logistic-function

#!/bin/bash

#########################################################
# The logistic function in GNU bash and bc
#########################################################
# Author: cgomesu
# Repo: https://github.com/cgomesu/bash-logistic-function
#########################################################


defaults () {
  if [[ -z $DEBUG ]]; then DEBUG='false'; fi
  if [[ -z "$x" || -z "$m" || -z "$L" || -z "$k" ]]; then err 'Missing mandatory parameters.'; fi
  if [[ -z $s ]]; then s=20; fi
  if [[ -z $S ]]; then S=2; fi
  if [[ $S -gt $s ]]; then err 'Option -S must be lower or equal to -s.'; fi
}

err () {
  if [[ $DEBUG = 'true' && -n "$1" ]]; then 
    echo '[logistic] There was an error: '"$1"
  fi; exit 1
}

############################################################
# The logistic function, f(x), has the following parameters:
# 
# x: value of a variable X
# m = x0: midpoint of X
# L: max value of f(x)
# k: growth rate
# 
# And is given by the equation
#
# f(x) = L / {1 + e^[-k * (x - m)]},
#
# in which 'e' is Euler's constant.
#
# MORE INFO: https://en.wikipedia.org/wiki/logistic_function
############################################################
logistic () {
  local EQUATION; local OUTPUT
  EQUATION="output=($L)/(1+e(-($k)*(($x)-($m))))"
  if ! OUTPUT=$(echo "scale=$s;$EQUATION;scale=$S;output/1" | bc -lq 2>/dev/null); then 
    err 'Unable to eval the equation.'
  fi
  echo "$OUTPUT"; return 0
}

usage () {
  printf "\nUsage:\n  %s -x VALUE -m VALUE -L VALUE -k VALUE [OPTIONS]\n" "$0"
  printf "\n  Logistic function:\n"
  echo '    -x  real*  value of a variable X'
  echo '    -m  real*  m = x0: Midpoint of X'
  echo '    -L  real*  max value of f(x)'
  echo '    -k  real*  growth rate'
  printf "\n  * acceptable inputs:\n"
  echo '    integers:       ..., -1, 0, 1, ...'
  echo '    fractions:      ..., -1/2, -.25, 0, .25, 1/2, ...'
  echo '    positive exps:  ..., "-(2^2)", 0, 2^2, ...'
  echo '    natural exps:   "e(VALUE)"'
  echo '    natural logs:   "l(VALUE)"'
  echo '    square roots:   "sqrt(VALUE)"'
  echo '    sines:          "s(VALUE)"'
  echo '    cosines:        "c(VALUE)"'
  echo '    arctangents:    "a(VALUE)"'
  printf "\n  Options:\n"
  echo '    -d       enable debug messages.'
  echo '    -h       show this help message.'
  echo '    -s  int  # of decimals to compute f(x). default: 20.'
  echo '    -S  int  # of decimals in the output. default: 2.'
  printf "\n  Example:\n"
  echo '    logistic-function -x .5 -m 0 -L 1 -k 1 -s 10 -S 4'
  printf "\nAuthor: cgomesu\nRepo: https://github.com/cgomesu/bash-logistic-function\n"
}

validate_integer () {
  if [[ -z "$1" || ! "$1" =~ ^[0-9]+$ ]]; then return 1; else return 0; fi
}

validate_parameter () {
  local REGEX_VALUE; local REGEX_MATLIB
  REGEX_VALUE="\-{0,1}([0-9]+|[0-9]+(\.|\/\-{0,1}|\^)[0-9]+|\.[0-9]+)"
  REGEX_MATLIB="\-{0,1}(e|l|sqrt|s|c|a)\($REGEX_VALUE\)"
  if [[ -z "$1" || ! "$1" =~ ^($REGEX_VALUE|$REGEX_MATLIB)$ ]]; then
    return 1
  else
    return 0
  fi
}


while getopts 'hdx:m:L:k:s:S:' OPT; do
  case ${OPT} in
    h)
      usage; exit 0
      ;;
    d)
      DEBUG='true'
      ;;
    x)
      x="$OPTARG"
      if ! validate_parameter "$x"; then err 'Invalid value for -x.'; fi
      ;;
    m)
      m="$OPTARG"
      if ! validate_parameter "$m"; then err 'Invalid value for -m.'; fi
      ;;
    L)
      L="$OPTARG"
      if ! validate_parameter "$L"; then err 'Invalid value for -L.'; fi
      ;;
    k)
      k="$OPTARG"
      if ! validate_parameter "$k"; then err 'Invalid value for -k.'; fi
      ;;
    s)
      s="$OPTARG"
      if ! validate_integer "$s"; then err 'Invalid value for -s.'; fi
      ;;
    S)
      S="$OPTARG"
      if ! validate_integer "$S"; then err 'Invalid value for -S.'; fi
      ;;
    \?)
      printf "\n!! INVALID OPTION !!\n"; usage; exit 1
      ;;
  esac
done

if ! command 2>/dev/null; then
  err 'Running command returns an error.'
elif [[ -z $(command -v bc 2>/dev/null) ]]; then
  err 'The GNU basic calculator (bc) is not installed or cannot be found in this users PATH.' 
fi

defaults
logistic

exit 0