Changed argument order of binning functions for consistency with other
math/statistics functions
This commit is contained in:
Neil Toronto
parent
af8d02146d
commit
04fbb02f63
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@ -74,13 +74,13 @@
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;; Bins
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(struct: (A B) sample-bin
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([values : (Listof A)] [weights : (U #f (Listof Nonnegative-Real))] [min : B] [max : B])
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([min : B] [max : B] [values : (Listof A)] [weights : (U #f (Listof Nonnegative-Real))])
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#:transparent)
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(: sample-bin-compact (All (A B) ((sample-bin A B) -> (sample-bin A B))))
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(define (sample-bin-compact bin)
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(let-values ([(xs ws) (count-samples (sample-bin-values bin) (sample-bin-weights bin))])
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(sample-bin xs ws (sample-bin-min bin) (sample-bin-max bin))))
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(sample-bin (sample-bin-min bin) (sample-bin-max bin) xs ws)))
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(: sample-bin-total (All (A B) ((sample-bin A B) -> Nonnegative-Real)))
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(define (sample-bin-total bin)
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@ -102,12 +102,12 @@
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(: bin-samples
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(All (A B)
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(case-> ((Sequenceof A) (Sequenceof A) (A A -> Any) -> (Listof (sample-bin A A)))
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((Sequenceof A) (Sequenceof B) (B B -> Any) (A -> B) -> (Listof (sample-bin A B))))))
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(case-> ((Sequenceof A) (A A -> Any) (Sequenceof A) -> (Listof (sample-bin A A)))
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((Sequenceof B) (B B -> Any) (Sequenceof A) (A -> B) -> (Listof (sample-bin A B))))))
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(define bin-samples
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(case-lambda
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[(xs bnds lte?) (bin-samples xs bnds lte? (λ: ([x : A]) x))]
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[(xs bnds lte? key)
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[(bnds lte? xs) (bin-samples bnds lte? xs (λ: ([x : A]) x))]
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[(bnds lte? xs key)
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(let* ([bnds (sort (sequence->list bnds) (λ: ([b1 : B] [b2 : B]) (and (lte? b1 b2) #t)))]
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[xs (sequence->list xs)]
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[xks (map (λ: ([x : A]) (cons x (key x))) xs)]
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@ -118,7 +118,7 @@
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(cond [(empty? xks) empty]
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[else (define min (cdr (first xks)))
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(define max (cdr (last xks)))
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(list (sample-bin (map (inst car A B) xks) #f min max))])]
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(list (sample-bin min max (map (inst car A B) xks) #f))])]
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[else
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(let: loop : (Listof (sample-bin A B)) ([min : (U #f B) #f]
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[max : B (first bnds)]
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@ -128,37 +128,37 @@
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(let-values ([(yks xks) (list-split-after xks (λ: ([xk : (Pair A B)])
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(lte? (cdr xk) max)))])
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(define maybe-bin
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(cond [min (list (sample-bin (map (inst car A B) yks) #f min max))]
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(cond [min (list (sample-bin min max (map (inst car A B) yks) #f))]
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[(empty? yks) empty]
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[else (list (sample-bin (map (inst car A B) yks) #f (cdr (first yks)) max))]))
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[else (list (sample-bin (cdr (first yks)) max (map (inst car A B) yks) #f))]))
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(cond [(empty? bnds)
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(cond [(empty? xks) (reverse (append maybe-bin bins))]
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[else
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(define bin2
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(sample-bin (map (inst car A B) xks) #f max (cdr (last xks))))
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(sample-bin max (cdr (last xks)) (map (inst car A B) xks) #f))
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(reverse (append (cons bin2 maybe-bin) bins))])]
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[else
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(loop max (first bnds) (rest bnds) xks (append maybe-bin bins))])))]))]))
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(: bin-weighted-samples
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(All (A B) (case-> ((Sequenceof A) (U #f (Sequenceof Real)) (Sequenceof A) (A A -> Any)
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(All (A B) (case-> ((Sequenceof A) (A A -> Any) (Sequenceof A) (U #f (Sequenceof Real))
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-> (Listof (sample-bin A A)))
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((Sequenceof A) (U #f (Sequenceof Real)) (Sequenceof B) (B B -> Any) (A -> B)
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((Sequenceof B) (B B -> Any) (Sequenceof A) (U #f (Sequenceof Real)) (A -> B)
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-> (Listof (sample-bin A B))))))
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(define bin-weighted-samples
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(case-lambda
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[(xs ws bnds lte?)
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(cond [ws (bin-weighted-samples xs ws bnds lte? (λ: ([x : A]) x))]
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[else (bin-samples xs bnds lte?)])]
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[(xs ws bnds lte? key)
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[(bnds lte? xs ws)
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(cond [ws (bin-weighted-samples bnds lte? xs ws (λ: ([x : A]) x))]
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[else (bin-samples bnds lte? xs)])]
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[(bnds lte? xs ws key)
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(cond [ws (let-values ([(xs ws) (sequences->weighted-samples 'bin-samples xs ws)])
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(define xws (map (inst cons A Nonnegative-Real) xs ws))
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(define xw-key (λ: ([xw : (Pair A Nonnegative-Real)]) (key (car xw))))
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(map (λ: ([bin : (sample-bin (Pair A Nonnegative-Real) B)])
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(define xws (sample-bin-values bin))
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(sample-bin (map (inst car A Nonnegative-Real) xws)
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(map (inst cdr A Nonnegative-Real) xws)
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(sample-bin-min bin)
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(sample-bin-max bin)))
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(bin-samples xws bnds lte? xw-key)))]
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[else (bin-samples xs bnds lte? key)])]))
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(sample-bin (sample-bin-min bin)
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(sample-bin-max bin)
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(map (inst car A Nonnegative-Real) xws)
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(map (inst cdr A Nonnegative-Real) xws)))
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(bin-samples bnds lte? xws xw-key)))]
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[else (bin-samples bnds lte? xs key)])]))
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@ -52,20 +52,23 @@ See @secref{stats:expected-values} for a discussion.
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(count-samples '(1 1 2 3 4) '(1/2 1/2 1 1 2))]
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}
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@defstruct*[sample-bin ([values (Listof A)]
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[weights (U #f (Listof Nonnegative-Real))]
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[min B] [max B])]{
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@defstruct*[sample-bin ([min B]
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[max B]
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[values (Listof A)]
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[weights (U #f (Listof Nonnegative-Real))])]{
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Represents a @italic{bin}, or a group of samples within an interval in a total order.
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The values and bounds have a different type to allow @racket[bin-samples] and
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@racket[bin-weighted-samples] to group elements based on a function of their values (a @racket[key],
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like in @racket[sort]).
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}
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@defproc*[([(bin-samples [xs (Sequenceof A)] [bounds (Sequenceof A)] [lte? (A A -> Any)])
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@defproc*[([(bin-samples [bounds (Sequenceof A)]
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[lte? (A A -> Any)]
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[xs (Sequenceof A)])
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(Listof (sample-bin A A))]
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[(bin-samples [xs (Sequenceof A)]
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[bounds (Sequenceof B)]
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[(bin-samples [bounds (Sequenceof B)]
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[lte? (B B -> Any)]
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[xs (Sequenceof A)]
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[key (A -> B)])
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(Listof (sample-bin A B))])]{
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Like @racket[(sort xs lte? #:key key)], but additionally groups samples into bins.
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@ -78,9 +81,9 @@ front.
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If some are greater than the largest bound, they are grouped into a single bin at the end.
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@examples[#:eval typed-eval
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(bin-samples '(0 1 2 3 4 5 6) '() <=)
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(bin-samples '(0 1 2 3 4 5 6) '(3) <=)
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(bin-samples '(0 1 2 3 4 5 6) '(2 4) <=)]
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(bin-samples '() <= '(0 1 2 3 4 5 6))
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(bin-samples '(3) <= '(0 1 2 3 4 5 6))
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(bin-samples '(2 4) <= '(0 1 2 3 4 5 6))]
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Note that @racket[bin-samples] always returns bins with @racket[#f] weights, meaning they contain
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unweighted samples.
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@ -103,15 +106,15 @@ Like @racket[bin-samples], but for weighted samples.
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@defproc[(sample-bin-compact [bin (sample-bin A B)]) (sample-bin A B)]{
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Compacts @racket[bin] by applying @racket[count-samples] to its values and weights.
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@examples[#:eval typed-eval
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(sample-bin-compact (sample-bin '(1 2 3 4 4) #f 1 4))]
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(sample-bin-compact (sample-bin 1 4 '(1 2 3 4 4) #f))]
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}
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@defproc[(sample-bin-total [bin (sample-bin A B)]) Nonnegative-Real]{
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If @racket[(sample-bin-weights bin)] is @racket[#f], returns the number of samples in @racket[bin];
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otherwise, returns the sum of their weights.
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@examples[#:eval typed-eval
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(sample-bin-total (sample-bin '(1 2 3 4 4) #f 1 4))
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(sample-bin-total (sample-bin-compact (sample-bin '(1 2 3 4 4) #f 1 4)))]
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(sample-bin-total (sample-bin 1 4 '(1 2 3 4 4) #f))
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(sample-bin-total (sample-bin-compact (sample-bin 1 4 '(1 2 3 4 4) #f)))]
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}
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@section[#:tag "stats:expected-values"]{Expected Values}
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@ -4,91 +4,91 @@
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typed/rackunit)
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(check-equal?
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(bin-samples '() '(5) <=)
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(bin-samples '(5) <= '())
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empty)
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(check-equal?
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(bin-samples '(4) '(5) <=)
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(list (sample-bin '(4) #f 4 5)))
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(bin-samples '(5) <= '(4))
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(list (sample-bin 4 5 '(4) #f)))
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(check-equal?
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(bin-samples '(5) '(5) <=)
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(list (sample-bin '(5) #f 5 5)))
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(bin-samples '(5) <= '(5))
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(list (sample-bin 5 5 '(5) #f)))
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(check-equal?
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(bin-samples '(6) '(5) <=)
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(list (sample-bin '(6) #f 5 6)))
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(bin-samples '(5) <= '(6))
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(list (sample-bin 5 6 '(6) #f)))
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(check-equal?
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(bin-samples '(4 5) '(5) <=)
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(list (sample-bin '(4 5) #f 4 5)))
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(bin-samples '(5) <= '(4 5))
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(list (sample-bin 4 5 '(4 5) #f)))
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(check-equal?
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(bin-samples '(5 6) '(5) <=)
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(list (sample-bin '(5) #f 5 5)
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(sample-bin '(6) #f 5 6)))
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(bin-samples '(5) <= '(5 6))
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(list (sample-bin 5 5 '(5) #f)
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(sample-bin 5 6 '(6) #f)))
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(check-equal?
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(bin-samples '(4 6) '(5) <=)
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(list (sample-bin '(4) #f 4 5)
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(sample-bin '(6) #f 5 6)))
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(bin-samples '(5) <= '(4 6))
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(list (sample-bin 4 5 '(4) #f)
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(sample-bin 5 6 '(6) #f)))
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(check-equal?
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(bin-samples '(4 5 6) '(5) <=)
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(list (sample-bin '(4 5) #f 4 5)
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(sample-bin '(6) #f 5 6)))
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(bin-samples '(5) <= '(4 5 6))
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(list (sample-bin 4 5 '(4 5) #f)
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(sample-bin 5 6 '(6) #f)))
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(check-equal?
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(bin-samples '() '(4 8) <=)
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(list (sample-bin '() #f 4 8)))
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(bin-samples '(4 8) <= '())
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(list (sample-bin 4 8 '() #f)))
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(check-equal?
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(bin-samples '(2) '(4 8) <=)
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(list (sample-bin '(2) #f 2 4)
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(sample-bin '() #f 4 8)))
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(bin-samples '(4 8) <= '(2))
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(list (sample-bin 2 4 '(2) #f)
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(sample-bin 4 8 '() #f)))
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(check-equal?
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(bin-samples '(4) '(4 8) <=)
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(list (sample-bin '(4) #f 4 4)
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(sample-bin '() #f 4 8)))
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(bin-samples '(4 8) <= '(4))
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(list (sample-bin 4 4 '(4) #f)
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(sample-bin 4 8 '() #f)))
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(check-equal?
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(bin-samples '(6) '(4 8) <=)
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(list (sample-bin '(6) #f 4 8)))
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(bin-samples '(4 8) <= '(6))
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(list (sample-bin 4 8 '(6) #f)))
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(check-equal?
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(bin-samples '(8) '(4 8) <=)
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(list (sample-bin '(8) #f 4 8)))
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(bin-samples '(4 8) <= '(8))
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(list (sample-bin 4 8 '(8) #f)))
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(check-equal?
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(bin-samples '(10) '(4 8) <=)
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(list (sample-bin '() #f 4 8)
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(sample-bin '(10) #f 8 10)))
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(bin-samples '(4 8) <= '(10))
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(list (sample-bin 4 8 '() #f)
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(sample-bin 8 10 '(10) #f)))
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(check-equal?
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(bin-samples '(4 8) '(4 8) <=)
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(list (sample-bin '(4) #f 4 4)
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(sample-bin '(8) #f 4 8)))
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(bin-samples '(4 8) <= '(4 8))
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(list (sample-bin 4 4 '(4) #f)
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(sample-bin 4 8 '(8) #f)))
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(check-equal?
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(bin-samples '(4 10) '(4 8) <=)
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(list (sample-bin '(4) #f 4 4)
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(sample-bin '() #f 4 8)
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(sample-bin '(10) #f 8 10)))
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(bin-samples '(4 8) <= '(4 10))
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(list (sample-bin 4 4 '(4) #f)
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(sample-bin 4 8 '() #f)
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(sample-bin 8 10 '(10) #f)))
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(check-equal?
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(bin-samples '(8 10) '(4 8) <=)
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(list (sample-bin '(8) #f 4 8)
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(sample-bin '(10) #f 8 10)))
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(bin-samples '(4 8) <= '(8 10))
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(list (sample-bin 4 8 '(8) #f)
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(sample-bin 8 10 '(10) #f)))
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(check-equal?
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(bin-samples '(4 8 10) '(4 8) <=)
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(list (sample-bin '(4) #f 4 4)
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(sample-bin '(8) #f 4 8)
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(sample-bin '(10) #f 8 10)))
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(bin-samples '(4 8) <= '(4 8 10))
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(list (sample-bin 4 4 '(4) #f)
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(sample-bin 4 8 '(8) #f)
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(sample-bin 8 10 '(10) #f)))
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(check-equal?
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(bin-samples '(1 1 2 2 2 3 4 5 5 5 5 6 7 8 9 9) '(3 8) <=)
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(list (sample-bin '(1 1 2 2 2 3) #f 1 3)
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(sample-bin '(4 5 5 5 5 6 7 8) #f 3 8)
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(sample-bin '(9 9) #f 8 9)))
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(bin-samples '(3 8) <= '(1 1 2 2 2 3 4 5 5 5 5 6 7 8 9 9))
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(list (sample-bin 1 3 '(1 1 2 2 2 3) #f)
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(sample-bin 3 8 '(4 5 5 5 5 6 7 8) #f)
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(sample-bin 8 9 '(9 9) #f)))
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