d3.layout.js

(function(){d3.layout = {};
// Implements hierarchical edge bundling using Holten's algorithm. For each
// input link, a path is computed that travels through the tree, up the parent
// hierarchy to the least common ancestor, and then back down to the destination
// node. Each path is simply an array of nodes.
d3.layout.bundle = function() {
  return function(links) {
    var paths = [],
        i = -1,
        n = links.length;
    while (++i < n) paths.push(d3_layout_bundlePath(links[i]));
    return paths;
  };
};

function d3_layout_bundlePath(link) {
  var start = link.source,
      end = link.target,
      lca = d3_layout_bundleLeastCommonAncestor(start, end),
      points = [start];
  while (start !== lca) {
    start = start.parent;
    points.push(start);
  }
  var k = points.length;
  while (end !== lca) {
    points.splice(k, 0, end);
    end = end.parent;
  }
  return points;
}

function d3_layout_bundleAncestors(node) {
  var ancestors = [],
      parent = node.parent;
  while (parent != null) {
    ancestors.push(node);
    node = parent;
    parent = parent.parent;
  }
  ancestors.push(node);
  return ancestors;
}

function d3_layout_bundleLeastCommonAncestor(a, b) {
  if (a === b) return a;
  var aNodes = d3_layout_bundleAncestors(a),
      bNodes = d3_layout_bundleAncestors(b),
      aNode = aNodes.pop(),
      bNode = bNodes.pop(),
      sharedNode = null;
  while (aNode === bNode) {
    sharedNode = aNode;
    aNode = aNodes.pop();
    bNode = bNodes.pop();
  }
  return sharedNode;
}
d3.layout.chord = function() {
  var chord = {},
      chords,
      groups,
      matrix,
      n,
      padding = 0,
      sortGroups,
      sortSubgroups,
      sortChords;

  function relayout() {
    var subgroups = {},
        groupSums = [],
        groupIndex = d3.range(n),
        subgroupIndex = [],
        k,
        x,
        x0,
        i,
        j;

    chords = [];
    groups = [];

    // Compute the sum.
    k = 0, i = -1; while (++i < n) {
      x = 0, j = -1; while (++j < n) {
        x += matrix[i][j];
      }
      groupSums.push(x);
      subgroupIndex.push(d3.range(n));
      k += x;
    }

    // Sort groups…
    if (sortGroups) {
      groupIndex.sort(function(a, b) {
        return sortGroups(groupSums[a], groupSums[b]);
      });
    }

    // Sort subgroups…
    if (sortSubgroups) {
      subgroupIndex.forEach(function(d, i) {
        d.sort(function(a, b) {
          return sortSubgroups(matrix[i][a], matrix[i][b]);
        });
      });
    }

    // Convert the sum to scaling factor for [0, 2pi].
    // TODO Allow start and end angle to be specified.
    // TODO Allow padding to be specified as percentage?
    k = (2 * Math.PI - padding * n) / k;

    // Compute the start and end angle for each group and subgroup.
    // Note: Opera has a bug reordering object literal properties!
    x = 0, i = -1; while (++i < n) {
      x0 = x, j = -1; while (++j < n) {
        var di = groupIndex[i],
            dj = subgroupIndex[di][j],
            v = matrix[di][dj],
            a0 = x,
            a1 = x += v * k;
        subgroups[di + "-" + dj] = {
          index: di,
          subindex: dj,
          startAngle: a0,
          endAngle: a1,
          value: v
        };
      }
      groups.push({
        index: di,
        startAngle: x0,
        endAngle: x,
        value: (x - x0) / k
      });
      x += padding;
    }

    // Generate chords for each (non-empty) subgroup-subgroup link.
    i = -1; while (++i < n) {
      j = i - 1; while (++j < n) {
        var source = subgroups[i + "-" + j],
            target = subgroups[j + "-" + i];
        if (source.value || target.value) {
          chords.push(source.value < target.value
              ? {source: target, target: source}
              : {source: source, target: target});
        }
      }
    }

    if (sortChords) resort();
  }

  function resort() {
    chords.sort(function(a, b) {
      return sortChords(
          (a.source.value + a.target.value) / 2,
          (b.source.value + b.target.value) / 2);
    });
  }

  chord.matrix = function(x) {
    if (!arguments.length) return matrix;
    n = (matrix = x) && matrix.length;
    chords = groups = null;
    return chord;
  };

  chord.padding = function(x) {
    if (!arguments.length) return padding;
    padding = x;
    chords = groups = null;
    return chord;
  };

  chord.sortGroups = function(x) {
    if (!arguments.length) return sortGroups;
    sortGroups = x;
    chords = groups = null;
    return chord;
  };

  chord.sortSubgroups = function(x) {
    if (!arguments.length) return sortSubgroups;
    sortSubgroups = x;
    chords = null;
    return chord;
  };

  chord.sortChords = function(x) {
    if (!arguments.length) return sortChords;
    sortChords = x;
    if (chords) resort();
    return chord;
  };

  chord.chords = function() {
    if (!chords) relayout();
    return chords;
  };

  chord.groups = function() {
    if (!groups) relayout();
    return groups;
  };

  return chord;
};
// A rudimentary force layout using Gauss-Seidel.
d3.layout.force = function() {
  var force = {},
      event = d3.dispatch("tick"),
      size = [1, 1],
      drag,
      alpha,
      friction = .9,
      linkDistance = d3_layout_forceLinkDistance,
      linkStrength = d3_layout_forceLinkStrength,
      charge = -30,
      gravity = .1,
      theta = .8,
      interval,
      nodes = [],
      links = [],
      distances,
      strengths,
      charges;

  function repulse(node) {
    return function(quad, x1, y1, x2, y2) {
      if (quad.point !== node) {
        var dx = quad.cx - node.x,
            dy = quad.cy - node.y,
            dn = 1 / Math.sqrt(dx * dx + dy * dy);

        /* Barnes-Hut criterion. */
        if ((x2 - x1) * dn < theta) {
          var k = quad.charge * dn * dn;
          node.px -= dx * k;
          node.py -= dy * k;
          return true;
        }

        if (quad.point && isFinite(dn)) {
          var k = quad.pointCharge * dn * dn;
          node.px -= dx * k;
          node.py -= dy * k;
        }
      }
      return !quad.charge;
    };
  }

  function tick() {
    var n = nodes.length,
        m = links.length,
        q,
        i, // current index
        o, // current object
        s, // current source
        t, // current target
        l, // current distance
        k, // current force
        x, // x-distance
        y; // y-distance

    // gauss-seidel relaxation for links
    for (i = 0; i < m; ++i) {
      o = links[i];
      s = o.source;
      t = o.target;
      x = t.x - s.x;
      y = t.y - s.y;
      if (l = (x * x + y * y)) {
        l = alpha * strengths[i] * ((l = Math.sqrt(l)) - distances[i]) / l;
        x *= l;
        y *= l;
        t.x -= x * (k = s.weight / (t.weight + s.weight));
        t.y -= y * k;
        s.x += x * (k = 1 - k);
        s.y += y * k;
      }
    }

    // apply gravity forces
    if (k = alpha * gravity) {
      x = size[0] / 2;
      y = size[1] / 2;
      i = -1; if (k) while (++i < n) {
        o = nodes[i];
        o.x += (x - o.x) * k;
        o.y += (y - o.y) * k;
      }
    }

    // compute quadtree center of mass and apply charge forces
    if (charge) {
      d3_layout_forceAccumulate(q = d3.geom.quadtree(nodes), alpha, charges);
      i = -1; while (++i < n) {
        if (!(o = nodes[i]).fixed) {
          q.visit(repulse(o));
        }
      }
    }

    // position verlet integration
    i = -1; while (++i < n) {
      o = nodes[i];
      if (o.fixed) {
        o.x = o.px;
        o.y = o.py;
      } else {
        o.x -= (o.px - (o.px = o.x)) * friction;
        o.y -= (o.py - (o.py = o.y)) * friction;
      }
    }

    event.tick({type: "tick", alpha: alpha});

    // simulated annealing, basically
    return (alpha *= .99) < .005;
  }

  force.nodes = function(x) {
    if (!arguments.length) return nodes;
    nodes = x;
    return force;
  };

  force.links = function(x) {
    if (!arguments.length) return links;
    links = x;
    return force;
  };

  force.size = function(x) {
    if (!arguments.length) return size;
    size = x;
    return force;
  };

  force.linkDistance = function(x) {
    if (!arguments.length) return linkDistance;
    linkDistance = d3.functor(x);
    return force;
  };

  // For backwards-compatibility.
  force.distance = force.linkDistance;

  force.linkStrength = function(x) {
    if (!arguments.length) return linkStrength;
    linkStrength = d3.functor(x);
    return force;
  };

  force.friction = function(x) {
    if (!arguments.length) return friction;
    friction = x;
    return force;
  };

  force.charge = function(x) {
    if (!arguments.length) return charge;
    charge = typeof x === "function" ? x : +x;
    return force;
  };

  force.gravity = function(x) {
    if (!arguments.length) return gravity;
    gravity = x;
    return force;
  };

  force.theta = function(x) {
    if (!arguments.length) return theta;
    theta = x;
    return force;
  };

  force.start = function() {
    var i,
        j,
        n = nodes.length,
        m = links.length,
        w = size[0],
        h = size[1],
        neighbors,
        o;

    for (i = 0; i < n; ++i) {
      (o = nodes[i]).index = i;
      o.weight = 0;
    }

    distances = [];
    strengths = [];
    for (i = 0; i < m; ++i) {
      o = links[i];
      if (typeof o.source == "number") o.source = nodes[o.source];
      if (typeof o.target == "number") o.target = nodes[o.target];
      distances[i] = linkDistance.call(this, o, i);
      strengths[i] = linkStrength.call(this, o, i);
      ++o.source.weight;
      ++o.target.weight;
    }

    for (i = 0; i < n; ++i) {
      o = nodes[i];
      if (isNaN(o.x)) o.x = position("x", w);
      if (isNaN(o.y)) o.y = position("y", h);
      if (isNaN(o.px)) o.px = o.x;
      if (isNaN(o.py)) o.py = o.y;
    }

    charges = [];
    if (typeof charge === "function") {
      for (i = 0; i < n; ++i) {
        charges[i] = +charge.call(this, nodes[i], i);
      }
    } else {
      for (i = 0; i < n; ++i) {
        charges[i] = charge;
      }
    }

    // initialize node position based on first neighbor
    function position(dimension, size) {
      var neighbors = neighbor(i),
          j = -1,
          m = neighbors.length,
          x;
      while (++j < m) if (!isNaN(x = neighbors[j][dimension])) return x;
      return Math.random() * size;
    }

    // initialize neighbors lazily
    function neighbor() {
      if (!neighbors) {
        neighbors = [];
        for (j = 0; j < n; ++j) {
          neighbors[j] = [];
        }
        for (j = 0; j < m; ++j) {
          var o = links[j];
          neighbors[o.source.index].push(o.target);
          neighbors[o.target.index].push(o.source);
        }
      }
      return neighbors[i];
    }

    return force.resume();
  };

  force.resume = function() {
    alpha = .1;
    d3.timer(tick);
    return force;
  };

  force.stop = function() {
    alpha = 0;
    return force;
  };

  // use `node.call(force.drag)` to make nodes draggable
  force.drag = function() {
    if (!drag) drag = d3.behavior.drag()
        .origin(Object)
        .on("dragstart", dragstart)
        .on("drag", d3_layout_forceDrag)
        .on("dragend", d3_layout_forceDragEnd);

    this.on("mouseover.force", d3_layout_forceDragOver)
        .on("mouseout.force", d3_layout_forceDragOut)
        .call(drag);
  };

  function dragstart(d) {
    d3_layout_forceDragOver(d3_layout_forceDragNode = d);
    d3_layout_forceDragForce = force;
  }

  return d3.rebind(force, event, "on");
};

var d3_layout_forceDragForce,
    d3_layout_forceDragNode;

function d3_layout_forceDragOver(d) {
  d.fixed |= 2;
}

function d3_layout_forceDragOut(d) {
  if (d !== d3_layout_forceDragNode) d.fixed &= 1;
}

function d3_layout_forceDragEnd() {
  d3_layout_forceDrag();
  d3_layout_forceDragNode.fixed &= 1;
  d3_layout_forceDragForce = d3_layout_forceDragNode = null;
}

function d3_layout_forceDrag() {
  d3_layout_forceDragNode.px = d3.event.x;
  d3_layout_forceDragNode.py = d3.event.y;
  d3_layout_forceDragForce.resume(); // restart annealing
}

function d3_layout_forceAccumulate(quad, alpha, charges) {
  var cx = 0,
      cy = 0;
  quad.charge = 0;
  if (!quad.leaf) {
    var nodes = quad.nodes,
        n = nodes.length,
        i = -1,
        c;
    while (++i < n) {
      c = nodes[i];
      if (c == null) continue;
      d3_layout_forceAccumulate(c, alpha, charges);
      quad.charge += c.charge;
      cx += c.charge * c.cx;
      cy += c.charge * c.cy;
    }
  }
  if (quad.point) {
    // jitter internal nodes that are coincident
    if (!quad.leaf) {
      quad.point.x += Math.random() - .5;
      quad.point.y += Math.random() - .5;
    }
    var k = alpha * charges[quad.point.index];
    quad.charge += quad.pointCharge = k;
    cx += k * quad.point.x;
    cy += k * quad.point.y;
  }
  quad.cx = cx / quad.charge;
  quad.cy = cy / quad.charge;
}

function d3_layout_forceLinkDistance(link) {
  return 20;
}

function d3_layout_forceLinkStrength(link) {
  return 1;
}
d3.layout.partition = function() {
  var hierarchy = d3.layout.hierarchy(),
      size = [1, 1]; // width, height

  function position(node, x, dx, dy) {
    var children = node.children;
    node.x = x;
    node.y = node.depth * dy;
    node.dx = dx;
    node.dy = dy;
    if (children && (n = children.length)) {
      var i = -1,
          n,
          c,
          d;
      dx = node.value ? dx / node.value : 0;
      while (++i < n) {
        position(c = children[i], x, d = c.value * dx, dy);
        x += d;
      }
    }
  }

  function depth(node) {
    var children = node.children,
        d = 0;
    if (children && (n = children.length)) {
      var i = -1,
          n;
      while (++i < n) d = Math.max(d, depth(children[i]));
    }
    return 1 + d;
  }

  function partition(d, i) {
    var nodes = hierarchy.call(this, d, i);
    position(nodes[0], 0, size[0], size[1] / depth(nodes[0]));
    return nodes;
  }

  partition.size = function(x) {
    if (!arguments.length) return size;
    size = x;
    return partition;
  };

  return d3_layout_hierarchyRebind(partition, hierarchy);
};
d3.layout.pie = function() {
  var value = Number,
      sort = d3_layout_pieSortByValue,
      startAngle = 0,
      endAngle = 2 * Math.PI;

  function pie(data, i) {

    // Compute the numeric values for each data element.
    var values = data.map(function(d, i) { return +value.call(pie, d, i); });

    // Compute the start angle.
    var a = +(typeof startAngle === "function"
        ? startAngle.apply(this, arguments)
        : startAngle);

    // Compute the angular scale factor: from value to radians.
    var k = ((typeof endAngle === "function"
        ? endAngle.apply(this, arguments)
        : endAngle) - startAngle)
        / d3.sum(values);

    // Optionally sort the data.
    var index = d3.range(data.length);
    if (sort != null) index.sort(sort === d3_layout_pieSortByValue
        ? function(i, j) { return values[j] - values[i]; }
        : function(i, j) { return sort(data[i], data[j]); });

    // Compute the arcs!
    var arcs = index.map(function(i) {
      return {
        data: data[i],
        value: d = values[i],
        startAngle: a,
        endAngle: a += d * k
      };
    });

    // Return the arcs in the original data's order.
    return data.map(function(d, i) {
      return arcs[index[i]];
    });
  }

  /**
   * Specifies the value function *x*, which returns a nonnegative numeric value
   * for each datum. The default value function is `Number`. The value function
   * is passed two arguments: the current datum and the current index.
   */
  pie.value = function(x) {
    if (!arguments.length) return value;
    value = x;
    return pie;
  };

  /**
   * Specifies a sort comparison operator *x*. The comparator is passed two data
   * elements from the data array, a and b; it returns a negative value if a is
   * less than b, a positive value if a is greater than b, and zero if a equals
   * b.
   */
  pie.sort = function(x) {
    if (!arguments.length) return sort;
    sort = x;
    return pie;
  };

  /**
   * Specifies the overall start angle of the pie chart. Defaults to 0. The
   * start angle can be specified either as a constant or as a function; in the
   * case of a function, it is evaluated once per array (as opposed to per
   * element).
   */
  pie.startAngle = function(x) {
    if (!arguments.length) return startAngle;
    startAngle = x;
    return pie;
  };

  /**
   * Specifies the overall end angle of the pie chart. Defaults to 2π. The
   * end angle can be specified either as a constant or as a function; in the
   * case of a function, it is evaluated once per array (as opposed to per
   * element).
   */
  pie.endAngle = function(x) {
    if (!arguments.length) return endAngle;
    endAngle = x;
    return pie;
  };

  return pie;
};

var d3_layout_pieSortByValue = {};
// data is two-dimensional array of x,y; we populate y0
d3.layout.stack = function() {
  var values = Object,
      order = d3_layout_stackOrders["default"],
      offset = d3_layout_stackOffsets["zero"],
      out = d3_layout_stackOut,
      x = d3_layout_stackX,
      y = d3_layout_stackY;

  function stack(data, index) {

    // Convert series to canonical two-dimensional representation.
    var series = data.map(function(d, i) {
      return values.call(stack, d, i);
    });

    // Convert each series to canonical [[x,y]] representation.
    var points = series.map(function(d, i) {
      return d.map(function(v, i) {
        return [x.call(stack, v, i), y.call(stack, v, i)];
      });
    });

    // Compute the order of series, and permute them.
    var orders = order.call(stack, points, index);
    series = d3.permute(series, orders);
    points = d3.permute(points, orders);

    // Compute the baseline…
    var offsets = offset.call(stack, points, index);

    // And propagate it to other series.
    var n = series.length,
        m = series[0].length,
        i,
        j,
        o;
    for (j = 0; j < m; ++j) {
      out.call(stack, series[0][j], o = offsets[j], points[0][j][1]);
      for (i = 1; i < n; ++i) {
        out.call(stack, series[i][j], o += points[i - 1][j][1], points[i][j][1]);
      }
    }

    return data;
  }

  stack.values = function(x) {
    if (!arguments.length) return values;
    values = x;
    return stack;
  };

  stack.order = function(x) {
    if (!arguments.length) return order;
    order = typeof x === "function" ? x : d3_layout_stackOrders[x];
    return stack;
  };

  stack.offset = function(x) {
    if (!arguments.length) return offset;
    offset = typeof x === "function" ? x : d3_layout_stackOffsets[x];
    return stack;
  };

  stack.x = function(z) {
    if (!arguments.length) return x;
    x = z;
    return stack;
  };

  stack.y = function(z) {
    if (!arguments.length) return y;
    y = z;
    return stack;
  };

  stack.out = function(z) {
    if (!arguments.length) return out;
    out = z;
    return stack;
  };

  return stack;
}

function d3_layout_stackX(d) {
  return d.x;
}

function d3_layout_stackY(d) {
  return d.y;
}

function d3_layout_stackOut(d, y0, y) {
  d.y0 = y0;
  d.y = y;
}

var d3_layout_stackOrders = {

  "inside-out": function(data) {
    var n = data.length,
        i,
        j,
        max = data.map(d3_layout_stackMaxIndex),
        sums = data.map(d3_layout_stackReduceSum),
        index = d3.range(n).sort(function(a, b) { return max[a] - max[b]; }),
        top = 0,
        bottom = 0,
        tops = [],
        bottoms = [];
    for (i = 0; i < n; ++i) {
      j = index[i];
      if (top < bottom) {
        top += sums[j];
        tops.push(j);
      } else {
        bottom += sums[j];
        bottoms.push(j);
      }
    }
    return bottoms.reverse().concat(tops);
  },

  "reverse": function(data) {
    return d3.range(data.length).reverse();
  },

  "default": function(data) {
    return d3.range(data.length);
  }

};

var d3_layout_stackOffsets = {

  "silhouette": function(data) {
    var n = data.length,
        m = data[0].length,
        sums = [],
        max = 0,
        i,
        j,
        o,
        y0 = [];
    for (j = 0; j < m; ++j) {
      for (i = 0, o = 0; i < n; i++) o += data[i][j][1];
      if (o > max) max = o;
      sums.push(o);
    }
    for (j = 0; j < m; ++j) {
      y0[j] = (max - sums[j]) / 2;
    }
    return y0;
  },

  "wiggle": function(data) {
    var n = data.length,
        x = data[0],
        m = x.length,
        max = 0,
        i,
        j,
        k,
        s1,
        s2,
        s3,
        dx,
        o,
        o0,
        y0 = [];
    y0[0] = o = o0 = 0;
    for (j = 1; j < m; ++j) {
      for (i = 0, s1 = 0; i < n; ++i) s1 += data[i][j][1];
      for (i = 0, s2 = 0, dx = x[j][0] - x[j - 1][0]; i < n; ++i) {
        for (k = 0, s3 = (data[i][j][1] - data[i][j - 1][1]) / (2 * dx); k < i; ++k) {
          s3 += (data[k][j][1] - data[k][j - 1][1]) / dx;
        }
        s2 += s3 * data[i][j][1];
      }
      y0[j] = o -= s1 ? s2 / s1 * dx : 0;
      if (o < o0) o0 = o;
    }
    for (j = 0; j < m; ++j) y0[j] -= o0;
    return y0;
  },

  "expand": function(data) {
    var n = data.length,
        m = data[0].length,
        k = 1 / n,
        i,
        j,
        o,
        y0 = [];
    for (j = 0; j < m; ++j) {
      for (i = 0, o = 0; i < n; i++) o += data[i][j][1];
      if (o) for (i = 0; i < n; i++) data[i][j][1] /= o;
      else for (i = 0; i < n; i++) data[i][j][1] = k;
    }
    for (j = 0; j < m; ++j) y0[j] = 0;
    return y0;
  },

  "zero": function(data) {
    var j = -1,
        m = data[0].length,
        y0 = [];
    while (++j < m) y0[j] = 0;
    return y0;
  }

};

function d3_layout_stackMaxIndex(array) {
  var i = 1,
      j = 0,
      v = array[0][1],
      k,
      n = array.length;
  for (; i < n; ++i) {
    if ((k = array[i][1]) > v) {
      j = i;
      v = k;
    }
  }
  return j;
}

function d3_layout_stackReduceSum(d) {
  return d.reduce(d3_layout_stackSum, 0);
}

function d3_layout_stackSum(p, d) {
  return p + d[1];
}
d3.layout.histogram = function() {
  var frequency = true,
      valuer = Number,
      ranger = d3_layout_histogramRange,
      binner = d3_layout_histogramBinSturges;

  function histogram(data, i) {
    var bins = [],
        values = data.map(valuer, this),
        range = ranger.call(this, values, i),
        thresholds = binner.call(this, range, values, i),
        bin,
        i = -1,
        n = values.length,
        m = thresholds.length - 1,
        k = frequency ? 1 : 1 / n,
        x;

    // Initialize the bins.
    while (++i < m) {
      bin = bins[i] = [];
      bin.dx = thresholds[i + 1] - (bin.x = thresholds[i]);
      bin.y = 0;
    }

    // Fill the bins, ignoring values outside the range.
    i = -1; while(++i < n) {
      x = values[i];
      if ((x >= range[0]) && (x <= range[1])) {
        bin = bins[d3.bisect(thresholds, x, 1, m) - 1];
        bin.y += k;
        bin.push(data[i]);
      }
    }

    return bins;
  }

  // Specifies how to extract a value from the associated data. The default
  // value function is `Number`, which is equivalent to the identity function.
  histogram.value = function(x) {
    if (!arguments.length) return valuer;
    valuer = x;
    return histogram;
  };

  // Specifies the range of the histogram. Values outside the specified range
  // will be ignored. The argument `x` may be specified either as a two-element
  // array representing the minimum and maximum value of the range, or as a
  // function that returns the range given the array of values and the current
  // index `i`. The default range is the extent (minimum and maximum) of the
  // values.
  histogram.range = function(x) {
    if (!arguments.length) return ranger;
    ranger = d3.functor(x);
    return histogram;
  };

  // Specifies how to bin values in the histogram. The argument `x` may be
  // specified as a number, in which case the range of values will be split
  // uniformly into the given number of bins. Or, `x` may be an array of
  // threshold values, defining the bins; the specified array must contain the
  // rightmost (upper) value, thus specifying n + 1 values for n bins. Or, `x`
  // may be a function which is evaluated, being passed the range, the array of
  // values, and the current index `i`, returning an array of thresholds. The
  // default bin function will divide the values into uniform bins using
  // Sturges' formula.
  histogram.bins = function(x) {
    if (!arguments.length) return binner;
    binner = typeof x === "number"
        ? function(range) { return d3_layout_histogramBinFixed(range, x); }
        : d3.functor(x);
    return histogram;
  };

  // Specifies whether the histogram's `y` value is a count (frequency) or a
  // probability (density). The default value is true.
  histogram.frequency = function(x) {
    if (!arguments.length) return frequency;
    frequency = !!x;
    return histogram;
  };

  return histogram;
};

function d3_layout_histogramBinSturges(range, values) {
  return d3_layout_histogramBinFixed(range, Math.ceil(Math.log(values.length) / Math.LN2 + 1));
}

function d3_layout_histogramBinFixed(range, n) {
  var x = -1,
      b = +range[0],
      m = (range[1] - b) / n,
      f = [];
  while (++x <= n) f[x] = m * x + b;
  return f;
}

function d3_layout_histogramRange(values) {
  return [d3.min(values), d3.max(values)];
}
d3.layout.hierarchy = function() {
  var sort = d3_layout_hierarchySort,
      children = d3_layout_hierarchyChildren,
      value = d3_layout_hierarchyValue;

  // Recursively compute the node depth and value.
  // Also converts the data representation into a standard hierarchy structure.
  function recurse(data, depth, nodes) {
    var childs = children.call(hierarchy, data, depth),
        node = d3_layout_hierarchyInline ? data : {data: data};
    node.depth = depth;
    nodes.push(node);
    if (childs && (n = childs.length)) {
      var i = -1,
          n,
          c = node.children = [],
          v = 0,
          j = depth + 1;
      while (++i < n) {
        d = recurse(childs[i], j, nodes);
        d.parent = node;
        c.push(d);
        v += d.value;
      }
      if (sort) c.sort(sort);
      if (value) node.value = v;
    } else if (value) {
      node.value = +value.call(hierarchy, data, depth) || 0;
    }
    return node;
  }

  // Recursively re-evaluates the node value.
  function revalue(node, depth) {
    var children = node.children,
        v = 0;
    if (children && (n = children.length)) {
      var i = -1,
          n,
          j = depth + 1;
      while (++i < n) v += revalue(children[i], j);
    } else if (value) {
      v = +value.call(hierarchy, d3_layout_hierarchyInline ? node : node.data, depth) || 0;
    }
    if (value) node.value = v;
    return v;
  }

  function hierarchy(d) {
    var nodes = [];
    recurse(d, 0, nodes);
    return nodes;
  }

  hierarchy.sort = function(x) {
    if (!arguments.length) return sort;
    sort = x;
    return hierarchy;
  };

  hierarchy.children = function(x) {
    if (!arguments.length) return children;
    children = x;
    return hierarchy;
  };

  hierarchy.value = function(x) {
    if (!arguments.length) return value;
    value = x;
    return hierarchy;
  };

  // Re-evaluates the `value` property for the specified hierarchy.
  hierarchy.revalue = function(root) {
    revalue(root, 0);
    return root;
  };

  return hierarchy;
};

// A method assignment helper for hierarchy subclasses.
function d3_layout_hierarchyRebind(object, hierarchy) {
  d3.rebind(object, hierarchy, "sort", "children", "value");

  // Add an alias for links, for convenience.
  object.links = d3_layout_hierarchyLinks;

  // If the new API is used, enabling inlining.
  object.nodes = function(d) {
    d3_layout_hierarchyInline = true;
    return (object.nodes = object)(d);
  };

  return object;
}

function d3_layout_hierarchyChildren(d) {
  return d.children;
}

function d3_layout_hierarchyValue(d) {
  return d.value;
}

function d3_layout_hierarchySort(a, b) {
  return b.value - a.value;
}

// Returns an array source+target objects for the specified nodes.
function d3_layout_hierarchyLinks(nodes) {
  return d3.merge(nodes.map(function(parent) {
    return (parent.children || []).map(function(child) {
      return {source: parent, target: child};
    });
  }));
}

// For backwards-compatibility, don't enable inlining by default.
var d3_layout_hierarchyInline = false;
d3.layout.pack = function() {
  var hierarchy = d3.layout.hierarchy().sort(d3_layout_packSort),
      size = [1, 1];

  function pack(d, i) {
    var nodes = hierarchy.call(this, d, i),
        root = nodes[0];

    // Recursively compute the layout.
    root.x = 0;
    root.y = 0;
    d3_layout_packTree(root);

    // Scale the layout to fit the requested size.
    var w = size[0],
        h = size[1],
        k = 1 / Math.max(2 * root.r / w, 2 * root.r / h);
    d3_layout_packTransform(root, w / 2, h / 2, k);

    return nodes;
  }

  pack.size = function(x) {
    if (!arguments.length) return size;
    size = x;
    return pack;
  };

  return d3_layout_hierarchyRebind(pack, hierarchy);
};

function d3_layout_packSort(a, b) {
  return a.value - b.value;
}

function d3_layout_packInsert(a, b) {
  var c = a._pack_next;
  a._pack_next = b;
  b._pack_prev = a;
  b._pack_next = c;
  c._pack_prev = b;
}

function d3_layout_packSplice(a, b) {
  a._pack_next = b;
  b._pack_prev = a;
}

function d3_layout_packIntersects(a, b) {
  var dx = b.x - a.x,
      dy = b.y - a.y,
      dr = a.r + b.r;
  return (dr * dr - dx * dx - dy * dy) > .001; // within epsilon
}

function d3_layout_packCircle(nodes) {
  var xMin = Infinity,
      xMax = -Infinity,
      yMin = Infinity,
      yMax = -Infinity,
      n = nodes.length,
      a, b, c, j, k;

  function bound(node) {
    xMin = Math.min(node.x - node.r, xMin);
    xMax = Math.max(node.x + node.r, xMax);
    yMin = Math.min(node.y - node.r, yMin);
    yMax = Math.max(node.y + node.r, yMax);
  }

  // Create node links.
  nodes.forEach(d3_layout_packLink);

  // Create first node.
  a = nodes[0];
  a.x = -a.r;
  a.y = 0;
  bound(a);

  // Create second node.
  if (n > 1) {
    b = nodes[1];
    b.x = b.r;
    b.y = 0;
    bound(b);

    // Create third node and build chain.
    if (n > 2) {
      c = nodes[2];
      d3_layout_packPlace(a, b, c);
      bound(c);
      d3_layout_packInsert(a, c);
      a._pack_prev = c;
      d3_layout_packInsert(c, b);
      b = a._pack_next;

      // Now iterate through the rest.
      for (var i = 3; i < n; i++) {
        d3_layout_packPlace(a, b, c = nodes[i]);

        // Search for the closest intersection.
        var isect = 0, s1 = 1, s2 = 1;
        for (j = b._pack_next; j !== b; j = j._pack_next, s1++) {
          if (d3_layout_packIntersects(j, c)) {
            isect = 1;
            break;
          }
        }
        if (isect == 1) {
          for (k = a._pack_prev; k !== j._pack_prev; k = k._pack_prev, s2++) {
            if (d3_layout_packIntersects(k, c)) {
              if (s2 < s1) {
                isect = -1;
                j = k;
              }
              break;
            }
          }
        }

        // Update node chain.
        if (isect == 0) {
          d3_layout_packInsert(a, c);
          b = c;
          bound(c);
        } else if (isect > 0) {
          d3_layout_packSplice(a, j);
          b = j;
          i--;
        } else { // isect < 0
          d3_layout_packSplice(j, b);
          a = j;
          i--;
        }
      }
    }
  }

  // Re-center the circles and return the encompassing radius.
  var cx = (xMin + xMax) / 2,
      cy = (yMin + yMax) / 2,
      cr = 0;
  for (var i = 0; i < n; i++) {
    var node = nodes[i];
    node.x -= cx;
    node.y -= cy;
    cr = Math.max(cr, node.r + Math.sqrt(node.x * node.x + node.y * node.y));
  }

  // Remove node links.
  nodes.forEach(d3_layout_packUnlink);

  return cr;
}

function d3_layout_packLink(node) {
  node._pack_next = node._pack_prev = node;
}

function d3_layout_packUnlink(node) {
  delete node._pack_next;
  delete node._pack_prev;
}

function d3_layout_packTree(node) {
  var children = node.children;
  if (children && children.length) {
    children.forEach(d3_layout_packTree);
    node.r = d3_layout_packCircle(children);
  } else {
    node.r = Math.sqrt(node.value);
  }
}

function d3_layout_packTransform(node, x, y, k) {
  var children = node.children;
  node.x = (x += k * node.x);
  node.y = (y += k * node.y);
  node.r *= k;
  if (children) {
    var i = -1, n = children.length;
    while (++i < n) d3_layout_packTransform(children[i], x, y, k);
  }
}

function d3_layout_packPlace(a, b, c) {
  var db = a.r + c.r,
      dx = b.x - a.x,
      dy = b.y - a.y;
  if (db && (dx || dy)) {
    var da = b.r + c.r,
        dc = Math.sqrt(dx * dx + dy * dy),
        cos = Math.max(-1, Math.min(1, (db * db + dc * dc - da * da) / (2 * db * dc))),
        theta = Math.acos(cos),
        x = cos * (db /= dc),
        y = Math.sin(theta) * db;
    c.x = a.x + x * dx + y * dy;
    c.y = a.y + x * dy - y * dx;
  } else {
    c.x = a.x + db;
    c.y = a.y;
  }
}
// Implements a hierarchical layout using the cluster (or dendogram) algorithm.
d3.layout.cluster = function() {
  var hierarchy = d3.layout.hierarchy().sort(null).value(null),
      separation = d3_layout_treeSeparation,
      size = [1, 1]; // width, height

  function cluster(d, i) {
    var nodes = hierarchy.call(this, d, i),
        root = nodes[0],
        previousNode,
        x = 0,
        kx,
        ky;

    // First walk, computing the initial x & y values.
    d3_layout_treeVisitAfter(root, function(node) {
      var children = node.children;
      if (children && children.length) {
        node.x = d3_layout_clusterX(children);
        node.y = d3_layout_clusterY(children);
      } else {
        node.x = previousNode ? x += separation(node, previousNode) : 0;
        node.y = 0;
        previousNode = node;
      }
    });

    // Compute the left-most, right-most, and depth-most nodes for extents.
    var left = d3_layout_clusterLeft(root),
        right = d3_layout_clusterRight(root),
        x0 = left.x - separation(left, right) / 2,
        x1 = right.x + separation(right, left) / 2;

    // Second walk, normalizing x & y to the desired size.
    d3_layout_treeVisitAfter(root, function(node) {
      node.x = (node.x - x0) / (x1 - x0) * size[0];
      node.y = (1 - node.y / root.y) * size[1];
    });

    return nodes;
  }

  cluster.separation = function(x) {
    if (!arguments.length) return separation;
    separation = x;
    return cluster;
  };

  cluster.size = function(x) {
    if (!arguments.length) return size;
    size = x;
    return cluster;
  };

  return d3_layout_hierarchyRebind(cluster, hierarchy);
};

function d3_layout_clusterY(children) {
  return 1 + d3.max(children, function(child) {
    return child.y;
  });
}

function d3_layout_clusterX(children) {
  return children.reduce(function(x, child) {
    return x + child.x;
  }, 0) / children.length;
}

function d3_layout_clusterLeft(node) {
  var children = node.children;
  return children && children.length ? d3_layout_clusterLeft(children[0]) : node;
}

function d3_layout_clusterRight(node) {
  var children = node.children, n;
  return children && (n = children.length) ? d3_layout_clusterRight(children[n - 1]) : node;
}
// Node-link tree diagram using the Reingold-Tilford "tidy" algorithm
d3.layout.tree = function() {
  var hierarchy = d3.layout.hierarchy().sort(null).value(null),
      separation = d3_layout_treeSeparation,
      size = [1, 1]; // width, height

  function tree(d, i) {
    var nodes = hierarchy.call(this, d, i),
        root = nodes[0];

    function firstWalk(node, previousSibling) {
      var children = node.children,
          layout = node._tree;
      if (children && (n = children.length)) {
        var n,
            firstChild = children[0],
            previousChild,
            ancestor = firstChild,
            child,
            i = -1;
        while (++i < n) {
          child = children[i];
          firstWalk(child, previousChild);
          ancestor = apportion(child, previousChild, ancestor);
          previousChild = child;
        }
        d3_layout_treeShift(node);
        var midpoint = .5 * (firstChild._tree.prelim + child._tree.prelim);
        if (previousSibling) {
          layout.prelim = previousSibling._tree.prelim + separation(node, previousSibling);
          layout.mod = layout.prelim - midpoint;
        } else {
          layout.prelim = midpoint;
        }
      } else {
        if (previousSibling) {
          layout.prelim = previousSibling._tree.prelim + separation(node, previousSibling);
        }
      }
    }

    function secondWalk(node, x) {
      node.x = node._tree.prelim + x;
      var children = node.children;
      if (children && (n = children.length)) {
        var i = -1,
            n;
        x += node._tree.mod;
        while (++i < n) {
          secondWalk(children[i], x);
        }
      }
    }

    function apportion(node, previousSibling, ancestor) {
      if (previousSibling) {
        var vip = node,
            vop = node,
            vim = previousSibling,
            vom = node.parent.children[0],
            sip = vip._tree.mod,
            sop = vop._tree.mod,
            sim = vim._tree.mod,
            som = vom._tree.mod,
            shift;
        while (vim = d3_layout_treeRight(vim), vip = d3_layout_treeLeft(vip), vim && vip) {
          vom = d3_layout_treeLeft(vom);
          vop = d3_layout_treeRight(vop);
          vop._tree.ancestor = node;
          shift = vim._tree.prelim + sim - vip._tree.prelim - sip + separation(vim, vip);
          if (shift > 0) {
            d3_layout_treeMove(d3_layout_treeAncestor(vim, node, ancestor), node, shift);
            sip += shift;
            sop += shift;
          }
          sim += vim._tree.mod;
          sip += vip._tree.mod;
          som += vom._tree.mod;
          sop += vop._tree.mod;
        }
        if (vim && !d3_layout_treeRight(vop)) {
          vop._tree.thread = vim;
          vop._tree.mod += sim - sop;
        }
        if (vip && !d3_layout_treeLeft(vom)) {
          vom._tree.thread = vip;
          vom._tree.mod += sip - som;
          ancestor = node;
        }
      }
      return ancestor;
    }

    // Initialize temporary layout variables.
    d3_layout_treeVisitAfter(root, function(node, previousSibling) {
      node._tree = {
        ancestor: node,
        prelim: 0,
        mod: 0,
        change: 0,
        shift: 0,
        number: previousSibling ? previousSibling._tree.number + 1 : 0
      };
    });

    // Compute the layout using Buchheim et al.'s algorithm.
    firstWalk(root);
    secondWalk(root, -root._tree.prelim);

    // Compute the left-most, right-most, and depth-most nodes for extents.
    var left = d3_layout_treeSearch(root, d3_layout_treeLeftmost),
        right = d3_layout_treeSearch(root, d3_layout_treeRightmost),
        deep = d3_layout_treeSearch(root, d3_layout_treeDeepest),
        x0 = left.x - separation(left, right) / 2,
        x1 = right.x + separation(right, left) / 2,
        y1 = deep.depth || 1;

    // Clear temporary layout variables; transform x and y.
    d3_layout_treeVisitAfter(root, function(node) {
      node.x = (node.x - x0) / (x1 - x0) * size[0];
      node.y = node.depth / y1 * size[1];
      delete node._tree;
    });

    return nodes;
  }

  tree.separation = function(x) {
    if (!arguments.length) return separation;
    separation = x;
    return tree;
  };

  tree.size = function(x) {
    if (!arguments.length) return size;
    size = x;
    return tree;
  };

  return d3_layout_hierarchyRebind(tree, hierarchy);
};

function d3_layout_treeSeparation(a, b) {
  return a.parent == b.parent ? 1 : 2;
}

// function d3_layout_treeSeparationRadial(a, b) {
//   return (a.parent == b.parent ? 1 : 2) / a.depth;
// }

function d3_layout_treeLeft(node) {
  var children = node.children;
  return children && children.length ? children[0] : node._tree.thread;
}

function d3_layout_treeRight(node) {
  var children = node.children,
      n;
  return children && (n = children.length) ? children[n - 1] : node._tree.thread;
}

function d3_layout_treeSearch(node, compare) {
  var children = node.children;
  if (children && (n = children.length)) {
    var child,
        n,
        i = -1;
    while (++i < n) {
      if (compare(child = d3_layout_treeSearch(children[i], compare), node) > 0) {
        node = child;
      }
    }
  }
  return node;
}

function d3_layout_treeRightmost(a, b) {
  return a.x - b.x;
}

function d3_layout_treeLeftmost(a, b) {
  return b.x - a.x;
}

function d3_layout_treeDeepest(a, b) {
  return a.depth - b.depth;
}

function d3_layout_treeVisitAfter(node, callback) {
  function visit(node, previousSibling) {
    var children = node.children;
    if (children && (n = children.length)) {
      var child,
          previousChild = null,
          i = -1,
          n;
      while (++i < n) {
        child = children[i];
        visit(child, previousChild);
        previousChild = child;
      }
    }
    callback(node, previousSibling);
  }
  visit(node, null);
}

function d3_layout_treeShift(node) {
  var shift = 0,
      change = 0,
      children = node.children,
      i = children.length,
      child;
  while (--i >= 0) {
    child = children[i]._tree;
    child.prelim += shift;
    child.mod += shift;
    shift += child.shift + (change += child.change);
  }
}

function d3_layout_treeMove(ancestor, node, shift) {
  ancestor = ancestor._tree;
  node = node._tree;
  var change = shift / (node.number - ancestor.number);
  ancestor.change += change;
  node.change -= change;
  node.shift += shift;
  node.prelim += shift;
  node.mod += shift;
}

function d3_layout_treeAncestor(vim, node, ancestor) {
  return vim._tree.ancestor.parent == node.parent
      ? vim._tree.ancestor
      : ancestor;
}
// Squarified Treemaps by Mark Bruls, Kees Huizing, and Jarke J. van Wijk
// Modified to support a target aspect ratio by Jeff Heer
d3.layout.treemap = function() {
  var hierarchy = d3.layout.hierarchy(),
      round = Math.round,
      size = [1, 1], // width, height
      padding = null,
      pad = d3_layout_treemapPadNull,
      sticky = false,
      stickies,
      ratio = 0.5 * (1 + Math.sqrt(5)); // golden ratio

  // Compute the area for each child based on value & scale.
  function scale(children, k) {
    var i = -1,
        n = children.length,
        child,
        area;
    while (++i < n) {
      area = (child = children[i]).value * (k < 0 ? 0 : k);
      child.area = isNaN(area) || area <= 0 ? 0 : area;
    }
  }

  // Recursively arranges the specified node's children into squarified rows.
  function squarify(node) {
    var children = node.children;
    if (children && children.length) {
      var rect = pad(node),
          row = [],
          remaining = children.slice(), // copy-on-write
          child,
          best = Infinity, // the best row score so far
          score, // the current row score
          u = Math.min(rect.dx, rect.dy), // initial orientation
          n;
      scale(remaining, rect.dx * rect.dy / node.value);
      row.area = 0;
      while ((n = remaining.length) > 0) {
        row.push(child = remaining[n - 1]);
        row.area += child.area;
        if ((score = worst(row, u)) <= best) { // continue with this orientation
          remaining.pop();
          best = score;
        } else { // abort, and try a different orientation
          row.area -= row.pop().area;
          position(row, u, rect, false);
          u = Math.min(rect.dx, rect.dy);
          row.length = row.area = 0;
          best = Infinity;
        }
      }
      if (row.length) {
        position(row, u, rect, true);
        row.length = row.area = 0;
      }
      children.forEach(squarify);
    }
  }

  // Recursively resizes the specified node's children into existing rows.
  // Preserves the existing layout!
  function stickify(node) {
    var children = node.children;
    if (children && children.length) {
      var rect = pad(node),
          remaining = children.slice(), // copy-on-write
          child,
          row = [];
      scale(remaining, rect.dx * rect.dy / node.value);
      row.area = 0;
      while (child = remaining.pop()) {
        row.push(child);
        row.area += child.area;
        if (child.z != null) {
          position(row, child.z ? rect.dx : rect.dy, rect, !remaining.length);
          row.length = row.area = 0;
        }
      }
      children.forEach(stickify);
    }
  }

  // Computes the score for the specified row, as the worst aspect ratio.
  function worst(row, u) {
    var s = row.area,
        r,
        rmax = 0,
        rmin = Infinity,
        i = -1,
        n = row.length;
    while (++i < n) {
      if (!(r = row[i].area)) continue;
      if (r < rmin) rmin = r;
      if (r > rmax) rmax = r;
    }
    s *= s;
    u *= u;
    return s
        ? Math.max((u * rmax * ratio) / s, s / (u * rmin * ratio))
        : Infinity;
  }

  // Positions the specified row of nodes. Modifies `rect`.
  function position(row, u, rect, flush) {
    var i = -1,
        n = row.length,
        x = rect.x,
        y = rect.y,
        v = u ? round(row.area / u) : 0,
        o;
    if (u == rect.dx) { // horizontal subdivision
      if (flush || v > rect.dy) v = v ? rect.dy : 0; // over+underflow
      while (++i < n) {
        o = row[i];
        o.x = x;
        o.y = y;
        o.dy = v;
        x += o.dx = v ? round(o.area / v) : 0;
      }
      o.z = true;
      o.dx += rect.x + rect.dx - x; // rounding error
      rect.y += v;
      rect.dy -= v;
    } else { // vertical subdivision
      if (flush || v > rect.dx) v = v ? rect.dx : 0; // over+underflow
      while (++i < n) {
        o = row[i];
        o.x = x;
        o.y = y;
        o.dx = v;
        y += o.dy = v ? round(o.area / v) : 0;
      }
      o.z = false;
      o.dy += rect.y + rect.dy - y; // rounding error
      rect.x += v;
      rect.dx -= v;
    }
  }

  function treemap(d) {
    var nodes = stickies || hierarchy(d),
        root = nodes[0];
    root.x = 0;
    root.y = 0;
    root.dx = size[0];
    root.dy = size[1];
    if (stickies) hierarchy.revalue(root);
    scale([root], root.dx * root.dy / root.value);
    (stickies ? stickify : squarify)(root);
    if (sticky) stickies = nodes;
    return nodes;
  }

  treemap.size = function(x) {
    if (!arguments.length) return size;
    size = x;
    return treemap;
  };

  treemap.padding = function(x) {
    if (!arguments.length) return padding;

    function padFunction(node) {
      var p = x.call(treemap, node, node.depth);
      return p == null
          ? d3_layout_treemapPadNull(node)
          : d3_layout_treemapPad(node, typeof p === "number" ? [p, p, p, p] : p);
    }

    function padConstant(node) {
      return d3_layout_treemapPad(node, x);
    }

    var type;
    pad = (padding = x) == null ? d3_layout_treemapPadNull
        : (type = typeof x) === "function" ? padFunction
        : type === "number" ? (x = [x, x, x, x], padConstant)
        : padConstant;
    return treemap;
  };

  treemap.round = function(x) {
    if (!arguments.length) return round != Number;
    round = x ? Math.round : Number;
    return treemap;
  };

  treemap.sticky = function(x) {
    if (!arguments.length) return sticky;
    sticky = x;
    stickies = null;
    return treemap;
  };

  treemap.ratio = function(x) {
    if (!arguments.length) return ratio;
    ratio = x;
    return treemap;
  };

  return d3_layout_hierarchyRebind(treemap, hierarchy);
};

function d3_layout_treemapPadNull(node) {
  return {x: node.x, y: node.y, dx: node.dx, dy: node.dy};
}

function d3_layout_treemapPad(node, padding) {
  var x = node.x + padding[3],
      y = node.y + padding[0],
      dx = node.dx - padding[1] - padding[3],
      dy = node.dy - padding[0] - padding[2];
  if (dx < 0) { x += dx / 2; dx = 0; }
  if (dy < 0) { y += dy / 2; dy = 0; }
  return {x: x, y: y, dx: dx, dy: dy};
}
})();