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

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)