3fca9080"
@@ -10208,6 +10239,11 @@ uncss@^0.17.2:
     postcss-selector-parser "6.0.2"
     request "^2.88.0"
 
+underscore@~1.4.4:
+  version "1.4.4"
+  resolved "https://registry.yarnpkg.com/underscore/-/underscore-1.4.4.tgz#61a6a32010622afa07963bf325203cf12239d604"
+  integrity sha1-YaajIBBiKvoHljvzJSA88SI51gQ=
+
 unicode-canonical-property-names-ecmascript@^1.0.4:
   version "1.0.4"
   resolved "https://registry.yarnpkg.com/unicode-canonical-property-names-ecmascript/-/unicode-canonical-property-names-ecmascript-1.0.4.tgz#2619800c4c825800efdd8343af7dd9933cbe2818"