"SICP Exercise" 144 Exercise 3.82

Exercise 3-82 Original

Exercise 3.82. Redo Exercise 3.5 on Monte Carlo integration in terms of streams. The stream version of Estimate-integral is not a argument telling how many trials to perform. Instead, it'll produce a stream of estimates based on successively more trials.

Code

  (define   ( Random-in-range  Low High)   (let    ( (range    ( -  High low) ) )   (+   low  (*    (random )  range) ) ) )   (define (random-number-pairs low1 high1 low2 high2)(cons-stream ( Cons (random-in-range low1 high1) (random-in-range low2 high2)) (random-number-pairs low1 high1 low2 high2                                             )))  (Define (Monte-carlo experiment-stream passed failed)           (define   ( next   Passed failed)   (cons-stream   (/  passed  ( +   passed failed) )   (monte-carlo   (stream-cdr  experiment-stream)  Passed failed) ) )           (if (stream-car experiment-stream)(next (+ passed 1 ) (failed)(next passed (+ failed 1)                                     )))  (Define (estimate-integral p x1 x2 y1 y2)          ( Let (Area  (* (- x2 x1) (- y2 y1))( randoms (random-number-pairs x1 x2 y1 y2                 )))                  (scale-stream (monte-carlo (stream-map p randoms)  0  0) area)))  (define (sum-of-square x y) ( + (* x x) (  * y y )))   (define  F  ( lambda   (x )   ( not   >   (  (-   (car  x)   1 )   (-   (cdr  x)   1 ) )   1 ) ) ) )   (define pi-stream (estimate-integral f 0  2  0  2))  

"SICP Exercise" 144 Exercise 3.82