lib/science/science.js

(function(){science = {version: "1.7.0"}; // 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;
};
science.vector = {};
science.vector.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.vector.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.vector.length = function(p) {
  return Math.sqrt(science.vector.dot(p, p));
};
science.vector.normalize = function(p) {
  var length = science.vector.length(p);
  return p.map(function(d) { return d / length; });
};
// 4x4 matrix determinant.
science.vector.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.vector.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.vector.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.vector.gaussjordan(m);

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

  return m;
};
science.vector.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.vector.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;
};
})()