diff -r efd9c589177a -r c0b4a8b5a012 toolkit/javascript/d3/lib/science/science.stats.js
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolkit/javascript/d3/lib/science/science.stats.js	Thu Apr 10 14:20:23 2014 +0200
@@ -0,0 +1,720 @@
+(function(){science.stats = {};
+// Bandwidth selectors for Gaussian kernels.
+// Based on R's implementations in `stats.bw`.
+science.stats.bandwidth = {
+
+  // Silverman, B. W. (1986) Density Estimation. London: Chapman and Hall.
+  nrd0: function(x) {
+    var hi = Math.sqrt(science.stats.variance(x));
+    if (!(lo = Math.min(hi, science.stats.iqr(x) / 1.34)))
+      (lo = hi) || (lo = Math.abs(x[1])) || (lo = 1);
+    return .9 * lo * Math.pow(x.length, -.2);
+  },
+
+  // Scott, D. W. (1992) Multivariate Density Estimation: Theory, Practice, and
+  // Visualization. Wiley.
+  nrd: function(x) {
+    var h = science.stats.iqr(x) / 1.34;
+    return 1.06 * Math.min(Math.sqrt(science.stats.variance(x)), h)
+      * Math.pow(x.length, -1/5);
+  }
+};
+science.stats.distance = {
+  euclidean: function(a, b) {
+    var n = a.length,
+        i = -1,
+        s = 0,
+        x;
+    while (++i < n) {
+      x = a[i] - b[i];
+      s += x * x;
+    }
+    return Math.sqrt(s);
+  },
+  manhattan: function(a, b) {
+    var n = a.length,
+        i = -1,
+        s = 0;
+    while (++i < n) s += Math.abs(a[i] - b[i]);
+    return s;
+  },
+  minkowski: function(p) {
+    return function(a, b) {
+      var n = a.length,
+          i = -1,
+          s = 0;
+      while (++i < n) s += Math.pow(Math.abs(a[i] - b[i]), p);
+      return Math.pow(s, 1 / p);
+    };
+  },
+  chebyshev: function(a, b) {
+    var n = a.length,
+        i = -1,
+        max = 0,
+        x;
+    while (++i < n) {
+      x = Math.abs(a[i] - b[i]);
+      if (x > max) max = x;
+    }
+    return max;
+  },
+  hamming: function(a, b) {
+    var n = a.length,
+        i = -1,
+        d = 0;
+    while (++i < n) if (a[i] !== b[i]) d++;
+    return d;
+  },
+  jaccard: function(a, b) {
+    var n = a.length,
+        i = -1,
+        s = 0;
+    while (++i < n) if (a[i] === b[i]) s++;
+    return s / n;
+  },
+  braycurtis: function(a, b) {
+    var n = a.length,
+        i = -1,
+        s0 = 0,
+        s1 = 0,
+        ai,
+        bi;
+    while (++i < n) {
+      ai = a[i];
+      bi = b[i];
+      s0 += Math.abs(ai - bi);
+      s1 += Math.abs(ai + bi);
+    }
+    return s0 / s1;
+  }
+};
+// Based on implementation in http://picomath.org/.
+science.stats.erf = function(x) {
+  var a1 =  0.254829592,
+      a2 = -0.284496736,
+      a3 =  1.421413741,
+      a4 = -1.453152027,
+      a5 =  1.061405429,
+      p  =  0.3275911;
+
+  // Save the sign of x
+  var sign = x < 0 ? -1 : 1;
+  if (x < 0) {
+    sign = -1;
+    x = -x;
+  }
+
+  // A&S formula 7.1.26
+  var t = 1 / (1 + p * x);
+  return sign * (
+    1 - (((((a5 * t + a4) * t) + a3) * t + a2) * t + a1)
+    * t * Math.exp(-x * x));
+};
+science.stats.phi = function(x) {
+  return .5 * (1 + science.stats.erf(x / Math.SQRT2));
+};
+// See <http://en.wikipedia.org/wiki/Kernel_(statistics)>.
+science.stats.kernel = {
+  uniform: function(u) {
+    if (u <= 1 && u >= -1) return .5;
+    return 0;
+  },
+  triangular: function(u) {
+    if (u <= 1 && u >= -1) return 1 - Math.abs(u);
+    return 0;
+  },
+  epanechnikov: function(u) {
+    if (u <= 1 && u >= -1) return .75 * (1 - u * u);
+    return 0;
+  },
+  quartic: function(u) {
+    if (u <= 1 && u >= -1) {
+      var tmp = 1 - u * u;
+      return (15 / 16) * tmp * tmp;
+    }
+    return 0;
+  },
+  triweight: function(u) {
+    if (u <= 1 && u >= -1) {
+      var tmp = 1 - u * u;
+      return (35 / 32) * tmp * tmp * tmp;
+    }
+    return 0;
+  },
+  gaussian: function(u) {
+    return 1 / Math.sqrt(2 * Math.PI) * Math.exp(-.5 * u * u);
+  },
+  cosine: function(u) {
+    if (u <= 1 && u >= -1) return Math.PI / 4 * Math.cos(Math.PI / 2 * u);
+    return 0;
+  }
+};
+// http://exploringdata.net/den_trac.htm
+science.stats.kde = function() {
+  var kernel = science.stats.kernel.gaussian,
+      sample = [],
+      bandwidth = science.stats.bandwidth.nrd;
+
+  function kde(points, i) {
+    var bw = bandwidth.call(this, sample);
+    return points.map(function(x) {
+      var i = -1,
+          y = 0,
+          n = sample.length;
+      while (++i < n) {
+        y += kernel((x - sample[i]) / bw);
+      }
+      return [x, y / bw / n];
+    });
+  }
+
+  kde.kernel = function(x) {
+    if (!arguments.length) return kernel;
+    kernel = x;
+    return kde;
+  };
+
+  kde.sample = function(x) {
+    if (!arguments.length) return sample;
+    sample = x;
+    return kde;
+  };
+
+  kde.bandwidth = function(x) {
+    if (!arguments.length) return bandwidth;
+    bandwidth = science.functor(x);
+    return kde;
+  };
+
+  return kde;
+};
+// Based on figue implementation by Jean-Yves Delort.
+// http://code.google.com/p/figue/
+science.stats.kmeans = function() {
+  var distance = science.stats.distance.euclidean,
+      maxIterations = 1000,
+      k = 1;
+
+  function kmeans(vectors) {
+    var n = vectors.length,
+        assignments = [],
+        clusterSizes = [],
+        repeat = 1,
+        iterations = 0,
+        centroids = science_stats_kmeansRandom(k, vectors),
+        newCentroids,
+        i,
+        j,
+        x,
+        d,
+        min,
+        best;
+
+    while (repeat && iterations < maxIterations) {
+      // Assignment step.
+      j = -1; while (++j < k) {
+        clusterSizes[j] = 0;
+      }
+
+      i = -1; while (++i < n) {
+        x = vectors[i];
+        min = Infinity;
+        j = -1; while (++j < k) {
+          d = distance.call(this, centroids[j], x);
+          if (d < min) {
+            min = d;
+            best = j;
+          }
+        }
+        clusterSizes[assignments[i] = best]++;
+      }
+
+      // Update centroids step.
+      newCentroids = [];
+      i = -1; while (++i < n) {
+        x = assignments[i];
+        d = newCentroids[x];
+        if (d == null) newCentroids[x] = vectors[i].slice();
+        else {
+          j = -1; while (++j < d.length) {
+            d[j] += vectors[i][j];
+          }
+        }
+      }
+      j = -1; while (++j < k) {
+        x = newCentroids[j];
+        d = 1 / clusterSizes[j];
+        i = -1; while (++i < x.length) x[i] *= d;
+      }
+
+      // Check convergence.
+      repeat = 0;
+      j = -1; while (++j < k) {
+        if (!science_stats_kmeansCompare(newCentroids[j], centroids[j])) {
+          repeat = 1;
+          break;
+        }
+      }
+      centroids = newCentroids;
+      iterations++;
+    }
+    return {assignments: assignments, centroids: centroids};
+  }
+
+  kmeans.k = function(x) {
+    if (!arguments.length) return k;
+    k = x;
+    return kmeans;
+  };
+
+  kmeans.distance = function(x) {
+    if (!arguments.length) return distance;
+    distance = x;
+    return kmeans;
+  };
+
+  return kmeans;
+};
+
+function science_stats_kmeansCompare(a, b) {
+  if (!a || !b || a.length !== b.length) return false;
+  var n = a.length,
+      i = -1;
+  while (++i < n) if (a[i] !== b[i]) return false;
+  return true;
+}
+
+// Returns an array of k distinct vectors randomly selected from the input
+// array of vectors. Returns null if k > n or if there are less than k distinct
+// objects in vectors.
+function science_stats_kmeansRandom(k, vectors) {
+  var n = vectors.length;
+  if (k > n) return null;
+  
+  var selected_vectors = [];
+  var selected_indices = [];
+  var tested_indices = {};
+  var tested = 0;
+  var selected = 0;
+  var i,
+      vector,
+      select;
+
+  while (selected < k) {
+    if (tested === n) return null;
+    
+    var random_index = Math.floor(Math.random() * n);
+    if (random_index in tested_indices) continue;
+    
+    tested_indices[random_index] = 1;
+    tested++;
+    vector = vectors[random_index];
+    select = true;
+    for (i = 0; i < selected; i++) {
+      if (science_stats_kmeansCompare(vector, selected_vectors[i])) {
+        select = false;
+        break;
+      }
+    }
+    if (select) {
+      selected_vectors[selected] = vector;
+      selected_indices[selected] = random_index;
+      selected++;
+    }
+  }
+  return selected_vectors;
+}
+science.stats.hcluster = function() {
+  var distance = science.stats.distance.euclidean,
+      linkage = "simple"; // simple, complete or average
+
+  function hcluster(vectors) {
+    var n = vectors.length,
+        dMin = [],
+        cSize = [],
+        distMatrix = [],
+        clusters = [],
+        c1,
+        c2,
+        c1Cluster,
+        c2Cluster,
+        p,
+        root,
+        i,
+        j;
+
+    // Initialise distance matrix and vector of closest clusters.
+    i = -1; while (++i < n) {
+      dMin[i] = 0;
+      distMatrix[i] = [];
+      j = -1; while (++j < n) {
+        distMatrix[i][j] = i === j ? Infinity : distance(vectors[i] , vectors[j]);
+        if (distMatrix[i][dMin[i]] > distMatrix[i][j]) dMin[i] = j;
+      }
+    }
+
+    // create leaves of the tree
+    i = -1; while (++i < n) {
+      clusters[i] = [];
+      clusters[i][0] = {
+        left: null,
+        right: null,
+        dist: 0,
+        centroid: vectors[i],
+        size: 1,
+        depth: 0
+      };
+      cSize[i] = 1;
+    }
+
+    // Main loop
+    for (p = 0; p < n-1; p++) {
+      // find the closest pair of clusters
+      c1 = 0;
+      for (i = 0; i < n; i++) {
+        if (distMatrix[i][dMin[i]] < distMatrix[c1][dMin[c1]]) c1 = i;
+      }
+      c2 = dMin[c1];
+
+      // create node to store cluster info 
+      c1Cluster = clusters[c1][0];
+      c2Cluster = clusters[c2][0];
+
+      newCluster = {
+        left: c1Cluster,
+        right: c2Cluster,
+        dist: distMatrix[c1][c2],
+        centroid: calculateCentroid(c1Cluster.size, c1Cluster.centroid,
+          c2Cluster.size, c2Cluster.centroid),
+        size: c1Cluster.size + c2Cluster.size,
+        depth: 1 + Math.max(c1Cluster.depth, c2Cluster.depth)
+      };
+      clusters[c1].splice(0, 0, newCluster);
+      cSize[c1] += cSize[c2];
+
+      // overwrite row c1 with respect to the linkage type
+      for (j = 0; j < n; j++) {
+        switch (linkage) {
+          case "single":
+            if (distMatrix[c1][j] > distMatrix[c2][j])
+              distMatrix[j][c1] = distMatrix[c1][j] = distMatrix[c2][j];
+            break;
+          case "complete":
+            if (distMatrix[c1][j] < distMatrix[c2][j])
+              distMatrix[j][c1] = distMatrix[c1][j] = distMatrix[c2][j];
+            break;
+          case "average":
+            distMatrix[j][c1] = distMatrix[c1][j] = (cSize[c1] * distMatrix[c1][j] + cSize[c2] * distMatrix[c2][j]) / (cSize[c1] + cSize[j]);
+            break;
+        }
+      }
+      distMatrix[c1][c1] = Infinity;
+
+      // infinity ­out old row c2 and column c2
+      for (i = 0; i < n; i++)
+        distMatrix[i][c2] = distMatrix[c2][i] = Infinity;
+
+      // update dmin and replace ones that previous pointed to c2 to point to c1
+      for (j = 0; j < n; j++) {
+        if (dMin[j] == c2) dMin[j] = c1;
+        if (distMatrix[c1][j] < distMatrix[c1][dMin[c1]]) dMin[c1] = j;
+      }
+
+      // keep track of the last added cluster
+      root = newCluster;
+    }
+
+    return root;
+  }
+
+  hcluster.distance = function(x) {
+    if (!arguments.length) return distance;
+    distance = x;
+    return hcluster;
+  };
+
+  return hcluster;
+};
+
+function calculateCentroid(c1Size, c1Centroid, c2Size, c2Centroid) {
+  var newCentroid = [],
+      newSize = c1Size + c2Size,
+      n = c1Centroid.length,
+      i = -1;
+  while (++i < n) {
+    newCentroid[i] = (c1Size * c1Centroid[i] + c2Size * c2Centroid[i]) / newSize;
+  }
+  return newCentroid;
+}
+science.stats.iqr = function(x) {
+  var quartiles = science.stats.quantiles(x, [.25, .75]);
+  return quartiles[1] - quartiles[0];
+};
+// Based on org.apache.commons.math.analysis.interpolation.LoessInterpolator
+// from http://commons.apache.org/math/
+science.stats.loess = function() {    
+  var bandwidth = .3,
+      robustnessIters = 2,
+      accuracy = 1e-12;
+
+  function smooth(xval, yval, weights) {
+    var n = xval.length,
+        i;
+
+    if (n !== yval.length) throw {error: "Mismatched array lengths"};
+    if (n == 0) throw {error: "At least one point required."};
+
+    if (arguments.length < 3) {
+      weights = [];
+      i = -1; while (++i < n) weights[i] = 1;
+    }
+
+    science_stats_loessFiniteReal(xval);
+    science_stats_loessFiniteReal(yval);
+    science_stats_loessFiniteReal(weights);
+    science_stats_loessStrictlyIncreasing(xval);
+
+    if (n == 1) return [yval[0]];
+    if (n == 2) return [yval[0], yval[1]];
+
+    var bandwidthInPoints = Math.floor(bandwidth * n);
+
+    if (bandwidthInPoints < 2) throw {error: "Bandwidth too small."};
+
+    var res = [],
+        residuals = [],
+        robustnessWeights = [];
+
+    // Do an initial fit and 'robustnessIters' robustness iterations.
+    // This is equivalent to doing 'robustnessIters+1' robustness iterations
+    // starting with all robustness weights set to 1.
+    i = -1; while (++i < n) {
+      res[i] = 0;
+      residuals[i] = 0;
+      robustnessWeights[i] = 1;
+    }
+
+    var iter = -1;
+    while (++iter <= robustnessIters) {
+      var bandwidthInterval = [0, bandwidthInPoints - 1];
+      // At each x, compute a local weighted linear regression
+      var x;
+      i = -1; while (++i < n) {
+        x = xval[i];
+
+        // Find out the interval of source points on which
+        // a regression is to be made.
+        if (i > 0) {
+          science_stats_loessUpdateBandwidthInterval(xval, weights, i, bandwidthInterval);
+        }
+
+        var ileft = bandwidthInterval[0],
+            iright = bandwidthInterval[1];
+
+        // Compute the point of the bandwidth interval that is
+        // farthest from x
+        var edge = (xval[i] - xval[ileft]) > (xval[iright] - xval[i]) ? ileft : iright;
+
+        // Compute a least-squares linear fit weighted by
+        // the product of robustness weights and the tricube
+        // weight function.
+        // See http://en.wikipedia.org/wiki/Linear_regression
+        // (section "Univariate linear case")
+        // and http://en.wikipedia.org/wiki/Weighted_least_squares
+        // (section "Weighted least squares")
+        var sumWeights = 0,
+            sumX = 0,
+            sumXSquared = 0,
+            sumY = 0,
+            sumXY = 0,
+            denom = Math.abs(1 / (xval[edge] - x));
+
+        for (var k = ileft; k <= iright; ++k) {
+          var xk   = xval[k],
+              yk   = yval[k],
+              dist = k < i ? x - xk : xk - x,
+              w    = science_stats_loessTricube(dist * denom) * robustnessWeights[k] * weights[k],
+              xkw  = xk * w;
+          sumWeights += w;
+          sumX += xkw;
+          sumXSquared += xk * xkw;
+          sumY += yk * w;
+          sumXY += yk * xkw;
+        }
+
+        var meanX = sumX / sumWeights,
+            meanY = sumY / sumWeights,
+            meanXY = sumXY / sumWeights,
+            meanXSquared = sumXSquared / sumWeights;
+
+        var beta = (Math.sqrt(Math.abs(meanXSquared - meanX * meanX)) < accuracy)
+            ? 0 : ((meanXY - meanX * meanY) / (meanXSquared - meanX * meanX));
+
+        var alpha = meanY - beta * meanX;
+
+        res[i] = beta * x + alpha;
+        residuals[i] = Math.abs(yval[i] - res[i]);
+      }
+
+      // No need to recompute the robustness weights at the last
+      // iteration, they won't be needed anymore
+      if (iter === robustnessIters) {
+        break;
+      }
+
+      // Recompute the robustness weights.
+
+      // Find the median residual.
+      var sortedResiduals = residuals.slice();
+      sortedResiduals.sort();
+      var medianResidual = sortedResiduals[Math.floor(n / 2)];
+
+      if (Math.abs(medianResidual) < accuracy)
+        break;
+
+      var arg,
+          w;
+      i = -1; while (++i < n) {
+        arg = residuals[i] / (6 * medianResidual);
+        robustnessWeights[i] = (arg >= 1) ? 0 : ((w = 1 - arg * arg) * w);
+      }
+    }
+
+    return res;
+  }
+
+  smooth.bandwidth = function(x) {
+    if (!arguments.length) return x;
+    bandwidth = x;
+    return smooth;
+  };
+
+  smooth.robustnessIterations = function(x) {
+    if (!arguments.length) return x;
+    robustnessIters = x;
+    return smooth;
+  };
+
+  smooth.accuracy = function(x) {
+    if (!arguments.length) return x;
+    accuracy = x;
+    return smooth;
+  };
+
+  return smooth;
+};
+
+function science_stats_loessFiniteReal(values) {
+  var n = values.length,
+      i = -1;
+
+  while (++i < n) if (!isFinite(values[i])) return false;
+
+  return true;
+}
+
+function science_stats_loessStrictlyIncreasing(xval) {
+  var n = xval.length,
+      i = 0;
+
+  while (++i < n) if (xval[i - 1] >= xval[i]) return false;
+
+  return true;
+}
+
+// Compute the tricube weight function.
+// http://en.wikipedia.org/wiki/Local_regression#Weight_function
+function science_stats_loessTricube(x) {
+  return (x = 1 - x * x * x) * x * x;
+}
+
+// Given an index interval into xval that embraces a certain number of
+// points closest to xval[i-1], update the interval so that it embraces
+// the same number of points closest to xval[i], ignoring zero weights.
+function science_stats_loessUpdateBandwidthInterval(
+  xval, weights, i, bandwidthInterval) {
+
+  var left = bandwidthInterval[0],
+      right = bandwidthInterval[1];
+
+  // The right edge should be adjusted if the next point to the right
+  // is closer to xval[i] than the leftmost point of the current interval
+  var nextRight = science_stats_loessNextNonzero(weights, right);
+  if ((nextRight < xval.length) && (xval[nextRight] - xval[i]) < (xval[i] - xval[left])) {
+    var nextLeft = science_stats_loessNextNonzero(weights, left);
+    bandwidthInterval[0] = nextLeft;
+    bandwidthInterval[1] = nextRight;
+  }
+}
+
+function science_stats_loessNextNonzero(weights, i) {
+  var j = i + 1;
+  while (j < weights.length && weights[j] === 0) j++;
+  return j;
+}
+// Welford's algorithm.
+science.stats.mean = function(x) {
+  var n = x.length;
+  if (n === 0) return NaN;
+  var m = 0,
+      i = -1;
+  while (++i < n) m += (x[i] - m) / (i + 1);
+  return m;
+};
+science.stats.median = function(x) {
+  return science.stats.quantiles(x, [.5])[0];
+};
+science.stats.mode = function(x) {
+  x = x.slice().sort(science.ascending);
+  var mode,
+      n = x.length,
+      i = -1,
+      l = i,
+      last = null,
+      max = 0,
+      tmp,
+      v;
+  while (++i < n) {
+    if ((v = x[i]) !== last) {
+      if ((tmp = i - l) > max) {
+        max = tmp;
+        mode = last;
+      }
+      last = v;
+      l = i;
+    }
+  }
+  return mode;
+};
+// Uses R's quantile algorithm type=7.
+science.stats.quantiles = function(d, quantiles) {
+  d = d.slice().sort(science.ascending);
+  var n_1 = d.length - 1;
+  return quantiles.map(function(q) {
+    if (q === 0) return d[0];
+    else if (q === 1) return d[n_1];
+
+    var index = 1 + q * n_1,
+        lo = Math.floor(index),
+        h = index - lo,
+        a = d[lo - 1];
+
+    return h === 0 ? a : a + h * (d[lo] - a);
+  });
+};
+// Unbiased estimate of a sample's variance.
+// Also known as the sample variance, where the denominator is n - 1.
+science.stats.variance = function(x) {
+  var n = x.length;
+  if (n < 1) return NaN;
+  if (n === 1) return 0;
+  var mean = science.stats.mean(x),
+      i = -1,
+      s = 0;
+  while (++i < n) {
+    var v = x[i] - mean;
+    s += v * v;
+  }
+  return s / (n - 1);
+};
+})()
\ No newline at end of file