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-;; Finite probability distributions
-
-;; by Konrad Hinsen
-;; last updated January 8, 2010
-
-;; Copyright (c) Konrad Hinsen, 2009-2010. All rights reserved.  The use
-;; and distribution terms for this software are covered by the Eclipse
-;; Public License 1.0 (http://opensource.org/licenses/eclipse-1.0.php)
-;; which can be found in the file epl-v10.html at the root of this
-;; distribution.  By using this software in any fashion, you are
-;; agreeing to be bound by the terms of this license.  You must not
-;; remove this notice, or any other, from this software.
-
-(ns
-  #^{:author "Konrad Hinsen"
-     :doc "Finite probability distributions
-           This library defines a monad for combining finite probability
-           distributions."}
-  clojure.contrib.probabilities.finite-distributions
-  (:use [clojure.contrib.monads
-	 :only (defmonad domonad with-monad maybe-t m-lift m-chain)]
-	 [clojure.contrib.def :only (defvar)]))
-
-; The probability distribution monad. It is limited to finite probability
-; distributions (e.g. there is a finite number of possible value), which
-; are represented as maps from values to probabilities.
-
-(defmonad dist-m
-  "Monad describing computations on fuzzy quantities, represented by a finite
-   probability distribution for the possible values. A distribution is
-   represented by a map from values to probabilities."
-  [m-result (fn m-result-dist [v]
-	      {v 1})
-   m-bind   (fn m-bind-dist [mv f]
-	      (reduce (partial merge-with +)
-		      (for [[x p] mv  [y q] (f x)]
-			{y (* q p)})))
-   ])
-
-; Applying the monad transformer maybe-t to the basic dist monad results
-; in the cond-dist monad that can handle invalid values. The total probability
-; for invalid values ends up as the probability of m-zero (which is nil).
-; The function normalize takes this probability out of the distribution and
-; re-distributes its weight over the valid values.
-
-(defvar cond-dist-m
-  (maybe-t dist-m)
-  "Variant of the dist monad that can handle undefined values.")
-
-; Normalization
-
-(defn- scale-by
-  "Multiply each entry in dist by the scale factor s and remove zero entries."
-  [dist s]
-  (into {}
-	(for [[val p] dist :when (> p 0)]
-	  [val (* p s)])))
-
-(defn normalize-cond [cdist]
-  "Normalize a probability distribution resulting from a computation in
-   the cond-dist monad by re-distributing the weight of the invalid values
-   over the valid ones."
-  (let [missing (get cdist nil 0)
-	dist    (dissoc cdist nil)]
-    (cond (zero? missing) dist
-	  (= 1 missing)   {}
-	  :else (let [scale  (/ 1 (- 1 missing))]
-		  (scale-by dist scale)))))
-
-(defn normalize
-  "Convert a weight map (e.g. a map of counter values) to a distribution
-   by multiplying with a normalization factor. If the map has a key
-   :total, its value is assumed to be the sum over all the other values and
-   it is used for normalization. Otherwise, the sum is calculated
-   explicitly. The :total key is removed from the resulting distribution."
-  [weights]
-  (let [total (:total weights)
-	w (dissoc weights :total)
-	s (/ 1 (if (nil? total) (reduce + (vals w)) total))]
-    (scale-by w s)))
-
-; Functions that construct distributions
-
-(defn uniform
-  "Return a distribution in which each of the elements of coll
-   has the same probability."
-  [coll]
-  (let [n (count coll)
-	p (/ 1 n)]
-    (into {} (for [x (seq coll)] [x p]))))
-
-(defn choose
-  "Construct a distribution from an explicit list of probabilities
-   and values. They are given in the form of a vector of probability-value
-   pairs. In the last pair, the probability can be given by the keyword
-   :else, which stands for 1 minus the total of the other probabilities."
-  [& choices]
-  (letfn [(add-choice [dist [p v]]
-	    (cond (nil? p) dist
-		  (= p :else)
-		        (let [total-p (reduce + (vals dist))]
-			  (assoc dist v (- 1 total-p)))
-		  :else (assoc dist v p)))]
-    (reduce add-choice {} (partition 2 choices))))
-
-(defn bernoulli
-  [p]
-  "Returns the Bernoulli distribution for probability p."
-  (choose p 1 :else 0))
-
-(defn- bc
-  [n]
-  "Returns the binomial coefficients for a given n."
-  (let [r (inc n)]
-     (loop [c 1
-	    f (list 1)]
-       (if (> c n)
-	 f
-	 (recur (inc c) (cons (* (/ (- r c) c) (first f)) f))))))
-
-(defn binomial
-  [n p]
-  "Returns the binomial distribution, which is the distribution of the
-   number of successes in a series of n experiments whose individual
-   success probability is p."
-  (let [q (- 1 p)
-	n1 (inc n)
-	k (range n1)
-	pk (take n1 (iterate #(* p %) 1))
-	ql (reverse (take n1 (iterate #(* q %) 1)))
-	f (bc n)]
-    (into {} (map vector k (map * f pk ql)))))
-
-(defn make-distribution
-  "Returns the distribution in which each element x of the collection
-   has a probability proportional to (f x)"
-  [coll f]
-  (normalize (into {} (for [k coll] [k (f k)]))))
-
-(defn zipf
-  "Returns the Zipf distribution in which the numbers k=1..n have
-   probabilities proportional to 1/k^s."
-  [s n]
-  (make-distribution (range 1 (inc n)) #(/ (java.lang.Math/pow % s))))
-
-(defn certainly
-  "Returns a distribution in which the single value v has probability 1."
-  [v]
-  {v 1})
-
-(with-monad dist-m
-
-  (defn join-with
-    "Returns the distribution of (f x y) with x from dist1 and y from dist2."
-    [f dist1 dist2]
-    ((m-lift 2 f) dist1 dist2))
-
-)
-
-(with-monad cond-dist-m
-  (defn cond-prob
-    "Returns the conditional probability for the values in dist that satisfy
-     the predicate pred."
-    [pred dist]
-    (normalize-cond
-      (domonad
-        [v dist
-	 :when (pred v)]
-	v))))
-
-; Select (with equal probability) N items from a sequence
-
-(defn- nth-and-rest [n xs]
-  "Return a list containing the n-th value of xs and the sequence
-   obtained by removing the n-th value from xs."
-  (let [[h t] (split-at n xs)]
-    (list (first t) (concat h (rest t)))))
-
-(with-monad dist-m
-
-  (defn- select-n [n xs]
-    (letfn [(select-1 [[s xs]]
-	      (uniform (for [i (range (count xs))]
-			 (let [[nth rest] (nth-and-rest i xs)]
-			   (list (cons nth s) rest)))))]
-      ((m-chain (replicate n select-1)) (list '() xs))))
-
-  (defn select [n xs]
-    "Return the distribution for all possible ordered selections of n elements
-     out of xs."
-    ((m-lift 1 first) (select-n n xs)))
-
-)
-
-; Find the probability that a given predicate is satisfied
-
-(defn prob
-  "Return the probability that the predicate pred is satisfied in the
-   distribution dist, i.e. the sum of the probabilities of the values
-   that satisfy pred."
-  [pred dist]
-  (apply + (for [[x p] dist :when (pred x)] p)))
-