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Matthew Butterick 10 years ago
parent c0c75ed55e
commit 9b3ecb9e06
1 changed files with 61 additions and 28 deletions
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quad/ocm-typed.rkt
Unescape Escape View File

@ -48,12 +48,12 @@ D. Eppstein, March 2002, significantly revised August 2005
(define-syntax-rule (vector-append-item xs value)
(vector-append xs (vector value)))
((inst vector-append Any) xs (vector value)))
(define-syntax-rule (vector-set vec idx val)
(begin
(vector-set! vec idx val)
vec))
(: vector-set (All (a) ((Vectorof a) Integer a -> (Vectorof a))))
(define (vector-set vec idx val)
(vector-set! vec idx val)
vec)
(define-syntax-rule (vector-cdr vec)
(vector-drop vec 1))
@ -152,14 +152,14 @@ D. Eppstein, March 2002, significantly revised August 2005
(define col (vector-ref col-indices col-idx))
(define idx-of-last-row
(cast (if (= col-idx (sub1 (vector-length col-indices)))
(vector-last row-indices)
(hash-ref (cast (hash-ref minima (vector-ref col-indices (add1 col-idx))) HashTableTop) 'row-idx)) Index-Type))
(vector-last row-indices)
(hash-ref (cast (hash-ref minima (vector-ref col-indices (add1 col-idx))) HashTableTop) 'row-idx)) Index-Type))
(define smallest-value-entry
((inst vector-argmin Make-Minimum-Input) (λ(x) (entry->value (car x)))
(for/vector : (Vectorof Make-Minimum-Input)
([row-idx (in-list ((inst dropf-right Index-Type) (vector->list row-indices) (λ(x) (not (= x idx-of-last-row)))))])
(cons (matrix-proc row-idx col) row-idx))))
(for/vector : (Vectorof Make-Minimum-Input)
([row-idx (in-list ((inst dropf-right Index-Type) (vector->list row-indices) (λ(x) (not (= x idx-of-last-row)))))])
(cons (matrix-proc row-idx col) row-idx))))
(! minima col (make-minimum smallest-value-entry)))
minima)
@ -169,13 +169,13 @@ D. Eppstein, March 2002, significantly revised August 2005
(define idx-of-last-col (sub1 (vector-length col-indices)))
(define (smallest-value-entry [col : Index-Type] [idx-of-last-row : Index-Type])
((inst argmin Make-Minimum-Input) (λ(x) (entry->value (car x)))
(for/list ([row-idx (stop-after (in-vector row-indices) (λ(x) (= idx-of-last-row x)))])
(cons (matrix-proc row-idx col) row-idx))))
(for/list ([row-idx (stop-after (in-vector row-indices) (λ(x) (= idx-of-last-row x)))])
(cons (matrix-proc row-idx col) row-idx))))
(for ([([col : Index-Type] col-idx) (in-indexed col-indices)] #:when (even? col-idx))
(define idx-of-last-row (cast (if (= col-idx idx-of-last-col)
(vector-last row-indices)
(hash-ref (cast (hash-ref minima (vector-ref col-indices (add1 col-idx))) HashTableTop) 'row-idx)) Index-Type))
(vector-last row-indices)
(hash-ref (cast (hash-ref minima (vector-ref col-indices (add1 col-idx))) HashTableTop) 'row-idx)) Index-Type))
(! minima col (make-minimum (smallest-value-entry col idx-of-last-row))))
minima)
@ -281,9 +281,8 @@ In addition, we keep a column index self._tentative, such that
(define-type Index-Type Nonnegative-Integer)
(define-type Matrix-Proc-Type (Index-Type Index-Type . -> . Any))
(define-type Entry->Value-Type (Any . -> . Flonum))
(define-type Indices-Type (Vectorof Index-Type))
(define o:min-values 0)
(define o:min-row-indices 1)
(define o:finished 2)
@ -337,11 +336,11 @@ In addition, we keep a column index self._tentative, such that
(for ([col (in-vector cols)])
(cond
[(>= col (vector-length (cast (ocm-ref ocm o:min-values) VectorTop)))
(ocm-set! ocm o:min-values (vector-append-item (ocm-ref ocm o:min-values) (@ (cast (@ minima col) HashTableTop) 'value)))
(ocm-set! ocm o:min-row-indices (vector-append-item (ocm-ref ocm o:min-row-indices) (@ (@ minima col) 'row-idx)))]
[(< ((ocm-ref ocm o:entry->value) (@ (@ minima col) 'value)) ((ocm-ref ocm o:entry->value) (vector-ref (ocm-ref ocm o:min-values) col)))
(ocm-set! ocm o:min-values (vector-set (ocm-ref ocm o:min-values) col (@ (@ minima col) 'value)))
(ocm-set! ocm o:min-row-indices (vector-set (ocm-ref ocm o:min-row-indices) col (@ (@ minima col) 'row-idx)))]))
(ocm-set! ocm o:min-values (vector-append-item (cast (ocm-ref ocm o:min-values) (Vectorof Any)) (@ (cast (@ minima col) HashTableTop) 'value)))
(ocm-set! ocm o:min-row-indices (vector-append-item (cast (ocm-ref ocm o:min-row-indices) (Vectorof Any)) (@ (cast (@ minima col) HashTableTop) 'row-idx)))]
[(< ((cast (ocm-ref ocm o:entry->value) Entry->Value-Type) (@ (cast (@ minima col) HashTableTop) 'value)) ((cast (ocm-ref ocm o:entry->value) Entry->Value-Type) (vector-ref (cast (ocm-ref ocm o:min-values) VectorTop) col)))
(ocm-set! ocm o:min-values ((inst vector-set Index-Type) (cast (ocm-ref ocm o:min-values) (Vectorof Index-Type)) col (cast (@ (cast (@ minima col) HashTableTop) 'value) Index-Type)))
(ocm-set! ocm o:min-row-indices ((inst vector-set Index-Type) (cast (ocm-ref ocm o:min-row-indices) (Vectorof Index-Type)) col (cast (@ (cast (@ minima col) HashTableTop) 'row-idx) Index-Type)))]))
(ocm-set! ocm o:finished next)]
[else
@ -350,12 +349,12 @@ In addition, we keep a column index self._tentative, such that
;; so we can clear out all our work from higher rows.
;; As in the fourth case, the loss of tentative is
;; amortized against the increase in base.
(define diag ((ocm-ref ocm o:matrix-proc) (sub1 next) next))
(define diag ((cast (ocm-ref ocm o:matrix-proc) Matrix-Proc-Type) (sub1 next) next))
(cond
[(< ((ocm-ref ocm o:entry->value) diag) ((ocm-ref ocm o:entry->value) (vector-ref (ocm-ref ocm o:min-values) next)))
[(< ((cast (ocm-ref ocm o:entry->value) Entry->Value-Type) diag) ((cast (ocm-ref ocm o:entry->value) Entry->Value-Type) (vector-ref (cast (ocm-ref ocm o:min-values) (Vectorof Any)) next)))
(log-ocm-debug "advance: second case because column minimum is on the diagonal")
(ocm-set! ocm o:min-values (vector-set (ocm-ref ocm o:min-values) next diag))
(ocm-set! ocm o:min-row-indices (vector-set (ocm-ref ocm o:min-row-indices) next (sub1 next)))
(ocm-set! ocm o:min-values (vector-set (cast (ocm-ref ocm o:min-values) (Vectorof Any)) next diag))
(ocm-set! ocm o:min-row-indices (vector-set (cast (ocm-ref ocm o:min-row-indices) (Vectorof Any)) next (sub1 next)))
(ocm-set! ocm o:base (sub1 next))
(ocm-set! ocm o:tentative next)
(ocm-set! ocm o:finished next)]
@ -363,8 +362,8 @@ In addition, we keep a column index self._tentative, such that
;; Third case: row i-1 does not supply a column minimum in
;; any column up to tentative. We simply advance finished
;; while maintaining the invariant.
[(>= ((ocm-ref ocm o:entry->value) ((ocm-ref ocm o:matrix-proc) (sub1 next) (ocm-ref ocm o:tentative)))
((ocm-ref ocm o:entry->value) (vector-ref (ocm-ref ocm o:min-values) (ocm-ref ocm o:tentative))))
[(>= ((cast (ocm-ref ocm o:entry->value) Entry->Value-Type) ((cast (ocm-ref ocm o:matrix-proc) Matrix-Proc-Type) (sub1 next) (cast (ocm-ref ocm o:tentative) Index-Type)))
((cast (ocm-ref ocm o:entry->value) Entry->Value-Type) (vector-ref (cast (ocm-ref ocm o:min-values) (Vectorof Any)) (cast (ocm-ref ocm o:tentative) Index-Type))))
(log-ocm-debug "advance: third case because row i-1 does not suppply a column minimum")
(ocm-set! ocm o:finished next)]
@ -378,4 +377,38 @@ In addition, we keep a column index self._tentative, such that
(log-ocm-debug "advance: fourth case because new column minimum")
(ocm-set! ocm o:base (sub1 next))
(ocm-set! ocm o:tentative next)
(ocm-set! ocm o:finished next)])]))
(ocm-set! ocm o:finished next)])]))
(: print (OCM-Type . -> . Void))
(define (print ocm)
(displayln (ocm-ref ocm o:min-values))
(displayln (ocm-ref ocm o:min-row-indices)))
(: smawky? ((Listof (Listof Real)) . -> . Boolean))
(define (smawky? m)
(: position-of-minimum ((Listof Real) . -> . Index-Type))
(define (position-of-minimum xs)
;; put each element together with its list index
(let ([xs : (Listof (Pairof Index-Type Real)) (map (inst cons Index-Type Real) (range (length xs)) xs)])
;; find the first one with the min value, and grab the list index
(car ((inst argmin (Pairof Index-Type Real)) cdr (filter (λ([x : (Pairof Index-Type Real)]) (not (negative? (cdr x)))) xs)))))
;; tests if penalty matrix is monotone for non-negative values.
(define increasing-minima? (apply <= (cast (map position-of-minimum m) (List* Real Real (Listof Real)))))
(define monotone? : Boolean
(for/and ([ridx (in-range 1 (length m))])
(for/and : Boolean ([cidx (in-range (sub1 (length (car m))))])
(cast (let* ([prev-row : (Listof Real) ((inst list-ref (Listof Real)) m (sub1 ridx))]
[row : (Listof Real) (list-ref m ridx)]
[a : Real (list-ref prev-row cidx)]
[b : Real (list-ref prev-row (add1 cidx))]
[c : Real (list-ref row cidx)]
[d : Real (list-ref row (add1 cidx))])
(if (andmap (λ([x : Real]) (not (negative? x))) (list a b c d)) ;; smawk disregards negative values
(cond
[(< c d) (if (< a b) #t (error (format "Submatrix ~a not monotone in ~a" (list (list a b) (list c d)) m)))]
[(= c d) (if (<= a b) #t (error (format "Submatrix ~a not monotone in ~a" (list (list a b) (list c d)) m)))]
[else #t])
#t)) Boolean))))
(and increasing-minima? monotone?))

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