[racket-dev] case-> and for/sum:

This looks like an instance of the problem Neil reported on Monday.

I'll discuss Neil's solution with Sam.

Vincent


At Thu, 3 Jan 2013 18:47:56 +0100,
Jens Axel Søgaard wrote:
> 
> Ignore the previous example. Here is the example again, now
> with correct usage of case-lambda. The for/sum problem remains.
> 
> /Jens Axel
> 
> 
> #lang typed/racket
> (require math)
> 
> (: matrix-solve-upper
>    (All (A) (case->
>              ((Matrix Real)   (Matrix Real)          -> (Matrix Real))
>              ((Matrix Real)   (Matrix Real)   (-> A) -> (U A (Matrix Real)))
>              ((Matrix Number) (Matrix Number)        -> (Matrix Number))
>              ((Matrix Number) (Matrix Number) (-> A) -> (U A (Matrix
> Number))))))
> (define matrix-solve-upper
>   ; solve the equation Ux=b
>   ; using back substitution
>   (case-lambda
>     [(U b)
>      (define (default-fail)
>        (raise-argument-error
>         'matrix-solve-upper
>         "The upper triangular matrix is not invertible." 0 U))
>      (matrix-solve-upper U b default-fail)]
>     [(U b fail)
>       (define m (matrix-num-rows U))
>       (define x (make-vector m 0))
>       (for ([i (in-range (- m 1) -1 -1)])
>         (define bi (matrix-ref b i 0))
>         (define Uii (matrix-ref U i i))
>         (when (zero? Uii) (fail))
>         (define x.Ui (for/sum ([j (in-range (+ i 1) m)])
>                        (* (matrix-ref U i j) (vector-ref x j))))
>         (vector-set! x i (/ (- bi x.Ui) Uii)))
>       (vector->matrix m 1 x)]))
> 
>  (define U (matrix [[4 -1 2  3]
>                     [0 -2 7 -4]
>                     [0  0 6  5]
>                     [0  0 0  3]]))
>  (define b (col-matrix [20 -7 4 6]))
>  b ; expected
>  (define x (solve-upper-triangular U b))
>  (matrix* U x)
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