sm.js

// Generated by CoffeeScript 1.7.1

/*
 * SM.js
 * (c) 2014 Kazuaki Tanida
 * This software can be freely distributed under the MIT license.
 */

(function() {
  var FI_G, ForgettingCurves, Item, MAX_AF, MAX_GRADE, MIN_AF, NOTCH_AF, OFM, RANGE_AF, RANGE_REPETITION, RFM, THRESHOLD_RECALL, error, exponentialRegression, fixedPointPowerLawRegression, linearRegression, linearRegressionThroughOrigin, main, mse, powerLawModel, powerLawRegression, sum,
    __bind = function(fn, me){ return function(){ return fn.apply(me, arguments); }; };

  this.SM = (function() {
    function SM() {
      this.data = __bind(this.data, this);
      this.discard = __bind(this.discard, this);
      this._update = __bind(this._update, this);
      this.answer = __bind(this.answer, this);
      this.nextItem = __bind(this.nextItem, this);
      this.addItem = __bind(this.addItem, this);
      this._findIndexToInsert = __bind(this._findIndexToInsert, this);
      this.requestedFI = 10;
      this.intervalBase = 3 * 60 * 60 * 1000;
      this.q = [];
      this.fi_g = new FI_G(this);
      this.forgettingCurves = new ForgettingCurves(this);
      this.rfm = new RFM(this);
      this.ofm = new OFM(this);
    }

    SM.prototype._findIndexToInsert = function(item, r) {
      var i, v, _i, _ref, _results;
      if (r == null) {
        r = (function() {
          _results = [];
          for (var _i = 0, _ref = this.q.length; 0 <= _ref ? _i < _ref : _i > _ref; 0 <= _ref ? _i++ : _i--){ _results.push(_i); }
          return _results;
        }).apply(this);
      }
      if (r.length === 0) {
        return 0;
      }
      v = item.dueDate;
      i = Math.floor(r.length / 2);
      if (r.length === 1) {
        if (v < this.q[r[i]].dueDate) {
          return r[i];
        } else {
          return r[i] + 1;
        }
      }
      return this._findIndexToInsert(item, (v < this.q[r[i]].dueDate ? r.slice(0, i) : r.slice(i)));
    };

    SM.prototype.addItem = function(value) {
      var item;
      item = new Item(this, value);
      return this.q.splice(this._findIndexToInsert(item), 0, item);
    };

    SM.prototype.nextItem = function(isAdvanceable) {
      if (isAdvanceable == null) {
        isAdvanceable = false;
      }
      if (0 === this.q.length) {
        return null;
      }
      if (isAdvanceable || this.q[0].dueDate < new Date()) {
        return this.q[0];
      }
      return null;
    };

    SM.prototype.answer = function(grade, item, now) {
      if (now == null) {
        now = new Date();
      }
      this._update(grade, item, now);
      this.discard(item);
      return this.q.splice(this._findIndexToInsert(item), 0, item);
    };

    SM.prototype._update = function(grade, item, now) {
      if (now == null) {
        now = new Date();
      }
      if (item.repetition >= 0) {
        this.forgettingCurves.registerPoint(grade, item, now);
        this.ofm.update();
        this.fi_g.update(grade, item, now);
      }
      return item.answer(grade, now);
    };

    SM.prototype.discard = function(item) {
      var index;
      index = this.q.indexOf(item);
      if (index >= 0) {
        return this.q.splice(index, 1);
      }
    };

    SM.prototype.data = function() {
      var item;
      return {
        requestedFI: this.requestedFI,
        intervalBase: this.intervalBase,
        q: (function() {
          var _i, _len, _ref, _results;
          _ref = this.q;
          _results = [];
          for (_i = 0, _len = _ref.length; _i < _len; _i++) {
            item = _ref[_i];
            _results.push(item.data());
          }
          return _results;
        }).call(this),
        fi_g: this.fi_g.data(),
        forgettingCurves: this.forgettingCurves.data(),
        version: 1
      };
    };

    SM.load = function(data) {
      var d, sm;
      sm = new SM();
      sm.requestedFI = data.requestedFI;
      sm.intervalBase = data.intervalBase;
      sm.q = (function() {
        var _i, _len, _ref, _results;
        _ref = data.q;
        _results = [];
        for (_i = 0, _len = _ref.length; _i < _len; _i++) {
          d = _ref[_i];
          _results.push(Item.load(sm, d));
        }
        return _results;
      })();
      sm.fi_g = FI_G.load(sm, data.fi_g);
      sm.forgettingCurves = ForgettingCurves.load(sm, data.forgettingCurves);
      sm.ofm.update();
      return sm;
    };

    return SM;

  })();

  RANGE_AF = 20;

  RANGE_REPETITION = 20;

  MIN_AF = 1.2;

  NOTCH_AF = 0.3;

  MAX_AF = MIN_AF * NOTCH_AF * (RANGE_AF - 1);

  MAX_GRADE = 5;

  THRESHOLD_RECALL = 3;

  Item = (function() {
    var MAX_AFS_COUNT;

    MAX_AFS_COUNT = 30;

    function Item(sm, value) {
      this.sm = sm;
      this.value = value;
      this.data = __bind(this.data, this);
      this.answer = __bind(this.answer, this);
      this._updateAF = __bind(this._updateAF, this);
      this._I = __bind(this._I, this);
      this.afIndex = __bind(this.afIndex, this);
      this.af = __bind(this.af, this);
      this.uf = __bind(this.uf, this);
      this.interval = __bind(this.interval, this);
      this.lapse = 0;
      this.repetition = -1;
      this.of = 1;
      this.optimumInterval = this.sm.intervalBase;
      this.dueDate = new Date(0);
      this._afs = [];
    }

    Item.prototype.interval = function(now) {
      if (now == null) {
        now = new Date();
      }
      if (this.previousDate == null) {
        return this.sm.intervalBase;
      }
      return now - this.previousDate;
    };

    Item.prototype.uf = function(now) {
      if (now == null) {
        now = new Date();
      }
      return this.interval(now) / (this.optimumInterval / this.of);
    };

    Item.prototype.af = function(value) {
      var a;
      if (value == null) {
        value = void 0;
      }
      if (value == null) {
        return this._af;
      }
      a = Math.round((value - MIN_AF) / NOTCH_AF);
      return this._af = Math.max(MIN_AF, Math.min(MAX_AF, MIN_AF + a * NOTCH_AF));
    };

    Item.prototype.afIndex = function() {
      var afs, i, _i, _results;
      afs = (function() {
        var _i, _results;
        _results = [];
        for (i = _i = 0; 0 <= RANGE_AF ? _i < RANGE_AF : _i > RANGE_AF; i = 0 <= RANGE_AF ? ++_i : --_i) {
          _results.push(MIN_AF + i * NOTCH_AF);
        }
        return _results;
      })();
      return (function() {
        _results = [];
        for (var _i = 0; 0 <= RANGE_AF ? _i < RANGE_AF : _i > RANGE_AF; 0 <= RANGE_AF ? _i++ : _i--){ _results.push(_i); }
        return _results;
      }).apply(this).reduce((function(_this) {
        return function(a, b) {
          if (Math.abs(_this.af() - afs[a]) < Math.abs(_this.af() - afs[b])) {
            return a;
          } else {
            return b;
          }
        };
      })(this));
    };

    Item.prototype._I = function(now) {
      var of_;
      if (now == null) {
        now = new Date();
      }
      of_ = this.sm.ofm.of(this.repetition, this.repetition === 0 ? this.lapse : this.afIndex());
      this.of = Math.max(1, (of_ - 1) * (this.interval(now) / this.optimumInterval) + 1);
      this.optimumInterval = Math.round(this.optimumInterval * this.of);
      this.previousDate = now;
      return this.dueDate = new Date(now.getTime() + this.optimumInterval);
    };

    Item.prototype._updateAF = function(grade, now) {
      var correctedUF, estimatedAF, estimatedFI, _i, _ref, _results;
      if (now == null) {
        now = new Date();
      }
      estimatedFI = Math.max(1, this.sm.fi_g.fi(grade));
      correctedUF = this.uf(now) * (this.sm.requestedFI / estimatedFI);
      estimatedAF = this.repetition > 0 ? this.sm.ofm.af(this.repetition, correctedUF) : Math.max(MIN_AF, Math.min(MAX_AF, correctedUF));
      this._afs.push(estimatedAF);
      this._afs = this._afs.slice(Math.max(0, this._afs.length - MAX_AFS_COUNT));
      return this.af(sum(this._afs.map(function(a, i) {
        return a * (i + 1);
      })) / sum((function() {
        _results = [];
        for (var _i = 1, _ref = this._afs.length; 1 <= _ref ? _i <= _ref : _i >= _ref; 1 <= _ref ? _i++ : _i--){ _results.push(_i); }
        return _results;
      }).apply(this)));
    };

    Item.prototype.answer = function(grade, now) {
      if (now == null) {
        now = new Date();
      }
      if (this.repetition >= 0) {
        this._updateAF(grade, now);
      }
      if (grade >= THRESHOLD_RECALL) {
        if (this.repetition < (RANGE_REPETITION - 1)) {
          this.repetition++;
        }
        return this._I(now);
      } else {
        if (this.lapse < (RANGE_AF - 1)) {
          this.lapse++;
        }
        this.optimumInterval = this.sm.intervalBase;
        this.previousDate = null;
        this.dueDate = now;
        return this.repetition = -1;
      }
    };

    Item.prototype.data = function() {
      return {
        value: this.value,
        repetition: this.repetition,
        lapse: this.lapse,
        of: this.of,
        optimumInterval: this.optimumInterval,
        dueDate: this.dueDate,
        previousDate: this.previousDate,
        _afs: this._afs
      };
    };

    Item.load = function(sm, data) {
      var item, k, v;
      item = new Item(sm);
      for (k in data) {
        v = data[k];
        item[k] = v;
      }
      item.dueDate = new Date(item.dueDate);
      if (item.previousDate != null) {
        item.previousDate = new Date(item.previousDate);
      }
      return item;
    };

    return Item;

  })();

  FI_G = (function() {
    var GRADE_OFFSET, MAX_POINTS_COUNT;

    MAX_POINTS_COUNT = 5000;

    GRADE_OFFSET = 1;

    function FI_G(sm, points) {
      var p, _i, _len, _ref;
      this.sm = sm;
      this.points = points != null ? points : void 0;
      this.data = __bind(this.data, this);
      this.grade = __bind(this.grade, this);
      this.fi = __bind(this.fi, this);
      this.update = __bind(this.update, this);
      this._registerPoint = __bind(this._registerPoint, this);
      if (this.points == null) {
        this.points = [];
        _ref = [[0, MAX_GRADE], [100, 0]];
        for (_i = 0, _len = _ref.length; _i < _len; _i++) {
          p = _ref[_i];
          this._registerPoint(p[0], p[1]);
        }
      }
    }

    FI_G.prototype._registerPoint = function(fi, g) {
      this.points.push([fi, g + GRADE_OFFSET]);
      return this.points = this.points.slice(Math.max(0, this.points.length - MAX_POINTS_COUNT));
    };

    FI_G.prototype.update = function(grade, item, now) {
      var expectedFI;
      if (now == null) {
        now = new Date();
      }
      expectedFI = (function(_this) {
        return function() {
          return (item.uf(now) / item.of) * _this.sm.requestedFI;

          /* A way to get the expected forgetting index using a forgetting curve
          curve = @sm.forgettingCurves.curves[item.repetition][item.afIndex()]
          uf = curve.uf (100 - @sm.requestedFI)
          return 100 - curve.retention (item.uf() / uf)
           */
        };
      })(this);
      this._registerPoint(expectedFI(), grade);
      return this._graph = null;
    };

    FI_G.prototype.fi = function(grade) {
      var _ref;
      if (this._graph == null) {
        this._graph = exponentialRegression(this.points);
      }
      return Math.max(0, Math.min(100, (_ref = this._graph) != null ? _ref.x(grade + GRADE_OFFSET) : void 0));
    };

    FI_G.prototype.grade = function(fi) {
      var _ref;
      if (this._graph == null) {
        this._graph = exponentialRegression(this.points);
      }
      return ((_ref = this._graph) != null ? _ref.y(fi) : void 0) - GRADE_OFFSET;
    };

    FI_G.prototype.data = function() {
      return {
        points: this.points
      };
    };

    FI_G.load = function(sm, data) {
      return new FI_G(sm, data.points);
    };

    return FI_G;

  })();

  ForgettingCurves = (function() {
    var FORGOTTEN, ForgettingCurve, REMEMBERED;

    FORGOTTEN = 1;

    REMEMBERED = 100 + FORGOTTEN;

    function ForgettingCurves(sm, points) {
      var a, i, p, partialPoints, r;
      this.sm = sm;
      if (points == null) {
        points = void 0;
      }
      this.data = __bind(this.data, this);
      this.registerPoint = __bind(this.registerPoint, this);
      this.curves = (function() {
        var _i, _results;
        _results = [];
        for (r = _i = 0; 0 <= RANGE_REPETITION ? _i < RANGE_REPETITION : _i > RANGE_REPETITION; r = 0 <= RANGE_REPETITION ? ++_i : --_i) {
          _results.push((function() {
            var _j, _results1;
            _results1 = [];
            for (a = _j = 0; 0 <= RANGE_AF ? _j < RANGE_AF : _j > RANGE_AF; a = 0 <= RANGE_AF ? ++_j : --_j) {
              partialPoints = points != null ? points[r][a] : (p = r > 0 ? (function() {
                var _k, _results2;
                _results2 = [];
                for (i = _k = 0; _k <= 20; i = ++_k) {
                  _results2.push([MIN_AF + NOTCH_AF * i, Math.min(REMEMBERED, Math.exp((-(r + 1) / 200) * (i - a * Math.sqrt(2 / (r + 1)))) * (REMEMBERED - this.sm.requestedFI))]);
                }
                return _results2;
              }).call(this) : (function() {
                var _k, _results2;
                _results2 = [];
                for (i = _k = 0; _k <= 20; i = ++_k) {
                  _results2.push([MIN_AF + NOTCH_AF * i, Math.min(REMEMBERED, Math.exp((-1 / (10 + 1 * (a + 1))) * (i - Math.pow(a, 0.6))) * (REMEMBERED - this.sm.requestedFI))]);
                }
                return _results2;
              }).call(this), [[0, REMEMBERED]].concat(p));
              _results1.push(new ForgettingCurve(partialPoints));
            }
            return _results1;
          }).call(this));
        }
        return _results;
      }).call(this);
    }

    ForgettingCurves.prototype.registerPoint = function(grade, item, now) {
      var afIndex;
      if (now == null) {
        now = new Date();
      }
      afIndex = item.repetition > 0 ? item.afIndex() : item.lapse;
      return this.curves[item.repetition][afIndex].registerPoint(grade, item.uf(now));
    };

    ForgettingCurves.prototype.data = function() {
      var a, r;
      return {
        points: (function() {
          var _i, _results;
          _results = [];
          for (r = _i = 0; 0 <= RANGE_REPETITION ? _i < RANGE_REPETITION : _i > RANGE_REPETITION; r = 0 <= RANGE_REPETITION ? ++_i : --_i) {
            _results.push((function() {
              var _j, _results1;
              _results1 = [];
              for (a = _j = 0; 0 <= RANGE_AF ? _j < RANGE_AF : _j > RANGE_AF; a = 0 <= RANGE_AF ? ++_j : --_j) {
                _results1.push(this.curves[r][a].points);
              }
              return _results1;
            }).call(this));
          }
          return _results;
        }).call(this)
      };
    };

    ForgettingCurves.load = function(sm, data) {
      return new ForgettingCurves(sm, data.points);
    };

    ForgettingCurve = (function() {
      var MAX_POINTS_COUNT;

      MAX_POINTS_COUNT = 500;

      function ForgettingCurve(points) {
        this.points = points;
        this.uf = __bind(this.uf, this);
        this.retention = __bind(this.retention, this);
        this.registerPoint = __bind(this.registerPoint, this);
      }

      ForgettingCurve.prototype.registerPoint = function(grade, uf) {
        var isRemembered;
        isRemembered = grade >= THRESHOLD_RECALL;
        this.points.push([uf, isRemembered ? REMEMBERED : FORGOTTEN]);
        this.points = this.points.slice(Math.max(0, this.points.length - MAX_POINTS_COUNT));
        return this._curve = null;
      };

      ForgettingCurve.prototype.retention = function(uf) {
        if (this._curve == null) {
          this._curve = exponentialRegression(this.points);
        }
        return (Math.max(FORGOTTEN, Math.min(this._curve.y(uf), REMEMBERED))) - FORGOTTEN;
      };

      ForgettingCurve.prototype.uf = function(retention) {
        if (this._curve == null) {
          this._curve = exponentialRegression(this.points);
        }
        return Math.max(0, this._curve.x(retention + FORGOTTEN));
      };

      return ForgettingCurve;

    })();

    return ForgettingCurves;

  })();

  RFM = (function() {
    function RFM(sm) {
      this.sm = sm;
      this.rf = __bind(this.rf, this);
    }

    RFM.prototype.rf = function(repetition, afIndex) {
      return this.sm.forgettingCurves.curves[repetition][afIndex].uf(100 - this.sm.requestedFI);
    };

    return RFM;

  })();

  OFM = (function() {
    var INITIAL_REP_VALUE, afFromIndex, repFromIndex;

    INITIAL_REP_VALUE = 1;

    afFromIndex = function(a) {
      return a * NOTCH_AF + MIN_AF;
    };

    repFromIndex = function(r) {
      return r + INITIAL_REP_VALUE;
    };

    function OFM(sm) {
      this.sm = sm;
      this.af = __bind(this.af, this);
      this.of = __bind(this.of, this);
      this.update = __bind(this.update, this);
      this.update();
    }

    OFM.prototype.update = function() {
      var a, decay, dfs, ofm0, r;
      dfs = (function() {
        var _i, _results;
        _results = [];
        for (a = _i = 0; 0 <= RANGE_AF ? _i < RANGE_AF : _i > RANGE_AF; a = 0 <= RANGE_AF ? ++_i : --_i) {
          _results.push(fixedPointPowerLawRegression((function() {
            var _j, _results1;
            _results1 = [];
            for (r = _j = 1; 1 <= RANGE_REPETITION ? _j < RANGE_REPETITION : _j > RANGE_REPETITION; r = 1 <= RANGE_REPETITION ? ++_j : --_j) {
              _results1.push([repFromIndex(r), this.sm.rfm.rf(r, a)]);
            }
            return _results1;
          }).call(this), [repFromIndex(1), afFromIndex(a)]).b);
        }
        return _results;
      }).call(this);
      dfs = (function() {
        var _i, _results;
        _results = [];
        for (a = _i = 0; 0 <= RANGE_AF ? _i < RANGE_AF : _i > RANGE_AF; a = 0 <= RANGE_AF ? ++_i : --_i) {
          _results.push(afFromIndex(a) / Math.pow(2, dfs[a]));
        }
        return _results;
      })();
      decay = linearRegression((function() {
        var _i, _results;
        _results = [];
        for (a = _i = 0; 0 <= RANGE_AF ? _i < RANGE_AF : _i > RANGE_AF; a = 0 <= RANGE_AF ? ++_i : --_i) {
          _results.push([a, dfs[a]]);
        }
        return _results;
      })());
      this._ofm = function(a) {

        /*
          O-Factor (given repetition, A-Factor and D-Factor) would be modeled by power law
          y = a(x/p)^b, a = A-Factor, b = D-Factor, x = repetition, p = 2 #second repetition number
            = (a/p^b)x^b
         */
        var af, b, model;
        af = afFromIndex(a);
        b = Math.log(af / decay.y(a)) / Math.log(repFromIndex(1));
        model = powerLawModel(af / Math.pow(repFromIndex(1), b), b);
        return {
          y: function(r) {
            return model.y(repFromIndex(r));
          },
          x: function(y) {
            return (model.x(y)) - INITIAL_REP_VALUE;
          }
        };
      };
      ofm0 = exponentialRegression((function() {
        var _i, _results;
        _results = [];
        for (a = _i = 0; 0 <= RANGE_AF ? _i < RANGE_AF : _i > RANGE_AF; a = 0 <= RANGE_AF ? ++_i : --_i) {
          _results.push([a, this.sm.rfm.rf(0, a)]);
        }
        return _results;
      }).call(this));
      return this._ofm0 = function(a) {
        return ofm0.y(a);
      };
    };

    OFM.prototype.of = function(repetition, afIndex) {
      return (repetition === 0 ? typeof this._ofm0 === "function" ? this._ofm0(afIndex) : void 0 : typeof this._ofm === "function" ? this._ofm(afIndex).y(repetition) : void 0);
    };

    OFM.prototype.af = function(repetition, of_) {
      var _i, _results;
      return afFromIndex((function() {
        _results = [];
        for (var _i = 0; 0 <= RANGE_AF ? _i < RANGE_AF : _i > RANGE_AF; 0 <= RANGE_AF ? _i++ : _i--){ _results.push(_i); }
        return _results;
      }).apply(this).reduce((function(_this) {
        return function(a, b) {
          if (Math.abs(_this.of(repetition, a) - of_) < Math.abs(_this.of(repetition, b) - of_)) {
            return a;
          } else {
            return b;
          }
        };
      })(this)));
    };

    return OFM;

  })();

  sum = function(values) {
    return values.reduce(function(a, b) {
      return a + b;
    });
  };

  mse = function(y, points) {
    var i;
    return sum((function() {
      var _i, _ref, _results;
      _results = [];
      for (i = _i = 0, _ref = points.length; 0 <= _ref ? _i < _ref : _i > _ref; i = 0 <= _ref ? ++_i : --_i) {
        _results.push(Math.pow(y(points[i][0]) - points[i][1], 2));
      }
      return _results;
    })()) / points.length;
  };

  exponentialRegression = function(points) {
    var X, Y, a, b, i, logY, n, p, sqSumX, sqX, sumLogY, sumSqX, sumX, sumXLogY, _y;
    n = points.length;
    X = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[0]);
      }
      return _results;
    })();
    Y = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[1]);
      }
      return _results;
    })();
    logY = Y.map(Math.log);
    sqX = X.map(function(v) {
      return v * v;
    });
    sumLogY = sum(logY);
    sumSqX = sum(sqX);
    sumX = sum(X);
    sumXLogY = sum((function() {
      var _i, _results;
      _results = [];
      for (i = _i = 0; 0 <= n ? _i < n : _i > n; i = 0 <= n ? ++_i : --_i) {
        _results.push(X[i] * logY[i]);
      }
      return _results;
    })());
    sqSumX = sumX * sumX;
    a = (sumLogY * sumSqX - sumX * sumXLogY) / (n * sumSqX - sqSumX);
    b = (n * sumXLogY - sumX * sumLogY) / (n * sumSqX - sqSumX);
    _y = function(x) {
      return Math.exp(a) * Math.exp(b * x);
    };
    return {
      y: _y,
      x: function(y) {
        return (-a + Math.log(y)) / b;
      },
      a: Math.exp(a),
      b: b,
      mse: function() {
        return mse(_y, points);
      }
    };
  };

  linearRegression = function(points) {
    var X, Y, a, b, i, n, p, sqSumX, sqX, sumSqX, sumX, sumXY, sumY;
    n = points.length;
    X = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[0]);
      }
      return _results;
    })();
    Y = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[1]);
      }
      return _results;
    })();
    sqX = X.map(function(v) {
      return v * v;
    });
    sumY = sum(Y);
    sumSqX = sum(sqX);
    sumX = sum(X);
    sumXY = sum((function() {
      var _i, _results;
      _results = [];
      for (i = _i = 0; 0 <= n ? _i < n : _i > n; i = 0 <= n ? ++_i : --_i) {
        _results.push(X[i] * Y[i]);
      }
      return _results;
    })());
    sqSumX = sumX * sumX;
    a = (sumY * sumSqX - sumX * sumXY) / (n * sumSqX - sqSumX);
    b = (n * sumXY - sumX * sumY) / (n * sumSqX - sqSumX);
    return {
      y: function(x) {
        return a + b * x;
      },
      x: function(y) {
        return (y - a) / b;
      },
      a: a,
      b: b
    };
  };

  powerLawModel = function(a, b) {
    return {
      y: function(x) {
        return a * Math.pow(x, b);
      },
      x: function(y) {
        return Math.pow(y / a, 1 / b);
      },
      a: a,
      b: b
    };
  };

  powerLawRegression = function(points) {
    var X, Y, a, b, i, logX, logY, model, n, p, sqSumLogX, sumLogX, sumLogXLogY, sumLogY, sumSqLogX;
    n = points.length;
    X = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[0]);
      }
      return _results;
    })();
    Y = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[1]);
      }
      return _results;
    })();
    logX = X.map(Math.log);
    logY = Y.map(Math.log);
    sumLogXLogY = sum((function() {
      var _i, _results;
      _results = [];
      for (i = _i = 0; 0 <= n ? _i < n : _i > n; i = 0 <= n ? ++_i : --_i) {
        _results.push(logX[i] * logY[i]);
      }
      return _results;
    })());
    sumLogX = sum(logX);
    sumLogY = sum(logY);
    sumSqLogX = sum(logX.map(function(v) {
      return v * v;
    }));
    sqSumLogX = sumLogX * sumLogX;
    b = (n * sumLogXLogY - sumLogX * sumLogY) / (n * sumSqLogX - sqSumLogX);
    a = (sumLogY - b * sumLogX) / n;
    model = powerLawModel(Math.exp(a), b);
    model.mse = function() {
      return mse(_y, points);
    };
    return model;
  };

  fixedPointPowerLawRegression = function(points, fixedPoint) {

    /*
      given fixed point: (p, q)
      the model would be: y = q(x/p)^b
      minimize its residual: ln(y) = b * ln(x/p) + ln(q)
        y_i' = b * x_i'
          x_i' = ln(x_i/p)
          y_i' = ln(y_i) - ln(q)
     */
    var X, Y, b, i, logQ, model, n, p, point, q;
    n = points.length;
    p = fixedPoint[0];
    q = fixedPoint[1];
    logQ = Math.log(q);
    X = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        point = points[_i];
        _results.push(Math.log(point[0] / p));
      }
      return _results;
    })();
    Y = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        point = points[_i];
        _results.push(Math.log(point[1]) - logQ);
      }
      return _results;
    })();
    b = linearRegressionThroughOrigin((function() {
      var _i, _results;
      _results = [];
      for (i = _i = 0; 0 <= n ? _i < n : _i > n; i = 0 <= n ? ++_i : --_i) {
        _results.push([X[i], Y[i]]);
      }
      return _results;
    })()).b;
    model = powerLawModel(q / Math.pow(p, b), b);
    return model;
  };

  linearRegressionThroughOrigin = function(points) {
    var X, Y, b, i, n, p, sumSqX, sumXY;
    n = points.length;
    X = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[0]);
      }
      return _results;
    })();
    Y = (function() {
      var _i, _len, _results;
      _results = [];
      for (_i = 0, _len = points.length; _i < _len; _i++) {
        p = points[_i];
        _results.push(p[1]);
      }
      return _results;
    })();
    sumXY = sum((function() {
      var _i, _results;
      _results = [];
      for (i = _i = 0; 0 <= n ? _i < n : _i > n; i = 0 <= n ? ++_i : --_i) {
        _results.push(X[i] * Y[i]);
      }
      return _results;
    })());
    sumSqX = sum(X.map(function(v) {
      return v * v;
    }));
    b = sumXY / sumSqX;
    return {
      y: function(x) {
        return b * x;
      },
      x: function(y) {
        return y / b;
      },
      b: b
    };
  };

  if (typeof module !== "undefined" && module !== null) {
    module.exports = {
      SM: this.SM,
      _test: {
        exponentialRegression: exponentialRegression,
        linearRegression: linearRegression,
        powerLawRegression: powerLawRegression,
        fixedPointPowerLawRegression: fixedPointPowerLawRegression,
        linearRegressionThroughOrigin: linearRegressionThroughOrigin
      }
    };
  }

  main = (function(_this) {
    return function() {
      var data, fs, gotoEnterance, mode, sm;
      fs = require('fs');
      console.log('(a)add, (n)next, (N)next advanceably, (s)save, (l)load, (e)exit');
      mode = ['entrance'];
      data = null;
      sm = new _this.SM();
      gotoEnterance = function() {
        mode = ['entrance'];
        data = null;
        return process.stdout.write('sm> ');
      };
      return process.stdin.on('readable', function() {
        var buf, chunk, g, input, item;
        chunk = process.stdin.read();
        input = chunk != null ? chunk.toString().trim() : void 0;
        switch (mode[0]) {
          case 'entrance':
            switch (input) {
              case 'a':
              case 'add':
                mode = ['add'];
                break;
              case 'n':
              case 'next':
                mode = ['next'];
                break;
              case 'N':
              case 'Next':
                mode = ['next', '_adv'];
                break;
              case 's':
              case 'save':
                mode = ['save'];
                break;
              case 'l':
              case 'load':
                mode = ['load'];
                break;
              case 'e':
              case 'exit':
                mode = ['exit'];
                break;
              case 'eval':
                mode = ['eval'];
                break;
              case 'list':
                mode = ['list'];
                break;
              default:
                gotoEnterance();
            }
        }
        switch (mode[0]) {
          case 'add':
            switch (mode[1]) {
              case void 0:
                data = {
                  front: null,
                  back: null
                };
                console.log('Enter the front of the new card:');
                return mode[1] = 'front';
              case 'front':
                data.front = input;
                console.log('Enter the back of the new card:');
                return mode[1] = 'back';
              case 'back':
                data.back = input;
                sm.addItem(data);
                return gotoEnterance();
            }
            break;
          case 'next':
            switch (mode[1]) {
              case void 0:
              case '_adv':
                data = sm.nextItem(mode[1] === '_adv');
                if (data == null) {
                  console.log("There is no card" + (sm.q.length > 0 ? ' that can be shown now. The next card is due at \"' + sm.q[0].dueDate.toLocaleString() + '\".' : '.'));
                  return gotoEnterance();
                } else {
                  console.log("How much do you remember [" + data.value.front + "]:");
                  return mode[1] = 'review';
                }
                break;
              case 'review':
                g = parseInt(input);
                if ((0 <= g && g <= 5)) {
                  sm.answer(g, data);
                  console.log("The answer was [" + data.value.back + "].");
                  return gotoEnterance();
                } else if (input === 'D') {
                  sm.discard(data);
                  return gotoEnterance();
                } else {
                  return console.log('The value should be from \'0\' (bad) to \'5\' (good). Otherwise \'D\' to discard:');
                }
            }
            break;
          case 'save':
            if (mode[1] == null) {
              console.log('enter file name to save configuration. (default name is [data.json]):');
              return mode[1] = true;
            } else {
              if (input === '') {
                input = 'data.json';
              }
              fs.writeFileSync(input, JSON.stringify(sm.data()));
              return gotoEnterance();
            }
            break;
          case 'load':
            if (mode[1] == null) {
              console.log('enter file name to load configuration. (default name is [data.json]):');
              return mode[1] = true;
            } else {
              if (input === '') {
                input = 'data.json';
              }
              buf = fs.readFileSync(input);
              data = JSON.parse(buf.toString());
              sm = _this.SM.load(data);
              return gotoEnterance();
            }
            break;
          case 'exit':
            if (mode[1] == null) {
              process.stdin.pause();
              return mode[1] = 'paused';
            }
            break;
          case 'eval':
            if (mode[1] == null) {
              return mode[1] = true;
            } else {
              console.log(eval(input));
              return gotoEnterance();
            }
            break;
          case 'list':
            console.log((function() {
              var _i, _len, _ref, _results;
              _ref = sm.q;
              _results = [];
              for (_i = 0, _len = _ref.length; _i < _len; _i++) {
                item = _ref[_i];
                _results.push(JSON.stringify(item.data()));
              }
              return _results;
            })());
            return gotoEnterance();
        }
      });
    };
  })(this);

  try {
    if ((typeof module !== "undefined" && module !== null) && (typeof require !== "undefined" && require !== null ? require.main : void 0) === module) {
      main();
    }
  } catch (_error) {
    error = _error;
    console.error("An error occured: " + error);
  }

}).call(this);