"use strict";


// A number of log probability density functions (PDF). Naming and parameterization
// should match R's, except for that all functions reside in an ld object (
// as in "log density"), so to get a normal log density you would write
// ld.norm(...).
// Most of the code below is directly taken from the great Jstat project
// (https://github.com/jstat/) which includes PDF for many common probability
// distributions. What I have done is only to convert these to log PDFs.

/*
Original work Copyright (c) 2013 jStat
Modified work Copyright (c) 2015 Rasmus Bååth 

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.

*/


// This boiler plate code here is taken from:
// https://github.com/umdjs/umd/blob/master/templates/returnExports.js
// It should make shure that module can be imported both in the browser,
// Node, and by using the Asynchronous Module Definition standard.
// If this module is loaded in the browser it will created the global
// object ld .
(function (root, factory) {
    if (typeof define === 'function' && define.amd) {
        // AMD. Register as an anonymous module.
        define([], factory);
    } else if (typeof module === 'object' && module.exports) {
        // Node. Does not work with strict CommonJS, but
        // only CommonJS-like environments that support module.exports,
        // like Node.
        module.exports = factory();
    } else {
        // Browser globals (root is window)
        root.ld = factory();
  }
}(this, function() {
  // Object to hold the functions to be exported.
  var ld  = {};
  
  ////////// Helper functions //////////
  //////////////////////////////////////
  
  var lgamma = function(x) {
    var j = 0;
    var cof = [
      76.18009172947146, -86.50532032941677, 24.01409824083091,
      -1.231739572450155, 0.1208650973866179e-2, -0.5395239384953e-5
    ];
    var ser = 1.000000000190015;
    var xx, y, tmp;
    tmp = (y = xx = x) + 5.5;
    tmp -= (xx + 0.5) * log(tmp);
    for (; j < 6; j++)
      ser += cof[j] / ++y;
    return log(2.5066282746310005 * ser / xx) - tmp;
  };
  ld.lgamma = lgamma;
  
  var lfactorial = function(n) {
    return n < 0 ? NaN : lgamma(n + 1);
  };
  ld.lfactorial = lfactorial;
  
  var lchoose = function(n, k){
    return lfactorial(n) - lfactorial(k) - lfactorial(n - k);
  };
  ld.lchoose = lchoose;
  
  var lbeta = function(a, b) {
    return lgamma(a) + lgamma(b) - lgamma(a + b);
  };
  ld.lbeta = lbeta;
  
  var log  = Math.log;
  var exp  = Math.exp;
  var abs  = Math.abs;
  var pow  = Math.pow;
  var sqrt = Math.sqrt;
  var pi   = Math.PI;
  
  ////////// Continous distributions //////////
  /////////////////////////////////////////////
  
  ld.beta = function(x, shape1, shape2) {
    if (x > 1 || x < 0) {
        return -Infinity;
    }
    if(shape1 === 1 && shape2 === 1) {
      return 0;
    } else {
      return (shape1 - 1) * log(x) + (shape2 - 1) * log(1 - x) - lbeta(shape1, shape2);  
    }
  };
  
  ld.cauchy = function(x, location, scale) {
    return log(scale) - log(pow(x - location, 2) + pow(scale, 2))  - log(pi);
  };
  
  ld.norm = function(x, mean, sd) {
      return -0.5 * log(2 * pi) -log(sd) - pow(x - mean, 2) / (2 * sd * sd);
  };

  // A bivariate Normal distribution parameterized by arrays of two means and SDs, and 
  // the correlation.
  ld.bivarnorm = function(x, mean, sd, corr) {
    var z = pow(x[0] - mean[0], 2) / pow(sd[0], 2) +
            pow(x[1] - mean[1], 2) / pow(sd[1], 2) - 
            (2 * corr * (x[0] - mean[0]) * (x[1] - mean[1])) / (sd[0] * sd[1]);
    var normalizing_factor = -( log(2) + log(pi) + log(sd[0]) + log(sd[1]) + 
                                0.5 * log(1 - pow(corr, 2)) ); 
    var bivar_log_dens = normalizing_factor - z / (2 * (1 - pow(corr, 2) ) ); 
    return bivar_log_dens;
  };
  

  ld.laplace = function(x, location, scale) {
    return (-abs(x - location)/scale) - log(2 * scale);
  };
  
  ld.dexp = ld.laplace;
  
  ld.gamma = function(x, shape, rate) {
    var scale = 1 / rate;
    if (x < 0) {
      return -Infinity;
    }
    if((x === 0 && shape === 1) ) {
      return -log(scale);
    } else {
      return (shape - 1) * log(x) - x / scale - lgamma(shape) - shape * log(scale);
    }
  };
  
  ld.invgamma = function(x, shape, scale) {
      if (x <= 0) {
        return -Infinity;
      }
      return -(shape + 1) * log(x) - scale / x - lgamma(shape) + shape * log(scale);
    };
  
  ld.lnorm =  function(x, meanlog, sdlog) {
    if (x <= 0) {
      return -Infinity;
    }
    return -log(x) - 0.5 * log(2 * pi) - log(sdlog) - 
            pow(log(x) - meanlog, 2) / (2 * sdlog * sdlog);
  };
  
  ld.pareto = function(x, scale, shape) {
    if (x < scale) {
      return -Infinity;
    }
    return log(shape) + shape * log(scale) - (shape + 1) * log(x);
  };
  
  ld.t  =  function(x, location, scale, df) {
    df = df > 1e100 ? 1e100 : df;
    return lgamma((df + 1)/2) - lgamma(df/2) - log(sqrt(pi * df) * scale) +
           log(pow(1 + (1/df) * pow((x - location)/scale, 2), -(df + 1)/2));
  };
  
  // This is a direct javascript translation of the R code used to evaluate
  // the log density of a weibull distribution: 
  // https://github.com/wch/r-source/blob/b156e3a711967f58131e23c1b1dc1ea90e2f0c43/src/nmath/dweibull.c
  ld.weibull = function(x, shape, scale) {
    if (x < 0) return -Infinity;
    if(x === 0 && shape < 1) return Infinity;
    var tmp1 = pow(x / scale, shape - 1);
    var tmp2 = tmp1 * (x / scale);
	  return -tmp2 + log(shape * tmp1 / scale);
  };
  
  // This is a direct javascript translation of the R code used to evaluate
  // the log density of a logistic distribution: 
  // https://github.com/wch/r-source/blob/b156e3a711967f58131e23c1b1dc1ea90e2f0c43/src/nmath/dlogis.c
  ld.logis = function(x, location, scale) {
    x = abs((x - location) / scale);
    var e = exp(-x);
    var f = 1.0 + e;
    return -(x + log(scale * f * f));    
  };

  ld.dirichlet = function(x, alpha) {
    var sum_alpha = 0;
    var sum_lgamma_alpha = 0;
    var sum_alpha_sub_1_log_x = 0;
    var n = alpha.length;
    for(var i = 0; i < n; i++) {
      sum_alpha += alpha[i];
      sum_lgamma_alpha += lgamma(alpha[i]);
      sum_alpha_sub_1_log_x += (alpha[i] - 1) * log(x[i]);
    }
    return lgamma(sum_alpha) - sum_lgamma_alpha + sum_alpha_sub_1_log_x;
  };
   
    
  ld.exp = function(x, rate) {
      return x < 0 ? -Infinity : log(rate) -rate * x;
  };
  
  ld.unif = function(x, min, max) {
      return (x < min || x > max) ? -Infinity : log(1 / (max - min));
  };
  
  ////////// Discrete distributions //////////
  ////////////////////////////////////////////
  
  ld.bern = function(x, prob) {
      return !(x === 0 || x === 1) ? -Infinity : log(x * prob + (1 - x) * (1 - prob));
  };
  
  ld.cat = function(x, probs) {
    if(x < 1 || x > probs.length) {
      return -Infinity;
    } else {
      return log( probs[x - 1] );
    }
  };
  
  ld.binom = function(x, size, prob) {
    if(x > size || x < 0) {
      return -Infinity;
    }
    if(prob === 0 || prob === 1) {
      return (size * prob) === x ? 0 : -Infinity;
    }
    return lchoose(size, x) + x * log(prob) + (size - x) * log(1 - prob);
  };
  
  var multinom = function(x, probs) {
    var n = x.length;
    var size = 0;
    var tmp_term = 0;
    for(var i = 0; i < n; i++) {
      if(probs[i] === 0) {
        if(x[i] !== 0) {
          return -Infinity;  
        }
      } else {
        size += x[i];
        tmp_term += x[i] * log(probs[i]) - lgamma(x[i] + 1);
      }
    }
    return lgamma(size + 1) + tmp_term ;
  };
  
  ld.nbinom = function(x, size, prob) {
    if(x < 0) {
      return -Infinity;
    }
    return lchoose(x + size - 1, size - 1) + x * log(1 - prob) + size * log(prob);
  };
  
  ld.hyper = function(x, m, n, k) {
    if(x < 0 || x > k) {
      return -Infinity;
    } else {
    return lchoose(m, x) + lchoose(n, k-x) - lchoose(m+n, k);
    }
  };
  
  ld.pois = function(x, lambda) {
      return x < 0 ? -Infinity : log(lambda) * x - lambda - lfactorial(x);
  };
  
  return ld;
}));