Vector
Implement a Vector class (or a set of functions) that models a Physical Vector. You should implement The four basic operations and a 'pretty print' function. Your Vector may be initialized in any reasonable way.
- Start and end points and direction - Angular coefficient and value (length)
The four operations to be implemented are:
- Vector+Vector addition
- Vector-Vector subtraction
- Vector*scalar multiplication
- Vector/scalar division
J
These are primitive (built in) operations in J:
<lang J> 5 7+2 3 7 10
5 7-2 3
3 4
5 7*11
55 77
5 7%2
2.5 3.5</lang>
A few things here might be worth noting:
J treats a sequences of space separated numbers as a single word, this is analogous to how languages which support a "string" data type support treating strings with spaces in them as single words. Put differently: '5 7' is a sequence of three characters but 5 7 (without the quotes) is a sequence of two numbers.
J uses the percent sign to represent division. This is a visual pun with the "division sign" or "obelus" which has been used to represent the division operation for hundreds of years.
In J, a single number (or single character) is special. It's not a treated as a sequence except in contexts where you explicitly declare it to be one (for example, by prefixing it with a comma). (If it were treated as a sequence the above operations would have been errors, because of the length mis-match.)
It's perhaps also worth noting that J allows you to specify complex numbers using polar coordinates, and complex numbers can be converted to vectors using the special token (+.) - for example:
<lang J> 2ad45 1.41421j1.41421
+. 2ad45
1.41421 1.41421
2ar0.785398
1.41421j1.41421
+. 2ar0.785398
1.41421 1.41421</lang>
In the construction of these numeric constants, ad is followed by an angle in degrees while ar is followed by an angle in radians. This practice of embedding letters in a numeric constant is analogous to the use of exponential notation when describing some floating point numbers.
Racket
We store internally only the x, y components and calculate the norm, angle and slope on demand. We have two constructors one with (x,y) and another with (slope, norm).
We use fl* and fl/ to try to get the most sensible result for vertical vectors.
<lang Racket>#lang racket
(require racket/flonum)
(define (rad->deg x) (fl* 180. (fl/ (exact->inexact x) pi)))
- Custom printer
- no shared internal structures
(define (vec-print v port mode)
(write-string "Vec:\n" port) (write-string (format " -Slope: ~a\n" (vec-slope v)) port) (write-string (format " -Angle(deg): ~a\n" (rad->deg (vec-angle v))) port) (write-string (format " -Norm: ~a\n" (vec-norm v)) port) (write-string (format " -X: ~a\n" (vec-x v)) port) (write-string (format " -Y: ~a\n" (vec-y v)) port))
(struct vec (x y)
#:methods gen:custom-write
[(define write-proc vec-print)])
- Alternative constructor
(define (vec/slope-norm s n)
(vec (* n (/ 1 (sqrt (+ 1 (sqr s)))))
(* n (/ s (sqrt (+ 1 (sqr s)))))))
- Properties
(define (vec-norm v)
(sqrt (+ (sqr (vec-x v)) (sqr (vec-y v)))))
(define (vec-slope v)
(fl/ (exact->inexact (vec-y v)) (exact->inexact (vec-x v))))
(define (vec-angle v)
(atan (vec-y v) (vec-x v)))
- Operations
(define (vec+ v w)
(vec (+ (vec-x v) (vec-x w))
(+ (vec-y v) (vec-y w))))
(define (vec- v w)
(vec (- (vec-x v) (vec-x w))
(- (vec-y v) (vec-y w))))
(define (vec*e v l)
(vec (* (vec-x v) l)
(* (vec-y v) l)))
(define (vec/e v l)
(vec (/ (vec-x v) l)
(/ (vec-y v) l)))</lang>
Tests <lang Racket>(vec/slope-norm 1 10)
(vec/slope-norm 0 10)
(vec 3 4)
(vec 0 10)
(vec 10 0)
(vec+ (vec/slope-norm 1 10) (vec/slope-norm 1 2))
(vec*e (vec/slope-norm 4 5) 2)</lang>
- Output:
Vec: -Slope: 1.0 -Angle(deg): 45.0 -Norm: 10.0 -X: 7.071067811865475 -Y: 7.071067811865475 Vec: -Slope: 0.0 -Angle(deg): 0.0 -Norm: 10 -X: 10 -Y: 0 Vec: -Slope: 1.3333333333333333 -Angle(deg): 53.13010235415597 -Norm: 5 -X: 3 -Y: 4 Vec: -Slope: +inf.0 -Angle(deg): 90.0 -Norm: 10 -X: 0 -Y: 10 Vec: -Slope: 0.0 -Angle(deg): 0.0 -Norm: 10 -X: 10 -Y: 0 Vec: -Slope: 1.0 -Angle(deg): 45.0 -Norm: 11.999999999999998 -X: 8.48528137423857 -Y: 8.48528137423857 Vec: -Slope: 4.0 -Angle(deg): 75.96375653207353 -Norm: 10.000000000000002 -X: 2.42535625036333 -Y: 9.70142500145332
Python
Implements a Vector Class that is initialized with origin, angular coefficient and value.
<lang python>class Vector:
def __init__(self,m,value):
self.m = m
self.value = value
self.angle = math.degrees(math.atan(self.m))
self.x = self.value * math.sin(math.radians(self.angle))
self.y = self.value * math.cos(math.radians(self.angle))
def __add__(self,vector):
"""
>>> Vector(1,10) + Vector(1,2)
Vector:
- Angular coefficient: 1.0
- Angle: 45.0 degrees
- Value: 12.0
- X component: 8.49
- Y component: 8.49
"""
final_x = self.x + vector.x
final_y = self.y + vector.y
final_value = pytagoras(final_x,final_y)
final_m = final_y / final_x
return Vector(final_m,final_value)
def __neg__(self):
return Vector(self.m,-self.value)
def __sub__(self,vector):
return self + (- vector)
def __mul__(self,scalar):
"""
>>> Vector(4,5) * 2
Vector:
- Angular coefficient: 4
- Angle: 75.96 degrees
- Value: 10
- X component: 9.7
- Y component: 2.43
"""
return Vector(self.m,self.value*scalar)
def __div__(self,scalar):
return self * (1 / scalar)
def __repr__(self):
"""
Returns a nicely formatted list of the properties of the Vector.
>>> Vector(1,10)
Vector:
- Angular coefficient: 1
- Angle: 45.0 degrees
- Value: 10
- X component: 7.07
- Y component: 7.07
"""
return """Vector:
- Angular coefficient: {}
- Angle: {} degrees
- Value: {}
- X component: {}
- Y component: {}""".format(self.m.__round__(2),
self.angle.__round__(2),
self.value.__round__(2),
self.x.__round__(2),
self.y.__round__(2))</lang>