CalcEntropyScriptsNetLogo.nlogo

;; just an experiment to calculate entropy from belief nets

extensions [
  matrix
]


turtles-own [
  myBeliefMatrix
  myIdentity
]

to go
  ask turtles [
    forward 1
  ]
end

to setup
  create-turtles 5
  createMatrices
  addDifferences
end

to createMatrices
  ask turtles [
    set myBeliefMatrix matrix:make-identity 9
    set myIdentity 1
  ]
end

to addDifferences
  ask turtles [
    repeat 9 [
      let i random 9
      let j random 9
      matrix:set myBeliefMatrix i j 1
    ]
  ]


end



to-report matrixAsVector [mat]
  let dims matrix:dimensions mat
  let rows item 0 dims
  let cols item 1 dims
  let vec []

  let i 0
  let j 0

  while [i < rows] [
    while [j < cols] [
      set vec lput matrix:get mat i j vec
      set j j + 1
    ]
    set j 0
    set i i + 1
  ]

  report vec
end


to-report totalGroupMatrix [group]
  let grouplist []
  ask turtles with [myIdentity = group][
    set grouplist lput matrixAsVector myBeliefMatrix grouplist
  ]
  report grouplist
end


to-report calculateBeliefEntropyBtwnGroupMembers [group]
  ;; basically, this function calculates the entropy for matrices drawn from a population
  ;; in this way it counts probabilities DOWN the columns of the matrix, rather than
  ;; across the row like a printing machine.
  ;; as such, be careful, many of the other functions here are not for calculating entropy
  ;; like that, rather they're calculating entropy within an agent, not within a population of
  ;; agents
  ;; ok, should I be removing the 0 items from the group? Or should I allow for calculations of
  ;; non-belief as well?
  let entropy 0
  let groupmat totalGroupMatrix group

  ;; now just for convenience sake (because I already wrote the other functions to calculate
  ;; things for matrices, conver that list of lists to a matrix
  let totalgroupmat matrix:from-row-list totalGroupMatrix group

  ;; now get a list of possible outcomes, i.e. the list of unique values
  ;; found in the matrix
  let poss_outcomes possible_outcomes_list matrixAsVector totalgroupmat
  set poss_outcomes remove 0 poss_outcomes

  let rows item 0 matrix:dimensions totalgroupmat
  let cols item 1 matrix:dimensions totalgroupmat

  let l length poss_outcomes
  let cnt 0
  let row_cnt 0
  let col_cnt 0
  let total_overall 0
  let instances_overall 0

  let probs_list_4_group []

  ;; now iterate through all the target probabilities
  while [cnt < l] [
    ;; and iterate through every row
    let tar item cnt poss_outcomes
    let instances 0
    let total rows
    while [col_cnt < cols] [
      ;; and iterate through every column
      while [row_cnt < rows][
        if matrix:get totalgroupmat row_cnt col_cnt = tar [
          set instances instances + 1
        ]
        set row_cnt row_cnt + 1
        ;; this is commented because its now set to rows
        ;;set total total + 1
      ]
      set col_cnt col_cnt + 1
      set row_cnt 0
      set probs_list_4_group lput (instances / total) probs_list_4_group
      set instances 0
    ]
    set cnt cnt + 1
  ]

  ;; what results is probs_list_4_group holding the probabilities that we need
  ;; in order to calculate the entropy now

  let l2 length probs_list_4_group
  let cnt2 0

  while [cnt2 < l2][
    let tarProb item cnt2 probs_list_4_group
    ifelse tarProb = 0[
      ;; do nothing, you can't calculate the probability of a 0 item
      set cnt2 cnt2 + 1
    ][
    set entropy (entropy + (tarProb * bounces_base_2 tarProb))
    set cnt2 cnt2 + 1
    ]
  ]

  report entropy
end

to-report avgBeliefMatrixEntropy
  let avgs []
  ask turtles [
    set avgs lput beliefMatrixEntropy myBeliefMatrix avgs
  ]
  ifelse empty? avgs [
    report 0][
    report mean avgs]
end

to-report beliefMatrixEntropy [mat]
  let h 0
  let probList probs_within_matrix myBeliefMatrix
  let l length probList
  let cnt 0

  while [cnt < l][
    let tarProb item cnt probList
    set h (h + (tarProb * bounces_base_2 tarProb))
    set cnt cnt + 1
  ]

  report h
end

to-report num_possible_outcomes [list-a]
  ;; report a list of list-a where all duplicates have been removed
  report length remove-duplicates list-a
end

to-report possible_outcomes_list [list-a]
  ;; reports an unsorted list of outcomes for a list.
  report remove-duplicates list-a
end

;; to calculate the number of bounces we calculate it as
;; the log of number of outcomes, which is 1/prob of outcome.

to-report bounces_base_2 [outcomes]
  report log (1 / outcomes) 2
end

to-report bounces_base_10 [outcomes]
  report log (1 / outcomes) 10
end

to-report bounces_base_e [outcomes]
  report log (1 / outcomes) e
end


to-report probs_within_matrix [gmat]
  ;; report a list of probabilities that all values exist within a given matrix
  let probs []
  ;; first get the size of the matrix
  let rows item 0 matrix:dimensions gmat
  let cols item 1 matrix:dimensions gmat

  ;; now get a list of possible outcomes, i.e. the list of unique values
  ;; found in the matrix
  let poss_outcomes possible_outcomes_list matrixAsVector gmat

  let cnt 0
  let lim length poss_outcomes
  ;; now loop through and record the probabilities of all of target_value in matrix
  while [cnt < lim] [
    let tar item cnt poss_outcomes
    set probs lput calculated_probability_matrix tar gmat probs
    set cnt cnt + 1
  ]
  ;; report the probabilities
  report probs
end


to-report calculated_probability_matrix [target_value matrix]
  ;; calculate the probability that you will see target_value in matrix

  let rows item 0 matrix:dimensions matrix
  let cols item 1 matrix:dimensions matrix

  let instances 0
  let total 0

  let i 0
  let j 0

  while [i < rows] [
    while [j < cols] [
      ;; now set directions for iterator
      if matrix:get matrix i j = target_value [
        set instances instances + 1
      ]
      set j j + 1
      set total total + 1
    ]
    set j 0
    set i i + 1
  ]

  report instances / total

end




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Setup
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BUTTON
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Show mean Entropy
show avgBeliefMatrixEntropy
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@#$#@#$#@
## WHAT IS IT?

(a general understanding of what the model is trying to show or explain)

## HOW IT WORKS

(what rules the agents use to create the overall behavior of the model)

## HOW TO USE IT

(how to use the model, including a description of each of the items in the Interface tab)

## THINGS TO NOTICE

(suggested things for the user to notice while running the model)

## THINGS TO TRY

(suggested things for the user to try to do (move sliders, switches, etc.) with the model)

## EXTENDING THE MODEL

(suggested things to add or change in the Code tab to make the model more complicated, detailed, accurate, etc.)

## NETLOGO FEATURES

(interesting or unusual features of NetLogo that the model uses, particularly in the Code tab; or where workarounds were needed for missing features)

## RELATED MODELS

(models in the NetLogo Models Library and elsewhere which are of related interest)

## CREDITS AND REFERENCES

(a reference to the model's URL on the web if it has one, as well as any other necessary credits, citations, and links)
@#$#@#$#@
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@#$#@#$#@
NetLogo 5.3.1
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