/**
 * Returns an array of numbers, starting at <tt>start</tt>, incrementing by
 * <tt>step</tt>, until <tt>stop</tt> is reached. The stop value is
 * exclusive. If only a single argument is specified, this value is interpeted
 * as the <i>stop</i> value, with the <i>start</i> value as zero. If only two
 * arguments are specified, the step value is implied to be one.
 *
 * <p>The method is modeled after the built-in <tt>range</tt> method from
 * Python. See the Python documentation for more details.
 *
 * @see <a href="http://docs.python.org/library/functions.html#range">Python range</a>
 * @param {number} [start] the start value.
 * @param {number} stop the stop value.
 * @param {number} [step] the step value.
 * @returns {number[]} an array of numbers.
 */
pv.range = function(start, stop, step) {
  if (arguments.length == 1) {
    stop = start;
    start = 0;
  }
  if (step == undefined) step = 1;
  if ((stop - start) / step == Infinity) throw new Error("range must be finite");
  var array = [], i = 0, j;
  stop -= (stop - start) * 1e-10; // floating point precision!
  if (step < 0) {
    while ((j = start + step * i++) > stop) {
      array.push(j);
    }
  } else {
    while ((j = start + step * i++) < stop) {
      array.push(j);
    }
  }
  return array;
};

/**
 * Returns a random number in the range [<tt>start</tt>, <tt>stop</tt>) that is
 * a multiple of <tt>step</tt>. More specifically, the returned number is of the
 * form <tt>start</tt> + <i>n</i> * <tt>step</tt>, where <i>n</i> is a
 * nonnegative integer. If <tt>step</tt> is not specified, it defaults to 1,
 * returning a random integer if <tt>start</tt> is also an integer.
 *
 * @param {number} [start] the start value value.
 * @param {number} stop the stop value.
 * @param {number} [step] the step value.
 * @returns {number} a random number between <i>start</i> and <i>stop</i>.
 */
pv.random = function(start, stop, step) {
  if (arguments.length == 1) {
    stop = start;
    start = 0;
  }
  if (step == undefined) step = 1;
  return step
      ? (Math.floor(Math.random() * (stop - start) / step) * step + start)
      : (Math.random() * (stop - start) + start);
};

/**
 * Returns the sum of the specified array. If the specified array is not an
 * array of numbers, an optional accessor function <tt>f</tt> can be specified
 * to map the elements to numbers. See {@link #normalize} for an example.
 * Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the sum of the specified array.
 */
pv.sum = function(array, f) {
  var o = {};
  return array.reduce(f
      ? function(p, d, i) { o.index = i; return p + f.call(o, d); }
      : function(p, d) { return p + d; }, 0);
};

/**
 * Returns the maximum value of the specified array. If the specified array is
 * not an array of numbers, an optional accessor function <tt>f</tt> can be
 * specified to map the elements to numbers. See {@link #normalize} for an
 * example. Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the maximum value of the specified array.
 */
pv.max = function(array, f) {
  if (f == pv.index) return array.length - 1;
  return Math.max.apply(null, f ? pv.map(array, f) : array);
};

/**
 * Returns the index of the maximum value of the specified array. If the
 * specified array is not an array of numbers, an optional accessor function
 * <tt>f</tt> can be specified to map the elements to numbers. See
 * {@link #normalize} for an example. Accessor functions can refer to
 * <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the index of the maximum value of the specified array.
 */
pv.max.index = function(array, f) {
  if (!array.length) return -1;
  if (f == pv.index) return array.length - 1;
  if (!f) f = pv.identity;
  var maxi = 0, maxx = -Infinity, o = {};
  for (var i = 0; i < array.length; i++) {
    o.index = i;
    var x = f.call(o, array[i]);
    if (x > maxx) {
      maxx = x;
      maxi = i;
    }
  }
  return maxi;
}

/**
 * Returns the minimum value of the specified array of numbers. If the specified
 * array is not an array of numbers, an optional accessor function <tt>f</tt>
 * can be specified to map the elements to numbers. See {@link #normalize} for
 * an example. Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the minimum value of the specified array.
 */
pv.min = function(array, f) {
  if (f == pv.index) return 0;
  return Math.min.apply(null, f ? pv.map(array, f) : array);
};

/**
 * Returns the index of the minimum value of the specified array. If the
 * specified array is not an array of numbers, an optional accessor function
 * <tt>f</tt> can be specified to map the elements to numbers. See
 * {@link #normalize} for an example. Accessor functions can refer to
 * <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the index of the minimum value of the specified array.
 */
pv.min.index = function(array, f) {
  if (!array.length) return -1;
  if (f == pv.index) return 0;
  if (!f) f = pv.identity;
  var mini = 0, minx = Infinity, o = {};
  for (var i = 0; i < array.length; i++) {
    o.index = i;
    var x = f.call(o, array[i]);
    if (x < minx) {
      minx = x;
      mini = i;
    }
  }
  return mini;
}

/**
 * Returns the arithmetic mean, or average, of the specified array. If the
 * specified array is not an array of numbers, an optional accessor function
 * <tt>f</tt> can be specified to map the elements to numbers. See
 * {@link #normalize} for an example. Accessor functions can refer to
 * <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the mean of the specified array.
 */
pv.mean = function(array, f) {
  return pv.sum(array, f) / array.length;
};

/**
 * Returns the median of the specified array. If the specified array is not an
 * array of numbers, an optional accessor function <tt>f</tt> can be specified
 * to map the elements to numbers. See {@link #normalize} for an example.
 * Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the median of the specified array.
 */
pv.median = function(array, f) {
  if (f == pv.index) return (array.length - 1) / 2;
  array = pv.map(array, f).sort(pv.naturalOrder);
  if (array.length % 2) return array[Math.floor(array.length / 2)];
  var i = array.length / 2;
  return (array[i - 1] + array[i]) / 2;
};

/**
 * Returns the unweighted variance of the specified array. If the specified
 * array is not an array of numbers, an optional accessor function <tt>f</tt>
 * can be specified to map the elements to numbers. See {@link #normalize} for
 * an example. Accessor functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the variance of the specified array.
 */
pv.variance = function(array, f) {
  if (array.length < 1) return NaN;
  if (array.length == 1) return 0;
  var mean = pv.mean(array, f), sum = 0, o = {};
  if (!f) f = pv.identity;
  for (var i = 0; i < array.length; i++) {
    o.index = i;
    var d = f.call(o, array[i]) - mean;
    sum += d * d;
  }
  return sum;
};

/**
 * Returns an unbiased estimation of the standard deviation of a population,
 * given the specified random sample. If the specified array is not an array of
 * numbers, an optional accessor function <tt>f</tt> can be specified to map the
 * elements to numbers. See {@link #normalize} for an example. Accessor
 * functions can refer to <tt>this.index</tt>.
 *
 * @param {array} array an array of objects, or numbers.
 * @param {function} [f] an optional accessor function.
 * @returns {number} the standard deviation of the specified array.
 */
pv.deviation = function(array, f) {
  return Math.sqrt(pv.variance(array, f) / (array.length - 1));
};

/**
 * Returns the logarithm with a given base value.
 *
 * @param {number} x the number for which to compute the logarithm.
 * @param {number} b the base of the logarithm.
 * @returns {number} the logarithm value.
 */
pv.log = function(x, b) {
  return Math.log(x) / Math.log(b);
};

/**
 * Computes a zero-symmetric logarithm. Computes the logarithm of the absolute
 * value of the input, and determines the sign of the output according to the
 * sign of the input value.
 *
 * @param {number} x the number for which to compute the logarithm.
 * @param {number} b the base of the logarithm.
 * @returns {number} the symmetric log value.
 */
pv.logSymmetric = function(x, b) {
  return (x == 0) ? 0 : ((x < 0) ? -pv.log(-x, b) : pv.log(x, b));
};

/**
 * Computes a zero-symmetric logarithm, with adjustment to values between zero
 * and the logarithm base. This adjustment introduces distortion for values less
 * than the base number, but enables simultaneous plotting of log-transformed
 * data involving both positive and negative numbers.
 *
 * @param {number} x the number for which to compute the logarithm.
 * @param {number} b the base of the logarithm.
 * @returns {number} the adjusted, symmetric log value.
 */
pv.logAdjusted = function(x, b) {
  if (!isFinite(x)) return x;
  var negative = x < 0;
  if (x < b) x += (b - x) / b;
  return negative ? -pv.log(x, b) : pv.log(x, b);
};

/**
 * Rounds an input value down according to its logarithm. The method takes the
 * floor of the logarithm of the value and then uses the resulting value as an
 * exponent for the base value.
 *
 * @param {number} x the number for which to compute the logarithm floor.
 * @param {number} b the base of the logarithm.
 * @returns {number} the rounded-by-logarithm value.
 */
pv.logFloor = function(x, b) {
  return (x > 0)
      ? Math.pow(b, Math.floor(pv.log(x, b)))
      : -Math.pow(b, -Math.floor(-pv.log(-x, b)));
};

/**
 * Rounds an input value up according to its logarithm. The method takes the
 * ceiling of the logarithm of the value and then uses the resulting value as an
 * exponent for the base value.
 *
 * @param {number} x the number for which to compute the logarithm ceiling.
 * @param {number} b the base of the logarithm.
 * @returns {number} the rounded-by-logarithm value.
 */
pv.logCeil = function(x, b) {
  return (x > 0)
      ? Math.pow(b, Math.ceil(pv.log(x, b)))
      : -Math.pow(b, -Math.ceil(-pv.log(-x, b)));
};

(function() {
  var radians = Math.PI / 180,
      degrees = 180 / Math.PI;

  /** Returns the number of radians corresponding to the specified degrees. */
  pv.radians = function(degrees) { return radians * degrees; };

  /** Returns the number of degrees corresponding to the specified radians. */
  pv.degrees = function(radians) { return degrees * radians; };
})();