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(module math mzscheme
; Usefull mathy functions for plots
(require
(lib "list.ss")
(lib "etc.ss")
(lib "math.ss"))
; using vectors for n-dimentional points
; vector-magnitude : (vectorof number) -> number
; computes the magnituded of the vector by using pythegorean theorem
(define (vector-magnitude vec)
(sqrt (foldl (lambda (item total) (+ (sqr item) total)) 0 (vector->list vec))))
; shortcuts to avoid writing ugly vector-ref code
(define (vector-x vec)
(vector-ref vec 0))
(define (vector-y vec)
(vector-ref vec 1))
(define (vector-z vec)
(vector-ref vec 2))
; make-vec : (number number -> number) (number number -> number) -> (vector -> vector)
(define (make-vec func1 func2)
(lambda (point) (vector (func1 (vector-x point) (vector-y point)) (func2 (vector-x point) (vector-y point)))))
; derivative : (number -> number) [number] -> (number -> number)
(define derivative
(opt-lambda (func [h .00000001])
(lambda (x) (/ (- (func (+ x h)) (func x)) h))))
; gradient : (number number -> number) [number] -> (vector -> vector)
(define gradient
(opt-lambda (func-3d [h .00000001])
(lambda (point) (vector ((derivative (lambda (x) (func-3d x (vector-y point))) h) (vector-x point))
((derivative (lambda (y) (func-3d (vector-x point) y)) h) (vector-y point))))))
(provide (all-defined)))
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