[clean-list] "dummies guide" to structuring a program for uniqueness typing

[Isaac Gouy]

Hi Diederik

> in word-frequency change
>          ht_buckets_to_list :: *[!Item a!] [Item a] -> [Item a]
> to
>          ht_buckets_to_list :: .[!Item a!] [Item a] -> [Item a]

That fixed the problem, but how can we describe this bug in a way that
someone like me can look through our code and see if we're making a
similar mistake?


> And for nbody look at my attached version where I think I was playing

> with some other aspect but which compiles successfully with 2.1.1

Compiled, and gave the correct answer - the fix will appear on the
website once we start timing again.


> For spectral norm if you could show your code I can probably resolve 

> the error for you.

This is how I'd left it-


module spectralnorm
import StdEnv, StdArrayExtensions

Start = AtAv n u v
   where 
   n = 100
   u = createUnboxedRealArr n 1.0
   v = createUnboxedRealArr n 0.0   

/*
Start = eigenvalue n (powerMethod 10 n (u,v)) 
   where 
   n = 2
   u = createUnboxedRealArr n 1.0
   v = createUnboxedRealArr n 0.0

   
eigenvalue n (u,v) = sqrt(vBv/vv)
   where      
   vBv = asum {a*b \\ a <-: u & b <-: v}   
   vv = asum {a*a \\ a <-: v}   
*/   
   

powerMethod 0 n (u,v) = (u,v)  
powerMethod step n (u,v) 
   # (u,v) = AtAv n u v 
   # (u,v) = AtAv n v u 
   = powerMethod (step-1) n (u,v)   
                                     
A i j = 1.0 / toReal ((i+j)*(i+j+1)/2 +i+1)

Av n v a = aloop (n-1) (n-1) v a
	where
	aloop n i v a
	  | i>=0 = aloop n (i-1) v {a&[i] = avsum i n v 0.0}
	         = a   
	         
	avsum i j v x
	  | j>=0 = avsum i (j-1) v (x+((A i j)*v.[j]))
	         = x

Atv n v a = aloop (n-1) (n-1) v a     
	where
	aloop n i v a
	  | i>=0 = aloop n (i-1) v {a&[i] = atvsum i n v 0.0}
	         = a   
	         
	atvsum i j v x
	  | j>=0 = atvsum i (j-1) v (x+((A j i)*v.[j]))
	         = x

AtAv n v a = (u, Atv n u a)
   where u = Av n v (createUnboxedRealArr n 0.0) 


		
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