@sgratzl/science/build/science.mjs

Scientific and statistical computing in JavaScript.

function ascending(a, b) {
  return a - b;
}

/**
 * Euler's constant.
 */
var EULER = .5772156649015329;

/**
Compute exp(x) - 1 accurately for small x.
 */
function expm1(x) {
  return x < 1e-5 && x > -1e-5 ? x + .5 * x * x : Math.exp(x) - 1;
}

function functor(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/
function hypot(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);
}

function quadratic() {
  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.
 */
function zeroes(n) {
  var i = -1,
      a = [];
  if (arguments.length === 1) while (++i < n) {
    a[i] = 0;
  } else while (++i < n) {
    a[i] = zeroes.apply(this, Array.prototype.slice.call(arguments, 1));
  }
  return a;
}

var version = "1.9.3"; // semver

function cross(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]];
}

function decompose() {
  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;
}

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) {

      do {
        // Compute implicit shift

        var g = d[l];
        var p = (d[l + 1] - g) / (2 * e[l]);
        var r = 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 = 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];
  }
}

// 4x4 matrix determinant.
function determinant(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];
}

function dot(a, b) {
  var s = 0,
      i = -1,
      n = Math.min(a.length, b.length);

  while (++i < n) {
    s += a[i] * b[i];
  }

  return s;
}

// 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
function gaussjordan(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;
}

function inverse(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.

  gaussjordan(m); // Remove identity matrix I to get A^-1.

  while (++i < n) {
    m[i] = m[i].slice(n);
  }

  return m;
}

function length(p) {
  return Math.sqrt(dot(p, p));
}

function multiply(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;
}

function normalize(p) {
  var length$$1 = length(p);
  return p.map(function (d) {
    return d / length$$1;
  });
}

function transpose(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
 */
function tridag(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];
  }
}



var lin_ = /*#__PURE__*/Object.freeze({
  cross: cross,
  decompose: decompose,
  determinant: determinant,
  dot: dot,
  gaussjordan: gaussjordan,
  inverse: inverse,
  length: length,
  multiply: multiply,
  normalize: normalize,
  transpose: transpose,
  tridag: tridag
});

// Based on implementation in http://picomath.org/.
function erf(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));
}

// Uses the Box-Muller Transform.

function gaussian() {
  var random = Math.random,
      mean = 0,
      sigma = 1,
      variance = 1;

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

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



var distribution_ = /*#__PURE__*/Object.freeze({
  gaussian: gaussian
});

// Welford's algorithm.
function mean(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;
}

// Also known as the sample variance, where the denominator is n - 1.

function variance(x) {
  var n = x.length;
  if (n < 1) return NaN;
  if (n === 1) return 0;
  var mean$$1 = mean(x),
      i = -1,
      s = 0;

  while (++i < n) {
    var v = x[i] - mean$$1;
    s += v * v;
  }

  return s / (n - 1);
}

function quantiles(d, quantiles) {
  d = d.slice().sort(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);
  });
}

function iqr(x) {
  var quartiles = quantiles(x, [.25, .75]);
  return quartiles[1] - quartiles[0];
}

// Based on R's implementations in `stats.bw`.
// Silverman, B. W. (1986) Density Estimation. London: Chapman and Hall.

function nrd0(x) {
  var lo;
  var hi = Math.sqrt(variance(x));
  if (!(lo = Math.min(hi, 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.

function nrd(x) {
  var h = iqr(x) / 1.34;
  return 1.06 * Math.min(Math.sqrt(variance(x)), h) * Math.pow(x.length, -1 / 5);
}

var bandwidth_ = /*#__PURE__*/Object.freeze({
  nrd0: nrd0,
  nrd: nrd
});

function euclidean(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);
}
function manhattan(a, b) {
  var n = a.length,
      i = -1,
      s = 0;

  while (++i < n) {
    s += Math.abs(a[i] - b[i]);
  }

  return s;
}
function minkowski(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);
  };
}
function chebyshev(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;
}
function hamming(a, b) {
  var n = a.length,
      i = -1,
      d = 0;

  while (++i < n) {
    if (a[i] !== b[i]) d++;
  }

  return d;
}
function jaccard(a, b) {
  var n = a.length,
      i = -1,
      s = 0;

  while (++i < n) {
    if (a[i] === b[i]) s++;
  }

  return s / n;
}
function braycurtis(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;
}

var distance_ = /*#__PURE__*/Object.freeze({
  euclidean: euclidean,
  manhattan: manhattan,
  minkowski: minkowski,
  chebyshev: chebyshev,
  hamming: hamming,
  jaccard: jaccard,
  braycurtis: braycurtis
});

function hcluster() {
  var distance = euclidean,
      linkage = "single"; // single, 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;
}

// See <http://en.wikipedia.org/wiki/Kernel_(statistics)>.
function uniform(u) {
  if (u <= 1 && u >= -1) return .5;
  return 0;
}
function triangular(u) {
  if (u <= 1 && u >= -1) return 1 - Math.abs(u);
  return 0;
}
function epanechnikov(u) {
  if (u <= 1 && u >= -1) return .75 * (1 - u * u);
  return 0;
}
function quartic(u) {
  if (u <= 1 && u >= -1) {
    var tmp = 1 - u * u;
    return 15 / 16 * tmp * tmp;
  }

  return 0;
}
function triweight(u) {
  if (u <= 1 && u >= -1) {
    var tmp = 1 - u * u;
    return 35 / 32 * tmp * tmp * tmp;
  }

  return 0;
}
function gaussian$1(u) {
  return 1 / Math.sqrt(2 * Math.PI) * Math.exp(-.5 * u * u);
}
function cosine(u) {
  if (u <= 1 && u >= -1) return Math.PI / 4 * Math.cos(Math.PI / 2 * u);
  return 0;
}

var kernel_ = /*#__PURE__*/Object.freeze({
  uniform: uniform,
  triangular: triangular,
  epanechnikov: epanechnikov,
  quartic: quartic,
  triweight: triweight,
  gaussian: gaussian$1,
  cosine: cosine
});

function kde() {
  var kernel = gaussian$1,
      sample = [],
      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 = functor(x);
    return kde;
  };

  return kde;
}

// http://code.google.com/p/figue/

function kmeans() {
  var 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;
}

function median(x) {
  return quantiles(x, [.5])[0];
}

// from http://commons.apache.org/math/

function loess() {
  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 medianResidual = median(residuals);
      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;
}

function mode(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];
}

function phi(x) {
  return .5 * (1 + erf(x / Math.SQRT2));
}

var distance = distance_;
var kernel = kernel_;
var distribution = distribution_;
var bandwidth = bandwidth_;

var stats_ = /*#__PURE__*/Object.freeze({
  distance: distance,
  kernel: kernel,
  distribution: distribution,
  bandwidth: bandwidth,
  erf: erf,
  hcluster: hcluster,
  iqr: iqr,
  kde: kde,
  kmeans: kmeans,
  loess: loess,
  mean: mean,
  median: median,
  mode: mode,
  phi: phi,
  quantiles: quantiles,
  variance: variance
});

var lin = lin_;
var stats = stats_;

export { lin, stats, version, ascending, EULER, expm1, functor, hypot, quadratic, zeroes };