/******************************************************************************\
*                                                                              *
*    SimpleCUDD library (www.cs.kuleuven.be/~theo/tools/simplecudd.html)       *
*  SimpleCUDD was developed at Katholieke Universiteit Leuven(www.kuleuven.be) *
*                                                                              *
*  Copyright Katholieke Universiteit Leuven 2008, 2009, 2010                   *
*                                                                              *
*  Author: Bernd Gutmann                                                       *
*  File: problogmath.c                                                         *
*  $Date:: 2010-12-17 12:21:58 +0100 (Fri, 17 Dec 2010)                      $ *
*  $Revision:: 5159                                                          $ *
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#include "problogmath.h"
#include "general.h"

double sigmoid(double x, double slope) {
  return 1.0 / (1.0 + exp(-x * slope));
}

// This function calculates the accumulated density of the normal distribution
// For details see G. Marsaglia, Evaluating the Normal Distribution, Journal of Statistical Software, 2004:11(4).
double Phi(double x)  {
  double s=x;
  double t=0.0;
  double b=x;
  double q=x*x;
  double i=1;

  // if the value is too small or too big, return
  // 0/1 to avoid long computations
  if (x < -10.0) {
    return 0.0;
  }

  if (x > 10.0) {
    return 1.0;
  }

  // t is the value from last iteration
  // s is the value from the current iteration
  // iterate until they are equal
  while(fabs(s-t) >= DBL_MIN) {
    t=s;
    i+=2;
    b*=q/i;
    s+=b;
  }

  return 0.5+s*exp(-0.5*q-0.91893853320467274178);
}

// integrates the normal distribution over [low,high]
double cumulative_normal(double low, double high, double mu, double sigma) {
  return Phi((high-mu)/sigma) - Phi((low-mu)/sigma);
}

// integrates the normal distribution over [-oo,high]
double cumulative_normal_upper(double high, double mu, double sigma) {
  return Phi((high-mu)/sigma);
}


// evaluates the density of the normal distribution
double normal(double x, double mu,double sigma) {
  double inner=(x-mu)/sigma;
  double denom=sigma*sqrt(2*3.14159265358979323846);
  return exp(-inner*inner/2)/denom;
}

double cumulative_normal_dmu(double low, double high,double mu,double sigma) {
  return normal(low,mu,sigma) - normal(high,mu,sigma);
}

double cumulative_normal_upper_dmu(double high,double mu,double sigma) {
  return  - normal(high,mu,sigma);
}


double cumulative_normal_dsigma(double low, double high,double mu,double sigma) {
  return (((mu-high)*normal(high,mu,sigma) - (mu-low)*normal(low,mu,sigma))/sigma);
}

double cumulative_normal_upper_dsigma(double high,double mu,double sigma) {
  return (mu-high)*normal(high,mu,sigma);
}


// this function parses two strings "$a;$b" and "???_???l$ch$d" where $a-$d are (real) numbers
// it is used to parse in the parameters of continues variables from the input file
density_integral parse_density_integral_string(char *input, char *variablename) {
  density_integral result;
  double sigma;
  int i;
  char garbage[64], s1[64],s2[64],s3[64],s4[64];

  if(sscanf(input, "%64[^;];%64[^;]", s1,s2) != 2) {
    fprintf(stderr, "Error at parsing the string %s in the function parse_density_integral_string\n",input);
    fprintf(stderr, "The string should contain 2 fields seperated by ; characters.\n");
    exit(EXIT_FAILURE);
  }

  if (!getRealNumber(s1, &result.mu)) {
    fprintf(stderr, "Error at parsing the string %s in the function parse_density_integral_string\n",input);
    fprintf(stderr, "%s is not a number\n",s1);
    exit(EXIT_FAILURE);
  }

  if (!getRealNumber(s2, &sigma) || sigma<=0.0) {
    fprintf(stderr, "Error at parsing the string %s in the function parse_density_integral_string\n",input);
    fprintf(stderr, "%s is not a number\n",s2);
    exit(EXIT_FAILURE);
  }
  result.log_sigma=log(sigma);

/*  if (result.sigma<=0) { */
/*     fprintf(stderr, "Error at parsing the string %s in the function parse_density_integral_string",input); */
/*     fprintf(stderr, "The value for sigma has to be larger than 0.\n"); */

/*     exit(EXIT_FAILURE); */
/*   } */

  if (sscanf(variablename,"%64[^lh]l%64[^lh]h%64[^lh]",garbage,s3,s4) != 3) {
    fprintf(stderr, "Error at parsing the string %s in the function parse_density_integral_string\n",variablename);
    fprintf(stderr, "The string should contain 2 fields seperated by ; characters.\n");
    exit(EXIT_FAILURE);
  }

  //  replace the d by . in s1 and s2
  for(i=0; s3[i]!='\0' ; i++) {
    if (s3[i]=='d') {
      s3[i]='.';
    }
    if (s3[i]=='m') {
      s3[i]='-';
    }
  }
  for(i=0; s4[i]!='\0' ; i++) {
    if (s4[i]=='d') {
      s4[i]='.';
    }
    if (s4[i]=='m') {
      s4[i]='-';
    }
  }

  if (!getRealNumber(s3, &result.low)) {
    fprintf(stderr, "Error at parsing the string %s in the function parse_density_integral_string\n",input);
    fprintf(stderr, "%s is not a number\n",s1);
    exit(EXIT_FAILURE);
  }

 if (!getRealNumber(s4, &result.high)) {
    fprintf(stderr, "Error ar parsing the string %s in the function parse_density_integral_string\n",input);
    fprintf(stderr, "%s is not a number\n",s1);
    exit(EXIT_FAILURE);
  }

  
  if (result.low>result.high) {
    fprintf(stderr, "Error ar parsing the string %s in the function parse_density_integral_string\n",input);
    fprintf(stderr, "The value for low has to be larger than then value for high.\n");
    fprintf(stderr, " was [%f, %f]\n",result.low, result.high);
    fprintf(stderr, " input %s \n",input);
    fprintf(stderr, " variablename %s \n",variablename);
 
    exit(EXIT_FAILURE);
  }

  
  return result;
}
