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#lang racket
(provide
width
make-center-width
center
make-center-percent
percent
pos?
neg?
mul-interval
div-interval
sub-interval
add-interval
make-interval
upper-bound
lower-bound
print-interval)
(define (width x)
(/ (- (upper-bound x) (lower-bound x)) 2))
(define (make-center-width c w)
(make-interval (- c w) (+ c w)))
(define (center i)
(/ (+ (lower-bound i) (upper-bound i)) 2))
(define (make-center-percent c p)
(let ((toler (* c (/ p 100.0))))
((lambda (a b)
(if (> a b)
(make-interval b a)
(make-interval a b)))
(- c toler)
(+ c toler))))
(define (percent i)
(let ((w (width i))
(c (center i)))
;; (newline) (print c)(println w)
;; not defined: percent of interval centered at zero
(if
(<= c 0)
0
(abs (* 100 (/ w c))))))
(define (pos? x)
(> x 0))
(define (neg? x)
(< x 0))
(define (mul-interval x y)
(cond
;; 1. all positive
((and
(pos? (lower-bound x))
(pos? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (lower-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y))))
;; 2. one lower-bound neg
((and
(neg? (lower-bound x))
(pos? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (lower-bound x) (upper-bound y))
(* (upper-bound x) (upper-bound y))))
;; 3. one lower-bound neg
((and
(pos? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (upper-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y))))
;; 4. one interval neg
((and
(neg? (lower-bound x))
(pos? (lower-bound y))
(neg? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y))))
;; 5. one interval neg
((and
(pos? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(neg? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y))))
;; 6. one interval neg, one interval crossing zero
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(neg? (upper-bound x))
(pos? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (upper-bound x) (lower-bound y))))
;; 7. one interval neg, one interval crossing zero
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(neg? (upper-bound y)))
(make-interval (* (upper-bound x) (upper-bound y))
(* (upper-bound x) (lower-bound y))))
;; 8. all neg
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(neg? (upper-bound x))
(neg? (upper-bound y)))
(make-interval (* (lower-bound x) (lower-bound y))
(* (upper-bound x) (upper-bound y))))
;; 9. both crossing zero
((and
(neg? (lower-bound x))
(neg? (lower-bound y))
(pos? (upper-bound x))
(pos? (upper-bound y)))
(make-interval ((lambda (a b) (if (< a b) a b))
(* (lower-bound x) (upper-bound y))
(* (upper-bound x) (lower-bound y)))
((lambda (a b) (if (> a b) a b))
(* (upper-bound x) (upper-bound y))
(* (lower-bound x) (lower-bound y)))))
;; 10. The case where one of the endpoints is neither negative or positive, 0
(else (mul-interval-min-max x y))))
(define (mul-interval-min-max x y)
(let ((p1 (* (lower-bound x) (lower-bound y)))
(p2 (* (lower-bound x) (upper-bound y)))
(p3 (* (upper-bound x) (lower-bound y)))
(p4 (* (upper-bound x) (upper-bound y))))
(make-interval (min p1 p2 p3 p4)
(max p1 p2 p3 p4))))
(define (div-interval x y)
(if (and (< 0 (lower-bound y)) (> 0 (upper-bound y)))
(error "Division by interval spanning zero")
(mul-interval
x
(make-interval
(/ 1.0 (upper-bound y))
(/ 1.0 (lower-bound y))))))
(define (sub-interval x y)
(make-interval (- (lower-bound x) (upper-bound y))
(- (upper-bound x) (lower-bound y))))
(define (add-interval x y)
(make-interval (+ (lower-bound x) (lower-bound y))
(+ (upper-bound x) (upper-bound y))))
(define (make-interval a b) (cons a b))
(define (lower-bound x) (car x))
(define (upper-bound x) (cdr x))
(define (print-interval x)
(newline)
(display "interval{")
(display (lower-bound x))
(display ",")
(display (upper-bound x))
(display "}")
(newline))
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