// Extend the Array class
Array.prototype.max = function () {
  return Math.max.apply(null, this);
};
Array.prototype.min = function () {
  return Math.min.apply(null, this);
};
Array.prototype.mean = function () {
  var i, sum;
  for (i = 0, sum = 0; i < this.length; i++)
    sum += this[i];
  return sum / this.length;
};
Array.prototype.pip = function (x, y) {
  var i, j, c = false;
  for (i = 0, j = this.length - 1; i < this.length; j = i++) {
    if (((this[i][1] > y) != (this[j][1] > y)) &&
      (x < (this[j][0] - this[i][0]) * (y - this[i][1]) / (this[j][1] - this[i][1]) + this[i][0])) {
      c = !c;
    }
  }
  return c;
}

var kriging = function () {
  var kriging = {};

  var createArrayWithValues = function (value, n) {
    var array = [];
    for (var i = 0; i < n; i++) {
      array.push(value);
    }
    return array;
  };

  // Matrix algebra
  kriging_matrix_diag = function (c, n) {
    var Z = createArrayWithValues(0, n * n);
    for (i = 0; i < n; i++) Z[i * n + i] = c;
    return Z;
  };
  kriging_matrix_transpose = function (X, n, m) {
    var i, j, Z = Array(m * n);
    for (i = 0; i < n; i++)
      for (j = 0; j < m; j++)
        Z[j * n + i] = X[i * m + j];
    return Z;
  };
  kriging_matrix_scale = function (X, c, n, m) {
    var i, j;
    for (i = 0; i < n; i++)
      for (j = 0; j < m; j++)
        X[i * m + j] *= c;
  };
  kriging_matrix_add = function (X, Y, n, m) {
    var i, j, Z = Array(n * m);
    for (i = 0; i < n; i++)
      for (j = 0; j < m; j++)
        Z[i * m + j] = X[i * m + j] + Y[i * m + j];
    return Z;
  };
  // Naive matrix multiplication
  kriging_matrix_multiply = function (X, Y, n, m, p) {
    var i, j, k, Z = Array(n * p);
    for (i = 0; i < n; i++) {
      for (j = 0; j < p; j++) {
        Z[i * p + j] = 0;
        for (k = 0; k < m; k++)
          Z[i * p + j] += X[i * m + k] * Y[k * p + j];
      }
    }
    return Z;
  };
  // Cholesky decomposition
  kriging_matrix_chol = function (X, n) {
    var i, j, k, sum, p = Array(n);
    for (i = 0; i < n; i++) p[i] = X[i * n + i];
    for (i = 0; i < n; i++) {
      for (j = 0; j < i; j++)
        p[i] -= X[i * n + j] * X[i * n + j];
      if (p[i] <= 0) return false;
      p[i] = Math.sqrt(p[i]);
      for (j = i + 1; j < n; j++) {
        for (k = 0; k < i; k++)
          X[j * n + i] -= X[j * n + k] * X[i * n + k];
        X[j * n + i] /= p[i];
      }
    }
    for (i = 0; i < n; i++) X[i * n + i] = p[i];
    return true;
  };
  // Inversion of cholesky decomposition
  kriging_matrix_chol2inv = function (X, n) {
    var i, j, k, sum;
    for (i = 0; i < n; i++) {
      X[i * n + i] = 1 / X[i * n + i];
      for (j = i + 1; j < n; j++) {
        sum = 0;
        for (k = i; k < j; k++)
          sum -= X[j * n + k] * X[k * n + i];
        X[j * n + i] = sum / X[j * n + j];
      }
    }
    for (i = 0; i < n; i++)
      for (j = i + 1; j < n; j++)
        X[i * n + j] = 0;
    for (i = 0; i < n; i++) {
      X[i * n + i] *= X[i * n + i];
      for (k = i + 1; k < n; k++)
        X[i * n + i] += X[k * n + i] * X[k * n + i];
      for (j = i + 1; j < n; j++)
        for (k = j; k < n; k++)
          X[i * n + j] += X[k * n + i] * X[k * n + j];
    }
    for (i = 0; i < n; i++)
      for (j = 0; j < i; j++)
        X[i * n + j] = X[j * n + i];

  };
  // Inversion via gauss-jordan elimination
  kriging_matrix_solve = function (X, n) {
    var m = n;
    var b = Array(n * n);
    var indxc = Array(n);
    var indxr = Array(n);
    var ipiv = Array(n);
    var i, icol, irow, j, k, l, ll;
    var big, dum, pivinv, temp;

    for (i = 0; i < n; i++)
      for (j = 0; j < n; j++) {
        if (i == j) b[i * n + j] = 1;
        else b[i * n + j] = 0;
      }
    for (j = 0; j < n; j++) ipiv[j] = 0;
    for (i = 0; i < n; i++) {
      big = 0;
      for (j = 0; j < n; j++) {
        if (ipiv[j] != 1) {
          for (k = 0; k < n; k++) {
            if (ipiv[k] == 0) {
              if (Math.abs(X[j * n + k]) >= big) {
                big = Math.abs(X[j * n + k]);
                irow = j;
                icol = k;
              }
            }
          }
        }
      }
      ++(ipiv[icol]);

      if (irow != icol) {
        for (l = 0; l < n; l++) {
          temp = X[irow * n + l];
          X[irow * n + l] = X[icol * n + l];
          X[icol * n + l] = temp;
        }
        for (l = 0; l < m; l++) {
          temp = b[irow * n + l];
          b[irow * n + l] = b[icol * n + l];
          b[icol * n + l] = temp;
        }
      }
      indxr[i] = irow;
      indxc[i] = icol;

      if (X[icol * n + icol] == 0) return false; // Singular

      pivinv = 1 / X[icol * n + icol];
      X[icol * n + icol] = 1;
      for (l = 0; l < n; l++) X[icol * n + l] *= pivinv;
      for (l = 0; l < m; l++) b[icol * n + l] *= pivinv;

      for (ll = 0; ll < n; ll++) {
        if (ll != icol) {
          dum = X[ll * n + icol];
          X[ll * n + icol] = 0;
          for (l = 0; l < n; l++) X[ll * n + l] -= X[icol * n + l] * dum;
          for (l = 0; l < m; l++) b[ll * n + l] -= b[icol * n + l] * dum;
        }
      }
    }
    for (l = (n - 1); l >= 0; l--)
      if (indxr[l] != indxc[l]) {
        for (k = 0; k < n; k++) {
          temp = X[k * n + indxr[l]];
          X[k * n + indxr[l]] = X[k * n + indxc[l]];
          X[k * n + indxc[l]] = temp;
        }
      }

    return true;
  }

  // Variogram models
  kriging_variogram_gaussian = function (h, nugget, range, sill, A) {
    return nugget + ((sill - nugget) / range) *
      (1.0 - Math.exp(-(1.0 / A) * Math.pow(h / range, 2)));
  };
  kriging_variogram_exponential = function (h, nugget, range, sill, A) {
    return nugget + ((sill - nugget) / range) *
      (1.0 - Math.exp(-(1.0 / A) * (h / range)));
  };
  kriging_variogram_spherical = function (h, nugget, range, sill, A) {
    if (h > range) return nugget + (sill - nugget) / range;
    return nugget + ((sill - nugget) / range) *
      (1.5 * (h / range) - 0.5 * Math.pow(h / range, 3));
  };

  // Train using gaussian processes with bayesian priors
  kriging.train = function (t, x, y, model, sigma2, alpha) {
    var variogram = {
      t: t,
      x: x,
      y: y,
      nugget: 0.0,
      range: 0.0,
      sill: 0.0,
      A: 1 / 3,
      n: 0
    };
    switch (model) {
      case "gaussian":
        variogram.model = kriging_variogram_gaussian;
        break;
      case "exponential":
        variogram.model = kriging_variogram_exponential;
        break;
      case "spherical":
        variogram.model = kriging_variogram_spherical;
        break;
    }
    ;

    // Lag distance/semivariance
    var i, j, k, l, n = t.length;
    var distance = Array((n * n - n) / 2);
    for (i = 0, k = 0; i < n; i++)
      for (j = 0; j < i; j++, k++) {
        distance[k] = Array(2);
        distance[k][0] = Math.pow(
          Math.pow(x[i] - x[j], 2) +
          Math.pow(y[i] - y[j], 2), 0.5);
        distance[k][1] = Math.abs(t[i] - t[j]);
      }
    distance.sort(function (a, b) {
      return a[0] - b[0];
    });
    variogram.range = distance[(n * n - n) / 2 - 1][0];

    // Bin lag distance
    var lags = ((n * n - n) / 2) > 30 ? 30 : (n * n - n) / 2;
    var tolerance = variogram.range / lags;
    var lag = createArrayWithValues(0, lags);
    var semi = createArrayWithValues(0, lags);
    if (lags < 30) {
      for (l = 0; l < lags; l++) {
        lag[l] = distance[l][0];
        semi[l] = distance[l][1];
      }
    } else {
      for (i = 0, j = 0, k = 0, l = 0; i < lags && j < ((n * n - n) / 2); i++, k = 0) {
        while (distance[j][0] <= ((i + 1) * tolerance)) {
          lag[l] += distance[j][0];
          semi[l] += distance[j][1];
          j++;
          k++;
          if (j >= ((n * n - n) / 2)) break;
        }
        if (k > 0) {
          lag[l] /= k;
          semi[l] /= k;
          l++;
        }
      }
      if (l < 2) return variogram; // Error: Not enough points
    }

    // Feature transformation
    n = l;
    variogram.range = lag[n - 1] - lag[0];
    var X = createArrayWithValues(1, 2 * n);
    var Y = Array(n);
    var A = variogram.A;
    for (i = 0; i < n; i++) {
      switch (model) {
        case "gaussian":
          X[i * 2 + 1] = 1.0 - Math.exp(-(1.0 / A) * Math.pow(lag[i] / variogram.range, 2));
          break;
        case "exponential":
          X[i * 2 + 1] = 1.0 - Math.exp(-(1.0 / A) * lag[i] / variogram.range);
          break;
        case "spherical":
          X[i * 2 + 1] = 1.5 * (lag[i] / variogram.range) -
            0.5 * Math.pow(lag[i] / variogram.range, 3);
          break;
      }
      ;
      Y[i] = semi[i];
    }

    // Least squares
    var Xt = kriging_matrix_transpose(X, n, 2);
    var Z = kriging_matrix_multiply(Xt, X, 2, n, 2);
    Z = kriging_matrix_add(Z, kriging_matrix_diag(1 / alpha, 2), 2, 2);
    var cloneZ = Z.slice(0);
    if (kriging_matrix_chol(Z, 2))
      kriging_matrix_chol2inv(Z, 2);
    else {
      kriging_matrix_solve(cloneZ, 2);
      Z = cloneZ;
    }
    var W = kriging_matrix_multiply(kriging_matrix_multiply(Z, Xt, 2, 2, n), Y, 2, n, 1);

    // Variogram parameters
    variogram.nugget = W[0];
    variogram.sill = W[1] * variogram.range + variogram.nugget;
    variogram.n = x.length;

    // Gram matrix with prior
    n = x.length;
    var K = Array(n * n);
    for (i = 0; i < n; i++) {
      for (j = 0; j < i; j++) {
        K[i * n + j] = variogram.model(Math.pow(Math.pow(x[i] - x[j], 2) +
            Math.pow(y[i] - y[j], 2), 0.5),
          variogram.nugget,
          variogram.range,
          variogram.sill,
          variogram.A);
        K[j * n + i] = K[i * n + j];
      }
      K[i * n + i] = variogram.model(0, variogram.nugget,
        variogram.range,
        variogram.sill,
        variogram.A);
    }

    // Inverse penalized Gram matrix projected to target vector
    var C = kriging_matrix_add(K, kriging_matrix_diag(sigma2, n), n, n);
    var cloneC = C.slice(0);
    if (kriging_matrix_chol(C, n))
      kriging_matrix_chol2inv(C, n);
    else {
      kriging_matrix_solve(cloneC, n);
      C = cloneC;
    }

    // Copy unprojected inverted matrix as K
    var K = C.slice(0);
    var M = kriging_matrix_multiply(C, t, n, n, 1);
    variogram.K = K;
    variogram.M = M;

    return variogram;
  };

  // Model prediction
  kriging.predict = function (x, y, variogram) {
    var i, k = Array(variogram.n);
    for (i = 0; i < variogram.n; i++)
      k[i] = variogram.model(Math.pow(Math.pow(x - variogram.x[i], 2) +
          Math.pow(y - variogram.y[i], 2), 0.5),
        variogram.nugget, variogram.range,
        variogram.sill, variogram.A);
    return kriging_matrix_multiply(k, variogram.M, 1, variogram.n, 1)[0];
  };
  kriging.variance = function (x, y, variogram) {
    var i, k = Array(variogram.n);
    for (i = 0; i < variogram.n; i++)
      k[i] = variogram.model(Math.pow(Math.pow(x - variogram.x[i], 2) +
          Math.pow(y - variogram.y[i], 2), 0.5),
        variogram.nugget, variogram.range,
        variogram.sill, variogram.A);
    return variogram.model(0, variogram.nugget, variogram.range,
        variogram.sill, variogram.A) +
      kriging_matrix_multiply(kriging_matrix_multiply(k, variogram.K,
          1, variogram.n, variogram.n),
        k, 1, variogram.n, 1)[0];
  };

  // Gridded matrices or contour paths
  kriging.grid = function (polygons, variogram, width) {
    var i, j, k, n = polygons.length;
    if (n == 0) return;

    // Boundaries of polygons space
    var xlim = [polygons[0][0][0], polygons[0][0][0]];
    var ylim = [polygons[0][0][1], polygons[0][0][1]];
    for (i = 0; i < n; i++) // Polygons
      for (j = 0; j < polygons[i].length; j++) { // Vertices
        if (polygons[i][j][0] < xlim[0])
          xlim[0] = polygons[i][j][0];
        if (polygons[i][j][0] > xlim[1])
          xlim[1] = polygons[i][j][0];
        if (polygons[i][j][1] < ylim[0])
          ylim[0] = polygons[i][j][1];
        if (polygons[i][j][1] > ylim[1])
          ylim[1] = polygons[i][j][1];
      }

    // Alloc for O(n^2) space
    var xtarget, ytarget;
    var a = Array(2), b = Array(2);
    var lxlim = Array(2); // Local dimensions
    var lylim = Array(2); // Local dimensions
    var x = Math.ceil((xlim[1] - xlim[0]) / width);
    var y = Math.ceil((ylim[1] - ylim[0]) / width);

    var A = Array(x + 1);
    for (i = 0; i <= x; i++) A[i] = Array(y + 1);
    for (i = 0; i < n; i++) {
      // Range for polygons[i]
      lxlim[0] = polygons[i][0][0];
      lxlim[1] = lxlim[0];
      lylim[0] = polygons[i][0][1];
      lylim[1] = lylim[0];
      for (j = 1; j < polygons[i].length; j++) { // Vertices
        if (polygons[i][j][0] < lxlim[0])
          lxlim[0] = polygons[i][j][0];
        if (polygons[i][j][0] > lxlim[1])
          lxlim[1] = polygons[i][j][0];
        if (polygons[i][j][1] < lylim[0])
          lylim[0] = polygons[i][j][1];
        if (polygons[i][j][1] > lylim[1])
          lylim[1] = polygons[i][j][1];
      }

      // Loop through polygon subspace
      a[0] = Math.floor(((lxlim[0] - ((lxlim[0] - xlim[0]) % width)) - xlim[0]) / width);
      a[1] = Math.ceil(((lxlim[1] - ((lxlim[1] - xlim[1]) % width)) - xlim[0]) / width);
      b[0] = Math.floor(((lylim[0] - ((lylim[0] - ylim[0]) % width)) - ylim[0]) / width);
      b[1] = Math.ceil(((lylim[1] - ((lylim[1] - ylim[1]) % width)) - ylim[0]) / width);
      for (j = a[0]; j <= a[1]; j++)
        for (k = b[0]; k <= b[1]; k++) {
          xtarget = xlim[0] + j * width;
          ytarget = ylim[0] + k * width;
          if (polygons[i].pip(xtarget, ytarget))
            A[j][k] = kriging.predict(xtarget,
              ytarget,
              variogram);
        }
    }
    A.xlim = xlim;
    A.ylim = ylim;
    A.zlim = [variogram.t.min(), variogram.t.max()];
    A.width = width;
    return A;
  };
  kriging.contour = function (value, polygons, variogram) {

  };

  // Plotting on the DOM
  kriging.plot = function (canvas, grid, xlim, ylim, colors) {
    // Clear screen
    var ctx = canvas.getContext("2d");
    ctx.clearRect(0, 0, canvas.width, canvas.height);

    // Starting boundaries
    var range = [xlim[1] - xlim[0], ylim[1] - ylim[0], grid.zlim[1] - grid.zlim[0]];
    var i, j, x, y, z;
    var n = grid.length;
    var m = grid[0].length;
    var wx = Math.ceil(grid.width * canvas.width / (xlim[1] - xlim[0]));
    var wy = Math.ceil(grid.width * canvas.height / (ylim[1] - ylim[0]));
    for (i = 0; i < n; i++)
      for (j = 0; j < m; j++) {
        if (grid[i][j] == undefined) continue;
        x = canvas.width * (i * grid.width + grid.xlim[0] - xlim[0]) / range[0];
        y = canvas.height * (1 - (j * grid.width + grid.ylim[0] - ylim[0]) / range[1]);
        z = (grid[i][j] - grid.zlim[0]) / range[2];
        if (z < 0.0) z = 0.0;
        if (z > 1.0) z = 1.0;

        ctx.fillStyle = colors[Math.floor((colors.length - 1) * z)];
        ctx.fillRect(Math.round(x - wx / 2), Math.round(y - wy / 2), wx, wy);
      }

  };


  return kriging;
}();