science.v1.js

(function(exports){
(function(exports){
science = {version: "1.9.1"}; // semver
science.ascending = function(a, b) {
  return a - b;
};
// Euler's constant.
science.EULER = .5772156649015329;
// Compute exp(x) - 1 accurately for small x.
science.expm1 = function(x) {
  return (x < 1e-5 && x > -1e-5) ? x + .5 * x * x : Math.exp(x) - 1;
};
science.functor = function(v) {
  return typeof v === "function" ? v : function() { return v; };
};
// Based on:
// http://www.johndcook.com/blog/2010/06/02/whats-so-hard-about-finding-a-hypotenuse/
science.hypot = function(x, y) {
  x = Math.abs(x);
  y = Math.abs(y);
  var max,
      min;
  if (x > y) { max = x; min = y; }
  else       { max = y; min = x; }
  var r = min / max;
  return max * Math.sqrt(1 + r * r);
};
science.quadratic = function() {
  var complex = false;

  function quadratic(a, b, c) {
    var d = b * b - 4 * a * c;
    if (d > 0) {
      d = Math.sqrt(d) / (2 * a);
      return complex
        ? [{r: -b - d, i: 0}, {r: -b + d, i: 0}]
        : [-b - d, -b + d];
    } else if (d === 0) {
      d = -b / (2 * a);
      return complex ? [{r: d, i: 0}] : [d];
    } else {
      if (complex) {
        d = Math.sqrt(-d) / (2 * a);
        return [
          {r: -b, i: -d},
          {r: -b, i: d}
        ];
      }
      return [];
    }
  }

  quadratic.complex = function(x) {
    if (!arguments.length) return complex;
    complex = x;
    return quadratic;
  };

  return quadratic;
};
// Constructs a multi-dimensional array filled with zeroes.
science.zeroes = function(n) {
  var i = -1,
      a = [];
  if (arguments.length === 1)
    while (++i < n)
      a[i] = 0;
  else
    while (++i < n)
      a[i] = science.zeroes.apply(
        this, Array.prototype.slice.call(arguments, 1));
  return a;
};
})(this);
(function(exports){
science.lin = {};
science.lin.decompose = function() {

  function decompose(A) {
    var n = A.length, // column dimension
        V = [],
        d = [],
        e = [];

    for (var i = 0; i < n; i++) {
      V[i] = [];
      d[i] = [];
      e[i] = [];
    }

    var symmetric = true;
    for (var j = 0; j < n; j++) {
      for (var i = 0; i < n; i++) {
        if (A[i][j] !== A[j][i]) {
          symmetric = false;
          break;
        }
      }
    }

    if (symmetric) {
      for (var i = 0; i < n; i++) V[i] = A[i].slice();

      // Tridiagonalize.
      science_lin_decomposeTred2(d, e, V);

      // Diagonalize.
      science_lin_decomposeTql2(d, e, V);
    } else {
      var H = [];
      for (var i = 0; i < n; i++) H[i] = A[i].slice();

      // Reduce to Hessenberg form.
      science_lin_decomposeOrthes(H, V);

      // Reduce Hessenberg to real Schur form.
      science_lin_decomposeHqr2(d, e, H, V);
    }

    var D = [];
    for (var i = 0; i < n; i++) {
      var row = D[i] = [];
      for (var j = 0; j < n; j++) row[j] = i === j ? d[i] : 0;
      D[i][e[i] > 0 ? i + 1 : i - 1] = e[i];
    }
    return {D: D, V: V};
  }

  return decompose;
};

// Symmetric Householder reduction to tridiagonal form.
function science_lin_decomposeTred2(d, e, V) {
  // This is derived from the Algol procedures tred2 by
  // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
  // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
  // Fortran subroutine in EISPACK.

  var n = V.length;

  for (var j = 0; j < n; j++) d[j] = V[n - 1][j];

  // Householder reduction to tridiagonal form.
  for (var i = n - 1; i > 0; i--) {
    // Scale to avoid under/overflow.

    var scale = 0,
        h = 0;
    for (var k = 0; k < i; k++) scale += Math.abs(d[k]);
    if (scale === 0) {
      e[i] = d[i - 1];
      for (var j = 0; j < i; j++) {
        d[j] = V[i - 1][j];
        V[i][j] = 0;
        V[j][i] = 0;
      }
    } else {
      // Generate Householder vector.
      for (var k = 0; k < i; k++) {
        d[k] /= scale;
        h += d[k] * d[k];
      }
      var f = d[i - 1];
      var g = Math.sqrt(h);
      if (f > 0) g = -g;
      e[i] = scale * g;
      h = h - f * g;
      d[i - 1] = f - g;
      for (var j = 0; j < i; j++) e[j] = 0;

      // Apply similarity transformation to remaining columns.

      for (var j = 0; j < i; j++) {
        f = d[j];
        V[j][i] = f;
        g = e[j] + V[j][j] * f;
        for (var k = j+1; k <= i - 1; k++) {
          g += V[k][j] * d[k];
          e[k] += V[k][j] * f;
        }
        e[j] = g;
      }
      f = 0;
      for (var j = 0; j < i; j++) {
        e[j] /= h;
        f += e[j] * d[j];
      }
      var hh = f / (h + h);
      for (var j = 0; j < i; j++) e[j] -= hh * d[j];
      for (var j = 0; j < i; j++) {
        f = d[j];
        g = e[j];
        for (var k = j; k <= i - 1; k++) V[k][j] -= (f * e[k] + g * d[k]);
        d[j] = V[i - 1][j];
        V[i][j] = 0;
      }
    }
    d[i] = h;
  }

  // Accumulate transformations.
  for (var i = 0; i < n - 1; i++) {
    V[n - 1][i] = V[i][i];
    V[i][i] = 1.0;
    var h = d[i + 1];
    if (h != 0) {
      for (var k = 0; k <= i; k++) d[k] = V[k][i + 1] / h;
      for (var j = 0; j <= i; j++) {
        var g = 0;
        for (var k = 0; k <= i; k++) g += V[k][i + 1] * V[k][j];
        for (var k = 0; k <= i; k++) V[k][j] -= g * d[k];
      }
    }
    for (var k = 0; k <= i; k++) V[k][i + 1] = 0;
  }
  for (var j = 0; j < n; j++) {
    d[j] = V[n - 1][j];
    V[n - 1][j] = 0;
  }
  V[n - 1][n - 1] = 1;
  e[0] = 0;
}

// Symmetric tridiagonal QL algorithm.
function science_lin_decomposeTql2(d, e, V) {
  // This is derived from the Algol procedures tql2, by
  // Bowdler, Martin, Reinsch, and Wilkinson, Handbook for
  // Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
  // Fortran subroutine in EISPACK.

  var n = V.length;

  for (var i = 1; i < n; i++) e[i - 1] = e[i];
  e[n - 1] = 0;

  var f = 0;
  var tst1 = 0;
  var eps = 1e-12;
  for (var l = 0; l < n; l++) {
    // Find small subdiagonal element
    tst1 = Math.max(tst1, Math.abs(d[l]) + Math.abs(e[l]));
    var m = l;
    while (m < n) {
      if (Math.abs(e[m]) <= eps*tst1) { break; }
      m++;
    }

    // If m == l, d[l] is an eigenvalue,
    // otherwise, iterate.
    if (m > l) {
      var iter = 0;
      do {
        iter++;  // (Could check iteration count here.)

        // Compute implicit shift
        var g = d[l];
        var p = (d[l + 1] - g) / (2 * e[l]);
        var r = science.hypot(p, 1);
        if (p < 0) r = -r;
        d[l] = e[l] / (p + r);
        d[l + 1] = e[l] * (p + r);
        var dl1 = d[l + 1];
        var h = g - d[l];
        for (var i = l+2; i < n; i++) d[i] -= h;
        f += h;

        // Implicit QL transformation.
        p = d[m];
        var c = 1;
        var c2 = c;
        var c3 = c;
        var el1 = e[l + 1];
        var s = 0;
        var s2 = 0;
        for (var i = m - 1; i >= l; i--) {
          c3 = c2;
          c2 = c;
          s2 = s;
          g = c * e[i];
          h = c * p;
          r = science.hypot(p,e[i]);
          e[i + 1] = s * r;
          s = e[i] / r;
          c = p / r;
          p = c * d[i] - s * g;
          d[i + 1] = h + s * (c * g + s * d[i]);

          // Accumulate transformation.
          for (var k = 0; k < n; k++) {
            h = V[k][i + 1];
            V[k][i + 1] = s * V[k][i] + c * h;
            V[k][i] = c * V[k][i] - s * h;
          }
        }
        p = -s * s2 * c3 * el1 * e[l] / dl1;
        e[l] = s * p;
        d[l] = c * p;

        // Check for convergence.
      } while (Math.abs(e[l]) > eps*tst1);
    }
    d[l] = d[l] + f;
    e[l] = 0;
  }

  // Sort eigenvalues and corresponding vectors.
  for (var i = 0; i < n - 1; i++) {
    var k = i;
    var p = d[i];
    for (var j = i + 1; j < n; j++) {
      if (d[j] < p) {
        k = j;
        p = d[j];
      }
    }
    if (k != i) {
      d[k] = d[i];
      d[i] = p;
      for (var j = 0; j < n; j++) {
        p = V[j][i];
        V[j][i] = V[j][k];
        V[j][k] = p;
      }
    }
  }
}

// Nonsymmetric reduction to Hessenberg form.
function science_lin_decomposeOrthes(H, V) {
  // This is derived from the Algol procedures orthes and ortran,
  // by Martin and Wilkinson, Handbook for Auto. Comp.,
  // Vol.ii-Linear Algebra, and the corresponding
  // Fortran subroutines in EISPACK.

  var n = H.length;
  var ort = [];

  var low = 0;
  var high = n - 1;

  for (var m = low + 1; m < high; m++) {
    // Scale column.
    var scale = 0;
    for (var i = m; i <= high; i++) scale += Math.abs(H[i][m - 1]);

    if (scale !== 0) {
      // Compute Householder transformation.
      var h = 0;
      for (var i = high; i >= m; i--) {
        ort[i] = H[i][m - 1] / scale;
        h += ort[i] * ort[i];
      }
      var g = Math.sqrt(h);
      if (ort[m] > 0) g = -g;
      h = h - ort[m] * g;
      ort[m] = ort[m] - g;

      // Apply Householder similarity transformation
      // H = (I-u*u'/h)*H*(I-u*u')/h)
      for (var j = m; j < n; j++) {
        var f = 0;
        for (var i = high; i >= m; i--) f += ort[i] * H[i][j];
        f /= h;
        for (var i = m; i <= high; i++) H[i][j] -= f * ort[i];
      }

      for (var i = 0; i <= high; i++) {
        var f = 0;
        for (var j = high; j >= m; j--) f += ort[j] * H[i][j];
        f /= h;
        for (var j = m; j <= high; j++) H[i][j] -= f * ort[j];
      }
      ort[m] = scale * ort[m];
      H[m][m - 1] = scale * g;
    }
  }

  // Accumulate transformations (Algol's ortran).
  for (var i = 0; i < n; i++) {
    for (var j = 0; j < n; j++) V[i][j] = i === j ? 1 : 0;
  }

  for (var m = high-1; m >= low+1; m--) {
    if (H[m][m - 1] !== 0) {
      for (var i = m + 1; i <= high; i++) ort[i] = H[i][m - 1];
      for (var j = m; j <= high; j++) {
        var g = 0;
        for (var i = m; i <= high; i++) g += ort[i] * V[i][j];
        // Double division avoids possible underflow
        g = (g / ort[m]) / H[m][m - 1];
        for (var i = m; i <= high; i++) V[i][j] += g * ort[i];
      }
    }
  }
}

// Nonsymmetric reduction from Hessenberg to real Schur form.
function science_lin_decomposeHqr2(d, e, H, V) {
  // This is derived from the Algol procedure hqr2,
  // by Martin and Wilkinson, Handbook for Auto. Comp.,
  // Vol.ii-Linear Algebra, and the corresponding
  // Fortran subroutine in EISPACK.

  var nn = H.length,
      n = nn - 1,
      low = 0,
      high = nn - 1,
      eps = 1e-12,
      exshift = 0,
      p = 0,
      q = 0,
      r = 0,
      s = 0,
      z = 0,
      t,
      w,
      x,
      y;

  // Store roots isolated by balanc and compute matrix norm
  var norm = 0;
  for (var i = 0; i < nn; i++) {
    if (i < low || i > high) {
      d[i] = H[i][i];
      e[i] = 0;
    }
    for (var j = Math.max(i - 1, 0); j < nn; j++) norm += Math.abs(H[i][j]);
  }

  // Outer loop over eigenvalue index
  var iter = 0;
  while (n >= low) {
    // Look for single small sub-diagonal element
    var l = n;
    while (l > low) {
      s = Math.abs(H[l - 1][l - 1]) + Math.abs(H[l][l]);
      if (s === 0) s = norm;
      if (Math.abs(H[l][l - 1]) < eps * s) break;
      l--;
    }

    // Check for convergence
    // One root found
    if (l === n) {
      H[n][n] = H[n][n] + exshift;
      d[n] = H[n][n];
      e[n] = 0;
      n--;
      iter = 0;

    // Two roots found
    } else if (l === n - 1) {
      w = H[n][n - 1] * H[n - 1][n];
      p = (H[n - 1][n - 1] - H[n][n]) / 2;
      q = p * p + w;
      z = Math.sqrt(Math.abs(q));
      H[n][n] = H[n][n] + exshift;
      H[n - 1][n - 1] = H[n - 1][n - 1] + exshift;
      x = H[n][n];

      // Real pair
      if (q >= 0) {
        z = p + (p >= 0 ? z : -z);
        d[n - 1] = x + z;
        d[n] = d[n - 1];
        if (z !== 0) d[n] = x - w / z;
        e[n - 1] = 0;
        e[n] = 0;
        x = H[n][n - 1];
        s = Math.abs(x) + Math.abs(z);
        p = x / s;
        q = z / s;
        r = Math.sqrt(p * p+q * q);
        p /= r;
        q /= r;

        // Row modification
        for (var j = n - 1; j < nn; j++) {
          z = H[n - 1][j];
          H[n - 1][j] = q * z + p * H[n][j];
          H[n][j] = q * H[n][j] - p * z;
        }

        // Column modification
        for (var i = 0; i <= n; i++) {
          z = H[i][n - 1];
          H[i][n - 1] = q * z + p * H[i][n];
          H[i][n] = q * H[i][n] - p * z;
        }

        // Accumulate transformations
        for (var i = low; i <= high; i++) {
          z = V[i][n - 1];
          V[i][n - 1] = q * z + p * V[i][n];
          V[i][n] = q * V[i][n] - p * z;
        }

        // Complex pair
      } else {
        d[n - 1] = x + p;
        d[n] = x + p;
        e[n - 1] = z;
        e[n] = -z;
      }
      n = n - 2;
      iter = 0;

      // No convergence yet
    } else {

      // Form shift
      x = H[n][n];
      y = 0;
      w = 0;
      if (l < n) {
        y = H[n - 1][n - 1];
        w = H[n][n - 1] * H[n - 1][n];
      }

      // Wilkinson's original ad hoc shift
      if (iter == 10) {
        exshift += x;
        for (var i = low; i <= n; i++) {
          H[i][i] -= x;
        }
        s = Math.abs(H[n][n - 1]) + Math.abs(H[n - 1][n-2]);
        x = y = 0.75 * s;
        w = -0.4375 * s * s;
      }

      // MATLAB's new ad hoc shift
      if (iter == 30) {
        s = (y - x) / 2.0;
        s = s * s + w;
        if (s > 0) {
          s = Math.sqrt(s);
          if (y < x) {
            s = -s;
          }
          s = x - w / ((y - x) / 2.0 + s);
          for (var i = low; i <= n; i++) {
            H[i][i] -= s;
          }
          exshift += s;
          x = y = w = 0.964;
        }
      }

      iter++;   // (Could check iteration count here.)

      // Look for two consecutive small sub-diagonal elements
      var m = n-2;
      while (m >= l) {
        z = H[m][m];
        r = x - z;
        s = y - z;
        p = (r * s - w) / H[m + 1][m] + H[m][m + 1];
        q = H[m + 1][m + 1] - z - r - s;
        r = H[m+2][m + 1];
        s = Math.abs(p) + Math.abs(q) + Math.abs(r);
        p = p / s;
        q = q / s;
        r = r / s;
        if (m == l) break;
        if (Math.abs(H[m][m - 1]) * (Math.abs(q) + Math.abs(r)) <
          eps * (Math.abs(p) * (Math.abs(H[m - 1][m - 1]) + Math.abs(z) +
          Math.abs(H[m + 1][m + 1])))) {
            break;
        }
        m--;
      }

      for (var i = m+2; i <= n; i++) {
        H[i][i-2] = 0;
        if (i > m+2) H[i][i-3] = 0;
      }

      // Double QR step involving rows l:n and columns m:n
      for (var k = m; k <= n - 1; k++) {
        var notlast = (k != n - 1);
        if (k != m) {
          p = H[k][k - 1];
          q = H[k + 1][k - 1];
          r = (notlast ? H[k + 2][k - 1] : 0);
          x = Math.abs(p) + Math.abs(q) + Math.abs(r);
          if (x != 0) {
            p /= x;
            q /= x;
            r /= x;
          }
        }
        if (x == 0) break;
        s = Math.sqrt(p * p + q * q + r * r);
        if (p < 0) { s = -s; }
        if (s != 0) {
          if (k != m) H[k][k - 1] = -s * x;
          else if (l != m) H[k][k - 1] = -H[k][k - 1];
          p += s;
          x = p / s;
          y = q / s;
          z = r / s;
          q /= p;
          r /= p;

          // Row modification
          for (var j = k; j < nn; j++) {
            p = H[k][j] + q * H[k + 1][j];
            if (notlast) {
              p = p + r * H[k + 2][j];
              H[k + 2][j] = H[k + 2][j] - p * z;
            }
            H[k][j] = H[k][j] - p * x;
            H[k + 1][j] = H[k + 1][j] - p * y;
          }

          // Column modification
          for (var i = 0; i <= Math.min(n, k + 3); i++) {
            p = x * H[i][k] + y * H[i][k + 1];
            if (notlast) {
              p += z * H[i][k + 2];
              H[i][k + 2] = H[i][k + 2] - p * r;
            }
            H[i][k] = H[i][k] - p;
            H[i][k + 1] = H[i][k + 1] - p * q;
          }

          // Accumulate transformations
          for (var i = low; i <= high; i++) {
            p = x * V[i][k] + y * V[i][k + 1];
            if (notlast) {
              p = p + z * V[i][k + 2];
              V[i][k + 2] = V[i][k + 2] - p * r;
            }
            V[i][k] = V[i][k] - p;
            V[i][k + 1] = V[i][k + 1] - p * q;
          }
        }  // (s != 0)
      }  // k loop
    }  // check convergence
  }  // while (n >= low)

  // Backsubstitute to find vectors of upper triangular form
  if (norm == 0) { return; }

  for (n = nn - 1; n >= 0; n--) {
    p = d[n];
    q = e[n];

    // Real vector
    if (q == 0) {
      var l = n;
      H[n][n] = 1.0;
      for (var i = n - 1; i >= 0; i--) {
        w = H[i][i] - p;
        r = 0;
        for (var j = l; j <= n; j++) { r = r + H[i][j] * H[j][n]; }
        if (e[i] < 0) {
          z = w;
          s = r;
        } else {
          l = i;
          if (e[i] === 0) {
            H[i][n] = -r / (w !== 0 ? w : eps * norm);
          } else {
            // Solve real equations
            x = H[i][i + 1];
            y = H[i + 1][i];
            q = (d[i] - p) * (d[i] - p) + e[i] * e[i];
            t = (x * s - z * r) / q;
            H[i][n] = t;
            if (Math.abs(x) > Math.abs(z)) {
              H[i + 1][n] = (-r - w * t) / x;
            } else {
              H[i + 1][n] = (-s - y * t) / z;
            }
          }

          // Overflow control
          t = Math.abs(H[i][n]);
          if ((eps * t) * t > 1) {
            for (var j = i; j <= n; j++) H[j][n] = H[j][n] / t;
          }
        }
      }
    // Complex vector
    } else if (q < 0) {
      var l = n - 1;

      // Last vector component imaginary so matrix is triangular
      if (Math.abs(H[n][n - 1]) > Math.abs(H[n - 1][n])) {
        H[n - 1][n - 1] = q / H[n][n - 1];
        H[n - 1][n] = -(H[n][n] - p) / H[n][n - 1];
      } else {
        var zz = science_lin_decomposeCdiv(0, -H[n - 1][n], H[n - 1][n - 1] - p, q);
        H[n - 1][n - 1] = zz[0];
        H[n - 1][n] = zz[1];
      }
      H[n][n - 1] = 0;
      H[n][n] = 1;
      for (var i = n-2; i >= 0; i--) {
        var ra = 0,
            sa = 0,
            vr,
            vi;
        for (var j = l; j <= n; j++) {
          ra = ra + H[i][j] * H[j][n - 1];
          sa = sa + H[i][j] * H[j][n];
        }
        w = H[i][i] - p;

        if (e[i] < 0) {
          z = w;
          r = ra;
          s = sa;
        } else {
          l = i;
          if (e[i] == 0) {
            var zz = science_lin_decomposeCdiv(-ra,-sa,w,q);
            H[i][n - 1] = zz[0];
            H[i][n] = zz[1];
          } else {
            // Solve complex equations
            x = H[i][i + 1];
            y = H[i + 1][i];
            vr = (d[i] - p) * (d[i] - p) + e[i] * e[i] - q * q;
            vi = (d[i] - p) * 2.0 * q;
            if (vr == 0 & vi == 0) {
              vr = eps * norm * (Math.abs(w) + Math.abs(q) +
                Math.abs(x) + Math.abs(y) + Math.abs(z));
            }
            var zz = science_lin_decomposeCdiv(x*r-z*ra+q*sa,x*s-z*sa-q*ra,vr,vi);
            H[i][n - 1] = zz[0];
            H[i][n] = zz[1];
            if (Math.abs(x) > (Math.abs(z) + Math.abs(q))) {
              H[i + 1][n - 1] = (-ra - w * H[i][n - 1] + q * H[i][n]) / x;
              H[i + 1][n] = (-sa - w * H[i][n] - q * H[i][n - 1]) / x;
            } else {
              var zz = science_lin_decomposeCdiv(-r-y*H[i][n - 1],-s-y*H[i][n],z,q);
              H[i + 1][n - 1] = zz[0];
              H[i + 1][n] = zz[1];
            }
          }

          // Overflow control
          t = Math.max(Math.abs(H[i][n - 1]),Math.abs(H[i][n]));
          if ((eps * t) * t > 1) {
            for (var j = i; j <= n; j++) {
              H[j][n - 1] = H[j][n - 1] / t;
              H[j][n] = H[j][n] / t;
            }
          }
        }
      }
    }
  }

  // Vectors of isolated roots
  for (var i = 0; i < nn; i++) {
    if (i < low || i > high) {
      for (var j = i; j < nn; j++) V[i][j] = H[i][j];
    }
  }

  // Back transformation to get eigenvectors of original matrix
  for (var j = nn - 1; j >= low; j--) {
    for (var i = low; i <= high; i++) {
      z = 0;
      for (var k = low; k <= Math.min(j, high); k++) z += V[i][k] * H[k][j];
      V[i][j] = z;
    }
  }
}

// Complex scalar division.
function science_lin_decomposeCdiv(xr, xi, yr, yi) {
  if (Math.abs(yr) > Math.abs(yi)) {
    var r = yi / yr,
        d = yr + r * yi;
    return [(xr + r * xi) / d, (xi - r * xr) / d];
  } else {
    var r = yr / yi,
        d = yi + r * yr;
    return [(r * xr + xi) / d, (r * xi - xr) / d];
  }
}
science.lin.cross = function(a, b) {
  // TODO how to handle non-3D vectors?
  // TODO handle 7D vectors?
  return [
    a[1] * b[2] - a[2] * b[1],
    a[2] * b[0] - a[0] * b[2],
    a[0] * b[1] - a[1] * b[0]
  ];
};
science.lin.dot = function(a, b) {
  var s = 0,
      i = -1,
      n = Math.min(a.length, b.length);
  while (++i < n) s += a[i] * b[i];
  return s;
};
science.lin.length = function(p) {
  return Math.sqrt(science.lin.dot(p, p));
};
science.lin.normalize = function(p) {
  var length = science.lin.length(p);
  return p.map(function(d) { return d / length; });
};
// 4x4 matrix determinant.
science.lin.determinant = function(matrix) {
  var m = matrix[0].concat(matrix[1]).concat(matrix[2]).concat(matrix[3]);
  return (
    m[12] * m[9]  * m[6]  * m[3]  - m[8] * m[13] * m[6]  * m[3]  -
    m[12] * m[5]  * m[10] * m[3]  + m[4] * m[13] * m[10] * m[3]  +
    m[8]  * m[5]  * m[14] * m[3]  - m[4] * m[9]  * m[14] * m[3]  -
    m[12] * m[9]  * m[2]  * m[7]  + m[8] * m[13] * m[2]  * m[7]  +
    m[12] * m[1]  * m[10] * m[7]  - m[0] * m[13] * m[10] * m[7]  -
    m[8]  * m[1]  * m[14] * m[7]  + m[0] * m[9]  * m[14] * m[7]  +
    m[12] * m[5]  * m[2]  * m[11] - m[4] * m[13] * m[2]  * m[11] -
    m[12] * m[1]  * m[6]  * m[11] + m[0] * m[13] * m[6]  * m[11] +
    m[4]  * m[1]  * m[14] * m[11] - m[0] * m[5]  * m[14] * m[11] -
    m[8]  * m[5]  * m[2]  * m[15] + m[4] * m[9]  * m[2]  * m[15] +
    m[8]  * m[1]  * m[6]  * m[15] - m[0] * m[9]  * m[6]  * m[15] -
    m[4]  * m[1]  * m[10] * m[15] + m[0] * m[5]  * m[10] * m[15]);
};
// Performs in-place Gauss-Jordan elimination.
//
// Based on Jarno Elonen's Python version (public domain):
// http://elonen.iki.fi/code/misc-notes/python-gaussj/index.html
science.lin.gaussjordan = function(m, eps) {
  if (!eps) eps = 1e-10;

  var h = m.length,
      w = m[0].length,
      y = -1,
      y2,
      x;

  while (++y < h) {
    var maxrow = y;

    // Find max pivot.
    y2 = y; while (++y2 < h) {
      if (Math.abs(m[y2][y]) > Math.abs(m[maxrow][y]))
        maxrow = y2;
    }

    // Swap.
    var tmp = m[y];
    m[y] = m[maxrow];
    m[maxrow] = tmp;

    // Singular?
    if (Math.abs(m[y][y]) <= eps) return false;

    // Eliminate column y.
    y2 = y; while (++y2 < h) {
      var c = m[y2][y] / m[y][y];
      x = y - 1; while (++x < w) {
        m[y2][x] -= m[y][x] * c;
      }
    }
  }

  // Backsubstitute.
  y = h; while (--y >= 0) {
    var c = m[y][y];
    y2 = -1; while (++y2 < y) {
      x = w; while (--x >= y) {
        m[y2][x] -=  m[y][x] * m[y2][y] / c;
      }
    }
    m[y][y] /= c;
    // Normalize row y.
    x = h - 1; while (++x < w) {
      m[y][x] /= c;
    }
  }
  return true;
};
// Find matrix inverse using Gauss-Jordan.
science.lin.inverse = function(m) {
  var n = m.length,
      i = -1;

  // Check if the matrix is square.
  if (n !== m[0].length) return;

  // Augment with identity matrix I to get AI.
  m = m.map(function(row, i) {
    var identity = new Array(n),
        j = -1;
    while (++j < n) identity[j] = i === j ? 1 : 0;
    return row.concat(identity);
  });

  // Compute IA^-1.
  science.lin.gaussjordan(m);

  // Remove identity matrix I to get A^-1.
  while (++i < n) {
    m[i] = m[i].slice(n);
  }

  return m;
};
science.lin.multiply = function(a, b) {
  var m = a.length,
      n = b[0].length,
      p = b.length,
      i = -1,
      j,
      k;
  if (p !== a[0].length) throw {"error": "columns(a) != rows(b); " + a[0].length + " != " + p};
  var ab = new Array(m);
  while (++i < m) {
    ab[i] = new Array(n);
    j = -1; while(++j < n) {
      var s = 0;
      k = -1; while (++k < p) s += a[i][k] * b[k][j];
      ab[i][j] = s;
    }
  }
  return ab;
};
science.lin.transpose = function(a) {
  var m = a.length,
      n = a[0].length,
      i = -1,
      j,
      b = new Array(n);
  while (++i < n) {
    b[i] = new Array(m);
    j = -1; while (++j < m) b[i][j] = a[j][i];
  }
  return b;
};
/**
 * Solves tridiagonal systems of linear equations.
 *
 * Source: http://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm
 *
 * @param {number[]} a
 * @param {number[]} b
 * @param {number[]} c
 * @param {number[]} d
 * @param {number[]} x
 * @param {number} n
 */
science.lin.tridag = function(a, b, c, d, x, n) {
  var i,
      m;
  for (i = 1; i < n; i++) {
    m = a[i] / b[i - 1];
    b[i] -= m * c[i - 1];
    d[i] -= m * d[i - 1];
  }
  x[n - 1] = d[n - 1] / b[n - 1];
  for (i = n - 2; i >= 0; i--) {
    x[i] = (d[i] - c[i] * x[i + 1]) / b[i];
  }
};
})(this);
(function(exports){
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];

      var 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) {
  var counts = {},
      mode = [],
      max = 0,
      n = x.length,
      i = -1,
      d,
      k;
  while (++i < n) {
    k = counts.hasOwnProperty(d = x[i]) ? ++counts[d] : counts[d] = 1;
    if (k === max) mode.push(d);
    else if (k > max) {
      max = k;
      mode = [d];
    }
  }
  if (mode.length === 1) return mode[0];
};
// 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);
};
science.stats.distribution = {
};
// From http://www.colingodsey.com/javascript-gaussian-random-number-generator/
// Uses the Box-Muller Transform.
science.stats.distribution.gaussian = function() {
  var random = Math.random,
      mean = 0,
      sigma = 1,
      variance = 1;

  function gaussian() {
    var x1,
        x2,
        rad,
        y1;

    do {
      x1 = 2 * random() - 1;
      x2 = 2 * random() - 1;
      rad = x1 * x1 + x2 * x2;
    } while (rad >= 1 || rad === 0);

    return mean + sigma * x1 * Math.sqrt(-2 * Math.log(rad) / rad);
  }

  gaussian.pdf = function(x) {
    x = (x - mean) / sigma;
    return science_stats_distribution_gaussianConstant * Math.exp(-.5 * x * x) / sigma;
  };

  gaussian.cdf = function(x) {
    x = (x - mean) / sigma;
    return .5 * (1 + science.stats.erf(x / Math.SQRT2));
  };

  gaussian.mean = function(x) {
    if (!arguments.length) return mean;
    mean = +x;
    return gaussian;
  };

  gaussian.variance = function(x) {
    if (!arguments.length) return variance;
    sigma = Math.sqrt(variance = +x);
    return gaussian;
  };

  gaussian.random = function(x) {
    if (!arguments.length) return random;
    random = x;
    return gaussian;
  };

  return gaussian;
};

science_stats_distribution_gaussianConstant = 1 / Math.sqrt(2 * Math.PI);
})(this);
})(this);